Axis 1 of twelve · ANA
Does the work feel necessary rather than assembled? The test is subtractive: what could be removed without loss? A work of high necessity resists the question — its parts are required by what it has to say, and its scale, however large, is compelled by the argument rather than permitted by it.
Caps the summit at 7.5. A work no part of which is required cannot be canon-forming, whatever else it achieves.
1754 works · cap · the rubric
Sophocles · Literature
9.5 · Tier V
Judged on the play, and on the Greek for the verbal part. The subtractive test fails almost everywhere, and the play states its own economy. It has one day: “hēd’ hēmera physei se kai diaphtherei”
“This day will reveal your birth and bring your ruin” (438). And it has one witness who serves twice: the survivor of the crossroads (118–119, 756) is the herdsman who carried the child (1123–1176), so one summons settles both questions. Even chance is spent on necessity. The Corinthian comes with good news (934) and brings the last proof. Held below the top by the length of the quarrel with Creon (513–677), and by a closing chorus (1524–1530) whose place in the play is disputed.
Leonardo da Vinci · Visual art
9.2 · Tier V
Judged on structure alone, figure by figure. The twelve are given by the subject; what Leonardo adds, the grouping in threes, is what makes them one event. Remove a triad and the wave breaks; remove a figure and its triad loses its turn toward the next. Peter’s knife foretells the garden, Judas’s bag the price, John’s leaning away the parting: each is the least mark that carries its meaning. The architecture is required too. The ceiling, the hangings and the side walls run into Christ’s head, and the central window gives him the only halo in the picture. What yields is the outer setting: the hangings could be simplified, the landscape thinned, and the lunettes are the patron’s heraldry rather than the argument.
Filippo Brunelleschi · Architecture
9.1 · Tier V
The site was fixed before the vault: a standing octagonal drum, and the commune’s oath to cover it without external buttresses. Remove the outer shell and the inner stands open to the weather and reads squat from the street; remove the inner and the outer cannot stand. Remove the hidden ribs and the webs lose their spine; remove the chains and the spread at the foot goes unresisted; remove the herringbone and, with no centering below, the courses have nothing to hold them while the mortar sets. Remove the lantern and the eye stands open. The height is compelled too: the sign had to be seen from the country round. What resists is the lantern’s niches, capitals and scrolls, which exceed their work.
Dante Alighieri · Literature
9.7 · Tier V
Only two passages in 14,233 lines recur verbatim, both deliberate formulas: Virgil’s two-line password to the guardians of Hell (Inf. III, V) and Aquinas glossing his own phrase (Par. X, XI). The scale is compelled. A journey through every condition of the soul needs every circle, and the canticles come out within thirty-eight lines of one another. The lectures that look removable carry the physics: the moon-spots of Par. II state the principle, “According to its goodness, dark and bright”, by which Heaven is ranked. Only the roll-calls yield to the subtractive test: the houses of Par. XVI, the princes of Purg. VII, a few hundred lines, and they hold the axis below the rest. Judged on the Italian, whose rhyme forces no padding: the composite rhymes and coinages add no lines.
William Shakespeare · Literature
9.3 · Tier V
The subtractive test finds less to remove here than in any other tragedy of its author. The play runs from the heath to the head on a pole, and nearly every scene turns the action: the prophecy (1.3), the letter and the invocation (1.5), the argument in which the deed is decided (1.7), the murder (2.2), the Porter, without whom the knocking has no body (2.3), Banquo’s death and Fleance’s escape (3.3), the feast (3.4), the second prophecy (4.1), and the slaughter of Macduff’s household (4.2), which turns a subject into an avenger. What could go is the Hecate scene (3.5) and Hecate’s lines in 4.1, which the action never needs, and, within the long English scene, the passage on Edward’s healing touch, a compliment to the reigning king that halts the play. Together they come to perhaps a twentieth of the text, and they hold the axis off the top.
Michelangelo · Visual art
9.2 · Tier V
Judged on structure alone. The subtractive test finds little to take away, because the work has already taken it. Goliath is gone, with the armour, the drapery and the head at the feet, and the sling runs from the raised left hand down the back, nearly out of sight. What is left is the minimum the subject needs: a body, a weapon held back, a face turned toward a threat. Much of the rest the stone compelled: the pose runs in the plane a shallow block allowed. What yields is the stump against the right leg, which the marble needs and the argument does not, and the large head and hands, which answer a distant view the work no longer has.
Ludwig van Beethoven · Music
9.1 · Tier V
The subtractive test meets resistance almost everywhere in the first movement. Everything grows from the four-note cell: the first theme, the horn call that opens the second group, the bass under the lyrical second theme, the development whittled to single chords passed between wind and strings, and the coda, which is a second development rather than a close. Nothing there is ornament. The scherzo is needed by the finale, which recalls it, and the transition is needed by both. The test finds give in two places: the Andante’s woodwind interlude and stretches of figuration, which could be shortened without breaking the argument, and the finale’s coda, which says the arrival more times than the argument requires.
Ludwig van Beethoven · Music
9.1 · Tier V
The subtractive test meets resistance wherever it is applied. Remove no. 3, eleven bars, and the D major dance drops into A major with no passage; remove no. 6 and the finale arrives without the lament that makes its violence an answer. The first join, a semitone from the fugue’s C sharp to the D of no. 2, makes the join part of the argument, and Beethoven’s direction that nothing pauses forbids the cut that separate movements would allow. The fugue holds nothing not built from its subject. The test finds give in two places: the Presto’s second statement of its trio, and the variation coda, the most separable stretch in the work.
Anonymous · Architecture
9.0 · Tier V
Run the subtractive test on the sanctuary. Take away the posts set in the earth, or the thatch, and the building no longer needs renewal. Take away the free-standing pillar at each gable and the roof loses the member that carries its ridge. Take away the empty site and the rite has nowhere to go: the bare ground beside the sanctuary is the most necessary thing in the plan. Take away the fences and the sanctuary becomes a granary in a field. Nothing is painted, carved or applied. Two things hold the axis below the top: the crossed finials and the billets on the ridge declare more than they carry, and the fences in succession are not each compelled. Use compels the rest: a dwelling for a kami who must be served daily and never seen.
Francis Ford Coppola · Film
9.0 · Tier V
Judged on structure, and the subtractive test finds almost nothing to remove; three hours are compelled. The wedding seats every person the plot will need, and each of its small scenes is a later scene’s premise: Luca Brasi rehearsing his thanks is the man who will be garrotted; Bonasera’s favour is repaid in the undertaker’s parlour; Fontane’s trouble sends Hagen to Hollywood. Fredo fumbling his gun at the fruit stand lays down in one shot the brother the second film must deal with. Sicily looks like an interlude and is not: it gives Michael a wife to lose and a country to inherit. The give is small. The Hollywood episode is a demonstration of method the plot could spare, and the Las Vegas visit is a transfer scene for the sequel’s business.
Aeschylus · Literature
9.5 · Tier V
Judged on the Greek, where the verbal test costs nothing: refrains and strophes repeat by design, and the compounds fold a phrase into a word. Each play’s action is required by the next. The killing at the door in the first is repeated in the second so that the third can refuse to repeat it. The kommos at the tomb (Cho. 306–478) circles its appeal to the dead father, but it is where a reluctant son is made a killer. What holds the axis is civic matter fixed to 458, the Argive alliance (Eum. 289–291, 667–673, 762–774) and Athena’s claim in the Troad (397–402), 29 lines in all, with the Herald’s Menelaus, who points to the lost satyr play.
Giotto di Bondone · Visual art
9.3 · Tier V
Judged on structure. The upper tier is what a hostile reader would cut first: an old man’s shame and return. Cut it and the chapel loses what it is for. Joachim is driven from the Temple because his offering is refused; across the arch, the middle tier ends with Christ driving the sellers out. The donor’s father was a usurer, and what a man may bring to the altar is the chapel’s own question, put first. The Virtues and Vices are the ground the history stands on; the Judgment is over the door. What yields: the inventory of busts in the bands; the coretti, which argue space rather than story; and the Hell, where incident multiplies past what the wall needs.
Gustave Flaubert · Literature
9.2 · Tier V
The subtractive test finds almost nothing to take. Flaubert worked by excision, and an episode that looks like a digression proves load-bearing. Charles’s schooldays and first marriage are required: Emma enters a life already formed as dull, and her story is enclosed in his. The agricultural show is the seduction’s instrument, not a set piece beside it. Hippolyte’s clubfoot is Charles’s one chance to become what she wants, and its failure turns her finally to Rodolphe. Binet’s lathe, the blind man, Lheureux’s scarves: each returns. The coda after her death delivers the world’s verdict. What holds the axis off the top is the vanished “nous” of the opening, a frame set up and dropped, and passages in the third part where the descent repeats its steps, one more loan, one more lie, a little past what the argument needs.
Euripides · Literature
9.2 · Tier V
The play is one movement of reversal, and almost nothing in it can be lifted out. The prologue states the god’s purpose and the shape of the end, and each scene between god and king turns the screw a notch: the king binds the stranger, and the stranger walks free; he threatens the women, and the herdsman shows them invincible; he would see them, and the god offers him the sight. The scene of the two old men in fawnskins looks removable and is not: it shows the accommodation with the god that Pentheus refuses and that saves neither of them. Held below the top by the second stasimon’s appeal to Thebes and the Dirce, which restates more than it moves, and by the inherited matter of the snake prophecy at the close.
Ancient Egyptian, under Khufu · Architecture
9.1 · Tier V
Run the subtractive test on the exterior and nothing yields: a true pyramid is four planes and a point, and with any part removed it is a broken one, not a smaller one. Its scale is not permitted by the argument but is the argument; the king’s permanence is stated as mass, and a smaller mass states less. Inside, the burial compels its own apparatus: a chamber high in the body needs a flat granite roof, the roof needs relief, the passage must be sealed from within, so the plugs need a magazine and the sealers an exit. What yields is below and beside, and buried: the rough chamber in the rock, the middle chamber whose purpose is unsettled, perhaps four of the five compartments. Whether these are an abandoned plan or one design is argued.
William Shakespeare · Literature
9.1 · Tier V
The subtractive test finds almost nothing idle. There is no subplot: Roderigo is Iago’s purse and his knife, Bianca carries the handkerchief to its last use in 4.1, and Emilia, who picks it up, is the one who unmakes the plot in 5.2. The case for cutting is the first act, and Boito and Verdi made it, beginning their opera in the Cypriot storm. What that cut loses shows the act is required. Brabantio’s parting warning, “She has deceived her father, and may thee” (1.3), is the seed Iago plants in 3.3 as “She did deceive her father, marrying you”; the Senate’s trust is the height Othello falls from; the wooing is the love the play destroys. What can go is small: the Clown’s two appearances, the musicians, and some of Iago’s rhymes on the quay.
Alban Berg · Music
9.1 · Tier V
Out of Büchner’s loose, unordered fragments Berg chose fifteen scenes and cut the rest, and every scene that remains does a job in one chain. The Captain’s mockery and the Doctor’s experiment wear Wozzeck down, the Drum Major takes Marie, the earrings betray her, the fight humiliates him, the knife follows, then the pond. The acts contract, from scenes of about seven and a half minutes in Act I to about four and a half in Act III. The subtractive test finds give in two places: the drunken apprentices’ mock sermon in the Act II tavern, a set piece the action could spare, and the Act II street scene, whose satire repeats Act I.
Jean Racine · Literature
9.1 · Tier V
The subtractive test finds almost nothing to take. The action is three speech acts, each drawn out under pressure: the confession to Œnone (I.3), the declaration to Hippolyte (II.5), the confession to Thésée (V.7). Each is made possible by the scene before. The false news of Thésée’s death (I.4) licenses the declaration; his return (III.3) turns it to crime and gives Œnone her opening. Hippolyte’s love for Aricie, often called a concession to gallant taste, bears weight: her line is under Thésée’s ban, and its discovery (IV.5 and 6) turns Phèdre from confession to jealousy and seals his death. The charges are small: the scene of Aricie and Ismène (II.1) and part of the lovers’ scene say in gallant idiom what needs fewer lines, and Théramène’s récit is longer than its news.
Caravaggio · Visual art
9.0 · Tier V
Judged on structure alone, figure by figure. The two who do not look up, the coin-counter and the old man in spectacles, cannot go: without them the call reaches the whole table; with them it can be missed. The boy and the youth on the stool carry the turn of attention toward the light, and the swords that say what room this is. The empty upper half is the space the light crosses; fill it and the beam has nowhere to travel. What gives is Peter. His echoing gesture hides Christ and gives the call a witness, but it doubles a hand that needed no doubling. He is the one figure the picture could lose.
Francisco Goya · Visual art
9.0 · Tier V
Judged on structure, zone by zone. The squad cannot go, nor the lantern that lights the victims and leaves the killers dark. The man in white is the present. The dead in the foreground are the past: remove them and the volley has no consequence. The file climbing from the city is the future: remove it and a procedure becomes an incident. The friar carries the Church to the point of death and leaves it helpless; even the unlit tower is required, the city’s sanctuary dark over what happens below. What yields is the back of the file and the hill, laid in summarily, where a few heads could be thinned without loss. The canvas needs nothing from its pendant.
Leo Tolstoy · Literature
9.0 · Tier V
The subtractive test finds little to take. The frame must come first: opening on the wake, with Pyotr Ivanovich calculating promotions and wrestling with a pouffe whose springs will not lie down, it shows Ivan Ilyich’s world going on exactly as he would have gone on, so that the life which follows is read as already judged. The two chapters of the life are required in their summary form: a life lived by decorum can be told only as a résumé, and the speed is the verdict. The fall while he shows the upholsterer how to hang the curtains must stay, since the wound comes from the apartment that was his pride. Held below the top by the narrator’s hand in chapters II and III, where the satire states what the scenes could carry, and by a few returns to the same insight in the middle chapters.
Andrei Rublev · Visual art
8.9 · Tier IV
The subtractive test is the history of the subject. The Hospitality of Abraham came to the painter with Abraham, Sarah, a servant, the slaughtered calf and a laden table, and as far as the panel shows he took all of them out. What remains cannot go. Remove the cup and the table is a meal, not a sacrifice; remove one of the house, the tree and the mountain and the correspondence of three signs to three persons breaks; remove the empty front of the table and the viewer has no place. Even the staffs are required: they are the vertical measure of the three, and the sign that they are travellers in Genesis and equals in rank. What gives is small: the cornices of the architecture and the folds of the left angel’s cloak are carried by rhythm more than by necessity.
Samuel Beckett · Literature
8.8 · Tier IV
The subtractive test finds almost nothing to take. The banana business looks like a clown’s turn bolted on, and it is not: the appetite that cannot leave the banana alone, the skin he slips on, the constipation the tape will mention, are the body the voice on the tape believed it had mastered, and the opening says in silence what the young voice will deny. The ledger gives the tape’s matter before it is heard, so that listening becomes recognition. The vision is required because it is skipped, the punt because its second hearing is the verdict. What holds the axis from the top is the new recording, where Fanny and the church visits run a few lines longer than the knowledge needs.
Homer · Literature
9.5 · Tier V
The design resists subtraction. The first four books show the house the hero’s absence has made, set Orestes as the pattern, and grow the son who will stand at the threshold. Nearly a fifth of the Greek lines recur verbatim, and by the subtractive test that is not padding: the speech introductions are how the medium marks speech, and the lines repeated at the recognitions make them recognitions. “And what so tedious as a twice-told tale?” (XII.452–453). What holds this axis lowest is small: the catalogue of heroines (XI.225–332), Theoclymenus’ pedigree and part of the second descent to the dead, under three per cent, with an epithet fitted to its slot (I.29) and a dropped plan (XVI.295–298).
John Milton · Literature
9.5 · Tier V
Judged partly on Milton’s verse, which barely yields to the subtractive test. In the 1667 text read, 0.35 per cent of words sit inside a repeated six-word sequence, and the whole lines that recur are deliberate. The scale is compelled: a poem of “Man’s first disobedience” (I.1) must show the first disobedience in Heaven before the second on Earth, with Chaos between. The devils’ catalogue (I.376–521) survives the test. What holds the axis lowest of the twelve is what does not: the Paradise of Fools (III.444–497), the puns of the war’s second day, “terms of weight, / Of hard contents” (VI.621–622), and the survey of Israel (XII.111–269). Together they come to perhaps three per cent of the poem.
Michelangelo · Visual art
9.5 · Tier V
Judged on structure alone. The nine Genesis scenes resist the subtractive test: they are the argument from first light to the first drunkenness, and the last, Noah exposed and covered by his sons (Gen 9:20–23), is the scene the visitor enters under. The seers hinge the story to waiting; the ancestors are the genealogy of Matthew 1, which the Christ cycle on the walls below requires; the four corner deliverances brace the vault. What yields is the third rank of ornament: the ten medallions, barely legible from the floor, the bronze nudes and the putti. And the number of seers is set by the window bays, a necessity of the building rather than the argument.
Anthemius of Tralles and Isidore of Miletus · Architecture
9.4 · Tier V
Judged on structure and use together. Take away a semidome and the dome loses its support to the east or west, and the nave shrinks to a square. Take away the exedrae and the semidomes lose their bracing and the space its widening. Take away the galleries and the cross-thrust loses a brace and the rite its place for the empress and the women. The narthexes are the threshold the entrance required. Nearly every major part answers a thrust and a rite at once. What resists is the cross-axis: flat tympana closing the north and south arches, and aisles whose divisions are ordered rather than required. And the scale answers an emperor’s ambition as well as his rite.
Richard Wagner · Music
9.4 · Tier V
The subtractive test meets resistance at every scale. Outwardly a drink, a torch, a wound and three ships are the whole action. Musically the work grows from the Prelude’s first two bars, and the deferral begun there is not discharged until the last page, so no act can end sooner than it does. Act III’s delirium runs in two waves, and the second, the curse on the drink, is the fever’s return. The test still finds give. Marke’s monologue states the Day’s claim at a length the drama has made plain, the lovers’ dispute on Day and Night argues in words what the harmony is doing, and theatres cut both for a century. On the music alone, two tenths higher.
Byzantine · Visual art
9.2 · Tier V
Judged on structure. Run the subtractive test field by field. Remove the lunettes and the Lamb has no history; remove the Lamb and the sacrifices have no end; remove the panels and the gifts are never brought; remove the conch and nothing is given back. The programme is one sentence, the Canon’s. The imperial panels are what a hostile reader would cut as propaganda, and they are what the logic needs most: without an offerer the sanctuary shows types with no antitype in the present, and Theodora’s chalice answers Justinian’s paten. What yields: the arch’s fifteen medallions, which are inventory; the vault’s garlands; a third Moses scene where two would witness; the cities, which are emblems; and a scale the building fixed.
Raphael · Visual art
9.1 · Tier V
Judged on structure. The argument is two men walking forward under an arch, one hand raised and one held level, and the building that makes their walk the axis of everything. Remove the architecture and they are a pair in a crowd; remove the steps and measurers and arguers share one floor. The corner groups are required: the tablet, the slate and the globes are the only places where knowledge is shown as an object. The statues name the two directions again; the cynic is the refusal every academy contains. What resists is the crowd: a third of the figures are there to be many. The added figure, unrequired by the design, is required by the picture, which without him has no solitary mind.
Mimar Sinan · Architecture
9.1 · Tier V
Take away a corner semidome and the octagon loses its brace to the square. Take away the turrets over the piers and the arch-heads lose the weight that holds their thrust down. Take away the galleries and the piers lose their tie to the outer wall, and the hall its side light. Take away the court and the ablution has no place and Friday no room. The piers are eight because eight arches of about twelve metres carry thirty-one metres of dome down near the walls. What resists is the minarets: the call needs one, and four, matched, at the hall’s corners, answer the composition and a sultan’s claim. The loge and the minbar’s carving exceed their use, and the scale is compelled by the claim more than by Edirne’s congregation.
Virginia Woolf · Literature
9.1 · Tier V
The test is subtractive, and it finds almost nothing to take. Each part requires the others: without the middle part the return has no loss to measure, and without the last the first part’s promises, the trip and Lily’s unfinished picture, go unpaid. Inside the first part the apparently incidental bears weight. The Grimm tale of the fisherman’s wife, read aloud to James, runs under the marriage it interrupts. Minta’s lost brooch is the price of her engagement, and the Rayleys’ failed marriage, reported ten years on, is the answer to Mrs Ramsay’s matchmaking. Tansley’s “Women can’t paint, women can’t write” is the sentence Lily paints against for a decade. What holds the axis a step below the top: some of Lily’s meditations in the last part restate questions already put; Bankes’s reflections are the loosest stretch of the first; and the alternation of boat and lawn is at moments a scheme followed rather than a necessity met.
Franz Kafka · Literature
9.0 · Tier V
The test is subtractive and finds almost nothing to take. The first sentence gives the transformation and the rest follows from it by necessity: the first part asks whether the household can admit what has happened, the second how it will live with it, the third how it will be rid of it. Each part needs its expulsion, and each expulsion is worse. The chief clerk’s visit is required, since it shows that Gregor’s first fear is for his job and that the firm comes to the door before the doctor; the furniture scene is required, since it is where the sister decides what he is; the lodgers and the violin bring the family’s new economy and Gregor’s last hunger into one room. The close is required too: without the family’s renewal the expulsion is not completed, and the story would end on pathos rather than disclosure. What holds the axis is the manner of the close, the tram ride into the country, which turns from Gregor to the family in a register more explicit than the rest.
Fan Kuan · Visual art
9.0 · Tier V
Judged on structure. The subtractive test removes almost nothing. Without the foreground boulders the eye has nothing to stand on before it climbs. Without the travellers the mountain loses its measure and becomes a rock face of no size. Without the temple roofs the human world is only traffic, with no place between road and peak where the order is acknowledged. Without the mist the mountain sits on the hill below it, an object rather than an apparition; without the waterfall the wall is mute. Each zone has an office. What could go is local, some trees on the rise and some scrub on the summit: texture, not incident.
Samuel Beckett · Literature
9.0 · Tier V
The subtractive test finds almost nothing loose. Every property is brought on to be used up: the painkiller is asked for at intervals until there is none; the toy dog is made, set up, falls, and is at last thrown away; the gaff is fetched to move the chair; the alarm clock is wound against Clov’s leaving and hung on the wall to be watched. Repetition is the play’s matter, not its padding: the questions come round because the day comes round. What holds the axis a step from the top is small. Beckett tightened the text himself for his Berlin production of 1967, and Nagg’s tailor story runs on after its frame has landed, though its length is half the joke.
Katsushika Hokusai · Visual art
8.9 · Tier IV
Judged on structure, element by element. Take away the great wave and there is no picture. Take away the boats and the wave has no size and no stake; it is a pattern. Take away one boat and the rhythm goes: three boats give three moments of one event, climbing, under, and coming through, a sequence held in an instant. Take away Fuji and the sheet loses its still point and its series. Take away the foreground swell and the rhyme between near water and far mountain, the picture’s one argument, is gone. The cartouche and signature are the only straight lines on the sheet, and the crest reaches toward them. What gives is small: the spray drops could be fewer, and later impressions stand without the pink sky, poorer but still the picture.
Giuseppe Verdi · Music
8.9 · Tier IV
Boito’s first decision is subtractive. Shakespeare’s Venetian act is cut whole, and the opera opens in the storm off Cyprus with no prelude, so the action begins as the hero lands. Every later scene has a job. The drinking song exists to make Cassio drunk; the drunkenness costs him his rank; the lost rank gives Desdemona her suit, and the suit gives Iago his evidence. The handkerchief changes hands inside the Act II quartet. The subtractive test finds give in three places: the homage chorus halts the action for a picture of Desdemona among islanders, though Iago’s asides keep it working; the bonfire chorus is a chorus round a fire; and the Act III concertato is static for its length.
Leonardo da Vinci · Visual art
8.9 · Tier IV
The subtractive test, passage by passage, and the panel resists it almost everywhere. The hands cannot go: they are the base of the pyramid and the one fixed thing against the unfixed face. The parapet and the bases of the two columns cannot go: they seat her in a loggia between the viewer’s space and the world’s, and give the land its distance. The land cannot go, nor either half of it, the winding road at the left and the bridge at the right meeting only behind her head. The veil, nearly invisible, carries the passage from hair to sky. What yields is small: the arm of the chair, so summary it nearly dissolves, and the long dark sleeve at the lower left. The scale is a portrait’s, compelled by its subject and not stretched.
F. Scott Fitzgerald · Literature
8.9 · Tier IV
The subtractive test finds almost nothing to take, and what looks removable turns out to bear weight. The roll of guests that opens chapter 4, set down on a timetable, reads as comic digression and is the list of those who came to the house and will not come to the funeral; one of them, Klipspringer, telephones in chapter 9 only to ask after his tennis shoes. Myrtle’s party in chapter 2 sets up the apartment, Tom’s violence and the garage the car will pass. Each of the nine chapters turns on one gathering, and none repeats another’s work. Held below the top: Michaelis’s account of Wilson’s night in chapter 8 is machinery delivered by report, and Nick’s “They were careless people, Tom and Daisy” (chapter 9) says what the scenes have shown.
Caravaggio · Visual art
8.8 · Tier IV
Judged figure by figure and void by void. The Baptist cannot go: he is the event, face down, wrists bound, his blood the one spill of red. The executioner cannot go: he holds the head down by the hair and reaches behind him for the short knife, the sword already on the ground, and the unfinished killing is the picture’s instant. The jailer’s pointing hand gives the death as instruction; the young woman with the basin is the reason and the receptacle; the old woman is the only feeling in the yard; the prisoners are the witnesses who cannot act. The emptiness is compelled too. What yields is the hanging rope and the ring, an accent rather than a requirement.
Franz Kafka · Literature
8.7 · Tier IV
The subtractive test finds almost nothing to take. The opening sentence sets the whole as the chronicle of a lost art, and every later part is required by that frame. The watchers who suspect him of secret eating are needed, since his torment is that no one can verify the one thing he does. The impresario’s forty days are needed, the market fixing the length of a vocation. The photographs that show weakness as the cause of his rage rather than its effect are needed, the misreading made into a business. The circus, the menagerie, the board no longer kept: each step of the decline is one step. The panther closes what the first sentence opened. Held a shade below the top because the middle account of the public’s changing taste is told in summary where a scene would cost nothing more.
Roman · Architecture
8.4 · Tier IV
The purpose is known, and it sets the form. The level of the channel is fixed by a fall of a few centimetres across the whole crossing, so the height of the bridge is given by the aqueduct’s line, not chosen. One arch could not rise forty-nine metres, so the height is divided into three tiers; the widest arch stands over the river, where floods must pass; the middle tier stands on the lower so that load comes down pier on pier; the small upper arches carry the narrow channel with the least stone. Nothing is ornament. What yields: the arches vary in width with the ground; the route that needed so high a crossing was one choice among routes; and the road deck adds a part the aqueduct never required.
Roman, under Hadrian · Architecture
9.3 · Tier V
Judged on structure, purpose and site. In the rotunda almost nothing yields to the subtractive test. The drum is as thick as the dome’s thrust requires, and hollowed by recesses where weight can go. The coffers order and lighten the dome, diminishing as it closes. The oculus removes the part least able to bear itself and is the only window: light, structure and meaning are one fact. Use is compelled too, one undivided room under one opening, a centre for an assembly or a cult. What yields is the junction. The porch is required as temple front and threshold, but the block with its second pediment shows two parts joined, not one compelled; the eight shrines are ordered rather than required.
Anonymous · Architecture
9.3 · Tier V
Judged on purpose, structure and site. The body of the church resists the subtractive test. The plan is compelled by the crypt beneath it and by what it serves: the double ambulatory carries pilgrims round the relic without crossing the canons’ choir, and the crypt takes them down to the well and the Virgin’s chapel. The section is compelled by structure: without the flyers the clerestory cannot stand so tall, and without the tribune nothing is lost, which is why the builders dropped it. The old front is kept by site and economy, and the bays fix the number of windows. What holds the axis is the narrative: many legend windows could carry another saint without loss, their subjects chosen by donors, and the porches were a change of plan.
Michelangelo · Visual art
9.3 · Tier V
Judged on structure alone, field by field. The lunettes cannot go: the cross and the column are the sign of the Son of Man appearing, and the judge’s gesture answers them. The resurrection, the ascent, the fall and Charon’s boat are four stations of one circuit; remove any one and the rotation breaks. The mouth of hell must open above the altar, and does. Bartholomew’s skin, the wall’s one signature, lies at Christ’s feet. What yields is the outer ring of the blessed, packed shoulder to shoulder in the upper zones, bodies more than persons: a third of them could be thinned with no loss of argument. The subject compels a multitude, not each member of it.
Iktinos and Kallikrates · Architecture
9.3 · Tier V
Judged on plan, structure and purpose. Within the Doric order every member is structural: column, architrave, triglyph and metope are the trabeated structure stated in stone, each required by the one above or below it. The plan is compelled by use. The front went from six columns to eight because the naos had to be wide enough for the statue and the colonnade returning behind it; the west room exists because a treasury was wanted. What holds the axis is the sculpture’s relation to use. The frieze, high on the cella wall behind the colonnade, cannot be read whole from anywhere a visitor stands; the backs of the pedimental figures are finished where no one could see them; and the Ionic frieze is an addition the Doric order does not ask for.
Sophocles · Literature
9.2 · Tier V
The subtractive test finds very little. The prologue’s two sisters set the two courses the play will test; the Guard’s two entrances put the burial and the capture in the city’s view; Haemon turns the conflict into the house, and Teiresias turns it to the gods. Eurydice, who speaks a handful of lines and goes in silence, completes Creon’s punishment: the man who set the city above kin is left with neither. Each part is required by the argument. Held below the top by three things: the first burial, dustless and unseen, never explained; the fourth stasimon, whose exempla bear on Antigone obliquely; and 904 to 920, where she reasons that a husband or a child could be replaced but a brother, her parents dead, could not. Aristotle knew those lines. They are the text, and they jar.
Ludwig van Beethoven · Music
9.2 · Tier V
Length is not charged; the question is whether the parts are required. The first movement resists the subtractive test almost everywhere. The C sharp of the seventh bar is the seed the movement spends its length resolving; the development’s new theme in E minor is required because the climax before it has broken the exposition’s material; the coda is not appendage but the place where the theme first sounds whole. The march’s fugato and its last crumbling of the theme bear load. The test finds give in two places: the finale’s chain of variations, whose fugatos, G minor episode and Poco andante could be reordered or shortened with less loss, and the scherzo, which could be exchanged for another of its kind with the cycle’s argument largely intact.
Sailendra · Architecture
9.2 · Tier V
Run the subtractive test downward from the top. The central stupa cannot go: the whole mass converges on it, and it is empty, which is the argument. The three rings cannot be two: their stupas stand in the ratio 4:3:2, and a series needs three terms. The square terraces cannot be fewer, since with the foot, the rings and the summit they make the count the path requires. The galleries’ blind walls are compelled by the purpose, and the scale by the hill the building clothes. What the test finds: the Jataka and Avadana layer could be thinned without loss of argument, and the Gandavyuha dwells on Maitreya’s tower at a length the walker feels. The builders ran the test themselves: the 160 panels of the foot were carved, then covered, and the bare platform is what their subtraction left.
Diego Velázquez · Visual art
9.2 · Tier V
Judged on structure alone, figure by figure. The infanta cannot go: she is the light. The two meninas frame her and give the picture its instant, one kneeling with the jar, one beginning to curtsey. The painter, the back of his canvas and the mirror are together the argument. Nieto in the far doorway is the second light and the depth of the house. The dog, the one creature not attending, cannot go, and Nicolasito’s foot on its back is the only movement in a stilled room. What yields is the pair in half shadow, above all the guardadamas, who could be removed without loss, and the two dark canvases over the mirror, required by the argument and illegible from the floor.
Samuel Beckett · Literature
9.1 · Tier V
The structure passes the subtractive test outright. Without the second act the play is one bad evening; with it, the evening is a law. Without Pozzo and Lucky the waiting has no measure: they pass, and change, and the waiters do not. Lucky’s speech is the only thinking the play allows, and cannot go; the Boy’s two visits are its hinges. What gives way is inside the acts. The routines, the boots, the hat, the carrots and turnips, the insults, the exercises, are modular: any one could be lost or moved without loss, and their order is permitted rather than compelled. The subject, time filled by interchangeable business, defends them as a class but not each item, and that holds the axis here.
Emily Brontë · Literature
9.1 · Tier V
The subtractive test finds little to take. Remove Lockwood and the book loses its first instrument: the outsider who misreads every relation at the Heights, taking the dead rabbits for cats and Cathy for Heathcliff’s wife (ch. 1 and 2), is how the reader enters a world that cannot be entered by sympathy. Remove the second generation and the revenge never meets its own failure; the book’s knowledge is that the pattern repeats and then, in Hareton and Cathy, breaks. Remove Isabella’s letter (ch. 13) and the marriage is told only from outside. What holds the axis lowest of the high figures is chapters 21 to 28, where the machinery of the revenge, the forced marriage, the will and the lawyer, takes more pages than its knowledge needs, and Linton Heathcliff is drawn in one peevish note for longer than one note sustains.
William Faulkner · Literature
9.1 · Tier V
Four tellings of one family’s fall, and the subtractive test asks whether any could go. None can. Benjy gives loss without understanding; Quentin understanding without the power to act; Jason the world of money without love; the fourth section the house seen at last from outside, with Dilsey. Each withholds what another gives, and Caddy, who has no section, exists only as their sum. Inside the first section the shifts of time are cued by sense, the fence, the golfers’ call of “caddie”, a smell, and none can be cut without the logic going. What holds the axis at 9.0: Quentin’s afternoon with the little Italian girl and the scene with Bland’s party run past their turn, and Jason’s monologue, required for its argument, repeats its grievances, the telegraph office, the cotton market, the money he is owed by the world, more often than the knowledge needs.
Alexander Pushkin · Literature
9.0 · Tier V
The severe case is that the Introduction’s catalogue of the city, its granite embankments, white nights, frost, balls, parades and the breaking of the Neva’s ice, is panegyric of a set kind that could be halved. The answer is in the structure: the catalogue is the claim the poem tests. It ends in a prayer that the vanquished element make peace with the city and that the Finnish waves forget their ancient enmity, and Part One opens by breaking that prayer. Cut it and the flood answers nothing. The two parts are matched, the river’s revolt against the city and the man’s against the founder. No episode is idle. What holds the axis a step from the top is one cut a reader could make without loss: the jibe in Part One at Count Khvostov, the poet who has already sung the disaster in immortal verses, a private joke the poem does not need.
Francesco Borromini · Architecture
9.0 · Tier V
The site compelled almost everything: a cramped corner at a crossroads, a fountain to be kept, a convent to be fitted beside the church, a patron too poor for marble. A nave would not fit and a circle would waste the length, so the oval; the corner is cut for the fountain and the cut becomes the tower; the material is brick and white stucco. Within that the geometry generates the parts. Take one group of columns away and the entablature’s wave breaks; take away the pendentives and the plan cannot become a ring for the dome; flatten the coffers and the dome loses its height. What yields: the medallion and angels on the façade, finished by another hand; the cherubs and garlands; the cloister’s alternating balusters, wit more than need.
John Milton · Literature
9.0 · Tier V
The subtractive test finds almost nothing idle in 193 lines, and the poem is built of the parts a critic would try to cut first: two digressions and a catalogue. Remove the passage on fame and the poem loses its first question, what a dedicated life is worth when “the blind Fury with th’ abhorred shears” cuts it before its harvest; King’s death matters because it might be Milton’s. Remove St Peter and it loses its second, why the faithful shepherd drowns while the “blind mouths” feed: an elegy for a cleric needs the indictment of the clergy. Held at 9.0 by the flowers, a later insertion in the manuscript, which the poem itself calls “false surmise”: ornament it must then cancel.
Umayyad, under Abd al-Malik · Architecture
8.9 · Tier IV
Judged on structure, purpose and site. The purpose is the Rock, and every part is placed by it. The circular arcade stands where the Rock ends and carries the drum and dome over it, so that the light falls on what the building exists to hold. The octagonal arcade and the outer wall make two rings of passage round it, so that the Rock is gone round, never faced from one end, and seen through the arcades from every point. Remove the outer ambulatory and the inner becomes a corridor; remove the dome and the centre is lost. What yields is small: the porches, needed as doors but not in their present form, and the reused columns, taken from what was to hand.
Anton Chekhov · Literature
8.9 · Tier IV
The subtractive test bites on almost nothing, and the figures who look like ornament are each a function of the argument. Yepikhodov, the clerk of “двадцать два несчастья” (twenty-two misfortunes), with his squeaking boots and a revolver he never fires, is the household’s incapacity made farce, and he stays on as the new owner’s steward. Pishchik, saved when the English find clay on his land, is the gentry economy surviving where it survives, by accident. Charlotta, with no passport and no known age, is rootlessness without sentiment. Firs’s forgotten method for drying cherries is the whole estate in four lines. What could go: part of Trofimov’s long speech in the second act, which states what the play shows, and perhaps the Passer-by, who is a device.
Jacques-Louis David · Visual art
8.9 · Tier IV
The subtractive test finds almost nothing to remove. Take away the empty wall and the picture loses its measure of what is gone: an absence over the dead man that fills more than half the field. Take away the crate and the dedication goes, and with it the work as a tombstone; the crate is also the poverty the picture argues. Without the letter the murder has no instrument of deceit, without the knife no instrument of death, and without the quill the arm is only an arm. What yields first is the banknote and its paper on the crate, which make explicit a charity the bare crate had already stated: the one place the picture speaks twice. The life size is compelled: it stands the viewer at the tub’s edge, as at a bier.
William Faulkner · Literature
8.9 · Tier IV
Fifty-nine sections in about ten days, and the subtractive test finds almost nothing to take. Every section is a turn of the road or a turn of a mind. The outer voices are not decoration: Samson, Armstid and Moseley give the coffin as the world smells it, which the family cannot say, and the book needs their view to measure the family’s. Cora Tull’s pieties are the book’s comedy and also the false reading of Addie that Addie’s own section answers. Cash’s numbered reasons, beginning “I made it on the bevel.”, are thirteen short lines that are his whole character. The length is compelled: a journey in fifty-nine stations, none of which idles. What holds the axis a step from the top: Whitfield’s single section is satire the book could compress, and MacGowan’s seduction of Dewey Dell in the drugstore runs coarser and longer than the arc requires.
Igor Stravinsky · Music
8.9 · Tier IV
Some twenty-two minutes on eleven verses, and the subtractive test meets resistance almost everywhere. Remove the first movement and the work loses the stranger’s plea, the condition the rest answers; the second movement’s last words, canticum novum, would promise a song with no need behind it. Remove the second and the work passes from plea to praise with no waiting and no rescue from the pit, de lacu miseriae. The third is the new song the second promised; it cannot go. Within movements the economy is severe. The give is in the Allegro, where a statement of the galloping blocks or a Laudate interjection could go without loss of argument, and in the coda, which could lose a cycle and keep its effect.
Chola bronze casters · Visual art
8.9 · Tier IV
Judged attribute by attribute, the figure resists subtraction almost everywhere. Take away the drum and creation goes; the fire, and destruction; the raised palm, the protection of what is; the dwarf under the foot, the ignorance overcome; the lifted foot and the hand that points to it, release, which is the image’s promise. The ring cannot go: it is the bounded world in which the dance happens and which the hands touch at their reach. The flying locks are the speed of the dance, the only measure of motion in a still metal figure. Removal fails at nearly every point, because the iconography is a sentence and each part a word in it. What yields is ornament: the jewellery, the count of flames, the detail of the sash.
Piero della Francesca · Visual art
8.8 · Tier IV
Judged element by element, and almost nothing yields. Remove the three men in the foreground and the panel is a small, exact Flagellation of the usual kind; remove the hall and it is an unexplained conversation in a street. The picture exists in the relation of the two, so both are required at their sizes. The column and its gilded idol fix Christ to the order of the hall. The man in the turban, seen from behind, is the one figure who watches, and he makes the scene something seen. Pilate, seated at the edge, is the authority that does nothing. The pavement makes the distance legible. What yields, slightly: the buildings of the street and the tree are permitted more than compelled.
Titian · Visual art
8.8 · Tier IV
Run the subtractive test register by register. The apostles are required: they are the earth the Virgin leaves and the only measure of her rising. The Virgin is the subject, and God the Father the destination without which the ascent has no end. Between the apostles’ heads and the cloud runs a strip of open sky, and that gap is the event: take it out and she is not leaving but floating. There is no landscape, no painted architecture, no donor and no saint outside the story; the frame is the architecture the painting refuses to contain. What yields is the crowd of child angels, more than a ring needs, and the angel with the crown, a second sign of an end God already states. The apostles are a group, and some could go unmissed.
Francisco Goya · Visual art
8.7 · Tier IV
Judged on the image as it stands, part by part. The eyes cannot go: wide, white-rimmed, looking past what the hands are doing, they are the picture, and without them this is an ogre at a meal. The hands cannot go; they grip the body at the waist so hard the fingers sink in, and the grip is the compulsion. The headless body, pale, small and already mostly gone, cannot go, nor the black, the only setting, which leaves the figure nowhere to be but the act. The crop is compelled: the head pressed to the top edge, the knees cut by the lower, the god too large for the field. What yields is little: the summary knees and lower legs, and a dark left part of the field that is not needed.
Anonymous (the Gawain poet) · Literature
8.7 · Tier IV
The test is subtractive, and the poem loses very little to it. The three days are built so that each of six strands is required by its pair: the deer hunted openly and the lady’s first open pursuit; the boar turning at bay and Gawain parrying her; the fox doubling and twisting and Gawain, on the third day, taking the girdle and hiding it. Remove the hunts and the bedroom loses its measure; remove the exchange of winnings and the girdle costs nothing. The pentangle passage, which looks like a digression, sets the standard of trawþe, truth and troth, by which the end will judge him; the seasons are the year he spends waiting for his death. Held below the top: the journey’s wildernesses and monsters pass in a list, the breaking of the deer runs long for its function, and Gawain’s turn against women after the Green Chapel is arguably more than the characterisation needs.
Wolfgang Amadeus Mozart · Music
8.7 · Tier IV
The subtractive test finds very little. In the first movement every contrast is used: the soft reply to the opening call returns as material the development breaks, and the comic tune that closes the exposition is not a garnish but the subject the development takes up; cut it and half the argument goes. In the finale the four-note motif and the four other themes are each built to fit the coda’s combination, so that without any one of them the coda cannot be written. The Trio’s anticipation of that motif makes the minuet a step toward the end. The give: the finale’s second repeat, which performers take or leave and the coda does not need, and the Andante’s long recapitulation, which restates more than it transforms.
Mark Rothko · Visual art
8.6 · Tier IV
Judged on the configuration, wall by wall. Take away the canvas on the entrance wall and the apse triptych faces a door instead of its answer. Take away a canvas from an angled wall and the enclosure opens: the octagon reads as eight walls with a gap, and the viewer is no longer held. Take away a side triptych and its opposite faces bare wall, and the cross-axis goes. There is no ornament to thin and no secondary rank; the whole is made by subtraction. What holds the axis is substitution, not removal: the four angled-wall canvases are close to interchangeable, and the canvases painted for the commission and not hung show that any one could have been another.
Joel Coen and Ethan Coen · Film
8.6 · Tier IV
Judged on structure and on the silences, which carry as much as the talk. The gas station coin toss establishes the law by which Carla Jean will later be offered her life; the Ellis scene, which a thriller would cut, is where the film says that what is coming was never waiting on anyone; both dreams are required, and the second needs the first. The motel vent, the transponder and the boots are each set down once and used. What counts against is weighed: Carson Wells gets a full scene with his employer and dies within a reel, and the Mexicans who kill Moss are a necessity with no face, so the refusal of the climax is also a convenience. Held at the figure because even the air through the opened vent is doing work.
Katsushika Hokusai · Visual art
8.4 · Tier IV
Tested by subtraction, element by element. The cone cannot go: it is the picture. The snow below the summit cannot go: it is the height, a mountain tall enough to hold snow in the warm months, and it is the season. The clouds cannot go: they are the fine wind of the title, the weather that clears the air, and their small repeated forms make the cone read as vast. The band of dots at the foot cannot go: it gives the mountain a base and the eye its one measure of size. The slope cannot be shortened without bringing the mountain back inside a frame it exceeds. What yields is the series’ furniture, cartouches and signature. Held below the top because a design so reduced leaves little to test.
Homer · Literature
9.6 · Tier V
The spine is as tight as any on the bench: a prize taken, the withdrawal, its cost counted in Achaean dead, the friend sent out in the hero’s armour, the return, the body given back. The long middle is compelled; the wrath has to be paid for at length. In the Greek the repetitions resist the subtractive test. Odysseus’ repeat of the gift-list cannot be cut without losing the line he leaves out (9.160), which Achilles answers (9.392). The messenger repetitions are the medium’s convention. What holds it lowest of the twelve is structural: Book X, 3.69 per cent of the lines, lifts out whole, and the Catalogue, 2.51 per cent, could be thinned.
William Shakespeare · Literature
9.5 · Tier V
Judged on the work for structure and on this text in part. The double plot passes the subtractive test outright: without Gloucester, Lear’s error is one man’s temper; with him it is a law, and “I stumbled when I saw” (4.1) answers “See better, Lear” (1.1). What holds the axis at 8.9 is the machinery and the text. Letters drive the plot; Kent keeps a disguise he never explains; Edgar withholds himself from his father and confesses it: “Never (O fault!) reveal’d myself unto him” (5.3). The conflation adds the Quarto’s 4.3, the Folio’s Merlin prophecy (3.2) and a Kent speech joined from both (3.1). On the work alone, two tenths higher.
Fyodor Dostoevsky · Literature
9.3 · Tier V
Length is not the question; whether each part is required by the one act is, and nearly every part is. Each subplot is a version of the murder. Dounia’s engagement to Luzhin repeats Sonia’s sale under a better name, and Raskolnikov says so (I.4). Luzhin’s economics of self-love is the theory as a businessman holds it. Svidrigaïlov is the theory lived without remorse, and his suicide answers the question the axe asked. The Marmeladovs are the “simple arithmetic!” (I.6) made into persons. What holds the axis lowest of the twelve is the slack the subtractive test still finds: Lebeziatnikov’s socialist chatter (V.1), Razumihin’s drunken lectures (II.4, III.1), the memorial dinner kept longer at farce than its turn needs (V.2), and an Epilogue whose summary hurries what it has to carry.
Ludwig van Beethoven · Music
9.3 · Tier V
The finale makes the first three movements required. Its recitative in cellos and basses calls up the first movement, the scherzo and a phrase of the Adagio and refuses each; cut any of them and the refusal points at nothing. The first movement grows from falling fourths and fifths over the open A–E, and its 547 bars hold no episode not built from that cell. Length is not charged. The subtractive test still finds give: the scherzo’s long repeats; the orchestral fugato after the tenor’s march; and the sketches, which plan an instrumental finale whose theme went into the A minor Quartet, Op. 132. The choral ending was chosen, not compelled.
Igor Stravinsky · Music
9.2 · Tier V
The work is short and nearly free of connective tissue; the subtractive test meets resistance at both ends of each part. Remove the Introduction and the Augurs’ chord has no waking world to break into; remove the Sage’s few bars and the Dance of the Earth loses the silence it erupts from; remove the Glorification and the Danse sacrale has no chosen one. The test finds give, and the form invites it: a work of juxtaposed blocks loses a block more easily than a sonata loses a paragraph. The Ritual of the Rival Tribes and the Ritual Action of the Ancestors each extend a state already set, and Spring Rounds could be shortened with little loss.
Franz Schubert · Music
9.2 · Tier V
Length is not charged: seventy minutes of walking is what the argument needs. The subtractive test meets resistance at every station that bears structure: no. 1, which sets the stranger walking; no. 5, the first offer of rest; no. 7, the crust over the torrent; no. 12, the calm worse than the storm; nos. 20 and 21, the signpost and the inn; no. 24. It finds give in three places: the two-part shape is the accident of the twelve poems Schubert found first; “Täuschung”, on a borrowed tune, and “Der stürmische Morgen” restate earlier songs; and “Rast” and “Die Post” repeat a strophe the ear already knows. The one change to Müller’s order, “Mut” before “Die Nebensonnen”, shows the ending was chosen.
Pablo Picasso · Visual art
9.1 · Tier V
Judged on structure alone, figure by figure. The mother and the burning figure are the two ends of the frieze: remove either and the field tips. The horse is the centre. The warrior, the one figure lying flat, is the base of the triangle, and the lamp-bearer and the electric light make its apex, the two kinds of seeing. The bull is the one figure that does not suffer, and is needed for that. Nine figures is close to the least the argument requires. What resists is at the margin. The bird on the table is small and hard to read as a figure, and could go with little loss; the door and the floor tiles are setting, not argument.
T. S. Eliot · Literature
9.1 · Tier V
The poem itself barely yields to the subtractive test. Pound’s cuts left four hundred and thirty-three lines from drafts nearly twice as long, and what remains is load: the ten lines of “Death by Water” are the drowned god the whole poem waits on; the pub monologue in “A Game of Chess” is the lower answer to the upper scene’s Cleopatra; the typist’s quatrains are the poem’s centre of desire without love. Even its quotations are joints, not ornament. What holds the axis is the notes, which are part of the work. Some are required, those on Weston, the Tarot, Tiresias and the Fire Sermon; many are permitted rather than compelled, a page reference or an anecdote about Shackleton. The poem alone would stand higher.
Édouard Manet · Visual art
8.9 · Tier IV
Judged figure by figure. The woman cannot go, and neither can her look: the picture is that look. The servant cannot go: she carries the bouquet, a visitor’s flowers, and so brings into the room the client who is not shown and who stands where the viewer stands. The cat cannot go: it answers the sleeping dog of Titian’s picture, fidelity turned into the creature of the night, and with the woman it is the only thing in the room that has noticed us. The slipper on one foot and the slipper fallen, the black ribbon at the throat, the bracelet, the flower in the hair: each says undressed, not nude, and each is a fact of price. The hand over the sex, flat and firm where Titian’s curls, is the argument. What yields is the dark ground at the right, where the servant’s face and the cat nearly drown and the curtain is a mass rather than a requirement.
Masaccio · Visual art
8.9 · Tier IV
Judged register by register, and nothing comes away. Remove the skeleton and the image loses the floor its ascent is measured from: the inscription speaks to the viewer in the second person, and every figure above is placed against that address. Remove the donors and the line between the painted chapel and the church goes, for they kneel exactly at the threshold, outside the pilasters, in our space and at our size. Remove the Virgin’s outward look and gesture and no figure stands between the viewer and the cross. The architecture is the instrument of the argument, and its scale, a chapel opened at life size in a flat wall, is compelled by the claim that the sacred stands in measured space continuous with ours. What gives is one figure: God stands on a ledge whose footing in the vault is never quite stated, and there the composition is permitted rather than compelled.
Euripides · Literature
8.9 · Tier IV
The subtractive test bites on rhetoric, not on structure. Remove the Nurse and the catastrophe has no agent: Phaedra has chosen silence and death, and only someone who loves her can break the silence for her. Remove the oath and Hippolytus has every reason to clear himself before Theseus, so the dispute of father and son has no lock. Remove the tablet and the dead woman cannot speak against the living man. The two halves are required as well: Aphrodite promises both deaths in the prologue, the woman’s and the young man’s, and the diptych is that promise kept. The servant’s prayer to Cypris in the first scene, asking her to forgive the young man’s pride, holds the whole play in a few lines. Held below the top by the length of Hippolytus’ tirade against women and of the dispute with his father, which say more than the action needs, and by a prologue that makes part of the first episode an exposition of what is already known.
Vincent van Gogh · Visual art
8.9 · Tier IV
Judged on the configuration. Remove the cypress and nothing on earth reaches the sky: the canvas becomes the sky study the painter first called it, and what it knows goes. Remove the village and no one sleeps under this sky; the spire that stops at the hills is the one measure of how far the human world gets. Remove the moon and the sky has no end at the right; remove the morning star and it has no beginning at the left; the spiral between them is the current they drive. Even the pale band on the horizon is required: it is the coming day, the night’s one edge. What gives is at the margin: the stars could be fewer or more, and the houses are a count, not a structure. The scale, small, is compelled; bigger, this sky would be décor.
Juan Rulfo · Literature
8.9 · Tier IV
The test is subtractive, and in so short a book it finds almost nothing to take. Every fragment works in two orders at once: it advances a life, and it adds a voice to the chorus that is the town. Remove Eduviges and the reader is never told, gently, that the living are not living; remove the night with Donis and his sister and Juan Preciado’s death has no cause; remove Father Rentería’s refused confession and the Church’s share in Pedro’s rule goes unshown; remove Abundio’s last visit and the book has no parricide to close it. The scale is compelled: a dead town speaks in fragments. What holds the axis below nine is the second half, where a few of the Media Luna’s business fragments tell what one scene could carry, and some of Susana’s monologues return to the same sea.
Michelangelo · Visual art
8.9 · Tier IV
Judged on structure, the subtractive test finds almost nothing to take. The group is a pyramid: the veiled head at the apex, the spread of the mantle at the base, the dead body across it as the one horizontal. Every great fold of the mantle is there to make that horizontal possible. The lap is enlarged far past nature and the cloth hides it; remove the drapery and the composition fails, because a grown man cannot lie across a woman’s knees at true proportion. The open left hand is the one gesture not needed for support, and it carries the meaning. What yields: the stump and rocky base, needed as ground but generic, and the small tumbling folds at the lower edge, which could be fewer.
Rogier van der Weyden · Visual art
8.9 · Tier IV
The subtractive test runs figure by figure, and almost nothing yields. Christ and the Virgin are the argument: two bodies falling on parallel diagonals, so that the son’s death and the mother’s swoon are one movement. John at the left and the Magdalene at the right are bent inward like brackets that close the frieze; remove either and the box opens. Joseph of Arimathea and Nicodemus are the labour of the body’s weight, and the young man on the ladder is the one reason the cross is still a cross. The skull carries the typology of Adam. What gives a little is the bearded man with the jar at the back right and, less, the holy woman in green behind the Virgin. The scale is compelled: the grief has to stand at the viewer’s height.
Yasujirō Ozu · Film
8.9 · Tier IV
Judged mainly on structure, with a verbal part in the repeated lines and the few speeches that state the film. Run the subtractive test scene by scene and the film resists it. The Atami night is the hinge, where the parents learn they have been paid to go away; without it the night at Ueno has no cause. Noriko’s day is the measure the children are weighed by. The bar is where Shūkichi’s disappointment in his son is spoken, so that his forgiveness is of a man he has judged. Osaka breaks the journey and places the third son. The great events are already removed: the journey out, the collapse, the death. What is charged: the cakes and the hairdressers’ meeting do one job twice, and Hattori’s wife is half a scene of furniture.
Ustad Ahmad Lahauri · Architecture
8.9 · Tier IV
Tested part by part. Take away the gateway and the garden has no threshold, and the verses that name it as paradise are gone. Take away the garden and the tomb is an object without an approach. The mosque is required by use, since prayer at a tomb needs it, and its place on the west by the direction of Mecca. The minarets serve no rite, but without them the plinth loses its frame and the white mass its measure. The double dome is compelled by two scales at once, the skyline and the chamber. What resists the test is the jawab: it answers the mosque and serves nothing that requires it, a necessity of the composition, not of the use. Ornament is sparing and gathered at thresholds.
Jan van Eyck · Visual art
8.9 · Tier IV
Judged object by object, because the painter put every object there to be read. Remove the mirror and the room has no back and no witness: it shows the couple from behind and two men at the threshold where the viewer stands. Remove the one lit candle and the room loses its sign that something is being marked in daylight. The joined hands and the raised right hand are the action; the dog is the one creature looking out. The pattens on the floor and the slippers by the far wall set the room’s depth and its owners’ ease. What yields is in the furnishings: the oranges, the brush by the bedpost and the prayer beads could be fewer without loss.
Nikolai Gogol · Literature
8.8 · Tier IV
The test is subtractive and finds almost nothing to take. The naming at the font, where the mother rejects a run of grotesque saints’ names from the calendar and the child is called after his father, must stay: it fixes a life given no choice from the first page. The mockery in the office must stay, since it carries the plea and the brother. The months of saving, walking on tiptoe to spare his soles, must stay, because the coat’s price is the measure of the loss. The theft, the significant person, the death and the ghost are one chain. The narrator’s digressions look removable and are not: they are the voice that ignores Akaky as the world does. What holds the axis is a handful of digressive runs, the party and some of the narrator’s asides about the ghost, which could be shortened with the knowledge unchanged.
Jean Racine · Literature
8.8 · Tier IV
The subtractive test finds the parts required. Take away any of the four principals and the chain is no longer a chain; take away the embassy and no one is forced to choose; take away the reversals of the second to fourth acts, in which Pyrrhus will give up the child, will not, will marry Hermione, will marry Andromaque, and Hermione’s order to kill has nothing to grow from. Even the confidants bear weight: Phoenix is the voice of the state Pyrrhus refuses, and Céphise is the one Andromaque trusts with the plan of her death (IV.1). The charges are real if light: the confidants are a convention, the exposition of I.1, Oreste telling Pylade what both already know, is the oldest device of the stage, and the turns can feel wound by the plot.
Herman Melville · Literature
8.8 · Tier IV
The test is subtractive and finds almost nothing to take. The materials are few and each is used twice: the formula; the walls, onto which the office looks and at the foot of which Bartleby dies; the copying that becomes the refusal to copy; the word “prefer” itself, which spreads through the office until Turkey and Nippers use it without noticing. The long opening portraits of Turkey and Nippers, whose tempers relieve each other morning and afternoon, look like the padding of a magazine sketch and are not: they set up an order in which every eccentricity is tolerated so long as copy is produced, which is the economy Bartleby breaks. What holds the axis is the coda. The rumour of the Dead Letter Office is told as hearsay after the death, and the story could be argued complete without it; it stays, because it gives the narrator his last failed explanation.
Anna Akhmatova · Literature
8.8 · Tier IV
The subtractive test finds almost nothing to take, and what each piece does is plain. The epigraph says where the speaker stood; the Preface says who asked for the poem and why; the Dedication turns the private wait into the common one; the ten numbered poems carry a single mind from the arrest through madness to the cross; the Epilogue makes the monument. Remove Crucifixion and the cycle loses its height and its law; remove the Preface and it loses its mandate. The scale is compelled: a cycle of fragments for a time when nothing longer could be held in memory. Held below 9.0 because VI, on the light weeks flying past, and IX, where madness spreads its wing, do work that V and VII do more strongly, and either could go with little lost.
Gustave Flaubert · Literature
8.8 · Tier IV
Within each tale the subtractive test is hard to pass. “Un cœur simple” compresses half a century into five sections and nothing in it is idle: the bull in the meadow, the walk to Honfleur, the whip across her face on the road, each is called on later. Its first sentence states the whole frame. “Saint Julien” has the inevitability of its prophecy, and every hunt is a step toward the bedroom. What holds the axis below the top is the book as a book: whether the triptych is required or three finished things bound together is a fair question, and “Hérodias” carries archaeological furniture (the citadel, the stores of arms, the factions at the banquet) that its drama does not all need.
Chantal Akerman · Film
8.8 · Tier IV
The design makes length the argument, and the subtractive test meets it. The first day’s tasks, shown whole and in their own time, are required, because the second and third days can only be read against them: an uncovered pot, a dropped spoon, a button not matched, hair out of place mean catastrophe only to a viewer who has learned the order. Remove the repetition and the deviation is invisible. The few scenes of speech are required too: the sister’s letter from Canada, the one other life on offer; the son’s talk in the dark, the one place the buried subject is spoken; the neighbour at the door, the world’s noise. What is charged: some errands of the first day extend the norm past the point where the viewer has it.
Anonymous · Architecture
8.8 · Tier IV
Judged on plan, section and site. Take away the compound piers and the double bay loses the springing of its vault; take away the cylinders and its two crossings of ribs have nothing to rest on but wall. Take away the galleries and the hidden bracing loses its roof, and the high vault its brace. The alternation that orders the eye is the alternation that carries the stone. The site compels the rest: a church on the neck of rock above the gorge, opposite the castle, with no room to spread. The Nine Altars was compelled, by the shrine’s crowds. What resists the test is in the church as it stands: the incised patterns, ordered rather than required, though they mark the rhythm; the Victorian screen and glass; Cosin’s font cover.
Anonymous · Architecture
8.8 · Tier IV
Run the subtractive test on the Western Precinct and it holds. Take away the pagoda and the precinct loses its relics and its vertical; take away the Kondō and it loses its images; take away the cloister and the pair is no longer a sacred enclosure but two buildings in a field. The Chūmon’s four bays and the post on its axis are compelled by the plan: the gate faces a pair, not a single object, and the post divides the approach between them. In the Eastern Precinct the octagon answers the circling of a memorial. What holds the axis is the Kondō’s upper storey and second roof, there for the profile, permitted by dignity rather than compelled by use; the Edo props answered need, not the first plan.
Béla Bartók · Music
8.8 · Tier IV
The subtractive test meets resistance in three of the four movements. The fugue cannot lose an entry: each adds the next fifth outward from A, and the last brings the climax, so a cut breaks the count the form is built on. The Adagio’s arch needs both its halves, and its centre is the panel the frame exists to hold. The finale’s return of the fugue subject, widened from chromatic to diatonic, is the work’s answer and cannot go. The give is in the second movement and the finale. The Allegro’s development runs longer than its argument needs, and the finale’s episodes are a chain of dances in which one more or fewer would be heard as different, not as wrong.
Johannes Brahms · Music
8.8 · Tier IV
The subtractive test meets resistance almost everywhere. The first movement drops the exposition repeat, the first of Brahms’s symphonies to do so, and nothing is said twice that the argument does not need; its chain of falling thirds is the source of every paragraph, the canonic close of the coda included. The finale cannot lose a variation without the arithmetic of the ground showing: thirty-one statements of eight bars, each a step in an accumulation, and the central E major group is the one place the pace changes. The give is in the third movement, whose high spirits stand outside the tragic frame and are answered by the key plan more than by the hearing.
Johannes Vermeer · Visual art
8.8 · Tier IV
Judged on structure. The sky cannot go: it is the source of the painting’s one event, the cloud whose passing puts the near town in shadow and the far town in sun. The water cannot go: it doubles the town and sets the viewer outside the walls. The town cannot be thinned: two gates, a bridge, the long outwork and two towers each hold a place in one horizontal, and the Nieuwe Kerk tower is the only vertical that reaches the light. The near bank is where the viewer stands, and its shadow measures the sun. The figures are the one give: they could be fewer, though they supply the scale and the picture’s only consciousness. Held short of the top for them, and for the ease with which one compact image passes the test.
Wong Kar-wai · Film
8.7 · Tier IV
Judged on structure and the cut. What was kept resists the subtractive test, because the repetitions are the content: the walk to the noodle stall, the passing on the stairs and the rain return, each in a different dress, and they are how the film counts time and shows two people circling what they will not do. The discovery through a handbag and a tie, each the double of a spouse’s, is the hinge. The rehearsals, where the pretence becomes the feeling, are required; the night trapped by the neighbours’ mahjong makes the building’s gaze a wall; and the coda is required, since a secret needs a place to be buried. What gives is the thin Singapore section and the employer’s affair, which doubles a theme the main story has already made.
Ludwig Mies van der Rohe · Architecture
8.7 · Tier IV
Judged on plan, section and structure, under purpose and site. The subtractive test is this building’s own method. Take away the onyx wall and the centre of the plan, the place of the chairs and the book, is gone. Take away the court and its figure and the route has no end. Take away the large pool and the podium loses its mirror and the roof its double. Take away the wall of light and the room has no light of its own. Take away one glass plane and a path closes. Eight columns set the roof; the travertine grid sets every wall’s length and place. What resists: the programme compelled almost nothing; each wall is required, but its exact position is compositional; and it is doubted that the eight columns alone carried the original roof, so the plainest necessity the building states was partly rhetoric.
Martin Scorsese · Film
8.7 · Tier IV
Judged on structure and on the cut. The film runs close to two and a half hours over thirty years, and almost nothing idles: Thelma Schoonmaker’s editing drops whole years in a freeze-frame and a line of narration, and each scene is kept only as long as it pays. The subtractive test is hard to pass. The Bamboo Lounge introductions, the painting at Tommy’s mother’s table, the garlic sliced with a razor in prison, Morrie’s wig commercial: each looks like colour and is load-bearing, since the texture is the argument, the life as a job and a pleasure. What gives: the affair with Janice runs slightly past its use, and the Tampa debt collection, with the lions, is an anecdote the film enjoys rather than needs. Those are weighed, and the figure stands high.
Hans Holbein the Younger · Visual art
8.6 · Tier IV
Judged by subtraction, and there is almost nothing to subtract. The body is the work. The slab carries it, and the white sheet crumpled under the back is the one soft thing, the only sign that hands laid him there. The lid is the argument of the format: without it the body lies in open air, a study; with it the dead man has no room, and the hair and the right hand spill over the edge because there is nowhere else for them to go. The wounds make this corpse this corpse, and the open eyes and mouth cannot go. What yields is at the margins: the inscription is a gloss rather than a structure, and the far end of the niche is permitted by the format more than compelled by it.
Anonymous · Architecture
8.6 · Tier IV
The subtractive test is the garden’s own method. Inside the wall there are fifteen stones, moss and gravel, and nothing else: no tree, no water, no lantern, no path. What remains carries the whole. Take away one group and the balance of the long rectangle tilts. Take away the moss and the stones become objects on a floor rather than land rising from a sea. Take away the wall and the gravel loses its edge and its scale against the trees beyond. The pull between the dense eastern group of five and the scattered groups to the west makes the field read as a field. Other arrangements might be proposed; nothing in this one is idle. Held short of the top only because its argument is small.
Louis Kahn · Architecture
8.6 · Tier IV
Run the subtractive test, and almost nothing is idle. Take away the slot and there is no light; take away the reflector and the light falls as glare on the floor; take away the cycloid and the light has no surface to spread over, for the curve’s low rise and steep sides were chosen to carry the day down the shell. Take away the channels and the services cut into the rooms; take away the courts and the field becomes a warehouse. The porches look superfluous, a vault with no room beneath, but they are the threshold and the statement of the unit. What yields: the number of vaults is ordered, not compelled; the vault’s form is compelled by light more than by structure; the partitions under each vault are arrangement.
Paul Cézanne · Visual art
8.4 · Tier IV
The subtractive test is the series’ own method: the painter ran it, from five figures to four to two, and this canvas is what survived the subtraction. Remove either player and there is no game and no confrontation. Remove the bottle and the axis goes: it stands on the centre line, the one vertical between two leaning masses, and its pale highlight is the brightest small note in the picture. Remove the pipe and the left player loses the one detail that sets him apart from his opponent. The table’s edge holds both. What yields is in the margins: the background is barely articulated and could be worked otherwise without loss, and the counts of folds and creases are not structural. The small scale is compelled, a closed world for two. Held below 9.0 because the parts are few and a few are slack; above The Large Bathers at 8.4, whose population is permitted.
Cistercian builders · Architecture
8.4 · Tier IV
Run the subtractive test on the church. Remove a bay of the aisle and its half barrel no longer leans against the nave vault; remove a window and the light that marks the hours is lost. There is no ornament to remove, since the rule had removed it before the builders began. The pointed section of the vault is the structure’s choice, not a style. The cloister is the clearest proof: its irregular plan is what the slope compelled, the galleries stepping down rather than the site being levelled. What resists: the stone belfry is a local licence, not a requirement, and the cloister piers carry more than the low vaults demand.
Li Chun · Architecture
8.2 · Tier IV
Judged on purpose, structure and site, the bridge yields almost nothing to the subtractive test. The low arch is compelled by the purpose: a road for carts across a river that floods, at a gradient a laden cart can climb, on one span that keeps piers out of the current. The spandrel openings are compelled twice, by weight, since they remove fill the arch need not carry and lighten the load on soft ground, and by flood, since they pass water a solid spandrel would dam. The shallow abutments follow from the soil. What yields: the carved balustrade could go and the bridge would carry as before, and the parallel rings answer the method of building, not the bridge.
James Joyce · Literature
9.5 · Tier V
Judged partly on Joyce’s English. Length is not a cost; the question is whether the parts are required. The scale is compelled: eighteen hours of one city, bound by refrains so exact that only 0.30 per cent of the words sit inside repeated ten-word runs, and every frequent repeat is deliberate, as with “What is home without Plumtree’s Potted Meat?” (Lotus Eaters, 5). The first nine episodes yield almost nothing to the subtractive test. What holds the axis at 8.8 is the second half: the Cyclops interpolations, the Bloomusalem pageant in Circe, the slang that ends Oxen and Ithaca’s longest inventories could each lose a third without losing a fact or a joke. Each parody is required; its length is not always.
Du Fu · Literature
9.2 · Tier V
At the scale of the poem the subtractive test fails almost everywhere. In “Spring View” every couplet does work no other could: the first sets the ruined state against the indifferent earth, the second turns it inward to flowers and tears, the third gives the war its time and its price, “烽火連三月，家書抵萬金”
“beacon fires have burned three months on end; a letter from home is worth ten thousand in gold”, and the fourth shrinks it to one body, white hair too thin for the hatpin. In seven regulated poems, 296 characters, no character repeats except in a chosen reduplicative binome. The sequences are each compelled. The body is not: it holds hundreds of poems of thanks, request and exchange whose loss would not change what Du Fu is, and they hold the axis below the single poems.
Gustav Mahler · Music
9.2 · Tier V
The test meets its hardest resistance in the outer movements. The first grows from four fragments heard before any theme, and every wave is built from them; the catastrophe is the opening rhythm returned in trombones and timpani, so no wave can go without the collapse losing its cause. The Adagio’s strophes thin on purpose, and the Adagissimo coda is where the claim is made; cut it and the work has an ending instead of a dying. Length is not charged. The test still finds give: the Ländler’s later returns, which state the coarseness past understanding, and the Rondo’s long counterpoint before its episode. Both are chosen; the charge is for the degree, not the choice.
Claude Debussy · Music
9.1 · Tier V
The subtractive test was applied once by the composer: four of the play’s nineteen scenes are gone, the servants’ two, Pelléas’s leave to go, the spinning scene, each a commentary, a delay or a doubled situation. What remains is a chain in which each small thing causes the next: the ring falls at noon, the horse falls at noon, the lost ring sends her to the cave with Pelléas, the hair brings Golaud’s laugh, the laugh the vaults and the warning, the warning the child at the window, the window Act IV. The orchestra plays for the words or stops. The test still finds give: the sheep scene, essential and separable, which houses cut; interludes whose length the stage set; the cave, a tableau. On the music alone, two tenths higher.
Matthias Grünewald · Visual art
9.1 · Tier V
Judged on structure. Closed, no field could go: the Crucifixion is the subject, Sebastian and Anthony are a hospital’s two intercessors against plague and fire, and the Lamentation completes the Passion at the height of the altar table. At the first opening the Annunciation, Nativity and Resurrection are the Incarnation’s three hinges, and the Concert is the threshold between two of them. The second opening is the house’s saint, his hermit and his torment. What holds the axis lowest, beside one other, is the shrine: carved before the painting was conceived, it is a given the painting was built round, not a necessity of its argument. Within the painting, the Concert’s tabernacle runs past what it needs, and the Annunciation is the field the sequence could most nearly lose.
Jorge Luis Borges · Literature
9.0 · Tier V
The prologue states the principle: “Desvarío laborioso y empobrecedor el de componer vastos libros” (a laborious and impoverishing madness, the composing of vast books). The stories obey it. Within each, the subtractive test finds nothing: “Las ruinas circulares” is a single movement from the landing in the unanimous night to the fire; “Funes el memorioso” has not a sentence beyond what the memory needs; the review form of “Pierre Menard” and of “Herbert Quain” removes the narrative padding a novel would carry. Across the book the test bites a little. “Herbert Quain” is slighter than its neighbours; “La forma de la espada” and “Tema del traidor y del héroe” spend their weight on a reversal; and of the stories added in 1956, “La secta del Fénix” is a riddle more than a story. The book returns to its labyrinths and mirrors often enough that one or two pieces could go with the knowledge unchanged.
Orson Welles · Film
9.0 · Tier V
Judged on structure. The newsreel is required: it gives the whole life in a few minutes so that the five accounts can be read against a public version. Each witness is required for a stretch no other covers: Thatcher for the boy and the money, Bernstein for the paper, Leland for the marriage and the campaign, Susan for the opera and Xanadu, Raymond for the end. Rosebud is required as the question that keeps the reporter moving and the answer the film gives only to the audience. The breakfast table and the Chicago review are compressions a longer film would have spread. The give is in display: the crane through the El Rancho skylight, the opera-house crane to the stagehands, flourishes that demonstrate the apparatus beyond what the argument needs.
Khmer, under Suryavarman II · Architecture
9.0 · Tier V
Run the subtractive test from the outside in. The moat cannot go: it is the ocean round the world. The causeway cannot go: it is the only way across, and the axis it lays down is the argument. The three galleries cannot go, because each is a range of the mountain and the ascent requires all three, and the five towers are Meru’s five peaks. Structure compels as much as meaning: the corbelled vault fixes the narrow width of every gallery, and the terraces fix the stepped mass. What resists the test is the wide precinct inside the outer wall, whose purpose has gone; the paired libraries and basins; and the ornament on nearly every surface. The devatas could be thinned without loss of argument.
Chola, under Rajaraja I · Architecture
9.0 · Tier V
Run the subtractive test from the gate. The two gateways frame the tower twice and set the axis. The second wall makes circumambulation a structure rather than a custom, and its passage is required by it. The tower is required: it is the mountain of which the sanctum is the cave. Two things resist the test. The miniature pavilions on the tiers repeat by rule, multiplied by a canon rather than an argument. And the height was permitted by a conquest treasury as much as compelled by the rite: the same worship would be served under a tower half as high. The full height is necessary to a statement, that the god stands at the summit of the realm, not to use.
Ludwig van Beethoven · Music
9.0 · Tier V
Length is not charged: the Ordinary has five parts, and Beethoven sets every clause. The subtractive test meets resistance at the hinges. The Kyrie’s three parts, with the Christe as the human plea between two addresses to the Lord, cannot lose one. The Credo’s repeated “Credo” is the frame that holds its many clauses; take it out and the movement becomes a list. The Praeludium stands where the elevation was silent and is the bridge the Benedictus descends from. The war in the Agnus Dei is what makes its prayer for peace a prayer. The test finds give in the Gloria, where some clauses are set at a pace that crowds rather than compels, and in the Credo’s closing double fugue, whose length the argument permits more than it requires.
Virginia Woolf · Literature
9.0 · Tier V
The test is subtractive, and it finds very little to take. The two strands are the argument: without Septimus the party is a comedy of manners, and without Clarissa his death is a case history. What looks detachable is mostly load-bearing. Lady Bruton’s luncheon, where she has a letter to the Times on emigration to Canada composed for her, is Bradshaw’s Proportion practised as policy. Miss Kilman’s afternoon with Elizabeth gives Clarissa her hated double and the next generation its one free ride, Elizabeth on an omnibus up the Strand. Even the ambulance that passes Peter carries Septimus’s body. What holds the axis below 9.0: Peter’s memory of Bourton returns to the same refusals more often than it needs; his dream of the solitary traveller, fine in itself, could go without the book losing a joint; and the satire of Hugh Whitbread runs longer than its point.
Gustav Mahler · Music
9.0 · Tier V
The subtractive test meets resistance at the ends. The first song states the case and the last answers it, and the funeral interlude that joins the two poems of “Der Abschied” is the death the text never names; remove it and the friend’s farewell becomes a scene, not a passing. The alternation of voices is required: the tenor’s songs are intoxication, the alto’s solitude and leave-taking, and the order sets them against each other. “Von der Jugend”, the shortest, is needed for its mirror. The give is in the middle: “Der Trunkene im Frühling” restates the first song’s answer in a lighter key, and the horsemen of “Von der Schönheit” are a genre picture more than a step.
Plato · Literature
8.9 · Tier IV
Take out any of the three speeches and the work stops being what it is. The oracle story (21a to 23b) is the warrant for the whole life: without it the examination is impertinence, with it obedience. The cross-examination of Meletus is required, the one place the method is performed rather than described, on the accuser, in court. The public record (31c to 33a) answers why a man so certain of his duty kept out of politics. The counter-penalty is the hinge, where the proposal of meals in the Prytaneum turns the defence into a refusal to bargain, and the farewell reads the death from the far side of it. Little is idle; some of it is longer than it need be. The cross-examination runs three arguments where one would convict Meletus of never having thought about the young: the horses and their trainers, the proof that no one corrupts willingly (25c to 26a), and the trap about the children of gods that ends in mules born of horses and asses (27d to e). The record under the democracy and the Thirty is a second answer to a question the first has settled, and the round of politicians, poets and craftsmen comes three times to the same result.
James Joyce · Literature
8.9 · Tier IV
The book was cut from Stephen Hero, the longer draft Joyce abandoned, and the cutting is its method: no exposition, no connective narrative between sections, each section the scene in which a stage of the soul is fixed. The subtractive test finds the spine required. Remove Clongowes and the later rebellion has no first injustice behind it: the unjust pandying and the walk to the rector’s room are the first refusal in small. Remove the Christmas dinner and nation and church never meet at the family table. Remove the sermons and the fourth chapter’s piety and the fifth chapter’s revolt have nothing to answer. The rhythm of rise and collapse requires each climax. What holds the axis a step below the top is the last chapter: the aesthetic discussion with Lynch, the walk with MacCann and the long exchange with Cranly carry more talk than the knowledge needs, and parts of the sermons repeat their terror after it has landed.
Toni Morrison · Literature
8.9 · Tier IV
The book is built of returns, and the test is whether the returns are required. They are. The killing in the shed is told in pieces, by Stamp Paid’s newspaper clipping, by schoolteacher’s cold eye, by Sethe circling the kitchen while Paul D waits, and each piece is needed because the act cannot be taken in at once, by him or by the reader. Remove Paul D’s chain gang in Georgia and the book loses the man’s half of what was done to bodies; remove the monologues of the second part and Beloved is never given her own voice or her other origin. What holds the axis a step below the top is a little that is permitted: Edward Bodwin’s ride to 124 in the third part, with its reflections on his father’s house, delays more than it adds; some memories of Sweet Home are told twice with less new each time; and the carnival and Paul D’s lodging in the church cellar are lighter than their place.
John Coltrane · Music
8.9 · Tier IV
Four parts in about thirty-three minutes, and the subtractive test finds almost nothing to take. The titles are an order of devotion, and each part is the stage it names. Remove Resolution and the turn from thanks to vow is skipped; remove Psalm and the pursuit ends in fury instead of prayer; remove Acknowledgement and the four-note figure the rest answers has no source. The material is small, a bass cell and three themes, and it is spent, not displayed. The test bites twice, and both times inside parts that are themselves compelled: Garrison’s unaccompanied solo closing Pursuance is longer than the bridge to Psalm needs, and Tyner’s solo in Resolution is the quartet’s ordinary excellence. No part could go.
Carl Theodor Dreyer · Film
8.9 · Tier IV
The trial ran over months in 1431; the film compresses it into what plays as one day, and the compression removes almost everything a trial film would carry: no witnesses, no journey, no battle, no king. What is left is a sequence in which each step is a new instrument of pressure: the question, the forged letter read by the false friend, the crown of straw, the wheel, the threat of dying without the sacrament, the open grave. Each turns the screw one notch. The abjuration is impossible without all of them, and the recantation impossible without the shorn head. What is charged: in the long interrogation some exchanges do the same work twice, and the riot after the burning runs a little past what it needs to show.
Leo Tolstoy · Literature
8.9 · Tier IV
Judged on the work for structure, and on the Russian in part. The subtractive test finds little. Each vantage carries a part of the argument the others cannot: the picket gives the common soldier’s war and Avdeev’s death; Avdeev’s village gives what the empire costs its own peasants, his wife’s relief at the news included; Nicholas and Shamil must both stand, because the book’s claim is that the two despots are one. The frame must stand, since without the thistle the death is an anecdote of the Caucasian War. Three places bite: the life Hadji Murat tells Loris-Melikov is long exposition by recital; the Tiflis chapters of cards, ball and theatre make their point before they end; and the Nicholas chapter presses the seduction and the vanity past what the parallel with Shamil requires.
Giuseppe Verdi · Music
8.9 · Tier IV
The subtractive test meets resistance along the spine. Act I is required by Act III: the party Violetta sings over in “Sempre libera” is the carnival that passes her window as she dies, and the “Di quell’amor” theme she mocks is the one the violins play under the letter. Remove the duet with Germont and the opera has no cause; remove the card game and the money thrown and the sacrifice has no visible price. The test finds give in three places: Alfredo’s and Germont’s cabalettas in Act II, long cut in common practice with little loss to the argument; the gypsy and matador choruses at Flora’s, which the plot waits through; and the second strophe of “Addio, del passato”, which restates the first.
Robert de Luzarches, Thomas and Renaud de Cormont · Architecture
8.9 · Tier IV
Run the subtractive test on the building as it stands. The plan resists it: a nave long enough for a city’s crowds and processions, an aisled transept, a double-aisled choir for the chapter, and an ambulatory and seven chapels by which pilgrims passed the relics. The elevation resists it most: arcade, triforium and clerestory are one bay repeated, and the arcade raised to about half the vault’s height makes nave and aisles one space rather than a tunnel with corridors. Outside, the flyers are the structure, and none can go. What yields is the west front above the portals: two galleries and a rose stacked to screen a nave taller than the front, and towers stopped short and unequal, recording the building’s history more than its need.
Guo Xi · Visual art
8.9 · Tier IV
Judged on the configuration. The central massif cannot go, nor its S-curve, which is the movement of the whole: rock rising out of mist, turning, rising again. The mist cannot go; it separates the stages of the ascent and makes the mass seem to breathe. The bare trees of the foreground give the scale and the season, at the first warmth. The three distances are each required, because the eye needs all three to travel: up the axis, into the right-hand cleft, out over water at the left. The small figures cannot go; without them nothing in the picture is a journey or a dwelling. What yields is extent at the margins, some subsidiary ridges and the far left recession, permitted by the format more than compelled by it.
Ming, under the Yongle Emperor · Architecture
8.9 · Tier IV
Run the subtractive test along the axis. The moat and the wall cannot go: the palace is defined by exclusion, and its name says so. The Meridian Gate, the Gate of Supreme Harmony and the Gate of Heavenly Purity cannot go, because each is a degree of access, and access is what the plan grades. The three halls cannot go, nor the one terrace that lifts the ritual of the state above everyone else’s ground. The division of Outer and Inner Court is compelled by the rule that the court stands in front and the residence behind. Structure compels as much: the timber frame on the bay module sets every hall’s proportion. What resists is repetition. The Six Eastern and Six Western Palaces and the ranks of side halls and storerooms could be thinned without loss of argument.
Johann Sebastian Bach · Music
8.9 · Tier IV
The large plan resists the subtractive test. The canons climb one interval at every third variation, unison to ninth, so no canon can go without breaking the ladder. Ten groups of three, two halves turning on the Ouverture, and thirty-two pieces answer the Aria’s thirty-two bars. The return is compelled by the first piece, whose tune the variations leave unheard until the end. The give is in the free variations: within a group the character piece and the virtuoso piece could change places, and to lose Var. 17 or Var. 20 would cost brilliance, not a step in the argument. Performances without most of the repeats lose less than their length.
Franz Kafka · Literature
8.8 · Tier IV
The test is subtractive, and at the scale of a story it finds almost nothing to take from the first four movements. The officer’s long exposition is the action: every part of the apparatus he explains is one the story later needs, from the Designer’s cogwheels to the felt gag in the mouth, and the condemned man’s dumb curiosity and the soldier’s boredom are timed against it. The reversal is prepared by the officer’s own principle, “Die Schuld ist immer zweifellos”, guilt is always beyond doubt, which he applies at last to himself. The teahouse grave, with its prophecy that the Commandant will return, is required, since it places the officer’s faith in a line of believers. What holds the axis is the last scene, the traveller warding the soldier and the condemned man off from the boat with a knotted rope, which repeats his refusal in action but is looser than all that precedes it.
Caravaggio · Visual art
8.8 · Tier IV
Judged part by part, by subtraction. Saul cannot go: he is the event. The horse cannot go: it is the reason the picture is not an icon, the mass of the ordinary world over the man, and its lifted hoof is the one act of care in the picture. The groom cannot go: he is the witness who sees nothing, and without him the conversion has no outside. The fallen helmet and sword are the soldier’s life laid down; the light is the only sign of heaven. What yields is the groom’s lower body, crowded behind the horse and hard to read, and the horse’s sheer extent, larger than the argument strictly compels.
Donatello · Visual art
8.8 · Tier IV
The subtractive test, part by part. The boy cannot go, nor the head: the work is the relation between them, a weight resting on a weight, the living foot on the dead face. The sword cannot go; it is too large for him, and that disproportion is the story told in one object. The stone cannot go, for it is the cause of which the sword is only the sequel. The wreathed hat cannot go: it shadows the face and turns the victory inward. The feather rising along the inside of the leg is the boldest part and the most argued, and it is required, the one place besides the foot where giant and boy touch. What yields is the small relief on the helmet, which the eye cannot read at viewing distance, and the boots, a decision of costume more than a necessity. Nothing is idle at the scale of the whole.
Albert Camus · Literature
8.8 · Tier IV
The test is subtractive, and it finds almost nothing to take. The vigil and the funeral must come first, because the second part will try them; the swim with Marie and the Fernandel film the next day are the prosecutor’s evidence before they are anything else; and Raymond’s letter, which Meursault writes because he has no reason not to, is the chain that leads to the beach. Salamano and his dog, which look like local colour, are the book’s other mourning: the old man abuses the dog for years, loses it and weeps, and Meursault, hearing him through the wall, thinks of his mother. The clipping about the Czech who returns home rich and is killed by his mother and sister, read and reread in the cell, is the novel’s own story inverted. The scale is compelled, since a life with no hidden depths needs no more pages. What the test can take is small: the little robot woman at Céleste’s, and part of the chaplain’s exchange, do work the action has already done.
Thomas Mann · Literature
8.8 · Tier IV
The subtractive test finds almost nothing loose in the first, third and fifth chapters. Each death figure is required: the red-haired stranger at the Munich chapel who starts the journey, the painted old man on the steamer who is Aschenbach’s own future, the gondolier who rows him where he does not mean to go and vanishes, the singer whose laugh is the plague’s. Each answers the others, and the last chapter gathers them. The failed departure, the luggage sent astray, is the hinge on which choice becomes fate; it cannot go. The charge falls on the second chapter and parts of the fourth. The account of the works and of their ethic of endurance, the motto “Durchhalten”
“Hold out” (II), is needed in substance, since the fall is measured from that height, but it is told as an essay and could be shorter; and the Platonic set pieces run longer than the action requires.
Herman Melville · Literature
8.8 · Tier IV
The test is subtractive and finds almost nothing to take, because the design is what the work says. Delano’s day must be long: the reader has to share his misreading for hours, and each spasm of suspicion, the men polishing hatchets, the boy struck with a knife, Atufal brought in chains every two hours, the old sailor’s knot, has to be raised and soothed by his good nature, or the reader is not implicated. The deposition must follow in its dry legal order, because only the master’s document can undo the master’s view, and it too is partial. The coda must stand, because it names the shadow. What holds the axis: the cycle of suspicion and reassurance turns once or twice more than the mechanism needs, and the deposition carries particulars, the inventory of the dead and some of the voyage before the revolt, that a reader feels as length.
Louis Kahn · Architecture
8.8 · Tier IV
Run the subtractive test, and it finds very little to take. The chamber is the centre and everything is ordered around it. The ambulatory makes a threshold between the city of offices and the room of assembly. The outer walls temper the light and heat of the climate before they reach the rooms. The lake sets the building apart from the city, cools the site and lifts it from water in a deltaic country. The cut openings are not ornament but the means of letting light through thick walls without letting the sun in. What resists: the mass and height of the ring exceed what the offices require, a scale permitted in part by the will to monument rather than compelled by use.
Sophocles · Literature
8.8 · Tier IV
The subtractive test finds little to cut. The prologue sets the lie and the young man’s reluctance in one exchange. The Merchant’s scene, which looks like an excursus, turns the screw: it tells Philoctetes he is hunted by the very men he is now trusting, and makes the lie unbearable to hold. The attack of the disease is the hinge on which the bow passes to Neoptolemus; without it the deception would succeed by plot instead of failing by pity. Each passage of the bow, given, kept and returned, is a required step. Held below 9.0: the abandonment is retold more than once, and the oracle’s terms (the bow, or the man?) are stated variously, so that some exposition seems placed for the plot’s convenience.
Jonathan Swift · Literature
8.8 · Tier IV
The test is subtractive and finds almost nothing to take. The opening scene must come first, because the projector’s pity is the bait: “It is a melancholy object to those, who walk through this great town”. The arithmetic must precede the proposal, because the proposal is its conclusion, and the horror is that it follows. The culinary particulars, “whether stewed, roasted, baked, or boiled”, are required because the reasoning must reach the kitchen to show where reasoning of this kind ends. The advantages, the refused alternatives and the close are each required. What holds the axis off the top: the rejected scheme for adolescents and the story of Psalmanazar are a second turn of the screw that a stricter economy could lose at little cost, and some of the six advantages repeat the shape of the one before.
Mimar Sinan · Architecture
8.8 · Tier IV
Run the subtractive test, and it bites on little. The central dome rests on four piers; the semidomes take its thrust on the qibla axis; the lateral thrust goes to buttresses drawn into the side walls and masked behind two-storey galleries, so that what elsewhere would be props reads as wall and loggia. The tympana carry no thrust and are opened to light. The court is required by a Friday congregation that overflows the hall; the minarets stand at its corners, where the call is given and the approach is framed. What resists is symbolic surplus: ten balconies are more than the call needs, and four tall towers serve rank as much as use. The plan, too, is a received scheme, chosen rather than compelled by this site.
Anonymous · Architecture
8.8 · Tier IV
Run the subtractive test. The lower chapel cannot go: it lifts the upper chapel to the king’s apartments and gives the household its own church, so the plan states rank by storey. The buttresses cannot go: once the wall is glass they are the structure. No window can go, since each holds a part of the history that runs to the relics. The tribune is the point the plan converges on; the apostles stand where the load comes down. What resists is surplus inside the glass: more than a thousand scenes, most unreadable from the floor, and a goldsmith’s profusion of gables and gilding beyond what the use compels.
Anonymous · Architecture
8.8 · Tier IV
The core resists the subtractive test, and the core is most of the building. The five vessels and the double ambulatory are required by a cathedral of a capital: a great clergy in the choir, a city’s crowd circulating round it. The height requires the flyers, the flyers the buttress piers, and the piers generate the chapels between them: one chain of necessity from plan to chevet. What holds the axis is the edges. The church stood for decades without a spire, and Viollet-le-Duc’s asserts the crossing without being required by it; the chimeras could go with nothing lost but the picturesque; the marble of the Vow fills a sanctuary the Gothic choir had defined; the 2024 furniture states a programme rather than answering a need.
Nick Cave and the Bad Seeds · Music
8.8 · Tier IV
The two-part plan is compelled. Eight short songs of vision come first, then three long pieces in which vision becomes knowledge, and the parable that closes Hollywood could stand nowhere earlier. Ghosteen Speaks gives the dead a voice and Leviathan answers it with love returned; together they are the hinge into the second part, and neither could be cut. The long pieces are not charged for their length, because their length is what they say. No track could go whole. The test finds give only in the middle of the first part, where Night Raid, Sun Forest and Galleon Ship share one register of drifting pads, a vision of flight or light and a refrain, and the three do the work of two. That thinning, not a removable song, holds it from the top.
Edvard Munch · Visual art
8.7 · Tier IV
Judged subtractively on the configuration. Remove the two walkers and the picture loses its second fact, that this happens to one person while the others, a few steps away, hear nothing; the cry becomes a state of the world rather than an isolation. Remove the railing and the one straight, made thing in the field goes, and with it the argument between the line that recedes in order and the curves that take the figure. Remove the sky and the cry has no source. Remove the hands and he is shouting, not hearing. The scale, small and close, is compelled: larger, the board would become a stage. What gives is at the margin: the shore is a count, not a structure, and passages of the fjord are filler between the bands.
Andrea Mantegna · Visual art
8.7 · Tier IV
Judged figure by figure, the picture is almost all requirement. Remove the slab and the body floats: it is the stone of anointing, and the corpse’s weight is known by what it rests on. Remove the shroud and the body becomes an anatomy study; its heavy folds make the legs a dead thing under cloth. The jar names the act, anointing for burial. The pillow raises the head just enough for the face to be seen down the length of the body, and the wounds sit where a viewer at the feet must meet them first. What yields is the mourners. The Virgin’s face is the human cost and cannot go, but the group is crowded, the third figure is a fragment, and the picture could stand, colder, as the body alone.
Masaccio · Visual art
8.7 · Tier IV
Tested by subtraction, the fresco gives up very little. The collector cannot go: he is the question, and his back, turned to us inside the ring, makes the viewer stand where he stands. Christ cannot go, nor the pointing that runs from his hand to Peter’s and on to the lake. Peter at the left and Peter at the right cannot go, for the miracle and the payment are the answer, and without them the centre is a dispute with no resolution. The ring is compelled by number and by its work: it closes on the stranger. What yields is small: heads at the back of the ring required by the count more than by the argument, the bare hills, and a building needed for the payment that holds nothing of its own.
Sophocles · Literature
8.7 · Tier IV
The subtractive test finds very little. The prologue must stand: Orestes’ plan of a false report of his own death is the engine of everything after. Chrysothemis comes twice and both visits are required: first as the sister who submits, carrying Clytemnestra’s offerings after the dream of the sceptre; then with the true news of the lock on the tomb, which Electra, already holding the false news, refuses, and which drives her to resolve on the killing alone. The agon with Clytemnestra must come before the false report so that the mother’s relief can be seen. The long speech of the chariot race at Delphi is the one place a reader asks whether so much is needed, and it is: its length makes a lie into a death. Held below 9 by that speech’s ornament and the second Chrysothemis scene’s length.
John A. Roebling and Washington Roebling · Architecture
8.7 · Tier IV
Judged on structure, purpose and site, and the river compels the first fact. A navigable tidal channel that would take no pier in midstream, and a clearance set for shipping, ask for one span of nearly sixteen hundred feet and towers tall enough to hang the deck some 135 feet over the water. The rest follows from tension and compression. Take away the anchorages and the cables have nothing to pull against; take away the towers and they have nothing to ride over. The stays and the stiffening truss answer the wind. The promenade is required by the purpose as the makers framed it. What yields: the stays double the suspenders’ work, an insurance more than a need; the pointed arches and cornices are a chosen dress; the approaches run long.
Caravaggio · Visual art
8.7 · Tier IV
Judged figure by figure. Christ cannot go: he is the light and the weight. Nicodemus cannot go: he carries the weight, and his outward look is the hinge to the viewer. John cannot go: his hand at the wound joins the bearing of the body to the sacrament. The Virgin, arms opened rather than raised, is the stillest grief, the Magdalene the inward one. The slab cannot go: it is altar, foundation and the floor the body will be laid on. What yields is Mary of Cleophas: her raised arms start the cascade, but they are the most theatrical gesture in the picture and the first a hostile eye would remove. The plant at the corner is a small surplus.
Henrik Ibsen · Literature
8.7 · Tier IV
Subtract anything and something breaks. The hat Hedda pretends to take for the maid’s is her contempt for the Tesman world in one gesture, and it is the first thing she does. The slippers Aunt Rina embroidered, which Tesman unwraps and Hedda will not look at, set the house’s sentiment against her. Thea’s account of Løvborg’s reform makes Hedda’s jealousy possible; the school memory of threatening to burn off Thea’s hair prepares the burning of the manuscript. The pistols are shown in the first act, fired in sport at Brack in the second, given to Løvborg in the third and traced by Brack in the fourth. What could go: the professorship thread, slack once Løvborg withdraws, and a little of Aunt Julle’s second visit.
Raphael · Visual art
8.7 · Tier IV
Judged figure by figure, the canvas resists subtraction. The Virgin is the event, a woman walking forward on cloud with the child held high. The child’s grave, direct look is the second face of the argument. Sixtus’s pointing hand is the hinge between the vision and the people before the altar, and his tiara on the ledge is the earthly office set down. Barbara looks down toward the place of the congregation and balances his upward look, so that the triangle of the three heads holds the whole. The curtains are the act of revelation; the ledge is the threshold. What yields is the pair of putti: the picture would stand without them, and the long history of their detachment as an image of their own proves it.
Neolithic builders · Architecture
8.7 · Tier IV
Run the subtractive test, and very little yields. The cairn is as massive as the vault requires: a corbelled roof stands because the weight round it holds each course. The passage is as long as it must be, and rises as it must, for the beam through the roof-box to reach the chamber floor and no further; lengthen it, shorten it or level it, and the solstice is lost. The roof-box exists because the rising passage would otherwise shade the chamber: a part compelled by the alignment. The kerb retains the mound and marks its edge, and its two grooved stones mark the axis. What yields: the carving is not required by structure, and its purpose is unknown; the three recesses follow the cross-plan of the type more than this tomb’s own end.
Caspar David Friedrich · Visual art
8.7 · Tier IV
Subtraction, part by part. The stack cannot go: it is the picture, a monument raised by no hand. The wreck cannot go: without it the canvas is a study of ice, and with it the stack becomes a grave. The distant bergs cannot go: they repeat the stack at the scale of the world and say the thing is no accident of one place. The open sky is the picture’s only release and the measure of how high the ice reaches. The scale is compelled: larger, the wreck would become an incident. What gives is the bottom edge, where the foreground is more an inventory of slabs than a structure and two or three could move without loss.
Édouard Manet · Visual art
8.7 · Tier IV
Judged on the configuration. The barmaid cannot go: she is the one thing not seen in glass, the only face that meets ours. The counter cannot go: it is the line of trade between her and the viewer, and the still life on it is the goods she stands among, at her height and in her colours. The mirror cannot go, and neither can its displacement: without the reflected back and the man in the hat the picture is a portrait of a girl at a bar. The trapeze artist’s feet carry the show no one is watching. What yields is at the margin: the balcony crowd could be thinner, the chandeliers fewer, and the bottles at the right edge are a second count of those at the left. The scale is compelled: near life size across a counter, at the distance of a customer.
Pieter Bruegel the Elder · Visual art
8.7 · Tier IV
Judged on the composition, since the panel has no words. Take away the hunters and the painting loses its entry, its human measure and its argument, the return with almost nothing. Take away the inn fire and the cold has no counterweight: the one warm field makes the white read as cold. Take away the trees and the eye has no ladder into the valley; take away the bird in flight and the drop is not crossed; take away the mountains and the world closes to a village. What yields is the incident of the far valley, the fallen skater and the small business of the ice and the houses: true to the day, and several pieces could go without loss. That additive habit, inherited from the calendar page, holds the axis below the top.
Piero della Francesca · Visual art
8.7 · Tier IV
Subtract, part by part. Christ cannot go: he is the axis and the whole act. The tomb cannot go: it is the threshold he crosses, and the foot raised on its rim shows the rising happening now, not reported after it. The four sleepers are required as four: two either side keep the pyramid whose apex is the head, and their four ways of sleeping, slumped, leaning, turned away, folded, are the human order’s one condition seen from four sides. The landscape is required: bare trees and trees in leaf, divided by the rising body, read the event in nature. What yields, slightly: the fourth soldier at the right, largely hidden and least distinct, and the painted frame, which places the work but argues nothing the picture does not.
Johannes Vermeer · Visual art
8.7 · Tier IV
Take each object away and ask. The curtain cannot go: it is the hand that has drawn the picture open, and the viewer’s place behind it. The painter’s back cannot go, for the picture is about a man whose face is withheld while he makes. The model is both the subject he paints and the subject of the picture, and her lowered eyes give the room its hush. The map carries the world the studio stands in; its crease and its border of towns make history geography. The unlit chandelier with its eagle is the one sign of a former sovereignty, and the cast mask is the art’s past, a dead face beside a living one. What yields a little is the still life on the table, where the silk and the folio could be fewer, and the foreground chair, which doubles the curtain’s work.
David Bowie · Music
8.7 · Tier IV
Seven tracks in about forty-one minutes, and the frame is lean. The title track must open: its rite sets the record’s terms, a death and a replacement, and its length is the rite’s. Lazarus must stand near the front, the plainest statement of the dying man. Dollar Days and I Can’t Give Everything Away must close, and they are joined, the one dissolving into the other. Girl Loves Me is required more than it looks: its slang swagger and its lost day (“did Monday go”) carry time slipping away in a language no one else speaks. The test bites only in the middle, where ’Tis a Pity She Was a Whore and Sue, songs first recorded in 2014, restate the band’s force more than they turn the argument.
Prince Hachijō Toshihito and Prince Toshitada · Architecture
8.7 · Tier IV
The parts are compelled by site, structure and purpose. The floors are raised against the river, and the pond, dug from low wet ground, is the one large figure every building faces. The timber stands on a proportional module, the post’s width setting the members’ sizes, so the rooms are the grid made visible. The moon platform exists for the moonrise; the stagger exists so that every principal room has the garden, the light and the air on two sides. Take away the Shōkintei and the circuit loses its culminating station and the stone bridge to it; take away the Sumiyoshi pine and the first view of the pond is spent at the gate. What resists is accretion: the Onrindō and the Shōiken are stations a circuit could do without, and the New Palace’s shelves and fittings are ordered rather than required.
Albrecht Dürer · Visual art
8.6 · Tier IV
Subtract, element by element, and almost nothing yields. The face cannot go: it is the claim. The frontality cannot go: it is the argument, and a turn of the head would make this a portrait like the painter’s own panel of 1498. The hand at the collar cannot go: it is the painter’s instrument, raised where the blessing hand of the holy face would be, and the one thing in the picture that is not symmetrical. The inscriptions sign the panel and turn likeness into statement; the dark ground removes place and time, as an icon’s gold does. What gives a little is the coat below the hand, a dark mass that carries less than its share.
August Strindberg · Literature
8.6 · Tier IV
Three people, one room, one night, no interval: each exchange tightens the next, and the subtractive test finds little to take. Julie’s command to dance, the cinder in Jean’s eye, his story of the boy who crawled through the privy and saw her in the rose garden, the two dreams, the seduction offstage, the plans for a hotel at Lake Como, the money, the greenfinch, the bell and the razor: remove one and a link in the necessity breaks. Even Kristin’s mime, which looks like a pause, is the play’s clock. What could go: part of Julie’s long account of how her mother raised her, which narrates what the play elsewhere shows, and a few turns late on where the contempt runs longer than the drama needs.
Nikolai Gogol · Literature
8.6 · Tier IV
The subtractive test finds almost nothing to take. The first line is the whole engine, “Я пригласил вас, господа, с тем, чтобы сообщить вам пренеприятное известие: к нам едет ревизор”
(I have invited you, gentlemen, to tell you a most unpleasant piece of news: an inspector is coming to us), and every scene after it turns the same screw. The officials’ reports in the first act set out what each has to hide; the second act must show Khlestakov starving and unpaid so that his terror can meet the Mayor’s; the lying of the third is the hinge; the bribes of the fourth are the town paying for its own fear; the betrothal of the fifth raises the Mayor to the height from which the letter drops him. Held below the top by the fourth act, which runs by repeating one action, and by Osip’s monologue (II.1), a set piece the plot could lose.
Salvador Dalí · Visual art
8.6 · Tier IV
Judged on the configuration. Remove the creature and no one sleeps: the watches melt over an empty shore, a still life of oddities, and the picture loses its centre and its reason. Remove the hard watch and its ants, and softness has no opposite; the one closed, hard timepiece being eaten is what makes the soft ones a release rather than a trick. Remove the tree and the block, and nothing hard holds the soft. Remove the lit cliffs, and the dream has no waking world at its edge. What gives is the count and the accessories: three soft watches where two would make the claim, a fly that repeats the ants, and the reflective plane at the right, which the composition uses and the meaning hardly needs. Required at the centre, accumulated at the margin.
Caspar David Friedrich · Visual art
8.6 · Tier IV
The picture is made by removal, and what is left resists removal almost entirely. Take the monk and the canvas becomes a weather study, a sea with no one to face it. Take the strip of shore and he has nowhere to stand and the viewer no ground. Take the dark band of sea and the sky has no depth to fall into: it is that band, nearly black, that makes the sky’s height felt. The scale is compelled: smaller, the emptiness would be a vignette; much larger, a decoration. The test bites in one place, the gulls, which could go though they give the only scale of the air and its only motion. They and the exact disposition of the cloud are permitted rather than required.
Donatello · Visual art
8.6 · Tier IV
One figure, and the subtractive test finds almost nothing to remove. The hair cannot go: it is her garment, her former beauty and the measure of her years in the desert in one material. The hands cannot go: their not quite meeting is the one movement in the figure, the place where its meaning turns from ruin to prayer. The face, with its open mouth and missing teeth, is the argument; the long bony feet are its foundation. The belt at the waist is the one ornament, and it is the hair again. The scale is compelled, a body confronting a body. What yields a little is the fall of hair over the lower legs, repeated more than required. So few parts leave necessity little to prove under strain.
Bong Joon-ho · Film
8.6 · Tier IV
Judged on structure and cut. The subtractive test finds almost nothing loose, because nearly every object is planted to be paid. The stone is given in the first act, floats up in the flood, is carried to the party and becomes the weapon turned on its bearer. The housekeeper’s expulsion is what sends her back to the doorbell. The Morse code tapped below the house is the code of the epilogue. The boy’s drawing of a “ghost”, dismissed as an invented diagnosis, is true. The line, seon, that the driver must never cross is the line the smell crosses. What gives: the rain that brings the Parks home is a hinge the world supplies too readily, the gymnasium says aloud what the flood has shown, and the epilogue’s voice-over spells out what the image carries.
Jean Racine · Literature
8.6 · Tier IV
The subtractive test finds almost nothing idle. Every scene turns one screw: the mother’s dawn vigil shows her already shut out; the night abduction of Junie gives Néron the desire that makes Britannicus a rival in love as well as in blood; the overheard scene makes Junie the instrument of her lover’s danger; the reconciliation Agrippine extorts and the two counsels of the fourth act set the hinge on which the poisoning swings. The principal figures are each required: without Burrhus and Narcisse the play has no moral alternative; without Junie, Néron’s turn has no private motive. Held below the top because the last movement, the flight to the Vestals and the people’s killing of Narcisse, is ordained by poetic justice more than compelled by the play’s logic, and Britannicus himself is thinner than his title, a necessary victim more than a necessary person.
John Fowler and Benjamin Baker · Architecture
8.6 · Tier IV
Judged on purpose, structure and site, and the site compels nearly everything: more than a mile of tidal water, a channel nearly 200 feet deep in places, an island at Inchgarvie where a central pier could stand, and a clearance of about 150 feet set by the Admiralty for the anchorage upstream, which rules out low arches and short spans. After the Tay the purpose was to cross and to be seen to be rigid, and the cantilever answers both. The subtractive test finds little to take: every member is a tube in compression or a lattice in tension. What holds it: the bridge is heavier than its loads require, a reassurance in steel. The excess is purpose, not ornament, and still excess.
Robert Bresson · Film
8.6 · Tier IV
Judged on structure and the cut, and the subtractive test finds little to take. Seventy-five minutes carry a fall, an education, a flight and a turn, and the film drops whatever does not move them: no planning is shown, no motive beyond the act, no city beyond stations, stairs and cafés. The Longchamp opening is required, since the end returns there; the mother’s death is required, since Michel stole from her and cannot weep at her funeral in the open; the café argument is the theory the rest refutes; the Gare de Lyon must be long. What gives: Jacques is a function more than a person, and the two years abroad, gone in a sentence, make the return to Jeanne arrive by notice rather than by consequence.
PJ Harvey · Music
8.6 · Tier IV
Twelve songs in about forty minutes, none an interlude, and the subtractive test mostly fails to find a cut. The title track must open, the country addressed and a cheerful tune turned against it. The Glorious Land states the record’s central figure, the land’s yield as maimed children, and must sit early. The Words That Maketh Murder is the eyewitness core; On Battleship Hill sets the record on a named hill of the dead; The Colour of the Earth must close, the voice handed to a man remembering a friend in the soil. The test bites only lightly. Bitter Branches and Hanging in the Wire share one image of soldiers strung across a landscape, and In the Dark Places restates the dead going under the hills. Nothing is padding.
The masons under Ismaila Traoré · Architecture
8.6 · Tier IV
Run the subtractive test, and almost every part answers with a reason. The platform is required by the flood. The thickness and batter of the walls are required by the strength of mud and by the heat. The pilasters stiffen the walls and carry the rain down between them. The toron are the scaffolding the annual replastering needs, left in the wall for good. The vents are the hall’s breath and light; the spouts keep water from the wall. The dense grid of piers is required by the span a palm beam can make. Use compels the rest: a hall for Friday prayer on its qibla, a court for the overflow, the qibla wall turned to the market. What yields is ordered rather than required: the pinnacles, the number and spacing of the towers, the symmetry of the eastern front.
Josquin des Prez · Music
8.6 · Tier IV
The subtractive test meets resistance because nothing in the mass is free material: every point of imitation is a phrase of the hymn, so to cut a passage is to cut a line of the chant from the argument. The Credo is the plainest evidence. Carrying more than half the text, it moves near syllabically and does not linger, and the one place it changes manner, Et incarnatus est, is the doctrinal centre of a mass on the hymn of the Body. The last Agnus releases the hymn in the top voice, a release the whole work has withheld. The give lies in the middle stretches of the Gloria and the Credo, where one point follows another by the logic of the text rather than of the whole. The liturgy fixes the order; only what Josquin made of it is credited.
Käthe Kollwitz · Visual art
8.5 · Tier IV
The subtractive test finds almost nothing to remove, because almost nothing was admitted. Eighteen years of making went mainly into taking away: earlier designs were given up, and what remains is two kneeling bodies and the dead in front of them. The son’s body is not in the work because the field is his body. Each figure is required: without the father the mother is a generic mourner; without the mother the father’s held rigidity has nothing to be held against. The interval is required too: push the bases together and the work says that grief is shared, which is what it refuses to say. What yields a little is the drapery of the mother, which reads as convention, and the bases, which are plain supports. A tenth under The Starry Night at 8.9; the small form makes the claim easier to meet.
Tadao Ando · Architecture
8.5 · Tier IV
Judged on structure, purpose and site. Run the subtractive test and almost nothing yields. Remove the oblique wall and the entry becomes a door in a box: the turn from street to dark, the compression before the room, is lost, and with it the slit of side light the wall makes where it meets the box. Remove the cross and there is no church, for the cross is the only sign and the chief light. Add a window and the cross becomes a decoration on a lit wall. Pews of scaffold board answer a budget, and their roughness answers the concrete. What resists: the glass in the cross is a compromise the form did not compel; the idea requires the dark room more than the use does; and a box so small makes necessity easy to keep.
Fra Angelico · Visual art
8.5 · Tier IV
The subtractive test is the fresco’s own method. The painter has already removed what the subject usually carries: the gold ground, the dove, the descending rays, God the Father in the sky. What is left is required. The loggia places the event in a building like the one the friar stands in, its columns answering Michelozzo’s cloister below. The fenced garden is the hortus conclusus and the outside the angel has come from. The barred window behind Mary is the cell, and the only opening onto anything beyond. The inscription turns the image into an instruction to a passing body. No part is idle. Held below 9.0 because the left bay and the garden strip carry less charge than the right, and the lower band of floor carries little.
Buster Keaton and Clyde Bruckman · Film
8.5 · Tier IV
Judged on structure, and the subtractive test barely bites. Every element of the prologue is spent later. The two loves, set in an early title as “his engine and” Annabelle’s picture, are taken together and recovered together; the recruiting office’s refusal and Annabelle’s condition make the whole chase a proof Johnnie does not know he is giving. The chase north and the chase south are one design, so that the ties, the uncoupled cars and the cannon going north return reversed going south. The night in enemy country is the hinge: under the Union table Johnnie hears the plan the battle will settle. What gives is small. Annabelle’s comic stoking runs long, and the closing battle repeats its business before the commission.
Giacomo Puccini · Music
8.5 · Tier IV
The libretto’s first decision is subtractive: Murger’s loose cycle of anecdotes becomes four tableaux and one couple set against another. Every Act I event has a job. The burnt manuscript makes the cold, Benoit’s visit empties the room, and the candle and the key bring Mimì to Rodolfo and keep her there. Act III depends on Act II, since Marcello and Musetta are now together and quarrelling, and their quarrel frames the lovers’ parting. Act IV’s horseplay is required: it is the play Musetta’s entrance breaks. The test finds give in Act II, where Parpignol and the crowd make a picture for longer than the action asks, and in Benoit’s scene, a comic number whose function a few lines would serve.
Constantin Brâncuși · Visual art
8.4 · Tier IV
Judged on the three phases of one form. Take away the cone of the foot and the form has no ground to leave: it stands, it does not rise. Take away the constriction above it and the body sits on its foot like a vase; the narrow neck is where the weight seems to let go. Take away the swelling of the body and the form is a rod; take away the oblique cut at the top and it ends where it should continue. Every part is required, and there are no other parts. What gives is substitution, which the series itself demonstrates: its versions, each a different setting of height, swell and foot, show that this proportion is one of several that work, not the only one. The form is compelled; its exact measure is chosen among neighbours.
Ernest Hemingway · Literature
8.4 · Tier IV
The subtractive test finds almost nothing to cut. The book is one action, and each part is required by it. The opening ashore sets the eighty-four days, the boy taken from the old man by his parents, and his poverty. The voyage needs its hours of patience before the strike, because the struggle is a test of duration. The sharks must come in sequence, first the single mako, the dentuso, then the shovel-nosed galanos, because the loss has to be slow to mean anything; and the coda must show the skeleton seen by people who cannot read it. The memories are few, the hand-wrestling at Casablanca and the lions on the African beach, and each returns at the end. What holds it below the top is repetition inside the monologue: the wish for the boy recurs past the point where it adds, and “the great DiMaggio” and his bone spur are returned to more often than the argument requires.
Barnett Newman · Visual art
8.4 · Tier IV
The subtractive test is the work’s own method: it was made by taking away nearly everything a painting had. What remains is a field and five lines, and each line bears load. Remove a zip and the intervals between the others change, so the measure of the whole changes, and the field becomes either a slab or a set of panels. Remove a metre of width and the field no longer outruns the eye at the close distance the painter asked for, and the encounter he built is lost. The red cannot be another colour without the canvas changing temperature. What holds the axis is substitution rather than removal: the zips could sit at other intervals without the work ceasing to be itself, and his other zip paintings show that the placement was judged, not compelled.
Three Kingdoms Korea · Visual art
8.4 · Tier IV
The subtractive test, part by part, and the figure resists it almost everywhere. The hand at the cheek is the thought: take it away and the figure merely sits. The crossed leg holds half the body withdrawn into meditation; the left foot on its lotus keeps the other half on the ground, so the figure is between staying and rising, and neither half can go. The hand on the ankle closes the circuit from hand to knee to foot. The bare torso lets the gesture read; the low crown lets the head stay a head; the skirt’s falling folds give the weight and calm the upper body lacks. What yields is little: some repeated folds at the back of the stool, the lotus of the footrest. Held below the top because the form is small and has few parts to test.
Robert Maillart · Architecture
8.4 · Tier IV
The subtractive test is the bridge’s whole argument. Take away the box walls toward the quarter points and the arch cannot carry an unbalanced load; take away the hinges and it must resist the temperature, shrinkage and settlement they were placed to release; thicken the crown and the economy that won the competition is gone. The parts are where force requires them and nowhere else, and the depth is spent where bending is greatest. Even the short, plain approach spans are compelled by the rock of the gorge. What holds the figure below the highest is that the necessity is single: the bridge has one task, to cross, and its parts are required by structure and site, not by a meaning. The rail and parapet are ordinary, and the curve of the approach is road geometry.
Knights Hospitaller builders · Architecture
8.2 · Tier IV
The purpose is the hardest any building serves: to keep a small number of men alive and in command of a pass against an army. Run the subtractive test. The talus cannot go: it thickens the base against mining, throws back what is dropped and makes the south face unclimbable. The birka cannot go: it is water in a siege and an obstacle at once. The outer wall cannot go: it makes the inner ward a second line commanding the first. The ramp is the entrance reduced to a killing ground; the stores and halls are the months a siege lasts; the chapel is required, for the garrison was a religious order. What yields is grace: the loggia’s tracery and the vaulted south-west chamber.
René Magritte · Visual art
8.1 · Tier IV
The subtractive test is close to the whole of this picture, because there is almost nothing to subtract. Remove the sentence and what is left is a primer card or a shop sign, with nothing to say. Remove the pipe and the sentence denies nothing: its first word points at a blank. Fill the ground with a table, a room and a shadow, and the pipe becomes a still life and the sentence a riddle about a room. The plain ground is required, and so is the schoolroom hand, which makes the words read as a lesson. What holds the axis below the top is substitution, not removal: the pipe is apt, a common thing and a sign of the ordinary man, and another object could stand in its place. Required in its parts, permitted in its choice of object.
Virgil · Literature
9.5 · Tier V
At the level of the line the subtractive test fails almost everywhere. One line in a hundred recurs whole in the Latin, against more than thirteen in the Iliad, and the returns that remain carry meaning. The large design is answered at every joint: Dido’s curse (4.625) by the Punic wars foretold in heaven (10.11–14), the footrace of V by Nisus and Euryalus in IX, Pallas entrusted (8.514–519), killed (10.479–505) and avenged (12.948–949). What holds it lowest of the twelve is local and structural. Book III carries removable matter, the Actian games (3.278–288) and the Sicilian coast-list (3.692–707); the catalogues and kill-lists could be thinned; and the poem is unrevised, with fifty-seven unfinished lines and four lines given verbatim to two speakers (1.530–533, 3.163–166), the marks of assembly.
Johann Sebastian Bach · Music
9.3 · Tier V
The narrative layer resists the subtractive test absolutely: Matthew 26 and 27 are set whole, and nothing in the Gospel is cut. The responses are placed with intent. The chorale “Ich bin’s, ich sollte büßen” answers the disciples’ “Herr, bin ich’s?” at once, and “Erbarme dich” follows Peter’s weeping where nothing else could. Length is not charged. The test finds real give in the arias: Mendelssohn cut many of them in 1829 and the work was still itself; the da capo returns repeat what was just heard; several numbers took new words in the Köthen funeral music of 1729; and Part I’s close was exchanged between versions. A movement that can be transplanted was not compelled by this work alone.
Franz Kafka · Literature
9.2 · Tier V
The test is subtractive, and most of what it touches proves required. The frame is compelled: an arrest without a charge must open and the quarry must close, since the book is the interval between an accusation and its sentence. The stations are required by what the book knows: the hearing shows the court as a crowd that applauds on cue, the flogger shows K.’s complaint falling as punishment on the warders, Titorelli’s acquittals give the law of the whole, Block shows what K. would become, and the cathedral states the law in a parable. The repetition of the middle is that law enacted: each approach returns K. to where he began, as the painter says of the postponement, so that the stations without progress are the argument and not the residue of a draft. What holds the axis at the foot of the twelve is a margin of accretion past that law: Huld’s accounts overlap Titorelli’s, the chapter on Fräulein Bürstner’s friend adds little, and the order of the middle is an editor’s.
Jan van Eyck · Visual art
9.2 · Tier V
Judged on structure alone. Closed, it passes the subtractive test: the Annunciation is the promise, the seers foresee it, the two Johns name the Church, the donors kneel; no field could go. In the open lower register the four groups on the wings converge on the Lamb, and the fountain carries the sacrifice toward the viewer; the lost Judges are required by that scheme. What holds the axis lowest is the joint between the registers: a row of near life-size figures on separate grounds above, one landscape of small figures below. The Deësis does not need the meadow, and the meadow does not need Adam and Eve.
Plato · Literature
9.1 · Tier V
Subtract and see what goes. The five speeches before Socrates are not ornament: each puts forward a claim the Socratic part takes up and corrects. Phaedrus’ love as the source of honour and self-sacrifice is the lowest rung; Pausanias’ two Aphrodites give the distinction between love of the body and love of the soul that the ladder rebuilds; Aristophanes’ halves give the doctrine of lack, which Diotima names and refuses (205d to e); Agathon confuses love with its object, and the questioning exposes it. The frame’s removes carry the theme of the intermediary, and Alcibiades is required as the particular love the ascent leaves behind. What holds the axis lower is Eryximachus’ medical cosmology, the speech most nearly removable, and Pausanias’ length.
Virgil · Literature
9.1 · Tier V
Subtract and test. The set pieces are not ornament: remove the portents at the end of the first book and the precepts lose the history they are given against; remove the plague and the stock-keeping of the third has no measure of what it guards; remove the Aristaeus and the poem has no answer to death. The alternation of the endings, dark, bright, dark, then death answered by birth, is a structure no book can leave. What holds the axis here is in the technical body: the catalogue of vines the poet himself says cannot be numbered (2.89 to 108), parts of the soil tests (2.177 to 258), the remedies for sheep (3.440 to 477), and weather lore carried over from Aratus rather than remade. They are a small fraction, and none is idle.
Euripides · Literature
9.0 · Tier V
The subtractive test mostly fails to find a removable part. The first line wishes the Argo had never sailed and sets the debt Jason will deny; Creon’s single day is the clock; the agon gives Jason his case so that the false reconciliation can turn his reasoning against him; the gifts need that scene, and the Tutor’s report that they were accepted sets off the monologue. Aristotle called the Aegeus scene irrational (Poetics 1461b), yet it is required twice: as the refuge without which the revenge is suicide, and as the sight of a king desperate for sons. What holds the axis below the others: Aegeus arrives by unprepared chance, the monologue as transmitted repeats itself, and the closing lines are generic.
James Joyce · Literature
9.0 · Tier V
The test is subtractive, and the book is mostly made of what cannot go. Inside the stories there is almost nothing to cut: “Eveline” runs to 1,827 words, and its last scene at the North Wall carries the whole of a life’s refusal. The order is argued: three stories in a boy’s first person, then youth, maturity and public life, the stories lengthening as the lives in them widen, then “The Dead”, which turns the book’s verdict back on the man best placed to deliver it. Remove “The Sisters” and the book loses its key words, paralysis, gnomon and simony. What holds the axis at 8.7 is the book’s history and one story. It grew by addition, from twelve stories to fifteen, so its scale was permitted before it was compelled; and “After the Race”, the thinnest of the fifteen, could go with the loss of one station, new Catholic money and the Continent, and little else.
Ludwig van Beethoven · Music
9.0 · Tier IV
Length is not charged: the scale is compelled by an argument that must travel from the fanfare’s assertion to F sharp minor, the farthest key of the work, and back by a search. The subtractive test meets resistance at the joints. The opening leap seeds the descending thirds; without the Adagio the fugue has nothing to answer; the Largo is the passage back, and without it the fugue arrives from nowhere. It finds give in three places: the Scherzo, brief and partly a parody of the opening, a lighter hinge than its place needs; the fugue’s long trilled sequences and middle episodes; and the maker’s own licence, for the London edition, to reorder the movements or drop the Largo or the fugue. Held below Winterreise’s 8.9 for that.
Fyodor Dostoevsky · Literature
8.9 · Tier IV
The subtractive test finds little to take. The two parts require each other: without the second, the doctrine of spite, the wall and the conscious mouse is a brilliant essay with no ground; without the first, the dinner and Liza are the anecdote of a mean clerk. The order is required too, since the theory must be heard before the reader can see that the young man enacted it. In the second part each scene readies the next: the collision shows the will that must not give way, the dinner shows it humiliated in company, the brothel shows it avenged on someone weaker, and Liza’s visit shows it destroying the one person who answered it. What the test finds is in the middle of the first part, where the chapters on advantage, history and the piano key circle one point more than once; much of the circling is earned, and some of it the book permits rather than compels.
Joseph Conrad · Literature
8.9 · Tier IV
The subtractive test finds almost nothing to take from the sequence. Each station is a stage of one disclosure: the women knitting black wool at the door of the office, the shelling of a continent from the sea, the grove where the worked-out labourers come to die, the accountant who keeps his books and his linen immaculate beside it, the manager whose only gift is that he is never ill. Remove any and the sequence loses a step in its argument that the enterprise is hollow at every level before Kurtz is reached. The frame is required too: the Thames at the close answers the Thames at the opening. What holds the axis is the prose’s own insistence, its words for the inscrutable and the unspeakable used more often than the knowledge needs, and a long middle of waiting at the Central Station that makes its point once more than it must.
Dante Alighieri · Literature
8.9 · Tier IV
The test is subtractive, and the narrative and the poems resist it. The screen ladies (V to X) look removable and are not: the pretended loves cost Dante the greeting (X), and its loss forces the turn to praise (XVIII). Sì lungamente is required because it is broken: death cuts the canzone off after one stanza (XXVII to XXVIII). The digression on personification (XXV) is the book’s poetics. What the test removes lies in the divisions, nearly a fifth of the words. Some bear weight, above all where Dante stops dividing (XXVI) and where he divides before the poem (XXXI); many, like that of Spesse fïate (XVI), restate the prose just read. The double sonnets of VII and VIII are the slackest verse.
Andrea Palladio · Architecture
8.9 · Tier IV
Judged on plan, section and structure under purpose and site. Take away one portico and the house has a back, and the argument, a house that faces the world equally, falls. Take away the hill and the four views that are the stated reason for the four loggias are gone. Turn the block square to the compass and two fronts never see the sun; the corners set to the cardinal points are compelled by climate. Put the kitchens on the principal floor and one front becomes a service front; the podium is required by the equality of the four. What resists: the symmetry is required by the idea more than by the life. Four identical porticoes answer four unequal views, one quarter is cold, the stairs are squeezed into the corners between circle and square, and the mezzanine is what the section left over.
Akira Kurosawa · Film
8.9 · Tier IV
Judged mainly on structure, with a small verbal part in the few speeches that turn the film. The three large parts are required, recruitment, preparation and battle, and their proportions are compelled, since the battle costs what the preparation built. Much that looks removable is not. The recruitment takes nearly an hour, but each test fixes a man: Gorobei laughs at the ambush behind the door, Kyūzō kills a man who forced the fight, Heihachi admits he is a middling swordsman. The armour scene looks like a digression and is the hinge. Length is not a cost in itself, and the shortened export versions are no evidence against the full one: cut, the film loses the proportions its argument needs. What gives is local: Kikuchiyo’s clowning repeats its effect, the comic business in the town and at the training runs past what it establishes, and the scenes in the flowers run longer than the ending needs. Each is a passage that could be shortened, not a part that could go.
Johannes Brahms · Music
8.9 · Tier IV
The order is required by the argument: the living mourn, all flesh withers, one man asks to know his end, the dwelling is longed for, the mourner is consoled, death is overcome, the dead are blessed. Cut the seventh movement and the blessing on those who mourn has no answer; the recall of the first movement’s close makes the bond audible. Length is not charged. The subtractive test still finds give. The work stood in six movements at Bremen in 1868 and was heard as whole, and the fifth completes the arch but was chosen, not compelled. The march of the second returns at length, and three movements end on the same turn.
Le Corbusier · Architecture
8.8 · Tier IV
Run the subtractive test; the parts are few, and each answers something. Remove the strip of light under the roof and the shell no longer floats: it becomes a lid on a box. Remove a tower and a side altar loses its only light. Remove the east choir and the building cannot serve the pilgrimage crowd, the reason it stands on the summit at all. The south wall’s depth makes its openings light-wells rather than windows, and the spout and basin carry the roof’s one gesture to the ground. What resists: light, liturgy and horizon compel the forms in their function, not in their exact curves, which another curve could have met; the pyramid and some outer furniture could go without great loss.
John Keats · Literature
8.8 · Tier IV
Taken poem by poem, the subtractive test nearly fails to find anything. To Autumn has no idle line: the first stanza loads, the second personifies, the third listens, and each is required by the turn from fullness to ending. The Urn moves from its question, “What men or gods are these?”, through the boughs that “cannot shed / Your leaves” to the emptied town and the address that closes it; remove a stanza and the argument breaks. Nightingale is one flight and one fall. Held at 8.7 by the body as a body: Psyche’s middle runs to inventory, its litany of what the goddess lacks said twice, and Indolence repeats its three figures across six stanzas whose order the manuscripts do not settle. These two hold about a third of the lines.
Jean Renoir · Film
8.8 · Tier IV
The subtractive test, scene by scene, and most of the film resists it. Le Bourget sets the one man who does not know the rules, telling a radio microphone that the woman he flew the Atlantic for did not come. Robert’s automata give the master his nature before he speaks. The car crash puts André’s despair and Octave’s place as go-between on the road. The servants’ table sets the second house beneath the first. The hunt is the hinge: the spyglass turns from a squirrel to a husband, and the slaughter rehearses the ending. What gives: the pursuit through the house runs past its point once its doubling of masters and servants is made, and some guests, Saint-Aubin above all and the gag figures at the fête, are furniture.
Martin Scorsese · Film
8.8 · Tier IV
Judged on structure and ellipsis, which carry the film’s necessity, and the subtractive test finds little to take. Each station is required: the Reeves decision, a man who wins and is not given what he has won; the “small hands”, which state the grievance; the pool, which sets possession going; the Fox fight, the one time he gives in and the one time he weeps; the television, where jealousy turns on the brother. Ellipsis does the cutting first: the war, the courtship and most of the title reign are absent. What gives is the Miami stretch. The club monologues and the under-age girls run on episode by episode, and a version that went from Vickie leaving to the cell would lose little.
Michelangelo · Architecture
8.8 · Tier IV
Judged on structure, purpose and site, which here bind hard. The site is a range of older cloister walls at an upper level: the hall takes its width and length from them, and its walls are thin because they stand on walls built for less. The pilaster frame is therefore both order and structure, and desks, windows, ceiling panels and floor panels all take the bay as their unit; remove one and the others lose their measure. The vestibule must climb from a lower floor to a higher one inside a small square, and the stair is the reason for the room. What yields: the consoles carry nothing and the tabernacles are blind, required by what the room says, not by what it holds up.
Sergei Eisenstein · Film
8.8 · Tier IV
Five acts, each with one action, and the subtractive test finds little to remove. The maggots are the cause: the doctor’s pince-nez folded into a lens, his verdict that the meat is fit, the soup refused, the plate inscribed with the prayer for daily bread smashed. The quarterdeck is the crisis: the tarpaulin thrown over the condemned, the one-word cry to the guards, the mutiny, Vakulinchuk’s death. The pier is the mourning that turns the city; the steps are the price the city pays; the squadron is the resolution. Each act requires the one before, and the argument cannot drop a step. What is charged: the speeches on the pier and some of the titles say what the images have shown, the provocateur’s moment repeats the work of the mourning, and the last act’s waiting is long for what it holds.
Ming, under the Yongle Emperor · Architecture
8.8 · Tier IV
Judged on purpose, structure and site, and the rite compels nearly everything. The emperor must come out to the south of the city, fast and offer, so there are a Hall of Abstinence, a music office and a slaughter pavilion, each where the sequence needs it. Heaven is worshipped in the open at the winter solstice, so the altar has no roof; the tablets must be kept, so the Vault stands beside it; the prayer for the harvest is made under a roof at the start of the year, so the hall stands at the other end of the axis. The numbers are required by the cosmology: a balustrade in tens would be wrong, not plainer. What yields: the hall’s three roofs are compelled by symbol more than by span, and the grove, the second wall and the length of the raised way are ordered by dignity.
Claude Debussy · Music
8.8 · Tier IV
Twenty-four minutes with very little that can be taken out. The first sketch is the strongest case: the fragments of its opening are the material of everything after, and the chorale at its end is prepared by the whole climb from dawn to noon, so the subtractive test finds nothing idle in it. The third sketch needs the first, calling back its opening in the low strings and closing on its chorale. The give is in two places. Jeux de vagues is the most separable panel, joined to the others by orchestral method and by derivations that are argued more than heard: the work would be smaller without it, not broken. And the composer cut the fanfares of 1905 in 1909, which some conductors restore without loss.
Safavid, under Shah Abbas I · Architecture
8.8 · Tier IV
Judged on plan and section, under purpose and site. The site set the problem: the king’s square runs on an axis Abbas drew, and the qibla lies far off it. Take away the vestibule and the turn, and the mosque either turns its back on the square or sets its congregation off the qibla; neither was possible, so the hinge is required. Take away the portal’s height and the square has no answer to the bazaar gate. Take away the outer shell and the sanctuary disappears from the square; take away the inner and the chamber is a well. The pool is required by ablution, the winter halls by an Isfahan winter, the madrasas by the teaching. What resists: the second pair of minarets, which the call does not need; the pattern of the skin, extensible as pattern is; and a scale set partly by a king’s wish for a monument.
Benjamin Britten · Music
8.8 · Tier IV
The large plan resists the subtractive test. Each Owen poem is set where the liturgy calls it. “Anthem for Doomed Youth” answers a prayer for eternal rest with “die as cattle”; the Calvary poem sits inside the Agnus Dei; the parable of Abram sits inside the promise to Abraham, so that removing either the fugue or the poem kills the other. “Strange Meeting” must come where the responsory begs deliverance from death, the only place the two soldiers meet the dead. Length is not charged. The give is in the Dies irae: four poems in more than a quarter of an hour, two of them tied loosely to the sequence, and long stretches for brass and chorus that restate. The Sanctus’s poem could change places without loss.
Inca, under Pachacuti · Architecture
8.8 · Tier IV
Judged on plan, section and structure, under purpose and site, and the site compels almost everything. Remove the terraces and the slope goes down the mountain with the first rains; they hold the ridge before they feed anyone. Remove the drains and the terraces fail. Remove the canal and there is no settlement, since the ridge has no water but its spring. The plaza had to be levelled on fill, the moat and wall had to part field from house, and each temple stands where its outcrop is. What resists is the estate’s own excess: some 200 buildings for a few hundred retainers, five ceremonial foci where one plaza would serve, and terraces that, on the usual estimates, could not have fed the estate, so that part of their extent is display. Scale here is compelled by the slope and permitted by the Inca.
Pierre Choderlos de Laclos · Literature
8.7 · Tier IV
The test is subtractive, and very little comes away. Every letter is an act: it informs, deceives, provokes or is intercepted, and many are written to be shown to a third party, so that what a letter says and what it does are both required. The double plot is compelled by the pact: the seduction of the Présidente de Tourvel, which is Valmont’s glory, and the corruption of Cécile Volanges, which is Merteuil’s revenge on Gercourt, are its two terms, and its collapse ends both. Even Merteuil’s long letter on her own formation is required, as the one account of how she was made. What holds the axis below the top is the middle of the Cécile and Danceny strand: ingenuous love repeated in kind, whose redundancy is partly the point and partly longueur.
Stanley Kubrick · Film
8.7 · Tier IV
Run the subtractive test and the three lines resist it, because each is one stage of a single mechanism: the base is the cause, the bomber the agent, the War Room the attempt at recall. Every obstacle is paid for: Ripper seals the base and impounds the radios, so the recall code lives only in his head; Mandrake must read it from his doodles; the Army must take the base so that Ripper dies; Guano must shoot open a Coke machine for the coins to call the President; the missile that misses the Leper Colony must wreck the CRM-114 and jam the bomb doors, so that Kong rides the bomb down. The Doomsday Machine closes every exit. What gives: some War Room business runs past its point, Turgidson’s telephone girlfriend and his wrestling with de Sadesky, and Strangelove’s arm is turned once or twice more than the joke needs.
Vittorio De Sica · Film
8.7 · Tier IV
Run the subtractive test scene by scene and almost nothing comes out without loss. The pawnshop is the economy of the film in one image: the family’s sheets go onto a wall of other families’ sheets, so the bicycle is bought back with the beds. The Santona is set up early so that the return to her measures how far Antonio has fallen from his own scorn. The Party hall, the mission church and the thief’s street each give a help that cannot help him, or his own face in another man’s poverty. What gives: the seminarians in the rain and the long rehearsal are colour past their work, and the score says twice what the images have said once.
Elia Kazan · Film
8.7 · Tier IV
Run the subtractive test and the spine resists it. The opening killing is the one Terry did not know he was helping, and everything after is his finding out what he did: Edie’s grief, the priest, the brother. Dugan’s death is required, since it proves that testifying gets a man killed and so makes Terry’s choice cost something real. The taxi is the hinge, where the past is named and the brother chooses to die for it. The roof and its birds are required twice, as Terry’s one place of care and as the form of his punishment. What gives is small: the sermon in the hold says at length what the film has shown, the hearing is procedure, and the wedding and the bar carry atmosphere.
Louis Kahn · Architecture
8.7 · Tier IV
Run the subtractive test, and it mostly holds. Take away the court and the two blocks are two laboratories. Take away the channel and the court loses the line that turns a void into a direction. Take away the studies and the scientist’s thought has nowhere to stand apart from the bench. The service floors are required by the purpose: they let a laboratory stay a laboratory for decades while its equipment turns over. The site compels the axis, laid toward the one horizon the mesa has. What resists: the outer elevations, and the stair and light courts along the flanks, are competent rather than compelled, and the laboratories are generic lofts, necessary as provision, not as form.
Auguste Rodin · Visual art
8.7 · Tier IV
The subtractive test finds almost nothing to take. There is a head and a robe, and the robe is the body. Remove the robe and the work is the nude studies, a squat, powerful, comic man in a wrestler’s stance: that was tried and set aside. Remove the backward lean and the mass stands as a column, a monument of the ordinary kind. Remove the empty sleeves and the cloak loses the sign that the arms are inside it. Remove the deep cutting of the eyes and mouth and the head no longer looks out of the mass at anything. Every part is required, and seven years of studies were spent finding what could go. Held below the top because so extreme a reduction leaves the test little to test: necessity in one mass is easier to keep than in Las Meninas, where many parts each earn their place.
Titian · Visual art
8.7 · Tier IV
Judged on the composition. Take away the hanging and the figure floats in a room with no near world to hold her; take away the room and she is the Dresden sleeper with her eyes opened. Take away the servants and the room has no time in it: they are looking for clothes, so the picture holds the interval before she is dressed. Take away the dog and the one other sleeper, which makes her waking visible, is lost. What yields is small: the plant on the sill and the column are emblem and furniture, and the roses do work the sheet and the hand already do. Held below the top because its necessity is that of one proposition, not of an argument with many parts.
Leonardo da Vinci · Visual art
8.7 · Tier IV
Judged figure by figure, gesture by gesture, and nothing human can go. Take John away and the Child blesses no one and the Virgin’s protecting hand has nothing to protect; take the Child and the hovering hand covers air; take the angel and the picture loses its one look outward and the hand that names John, so the circuit closes inside the group and the viewer is shut out. The six acting hands are one sentence read downward through the centre. The grotto is required too: the subject is a meeting in the wilderness, and the cave gives the figures their dark ground and their shelter. What yields is the setting’s extent: the far peaks and the water, evocative rather than compelled, and the ledges above the group, which could be trimmed. The angel’s point can be called redundant beside the gazes.
Anton Chekhov · Literature
8.7 · Tier IV
The subtractive test finds very little to take. Each of the nine is load-bearing in the household’s economy of service. Maria Vasilyevna, reading her pamphlets at the margin of the action, is the living form of the idolatry that consumed Vanya’s twenty-five years; remove her and the professor’s cult has no priest. Telegin, sponging and loyal, keeps faith with a wife who ran off the day after the wedding, the comic mirror of Yelena’s faithfulness to a husband she does not love. Marina’s tea and knitting are the play’s clock. The four acts are arrival, night, crisis and departure, and none could go. Held below the top because Astrov’s forest argument is put twice at length, and some of the first act’s talk sets out what the action later shows.
Mexica · Visual art
8.7 · Tier IV
Judged element by element. The decapitation cannot go: the face of meeting serpents is the work’s central act, a body whose head is made of its own blood. The claws cannot go: they make the figure a devourer, the earth’s teeth at the ends of the arms. The necklace of hands and hearts and the skull is the payment the earth demands, laid where a mother’s breast is, and the slack breasts are the other half of the same sentence. The serpent skirt is the figure’s name. The underside looks idle until one asks what the statue stands on. What yields: the back is less tightly argued than the front, and the feet’s detail could thin without loss.
Albert Camus · Literature
8.7 · Tier IV
The test is subtractive, and it finds very little. The book is one manoeuvre, and each episode is a step in it: the opening offer in the bar, the portrait of the advocate of widows and orphans, the laugh on the Pont des Arts, the confession of the night on the bridge, the theory of universal guilt, the cupboard and the panel, and the turn on the listener. Remove the laugh and the confession has no trigger; remove the panel and the judge-penitent has no emblem; remove the listener’s last revelation and the trap does not close. What the test can take lies in the long middle, where the catalogue of vanities and seductions runs on after its point is made, and in aphorisms that repeat a turn already made; the camp anecdote arrives late, though it earns its place. Perhaps a twentieth of the whole is permitted rather than compelled.
The Cure · Music
8.7 · Tier IV
Twelve tracks in about seventy-two minutes, and the longest stretches are the hardest to cut. The introductions look removable and are not: the voice that arrives late out of the wall of “Plainsong” is the album’s argument, a self arriving in its weather and losing to it. The three short songs are the counterweight; without “Lovesong” the record never states what is being lost. From “Prayers for Rain” to “Untitled” each track is a stage of one descent, and none could be moved forward. Across seventy-two minutes the test bites once, at “Last Dance”, which repeats the regret of “Pictures of You” at lower pressure, and that one give holds it from the top. The vinyl LP’s omission of it and “Homesick” is counted once, not as proof of an anthology.
Donato Bramante · Architecture
8.6 · Tier IV
Judged on purpose, structure and site. The building marks a spot, and almost everything follows from that. A round plan has no front and no end, so the eye and the body are gathered on one centre, the place of the cross, which the crypt marks below and the lantern above. The peristyle makes it a temple, legible whole from every side; the drum lifts the dome so that it reads above the colonnade; the order and its frieze carry the dedication. The parts are proportioned from a single module, so that a change in one would unsettle all. What yields: the ambulatory of the peristyle is too narrow to be used and is there to be seen, and the cella is so small that its use is token. The necessity is commemorative and visual more than practical, which holds it off the top.
Henri Matisse · Visual art
8.6 · Tier IV
Judged on the composition, since the canvas has no words. The subtractive test finds almost nothing to take away. Five figures: four would close into a static square, six would crowd the ring into a frieze. Three colours: a fourth, a cast shadow, a flower, a tree, would put the scene somewhere and end its claim to be everywhere. The hill is one curve, because the dancers need ground to push against and nothing more. Even the apparent accident is required: close the gap between the two hands at the front left and the ring becomes an emblem, a closed wheel. The charge is small. The exact postures of the rear figures could vary without loss; their necessity is rhythmic, not particular.
Bureau of Reclamation, with Gordon Kaufmann · Architecture
8.6 · Tier IV
Judged on purpose, structure and site, the dam passes the subtractive test as few buildings can. The curve in plan is the arch, carrying the water’s thrust to the canyon walls; the thickening from about 45 feet at the crest to about 660 at the base is gravity answering depth; the towers stand where the water must be drawn, the spillways where floods must pass, the powerhouse where the penstocks fall. Kaufmann’s treatment was itself subtraction, leaving the forms the purpose required. What yields: the powerhouse is given more height and wall than its turbines need; the figures, the star chart and the reliefs could go and the dam would work as before; and the height was partly chosen, set for storage the river has not always filled.
Bob Dylan · Music
8.6 · Tier IV
Ten songs in about fifty-two minutes, and the subtractive test finds little to take. Tangled Up in Blue must open: it holds the whole story in one song, a love lost and found across years and towns, and the rest of the record are its facets. Idiot Wind is the hinge of side one, the rage the other songs answer; If You See Her, Say Hello and Shelter from the Storm are its counterweights, tenderness and grace. Buckets of Rain is the compelled end, a shrug after the storm. The test bites twice: Meet Me in the Morning is a plain twelve-bar blues that restates a mood without a turn, and Lily, Rosemary and the Jack of Hearts plays the record’s triangle as a story with masks, but its near nine minutes are permitted more than compelled.
Natsume Sōseki · Literature
8.6 · Tier IV
Subtract, and almost nothing goes without loss. The beach at Kamakura, the monthly visits to the grave at Zōshigaya, Sensei’s refusals, his remark that ordinary good men turn bad at the decisive moment and his one-word cause, money: each is a seed the testament harvests. Part II, which a hasty reader takes for an interlude, is required. The father’s slow dying of a kidney illness is set against the Emperor’s death and Nogi’s, so that three deaths of the old order are lined up before the fourth arrives by post, and the young man’s choice to board the Tokyo train and leave his father dying is the act by which he becomes the heir the letter addresses. What could go is small: a few chapters of family talk about his career and his brother, and the length at which the uncle’s swindle is told.
Frank Lloyd Wright · Architecture
8.6 · Tier IV
Judged on plan, section and structure, under purpose and site. Take away the cantilever and the living room sits on the bank looking at the falls, the house the client expected. Take away the stone core and the trays have nothing to hang from. Take away the boulder and the hearth is a fireplace, not the rock of the site. Take away the hatch and the stair, and the house over the water has no way down to it. The levels follow the ledges of the rock, and the trays repeat them. What resists the test: the upper terraces multiply beyond what the rooms need, compelled by the composition more than the use; the guest house and its walk are a building a smaller programme would not require; and the structure was made to serve the cantilever rather than compelled by it, and did not quite.
Joy Division · Music
8.6 · Tier IV
Ten tracks in about thirty-nine minutes, and nearly every one is required by what the record has to say. Disorder must open: a plea for “a guide to come” over a fast, bright bass, the one forward motion the record allows, and the rest is that guide failing to arrive. New Dawn Fades must close Outside, the slow gathering the side has withheld; She’s Lost Control must open Inside, the record’s clearest statement turned onto another person. I Remember Nothing is the compelled end. Candidate is static by design and earns its place by that stasis. The test bites once, on the second side, where Wilderness, the slightest song, runs into Interzone, an older song that adds energy and no meaning.
Roman Polanski · Film
8.6 · Tier IV
Judged on structure and on the screenplay’s economy. Run the subtractive test and the plot resists it: almost every object planted is paid. The broken taillight lets Gittes follow Evelyn; a cheap watch under a tyre times Mulwray’s night visits; the obituary column names the dead men who own the Valley; the gardener’s “bad for glass” sends Gittes to the pond, and the bifocals in it are Cross’s, not Mulwray’s. Salt water in a man found in a fresh reservoir is the hinge of the whole. The farmers, the rest home and the Albacore Club, which look like digressions, are the public crime the private one mirrors. What gives: the orange-grove chase repeats the reservoir’s work, and the land fraud is laid out in more detail than the drama needs.
Yasujirō Ozu · Film
8.6 · Tier IV
Judged mainly on structure. Run the subtractive test scene by scene and the film resists it, because each scene moves one piece of a single decision. The bicycle ride to the sea shows the possibility that Hattori is, and the next scene removes it: he is engaged. The Noh performance turns the father’s remarriage from rumour to a face across a theatre. Aya’s flat shows the one other life Noriko knows. The Kyoto journey is required, because the film must give father and daughter one last time together before it takes it away. What is charged: the opening tea ceremony runs long as a frame, Aunt Masa’s purse at the shrine is comic business the plot does not need, the Noh holds its stage action longer than its job requires, and the father’s speech at the inn says what the film has already shown.
Mohammad Reza Isfahani, under Shah Abbas I · Architecture
8.6 · Tier IV
Judged on structure, purpose and site. The portal must face the square, for the mosque is a member of the square’s plan, answering the palace opposite; the chamber must face Mecca; the bent passage is the only thing that can reconcile the two, so it is compelled, not chosen for effect. The absence of court, iwans and minaret is itself required: a mosque of one room, for prayer and not for the assembly of a city, has no use for a minaret calling a public that does not gather there. The eight arches are what a square needs to carry a circle; the tile is the whole interior surface, structure outlined in colour. What resists: the outside of the dome is a display to the square, not a requirement of the room it covers, and the inscriptions are denser than any visitor reads. The necessity lies in the plan and the passage; the structure is conventional.
Radiohead · Music
8.6 · Tier IV
Ten tracks in about forty-two minutes, and almost nothing can go. The band’s own subtraction is on record: eight songs from the same years were left off and issued separately on a second disc, and the album is the better for each absence. Within the songs the form is economical. 15 Step states its pulse and its argument in under four minutes, Nude has been reduced to a voice, a bass line and strings, and Videotape is little but piano, voice and a few percussive strokes. Faust Arp, the shortest track, looks removable and is not: it holds the hinge between two equal halves. The test bites once, at Bodysnatchers, the one track whose loss the record’s argument would survive.
Alberto Giacometti · Visual art
8.5 · Tier IV
Judged by the subtractive test, which the figure has already applied to itself: Giacometti took away until what remained could not be thinned further without ceasing to stand. Remove the stride and this is one of his standing women, and the claim on movement goes. Remove the weight of the feet and the base and the thinness has nothing to rise from; the feet make the figure walk on the ground rather than float. Remove the forward lean and it marches instead of going on. Nothing ornamental is left to remove. What holds the axis is substitution: Walking Man II, made the same year with another surface and stance, shows that this figure’s particulars were one choice among close neighbours, and the surface, worked everywhere, is permitted in its detail rather than compelled at each point.
Anselm Kiefer · Visual art
8.5 · Tier IV
The subtractive test on a single image. The hall cannot go: it is the work’s body and its accusation, a memorial to the soldiers of the Reich. The perspective cannot go: it carries the viewer into the crypt, toward the one light. The flames cannot go: without them the hall is a ruin; with them it is a sanctuary and a furnace at once. The name cannot go: without it the canvas is the Reich’s hall, blackened; with it the hall belongs to the ashen-haired woman of Celan’s poem, and the whole image turns. Four elements, each required, and nothing added beside them. What yields is the surface below the level of the image: the incident of crust, drip and stain is not, patch by patch, required, and some of it reads as material for its own sake.
George Orwell · Literature
8.5 · Tier IV
The test is subtractive, and in thirty thousand words it finds almost nothing to take. Each incident carries a stage of the argument and stands where the argument needs it. Old Major’s dream gives the revolution its promise, so that every later betrayal can be measured against it. Mollie, leaving for sugar and ribbons, is the one animal who goes over to the enemy for comfort; Moses, flying off and returning, is religion tolerated when it is useful. The windmill joins labour, technology and propaganda in one object, built, blown down and built again. The hens’ rebellion over their eggs must come before the confessions, since it supplies the first victims; Boxer’s sale must come last before the end. Charged: the timber deal and the forged banknotes are compelled more by the historical key than by the fable’s own need, and chapter X compresses years into summary.
Francis Bacon · Visual art
8.5 · Tier IV
Judged on the panels one by one and as a set. Remove a panel and the triad goes: the mourners at the foot of a cross are three by tradition, the Furies are three, and the triptych is the form that carries both. Remove the orange and the figures lose the one element common to all three, the airless field that isolates and binds them. Remove the table, the plinth and the grass and the figures float; the panels stop being stages. Within each panel nothing ornamental remains. What holds the axis is substitution: the left figure’s drapery and the supports read as found rather than compelled, the title’s own word, studies, admits the configuration was provisional, and the restatement of 1988 held the composition at another scale and colour.
Jane Austen · Literature
8.5 · Tier IV
The subtractive test finds very little, because each set piece does double work. The assembly plants the slight that Elizabeth’s prejudice feeds on and that Darcy’s pride must answer for. Collins’s proposal (chapter 19) is farce and also the hinge that sends him to Charlotte Lucas, whose marriage (22) is the novel’s counter-argument and gives Elizabeth her reason to be at Hunsford when Darcy proposes (34). Lydia’s elopement looks like a late subplot and is the test of everything: it proves Wickham’s character, exposes the family as Darcy’s letter said it would, and gives Darcy the act by which his change is shown. Austen’s own account of the revision, the book “lopt and cropt”, is the measure. What the test can take is small: some of Mary’s moralising, some of Kitty, a few chapters of visiting at Hunsford. The tidy distributions of the last chapter are permitted rather than compelled.
Diego Velázquez · Visual art
8.5 · Tier IV
Apply the subtraction test and almost nothing yields. The hanging cannot go: it is the red ground against which the red of the office and the red of the face must be told apart, and the picture’s argument is that they almost cannot be. The chair cannot go: it is the throne cut down to a seat, its gilt finial the one hard ornament beside the head. The paper cannot go: the one object, the business of the court in a white fold. The ring cannot go. The white rochet is the cool that makes the reds burn. What holds the figure below the top is the lower field of white lace and drapery, compelled as a counterweight but painted at more length than the meaning needs.
Polykleitos the Younger (attributed) · Architecture
8.5 · Tier IV
Run the subtractive test, and almost nothing yields, because almost nothing here is for any purpose but seeing and hearing. Each row exists because a body must sit there at a set height above the one below; each stairway, because those bodies must reach their seats and leave; the drain, because a bowl of stone gathers rain. The scale is compelled by the festival audience it held and by the reach of one voice. What holds it below the top: the upper cavea, though it obeys the same law, enlarges a finished form rather than supplying a part the first required, and with the stage building lost, necessity is read on the bowl and the circle alone.
Gabriel García Márquez · Literature
8.5 · Tier IV
The book’s premise is necessity, and the subtractive test finds almost nothing to take. Each of the five chapters is required by the reconstruction. The first gives the victim’s last morning, so that the reader walks beside a man the whole town knows is to die. The second gives the wedding, because the killing has no cause without the returned bride. The third is the long middle in which the twins tell everyone what they mean to do, and it must be long, because its length is the indictment. The fourth gives the autopsy and Angela Vicario’s later life, the consequence before the act; the fifth keeps the killing for the last pages, so that knowledge has done all its work before the knife does. The minor persons, Clotilde Armenta, the mayor Lázaro Aponte, Father Amador, Victoria Guzmán and Divina Flor, each carry one failure to act. What holds the axis below the summit is a little looseness: a few of the narrator’s family digressions and the catalogue of the wedding feast run freer than the rest.
Piet Mondrian · Visual art
8.4 · Tier IV
Judged unit by unit, as the painter’s method invites, since every position was worked for balance. Take away a yellow line and the field loses a beat and a boundary; the lines are few enough that each is structural. Take away one of the large rectangles that sit across the grid and the rhythm loses one of its slow accents against the fast pulse of the small units, and the balance tilts, which the whole method was built to prevent. Take away the absent black and nothing is missing, which is the point. What yields is the small unit: whether a given square is red, blue or grey, and exactly where, could change in places without loss, and the moving tapes show that position was searched for rather than given.
Leonardo da Vinci · Visual art
8.4 · Tier IV
Judged on structure alone, and very little can go. The turn of the head is the event: without it the panel is a court likeness. The ermine cannot go: it is a second body repeating hers, the twist of its neck answering hers and its raised paw answering her hand, so that the picture is two attentive creatures facing one way. The hand cannot go: it joins woman and animal, and its long fingers, articulated at every joint, are the one moving thing on the panel. The light from the upper left is at once the reason for the turn and the means of the modelling. What yields: the necklace’s second loop, the ribbons and the slashed sleeve, permitted rather than compelled, and an animal larger than any ermine, its scale argued by emblem, not by necessity.
Hasegawa Tōhaku · Visual art
8.4 · Tier IV
The test is subtractive, and the work is already the result of subtraction: no figure, no hut, no shore, no path, no colour, no gold. What remains is pines, the air between them and one far peak, and each is required. Take away the peak and the left screen loses its depth and its season; take away the dark near grove at the right and the pair has no foreground from which the mist recedes; take away the emptiness and there is no work. What holds the axis below the top is length. The groves are a sequence along twelve panels, and a sequence of like units can lose one without collapse; and the joins, where the composition does not run cleanly from panel to panel, show that the order of the parts was not wholly fixed by the work itself.
Edith Wharton · Literature
8.4 · Tier IV
Subtract, and very little goes without loss. The opening at the Academy of Music sets every term: the boxes, the opera glass, Faust sung in Italian to an English-speaking audience, the lilies of the valley, the arrival of the Countess Olenska in the Mingott box. The genealogies supplied by Sillerton Jackson and Lawrence Lefferts look like ornament and are not: they are the court record by which Ellen is tried, and the trial is the plot. The archery at Newport, the parasol at the Blenkers’, the interview in Boston with M. Rivière, each moves the noose a turn. What could go is small: some of the inventory of drawing rooms in Book I, part of Archer’s reflection on his reading and his club, and Ned Winsett, whose case for public life is stated more than made necessary.
The Strokes · Music
8.4 · Tier IV
Eleven short tracks, and inside each song the subtractive test finds almost nothing: no introduction is padded, no solo outstays its few bars, and every song stops when its last chorus has landed. Is This It must open, a slow, loping title song that asks the record’s question before the speed starts. Last Nite and Hard to Explain are the record’s two cores and could not go. Take It or Leave It must close, the one place the voice is pushed to a shout, an ultimatum after ten tracks of shrugging. Economy is the record’s first virtue and it is nearly complete. The test bites only across the sequence: Soma, Alone, Together and Trying Your Luck share one tempo, one texture and one stance, and any one of them could go with little lost.
Rembrandt van Rijn · Visual art
8.4 · Tier IV
Judged figure by figure, the canvas resists subtraction nearly everywhere. The chairman at the centre with the open book is the axis of the bench. The syndic half risen at the left is the instant: take him away and the picture is a row; with him it is a moment broken off. The servant behind, bareheaded and lower in rank, is the vertical that keeps the frieze from going flat, and the one face not of the board. The red carpet is the field of light from which every black coat is read; without it the black is a mass. What yields is little: the syndic at the far right sits nearest to repeating his neighbour, and the carved detail of the panelling is permitted rather than compelled.
Alberto Burri · Visual art
8.4 · Tier IV
The subtractive test finds little to take. Each white mass stands for a block of houses that stood there; each fissure is a street that was walked. Remove the plan of the town and the work is a pattern on a hill, a crackle enlarged; remove the rubble inside and it is a monument laid on a site rather than a burial of it; remove the walk and it is an image seen from the air. Remove the whiteness and the shroud goes. Raise the blocks above the head and the walker loses the slope and the sky; lower them to the knee and the town is only a map. The parts are few, and the few are required. What gives a little is the extent of the field, which the town sets but which is not argued at every edge.
Kazimir Malevich · Visual art
8.3 · Tier IV
The subtractive test returns its strongest answer and its hardest question. Nothing can be removed: take away the white and the square is no longer a figure on a ground but a monochrome, a different and later proposition, Rodchenko’s of 1921; take away the black and there is a white canvas; set the square at an edge and it becomes a shape in a composition rather than the zero of composition. The smallness of means is compelled by the argument, which is reduction, not permitted by it. The hard question is substitution, and it holds the axis: the later versions, made at more than one size, show that not every measure was fixed. What is necessary is the relation, and necessity bought with almost no parts is easier than necessity across a crowded whole.
Johannes Vermeer · Visual art
8.3 · Tier IV
Take each object away and ask. The woman cannot go, nor the stream, which is the instant. The window is the light, and its one broken pane is the sign that the light comes in from outside, through something used. The bread is the second subject of the light, where the picture is looked at hardest. The bare wall cannot go: it is the field for her silhouette, and its nails and holes make it a wall rather than a ground. What yields: the basket and the pail on the wall, and the foot warmer and the tiles at the floor, which could be lost at some cost to the room’s completeness and to an undertone, not to the act. Required in the main; not every object at once.
Charles Rennie Mackintosh · Architecture
8.3 · Tier IV
Judged on purpose, structure and site, and the building resists the subtractive test almost everywhere. The brief asked for a plain building with north light for its studios, and the north front is that light: windows as large as the wall allows, their mullions and iron the means of the glass. The slope compels the south, the building dropping storeys down the hill, sheer because the site is. The east and west fronts differ because their rooms differ, the library’s height and light producing the west façade’s tall oriels. The phasing compelled the asymmetry: the entrance stands where the first half’s money ended. What yields is small: the entrance’s curving stone and ironwork, the tower over the stair, the finials, and the Hen Run, a delight a corridor did not strictly need.
Piet Mondrian · Visual art
8.1 · Tier IV
Judged by subtraction, and the canvas has almost nothing to subtract. Take away the blue and the red has nothing to answer it across the diagonal; the field tips to the upper right. Take away the yellow and the lower right corner, the one place where the red’s weight comes down to the edge, goes slack. Move one black band by its own width and the proportions of four planes change at once. The scale is compelled: the red is large against the body without becoming a wall. What holds the axis below the top lies beside the canvas, not in it. The painter made dozens of compositions on this law in these years; the necessity is the system’s, and this canvas is one exact solution among a family of solutions.
Michel Virlogeux and Norman Foster · Architecture
8.1 · Tier IV
Judged on structure, purpose and site, the subtractive test finds almost nothing to take away. The route had to cross a gorge some 2.5 kilometres wide between two plateaus without descending into the valley, so the height is compelled by the land, not chosen for effect. The equal spans of 342 metres make the piers as few as the deck allows; each pier’s height is set by the ground beneath it, not by composition. The split upper leaves are required by the continuous deck’s movement in heat, and become the piers’ taper only because they are required. What yields: the masts’ height and their inverted Y are partly a figure, the deck’s slight curve is drawn for the view of the bridge as well as for the road, and the wind screens are a concession added to the form, not drawn out of it.
Anonymous · Literature
9.5 · Tier V
The core passes the subtractive test. Without the prologue no one knows what Job cannot know, that he is struck “without cause” (2:3); without the dialogue the verdict of 42:7 has nothing to approve; without the third chapter the speeches from the storm answer nothing. The friends’ repetition is their position, and the cycles shrink as it runs out: 2,051, 1,349 and 843 words. What holds the axis lowest of the twelve is Elihu: 165 verses, 15.4 per cent of the book, named nowhere else. Job never answers him, God answers Job as if he had not spoken, and the verdict passes him over.
Richard Wagner · Music
9.5 · Tier V
Length is not the charge, and most of the length is compelled. Rheingold is needed because the theft and the contract are the first cause; Walküre because the god’s free hero must be shown to be unfree; Siegfried because the truly free hero must exist before he can be destroyed. The subtractive test finds give in one recurring place: the narrations. The text was written backward, so the later dramas recount what the earlier ones stage. Wotan’s monologue changes the story as it tells it; the riddle game in Siegfried Act I, the Norns and Waltraute mostly go over the ground again. The Gibichung plot turns on a drug of forgetting the rest of the cycle does not need. These hold the axis at the lowest of the twelve.
Fyodor Dostoevsky · Literature
9.5 · Tier V
Judged on the work. Its verbal part lies in the Russian, beyond this reading, and is neither charged nor credited. Length is not a cost, and three stretches that look removable fail the subtractive test. The church-court debate plants Paissy’s “third temptation of the devil” (Pt. I, Bk. II, ch. 5), on which the Legend builds; the sermon to village priests plants the “little tiny seed” (Pt. II, Bk. VI, ch. 1) that the speech at the stone gathers in; the failed loans fix the moneyless afternoon in evidence. What holds the axis at 8.6 is what does give way: Rakitin’s verses told twice, the market pranks of Book X, the officials’ pedigrees, and the trial’s choruses and retellings, which “had little to do with the case in hand” (Pt. IV, Bk. XII, ch. 6). Together they come to perhaps a twentieth of the book.
William Shakespeare · Literature
9.5 · Tier V
The design passes the subtractive test: three sons of murdered fathers, Hamlet, Laertes and Fortinbras, and a fourth in the Player’s Pyrrhus. Without Laertes the end has no instrument; without Fortinbras no one inherits “the election” (5.2). Hamlet names the method: “by the image of my cause I see / The portraiture of his” (5.2). What holds the axis at 8.6 is the matter around the design: Reynaldo, the embassy, a dumb show that tells the Mousetrap before it is played, pirates who exist to bring Hamlet home, Osric. The conflation adds 2,061 words found in only one early printing. On the work alone, two tenths higher.
Marcel Proust · Literature
9.4 · Tier V
Length is not a cost; the question is whether the parts are required. The scale is compelled: time is regained only after it has been spent, and the faces aged in the last volume work only because they have been carried through every volume before it. Un amour de Swann is the template for every later love, and the boy’s love for Gilberte rehearses its law: “it was I alone who loved.” (Noms de pays : le nom). What holds the axis at 8.6 is the Albertine cycle, which restates Swann’s law of jealousy round after round in the fifth and sixth volumes. In his last typescript of the sixth Proust cut it heavily. His own cut is the evidence: perhaps a tenth of the whole could go.
Murasaki Shikibu · Literature
9.3 · Tier V
Length is not a cost, and the scale is compelled: the subject is recurrence, and recurrence needs time to happen in. Genji wrongs his father with Fujitsubo (ch. 5, 7) and is wronged the same way, decades later, by Kashiwagi and the Third Princess (ch. 34–36); the substitutions run from the Kiritsubo consort to Fujitsubo, Murasaki and the Third Princess, and again at Uji. What holds the axis lowest of the twelve is matter the tale could lose. Sixteen chapters of the first part form a side strand that lifts out without breaking the main plot, the Tamakazura chapters (22–31) its largest block. The bridge chapters, Takekawa above all, could go with little loss, and the inventories of robes, gifts and ranks run longer than their meaning.
Plato · Literature
9.2 · Tier V
Subtract and see what goes. The first word, “katebēn”
“I went down” (327a), is answered in Book VII by the order to the freed prisoner, “katabateon”
“you must go down” (520c): the setting is the cave the dialogue later describes. Book I cannot be cut, for its failure is why Glaucon demands a longer account; Books VIII and IX are required by his question, whether the just life is happier, which only the tyrant’s portrait answers. What holds the axis lowest of the twelve is matter permitted rather than compelled: Book III’s rules on modes, rhythms and diet, the nuptial number (546), and the second treatment of poetry in Book X, which Er defends but whose joint still shows.
William Shakespeare · Literature
9.2 · Tier V
The first part passes the subtractive test almost whole. Every strand answers another: the robbery at Gad’s Hill against the rebels dividing the kingdom on a map (1 Henry IV, 3.1); the play extempore in the tavern (2.4) against the King’s interview with his son (3.2); Hotspur’s honour against Falstaff’s catechism, “What is honour? A word” (5.1). The second part replays the first one’s movement, and much of the replay is purpose, since its subject is time that will not move as kings intend; Shallow’s scenes are required by it. What holds the axis lowest of the twelve is what is not required: some of Pistol’s ranting, the long rebel councils (2 Henry IV, 1.3 and 4.1), and the Epilogue’s dance and its notice of a play to come. About a twentieth of the whole could go without loss.
Wolfgang Amadeus Mozart · Music
9.2 · Tier V
The action is a seducer’s last day, and he fails at every attempt the stage shows: Anna drives him from her house, Elvira breaks in on Zerlina after No. 7, Zerlina screams at the ball, and Masetto’s arrival cuts short the serenade to Elvira’s maid. The run of failure is the plot, and it ends at the table; the Commendatore dies in No. 1 so that No. 24 can happen. What holds the axis here is the number form and the version. The Act II middle, a chain of disguises, captures and escapes, is the most separable stretch, and Ottavio’s two arias halt the action. On the Prague score alone, two tenths higher.
Johann Sebastian Bach · Music
9.2 · Tier V
Length is not charged. The subtractive test meets its hardest resistance in the Symbolum Nicenum: remove the Et incarnatus and the Crucifixus is no longer the centre of nine; the Gratias and the Dona nobis require each other across ninety minutes. The give is documented, not supposed. The Missa of 1733 stood alone as a complete Lutheran Mass, the Sanctus stood alone from 1724, and C. P. E. Bach gave the Credo by itself in 1786. The Gloria’s clauses each have a number because the Dresden plan says so, the Osanna returns because the liturgy says so, and eight movements were first compelled by other words. The whole is necessary; several of its parts were not necessary to it.
Plato · Literature
9.1 · Tier V
Subtract and see what goes. Remove the frame and the work loses its tense: Phaedo telling it afterward makes every argument a thing remembered beside a body. Remove the Delian ship (58a to c) and the month that lets the conversation happen is unexplained. Remove the objections of Simmias and Cebes and the earlier proofs stand untested, which the dialogue cannot allow; the despair they cause (88c) is what the passage on misology answers. Remove the myth and the work ends in a proof it has itself called short of certain (107b). What holds the axis lowest of the gated axes is length: the cyclical argument (70c to 72e) and parts of the argument from affinity run longer than their weight, and the refutation of attunement gives three arguments where one carries the point (91c to 95a).
William Faulkner · Literature
9.1 · Tier V
The test is subtractive, and it is harder here than it looks, because the book tells one story four times. Remove Mr. Compson’s three chapters and the wrong theory goes with them, the octoroon mistress and the bigamy, which the right one must overturn: the book needs the error so that the truth about Bon’s blood lands as a reversal and not as a fact. Remove Rosa’s fifth chapter and her long grievance is an anecdote; remove Shreve and Quentin has no one to tell it to and no one to contradict him. The parts are required. What holds the axis at the foot of the twelve is the sentence, not the structure: the rhetoric says some things three times within a clause, a vocabulary of intensity recurs past its use, and Mr. Compson’s chapter on the wedding and the town spends more than it buys. A tenth or so of the verbal mass is permitted rather than compelled.
Teotihuacano · Architecture
9.1 · Tier V
Run the subtractive test from the plan inward. The orientation cannot go: every wall obeys it, and the river was bent to it. The Avenue cannot go: it lays the Moon against Cerro Gordo and holds the city’s two halves. The Sun stands over the cave; the Ciudadela is the crossing of the two avenues and the state’s seat. The compounds are compelled by the people they housed; their uniformity is the plan’s argument. What resists, and holds the axis lowest of the twelve: the small pyramids ranged round the Ciudadela, more than the enclosure needs; the three-temple complexes repeated along the Avenue; the Moon’s seven bodies; the platforms set before the Sun and the Feathered Serpent by later politics; five centuries of addition. A city built by generations is in part assembled; this one was assembled to one rule from the start.
George Eliot · Literature
9.1 · Tier V
Length is not a cost; the question is what could go, and the four strands cannot. Lydgate’s marriage is the measure of Dorothea’s, since each marries an idea of the other; Fred’s redemption by work is the measure of Lydgate’s fall by debt; and Bulstrode’s exposure breaks Lydgate and calls Dorothea out of her grief. Featherstone’s two wills, which seem a comic subplot of greedy kin, bring Raffles to Stone Court and so bring down the bank. What holds the axis lowest of the twelve, level with The Archetypal Deep, is slack of about a twentieth: the Featherstone relatives and the funeral told at more length than the comedy needs, Mr Brooke’s candidacy and the Pioneer, the Garths’ goodness said more than once, and commentary where a scene has done its work.
William Blake · Literature
9.0 · Tier V
Inside the poem, necessity is near absolute. The Sick Rose has eight lines and none can go: “O Rose thou art sick. / The invisible worm, / That flies in the night / In the howling storm”. London uses one word twice, for the street and for the river, because the repetition is the argument: both are owned. The pairs are required, since each half of a pair means what it means against the other. The test cuts at the level of the book. Blake moved four poems between the halves, reordered plates from copy to copy, etched “A Divine Image” and left it out, and added To Tirzah later: the sequence was not compelled. Some songs are slight, The Blossom, Laughing Song, The Lilly, My Pretty Rose Tree, The Angel, and their loss would cost a tone more than a meaning. Innocence’s slight songs are required as a state, which lightens the charge without removing it.
Alfred Hitchcock · Film
9.0 · Tier V
Judged on structure, since the dialogue is functional and carries little of the meaning. The second half is built from the first, so almost every first-half scene is required twice: once as event, once as the template the remaking copies. Ernie’s, the grey suit, the bun and the tower are each set down so they can be repeated. Midge looks removable and is not: she is the one woman who offers Scottie herself, and he refuses her for an image. The give is real and is weighed in full. The vanishing at the McKittrick Hotel is never explained, kept for an uncanny effect the plot cannot account for. And the exposition at Elster’s office and in the bookshop is laid out in plain talk.
Cormac McCarthy · Literature
9.0 · Tier V
The test is subtractive, and the book resists it more than a picaresque should. Its argument is that violence is not an episode in the conquest of the West but its substance, and the argument is made by repetition: massacre after massacre, ride after ride, nothing learned and nothing ending. Cut the repetition and the argument becomes an anecdote; three massacres chosen would tell a story of escalation the book denies. The set pieces are each required: the revival, the Comanche, the powder, the war speech, the crossing, the jakes. What holds the axis at the foot of the twelve is the middle, where the rides between Chihuahua and the crossing return to desert, water and slaughter without adding a turn, perhaps a tenth of the whole, and the kid’s thread, thin across the long passages from which he is absent.
Richard Wagner · Music
9.0 · Tier V
Length is not charged: the slowness is the argument, and Gurnemanz says as much when he tells Parsifal that here time becomes space. The subtractive test meets resistance at every structural point: the wounded king’s bath, the swan, the first ceremony watched without understanding, the flower maidens, the kiss and the cry “Die Wunde!”, the spear caught in the air, the Good Friday meadow, the second ceremony. Each event is required by the next. It finds give in Gurnemanz: the Act I narration lays out Titurel, Klingsor, the lost spear and the prophecy at length to squires who in part know it, and Act III tells again what the interval held. The first ceremony runs beyond its dramatic need. Held below Otello’s 9.1, whose libretto was cut harder.
Wolfgang Amadeus Mozart · Music
9.0 · Tier V
The machine is tight. The first duet measures the room the Count has given the couple, “Cinque, dieci” (“Five, ten”), and the room’s place between the Count’s door and the Countess’s is the plot. Cherubino hidden in Act I sets up the closet in Act II; the closet yields the jumping page, the crushed flowers and the commission without a seal; the commission and Marcellina’s contract drive the trial; the trial yields the recognition; the letter duet yields the pin whose loss opens Act IV. Almost every recitative pays a thread forward. The give is in three places: Marcellina’s and Basilio’s Act IV arias, cut in most houses with little loss; Bartolo’s vengeance aria, a buffo calling card more than a move; and the Act III chorus and fandango, ceremony the plot passes through.
Samuel Beckett · Literature
8.9 · Tier IV
The test is subtractive, and the book invites it openly: its matter is a voice that cannot stop, so it may be asked why it does not stop sooner. The answer is the argument. The voice is under orders to speak until it has said itself, and it cannot; an ending reached because enough had been said would refute the book. The argument sets the length, and the length is modest. Each part takes away one more surrogate: the opening questions and hypotheses, the earlier heroes, Mahood twice, Worm, the last sentence. What gives way is the long middle, where cycles about the masters and the pensum come round without turning and the Worm section restates an impasse rather than deepening it: perhaps a tenth of the book is allowed rather than required.
Samuel Beckett · Literature
8.9 · Tier IV
The halves need each other. Take away Moran and Molloy’s monologue is a voice without a measure; take away Molloy and Moran’s decline has nothing to decline toward. Inside each half the test is harder. The first part is picaresque in build, a run of encounters, the two walkers seen at evening, the policeman and the papers, Lousse and her dog, Ruth or Edith, the charcoal-burner, the crawl through the forest, and several could go without breaking the line. What resists subtraction is that the digressions are the matter: the sixteen sucking stones sent round four pockets, the count of farts reduced to an hourly average, the mother addressed by knocks on her skull are not ornaments on a story but the whole equipment of the mind that tells it. Held below the top because the Lousse interlude and parts of Moran’s journey run longer than their work.
Arthur Rimbaud · Literature
8.9 · Tier IV
The test is subtractive, and a book this compressed is hard put to pass it; it mostly resists. Each part is a stage of one trial: the prologue’s verdict, the inheritance of “Mauvais sang”, the poison of “Nuit de l’enfer”, the two crimes confessed in the two “Délires”, the love and the poetics, three short attempts at escape in “L’Impossible”, “L’Éclair” and “Matin”, and the leave-taking of “Adieu”. Remove “Alchimie du verbe” and the book loses its confession of the poetics; remove “Vierge folle” and it loses the other self who judges him. What the test can take lies in “Mauvais sang”, whose eight movements wander, from the Gaul to the crusader, the convict and the landing of the whites, and could lose one without loss, and in “L’Impossible” and “L’Éclair”, which argue the same case twice.
Anonymous, under King Lalibela · Architecture
8.9 · Tier IV
Run the subtractive test, which here takes a literal form: every part is what was left when everything else was taken away, so nothing was added that could now be removed. The sanctuary that holds the tabot, the three-part plan of Ethiopian worship, the court that frees the monolith, the trench that drains it and brings the worshipper to the door: liturgy, rock and rain compel them. What yields is the vocabulary of memory. Beam-ends, recessed courses and window frames copy the timber-and-stone building of Aksum in a material that does not need them, required by meaning and not by structure. And the complex is accretive: the number and placing of the churches follow dedication and history more than necessity.
Herman Melville · Literature
8.9 · Tier IV
Most of the whole resists the subtractive test. The stutter is planted early, the work of “the envious marplot of Eden” (ch. II); it returns in the fore-chains as “D-D-Damme” (ch. XII), and in the cabin it is the blow itself: “Could I have used my tongue I would not have struck him.” (ch. XVIII). The soup, the Dansker’s warning and the afterguardsman’s guineas are each required, and so are the sequels, “Three brief chapters will suffice.” (ch. XXIV), which carry the verdict of record and memory. What does not resist is part of the essay: most of the Nelson chapter, by the narrator’s own account a “literary sin” (ch. IV); the sailors as “a juvenile race” (ch. XIV); the Somers paragraph; Vere introduced a second time, “to fill out that sketch” (ch. VI). Perhaps a twentieth could go; from the soup to the burial there is no slack.
Pieter Bruegel the Elder · Visual art
8.9 · Tier IV
Judged on the configuration, since the panel has no words. The tower cannot go, nor the rock it is cut into: the building swallows a mountain, and that is half the argument. The harbour cannot go: ships, rafts and cranes feed stone and timber to the base, so the tower is supplied by a living economy and not by a miracle. The city cannot go, since it gives the tower its scale. The king and the kneeling masons cannot go: the only figures large enough to read as persons, they are the will that orders the whole. What gives is the detail. The small labours are each true, but their number is a density rather than a structure: a third of them could be other labours and the panel would know the same thing.
Vladimir Nabokov · Literature
8.9 · Tier IV
The test is subtractive, and it bites less here than on almost any novel of the book’s size, because the book is two texts locked together and each is the other’s evidence. The poem cannot go: it is the thing commented on, and its plain grief is the measure of the commentator’s appropriation. The Zemblan romance cannot go: it is what Kinbote reads into the poem, and the book’s argument lives in the gap. The notes on the assassin, placed so that he draws nearer as the poem nears its end, carry the plot; even the index closes the book in Kinbote’s voice and gives his last disguises away. Where the test bites: the palace and escape notes run longer than the counterpoint needs, the king’s amours repeat one joke, and some notes are wordplay that the design permits rather than compels, perhaps a tenth of the whole.
The Beatles · Music
8.9 · Tier IV
Fourteen tracks in about thirty-five minutes, and no song outstays its idea; eight run under two and a half minutes. Nothing in “Eleanor Rigby” or “For No One” can go: each verse of the first moves its story a step, and two verses and a horn solo carry the whole of the second. The frame is required, with the state’s demand in “Taxman” at the opening and the dissolved self of “Tomorrow Never Knows” at the close. The test bites in three places, all on the second side. “Doctor Robert”, “And Your Bird Can Sing” and “Good Day Sunshine” could go with little loss to what the record argues.
Gian Lorenzo Bernini · Visual art
8.9 · Tier IV
Judged on the configuration. Take away the Cornaro and the vision has no witnesses and the chapel is no longer a tomb: both its purposes go. Take away the skeletons in the floor and the dead under the vision go with the lowest order. Take away the opened vault and the light has its source in a window, not in the work; take away the rays and the light is invisible. What gives is number and abundance. There are eight Cornaro because the family had eight to name, and one or two could go without loss. The coloured revetment is richness, and the habit’s folds, compelled because they hide the body, are more than the argument needs.
Vladimir Nabokov · Literature
8.9 · Tier IV
The test is subtractive, and the book resists it because so much that looks like ornament is wiring. A class list read for its comedy names Aubrey McFate, whom Humbert makes the name of his fate; a Who’s Who in the Limelight entry in the prison library names Quilty before the reader can know him; Quilty’s play shares its title with the hotel of the first night; the foreword gives away Dolores’s death under a name learned only in Part Two. Cut any of these and a strand of the design goes slack. What holds the axis is in Part Two: the motel catalogues of the first journey and the pursuit of the second are long by design, since tedium and dread are the meaning, but a few pages of each could go without loss.
Francis Ford Coppola · Film
8.9 · Tier IV
The two strands require each other. Without the father, the son’s 1958 is a crime drama about a hard man; without the son, the father’s 1917 is an immigrant romance. The scene that binds them is required too: Michael asking his mother what his father thought “deep in his heart”, and the cut that answers him with 1917. So is the 1941 coda, the only sight of the family whose loss the film measures. Length is not charged. The subtractive test still finds give: the Geary brothel episode exists for leverage; the Rosato brothers, Roth’s double game and the Pentangeli garrotting are machinery a clearer plot would not miss; the landlord episode is charming and detachable.
Pablo Picasso · Visual art
8.8 · Tier IV
Judged on the configuration as it stands, and the studies show the subtractive test already run by the painter: the sailor at the centre and the student at the left were taken out, and the room lost its story and kept its encounter. What is left resists removal at the main joints. Without the squatting figure the picture loses its most violent turn and the lower right goes slack; without the ledge of fruit nothing comes out to meet the viewer; without the curtain-puller nothing opens the scene. Where it gives: the two central women are close to a pair, and one could go with the frontal stare kept; the drapery at the upper left is filler beside that at the right. The scale is compelled: smaller, the stare would stop at the frame.
Built for Abbot Suger · Architecture
8.8 · Tier IV
Run the subtractive test on each campaign. The chevet resists it: the double ambulatory and the merged crown of chapels exist to let light pass unbroken round the relics of Denis and his companions, raised from the crypt to the upper choir, and the thin monolithic columns exist so that nothing stands between the windows and the eye. The crypt cannot go: it is the martyr’s tomb, the reason for the church. The width of the thirteenth-century transept is compelled by a use, the royal tombs laid out under Louis IX. What yields is at the joins: the fortress-like west block, the narthex bays kept rather than required, the Renaissance tombs and the nineteenth-century additions present by accretion. Each part has its reason; the whole was not conceived at once.
Luigi Pirandello · Literature
8.8 · Tier IV
The bones of the play bear the subtractive test. Remove the rehearsal of Il giuoco delle parti and the Characters arrive in no theatre. Remove Madama Pace and the one scene they live for has nowhere to happen. Remove the Son, who refuses to act his part, and the play loses its proof that a character can be fixed in refusal as well as in suffering. Each of the six is required by the family scenario and by the argument at once. What holds the axis below the high eights is the Father: his speeches on the many selves, on the single moment by which a man is judged, and on the character’s advantage over the actor are each necessary, but stated, restated and argued back at a length the play does not need.
Chinua Achebe · Literature
8.8 · Tier IV
The test is subtractive, and the spine passes it. Take out Ikemefuna and Nwoye has no wound to carry into the church. Take out Ezeudu’s warning to Okonkwo to take no hand in the boy’s death, and the gun that goes off at Ezeudu’s funeral is only chance, not a debt paid. Take out the exile and the return has nothing to measure what was lost. Most of Part One’s set pieces bear weight: the egwugwu return as the mask that Enoch tears away, the locusts return when the oracle of Abame, as Obierika reports it, names the white men locusts. What holds the axis here is two or three chapters of custom shown for its own sake, and the haste of Part Three.
Johann Wolfgang von Goethe · Literature
8.8 · Tier IV
The subtractive test finds little to remove from Book One: the arrival, the spring at the well, the children, the bread cut at the door, the ball and the thunderstorm, Albert’s return, the quarrel over suicide with a pistol held to the temple, the flight. Each step closes a door. Book Two is where the test bites. The embassy, the pedantic envoy and the snub at Count C.’s are required, since they show that the world outside Lotte has no place for him either, but the stretch runs a little past its work. The Ossian reading, several pages of Goethe’s own version of the songs of Selma, is the climax of shared feeling and must stand; at its length it is permitted more than compelled. The peasant lad added in 1787 earns his place.
Rembrandt van Rijn · Visual art
8.8 · Tier IV
Judged figure by figure. The father and the son cannot go: the embrace is the work, and every part of it is required, the bent head, the two hands, the son’s face pressed into the father’s body so that it is half lost, the bare sole turned to the viewer, the fallen shoe. The elder son cannot go: the parable’s second half is his, and his height, his lit face and the gap of dark floor between him and the embrace are the picture’s other argument. The great dark above is required too; it encloses the embrace. What yields is in the middle and the shadow: the seated man would be missed as a witness, not as a meaning, and the faces behind are below necessity.
Sappho · Literature
8.8 · Tier IV
Within the poems that survive whole or nearly whole, the subtractive test finds almost nothing to remove. The poem of the man “equal to the gods” is a list of symptoms in which each item is required: the tongue, the thin fire under the skin, the eyes that see nothing, the roaring ears, sweat, trembling, and last “chlōrotera de poias / emmi”
“greener than grass I am”, each step further from speech and nearer death. The hymn to Aphrodite needs every stanza: invocation, remembered descent, the goddess’s speech, the present plea. The priamel of fragment 16 has no idle member. What holds the axis here: necessity can be shown for perhaps a dozen poems, and across most of the body the question cannot be asked.
Akira Kurosawa · Film
8.8 · Tier IV
The subtractive test finds little to take. Each of the four accounts is required, because each makes the same death serve a different vanity: the bandit’s duel makes him a hero, the wife’s swoon makes her a victim, the husband’s suicide makes him a samurai, and the woodcutter’s farce strips all three. Remove one and the pattern, each teller claiming the killing or its honour, does not form. The woodcutter’s long, wordless walk into the forest looks subtractable and is not: it sets the light the accounts are played in and makes him the man who found the body, and so the last suspect. What gives: the commoner’s lines state what the accounts have already shown, and the coda with the abandoned child does one job, answering the commoner, at more length than it needs.
Alan Moore and Dave Gibbons · Literature
8.8 · Tier IV
The subtractive test is unusually hard to pass against this book, because the grid of nine panels makes each page a fixed budget, and the book spends it with very little slack. The background is load-bearing: the newsstand at the corner of 40th Street and 7th Avenue, its vendor and the boy reading the pirate comic, recurs in nearly every chapter and is where the end falls. Most of the back matter is required: Under the Hood gives the first generation of masks the history the main narrative cannot stop to give; the psychiatric file makes the turn of chapter VI possible; the pirate comic is the book’s moral double. What could go: some back matter is fill, the ornithology article and the number of The New Frontiersman doing less than the rest; Veidt’s account of his own life runs longer than the reader needs; and the mechanics of the island and the creature are told at a length the idea does not compel.
Giovanni Bellini · Visual art
8.8 · Tier IV
The subtractive test bites less than one expects of a picture so full of things. The saint cannot go, nor the light, nor the empty sandals: the shoes put off are the act, and the open hands are its answer. The cell, the desk, the book and the skull are his life in four objects: shelter, study, scripture, death. The donkey is the beast that carries him, left in the field; the town behind is the world he left, still visible and still in order. What yields is the inventory at the edges: some of the plants, the shepherd’s flock and the lesser creatures could be thinned without loss, and part of the pleasure is a cataloguing pleasure. Compelled at its centre, permitted in its margins.
Hans Holbein the Younger · Visual art
8.8 · Tier IV
The subtractive test, object by object. The skull cannot go: it is the picture’s second subject and the reason for its floor. The crucifix cannot go: it is the third viewpoint, from which the other two are judged, set exactly where an inventory would miss it. The two men cannot go, nor their ages: youth written down beside a death that has to be found. The lute with its broken string and the hymnbook carry the church’s discord in 1533. What yields is the upper shelf taken item by item: the quadrant, the polyhedral dial and the torquetum make one argument, the measure of the heavens, three or four times, and the case of flutes is a second instrument where the lute carries the meaning.
Byzantine, under Bishop Ecclesius and Justinian · Architecture
8.8 · Tier IV
Judged on structure, purpose and site. The core resists the subtractive test. The light dome of tubes is what lets the walls stay thin and open; the exedrae are screens and buttresses at once, curving their columns into the ambulatory, where they take the outward push and let light and sight through; the gallery answers a use that divided the congregation by sex and rank. The presbytery is the place of the altar, and nothing in its mosaic is surplus: every scene is a sacrifice or an offering, set round the table where the offering is made. What yields: the narthex is joined to the octagon, not required by it; the presbytery is added to a figure that does not ask for one; and the plain exterior is what the interior left over.
Diego Velázquez · Visual art
8.8 · Tier IV
Judged on the configuration. The two rooms cannot be separated: take the alcove away and the canvas is a genre scene, as it was read for two centuries; take the workroom away and it is a court visit to a tapestry, a document. The wager is their joining. The two principal spinners are required: the old woman at the wheel and the young one at the right are Pallas disguised and Arachne, the contest at its beginning, while the alcove holds its end. The Titian is required, since Arachne’s offence was to weave the loves of the gods. What yields: the woman with the curtain, the one stooping, the cat and the ladder are furniture more than argument, and the viol is an enigma more than a necessity.
Isaac Babel · Literature
8.8 · Tier IV
The subtractive test on a single story is nearly unanswerable. “My First Goose”, a page and a half, cannot lose a sentence: the newcomer’s spectacles, his trunk thrown into the street by the Cossacks, the goose crushed under his boot, the old woman, the shared cabbage soup, Lenin’s speech read aloud and the closing line of the heart form one chain. “Crossing the Zbrucz” is as tightly bound. The arrangement is required too: the first story opens on an old Jew with his throat cut, and the last closes on a dead Jewish soldier of the Red Army. The test bites in the middle of the book, where a few campaign stories carry the war forward without the fusion of the best, and their order could be varied without loss.
Andrei Tarkovsky · Film
8.8 · Tier IV
Judged on structure and duration. The film is one journey, and the subtractive test finds little to take out of its line. The domestic opening sets the wife and child the close returns to; the bar names the two clients; the cordon and the trolley make the crossing; each stage in the Zone tests one of the three; Porcupine’s story is the key to the Room and to the ending; the wife’s speech and the glasses answer the Stalker’s despair. The long takes are the waiting the Zone demands, and their length is compelled. What gives: the Writer’s tirades restate his position, the Professor’s arguments are partly exposition, and the rest stop in the first part is longer than its work.
Francesco Borromini · Architecture
8.8 · Tier IV
Judged on plan, structure and site under purpose, much is compelled. The site gives a narrow plot closing a long court, approached on one axis, its concave end already set by the courtyard; a centralised church answers it, and the altar lobe on the axis receives the court’s whole length. Inside, the subtractive test meets resistance: remove one lobe and the star fails, and with it the law by which the dome closes; remove the continuous entablature and the six lobes become six chapels round a hexagon; remove the drum outside and the dome’s thrust has nothing to hold it. What yields: the geometry is required by the idea more than by the use. A university chapel needed one room and an altar, not a star; the three alternating lobes add no function; the spiral is compelled by meaning, not by structure.
El Greco · Visual art
8.8 · Tier IV
Judged figure by figure. The count in his armour and the two saints in gold cannot go: they are the event. The boy at the lower left cannot go: he points, he looks out, and he ties the painter’s household to the burial. The priest in the surplice at the right, reading the office and looking up, is the one man below who turns toward heaven, and he is the hinge between the zones. The angel and the soul are the only thing that crosses, and the intercession above is required by what the picture argues. What yields is population: the frieze is required as a body, the community that witnesses, but any one head could go, and the crowd of the blessed thins into filler at its edges. The life size below is compelled.
Albrecht Dürer · Visual art
8.8 · Tier IV
Take the figures away one by one. The knight is the work. Death and the Devil cannot go, for the title names them, and without them the rider is a portrait of armour. The hourglass, held up into his face and unregarded, is the hinge of the whole. The skull at the lower left is the road behind him, and the tablet beside it sets the date and the maker in the same ground. The gorge confines him and the castle gives the road its end. The dog, the lizard and some of the vegetation are emblems added to the scheme, and the eye could lose one without feeling a gap. Tight, short of the top.
Titian · Visual art
8.8 · Tier IV
Judged figure by figure. Marsyas cannot go: the inverted body is the picture’s axis and its event. The two flayers cannot go: one in reverent closeness at the chest, one at the leg like a butcher, they are the two faces of the punishment, care and labour. The musician cannot go: music continues while a musician is skinned, and that is the argument. Midas cannot go; he is the one who thinks, and the picture’s weight moves to him. The small dog at the blood says what the body now is. What yields is the boy with the large dog at the right, which repeats the dog’s office, and the satyr with the bucket, a help carried over from the inherited design. Required at its core, permitted at two points.
Roman, under Vespasian and Titus · Architecture
8.8 · Tier IV
Judged on structure, purpose and site. The purpose is to bring a city’s crowd in, seat it by rank in sight of one floor and send it out again, and almost the whole fabric is compelled by it. The eighty arches, the annular corridors and the stairs between the radial walls are the circulation, each numbered entrance bound to a stair and a zone. The radial walls carry the raked seating and the routes at once. The ellipse gives combat its long axis and every seat a view; the hypogeum serves the appearances from below; the attic carries the awning. What fails the subtractive test is the skin: the engaged orders bear nothing, and the bay would stand without them.
Miles Davis · Music
8.8 · Tier IV
Five tracks in about forty-six minutes, and the subtractive test finds little to take. Inside the pieces almost nothing is written that could go: “So What” is a bass figure and a two-chord reply, and “Flamenco Sketches” is a sequence of five scales. The frames are as small as frames can be and still hold a performance. The solos are long, and the length is the argument, since a scale held for as long as the player chooses means nothing unless it is held. The test bites once. “Freddie Freeloader”, a B flat blues played as the hard bop of the day, could go, but it is the plain ground that “All Blues” turns into a vamp.
Jean d'Orbais, Jean le Loup, Gaucher de Reims and Bernard de Soissons · Architecture
8.8 · Tier IV
Run the subtractive test. The structure resists it almost everywhere: the flying buttresses are the thrust of the vault made visible, and the tabernacles that crown their piers, each sheltering an angel, are weight set where weight is needed, so that the sculpture there is also load. The plan is compelled by use: a long nave for the coronation procession, a deep choir for the clergy and the rite, a crossing where the throne stood. What yields is the abundance. Some 2,300 figures, the inner west wall in niches, angels and kings repeated: much is ordered rather than required, and a smaller programme would say the same. The upper façade and the unspired towers read as continuation more than necessity.
Nirvana · Music
8.8 · Tier IV
Twelve tracks in about forty-two minutes, and within the songs nothing is spare. “Smells Like Teen Spirit” has four chords, a verse, a pre-chorus and a chorus, and the quiet verse exists to make the chorus land. “Polly” is two chords’ worth of flat strumming because the flatness is the horror, and “Something in the Way” could only close the record. No track outstays its idea; the longest, the opener, runs about five minutes, and the frame, each side ending on its quietest song, is designed. The test bites in one place, and that is what holds the figure. “Breed”, “Territorial Pissings” and “Stay Away” do one job, fast, loud and sardonic, and two of the three could go with little loss.
U2 · Music
8.8 · Tier IV
Eleven tracks in about fifty minutes, and most of them pass the subtractive test. The opening is compelled: the record’s longing is in its delay, and nothing after it could stand first. Bullet the Blue Sky and Running to Stand Still are required by the America the album means to show, and Red Hill Mining Town, though its lyric is the weakest of the political songs, is the only song of labour. In God’s Country restates the opening’s desert, but in the plainest terms the record has, and at the point where side two begins its descent. The test bites once, at Trip Through Your Wires, a short harmonica blues the album never returns to.
Radiohead · Music
8.8 · Tier IV
Twelve tracks in fifty-three minutes, and most of them pass the subtractive test. The recitation looks the most removable and is the least: it runs under two minutes and is the only track without a sung voice, which is why it can carry the turn, and without it the synthetic voice of the second track has nowhere to arrive. The six-minute second track earns its length section by section, and the slow closing track, which asks the listener to slow down, could not sit anywhere else. The test bites in two places. The eighth track states as slogans what the seventh and tenth enact, and the third repeats the rescue fantasies around it.
Krzysztof Kieślowski · Film
8.8 · Tier IV
The subtractive test bites at two levels. Within Blue almost nothing gives: the sugar cube, the mouse, the petition and the visits to the mother are each a station of Julie’s attempt to want nothing, and each is undone. Red is nearly as tight, since every crossing of Valentine and Auguste argues that a life can be lived again in another. Remove White and the triad loses equality, its only comic register and a couple on the ferry, so the design requires it, and the three are compelled together. The give is local, in one film’s machinery, and nothing in the whole depends on it. What holds the axis here is that slack: the bodyguard work, the land deal and the Russian corpse are machinery for a fortune the comedy needs only as fact. Parts of the bond are ligature, and the ferry, compelled by Red, is only permitted by Blue.
Auguste Rodin · Visual art
8.7 · Tier IV
The number is given by the story, and the work takes the number seriously: six men, not a hero and his following. Put each to the subtractive test. Eustache de Saint-Pierre, old, stooped, eyes down, walking first, cannot go: he is the decision already made. Jean d’Aire, rigid, the key across his body, cannot go: he is the decision held by will. The man with his head in his hands cannot go: he is the decision unbearable. The two who turn back and the one who raises an open hand are the doubt and the farewell. What gives is the arrangement. Each figure stands alone and was enlarged and cast singly, so the composition scored is one of several the figures would allow. The figures are required; their exact placing less so.
Hans Scharoun · Architecture
8.7 · Tier IV
Judged on purpose, structure and site, and the room passes the subtractive test almost whole. Put the music at the centre and ask that every listener be near it and see it, and the terraces, the tilts of the blocks, the seats behind the orchestra, the tent of the ceiling and the reflectors over the platform each follow; take one away and the hall loses its sight lines, its nearness or its sound. The exterior is the room’s consequence: the roof follows the ceiling and the walls fold round the terraces, so nothing is a front put on for the street. The foyer is compelled by the section, occupying the space under the raked seating, its stairs the paths to the blocks above. What holds the axis below 9.0: the foyer’s profusion of stairs, levels and bridges exceeds what circulation needs, and the irregularity of the blocks is partly composition rather than acoustics or sight.
Théodore Géricault · Visual art
8.7 · Tier IV
Judged on the configuration. The raft cannot go, nor its tilt toward us, the near edge almost at the frame, so that the sea comes to our feet. The mast and sail cannot go: they are the second vector, pulling left while the bodies strain right, and the picture is the contest of the two. The father with his dead son cannot go: he is the stillness against which the climb is measured. The dead sliding into the sea at the bottom edge, the climb, the figure at its apex and the speck of the Argus cannot go. Below that the test gives a little. In the shadowed middle near the mast one or two figures could be taken out and the pyramid would still rise; the crowd there supplies mass more than meaning.
Anton Chekhov · Literature
8.7 · Tier IV
The subtractive test finds very little. Each sister is a different answer to one question: Olga by duty, Masha by passion, Irina by work and then by a marriage of resignation; and Andrei is the fourth answer, the talent that becomes a council clerk with a mortgaged house. Natasha is required as the force that takes the house room by room; Vershinin as the philosopher of the future whose love for Masha cannot leave his own marriage; Tuzenbach and Solyony as the triangle around Irina that ends in the duel. Remove an act and the erosion jumps a step. The margin: Fedotik and Rode are nearly interchangeable, and Vershinin’s two speeches on the centuries ahead cover overlapping ground.
Flannery O'Connor · Literature
8.7 · Tier IV
The test is subtractive, and in the strong stories it finds nothing. The title story’s first pages, the cat hidden in the basket and the grandmother’s lie about a secret panel, are the mechanism of the crash: every comic detail is a fuse. “Good Country People” spends its first third on Mrs. Hopewell’s platitudes and Mrs. Freeman’s appetites, and the whole of it is needed, because the seduction in the hayloft reverses exactly the pieties set up there. “The Displaced Person” is long, and its length is compelled: three women’s views of one man must be built before the tractor can roll. What holds the axis are the two slight stories. “A Stroke of Good Fortune” is a single joke on the denial of a pregnancy, and “A Late Encounter with the Enemy” a single irony on a Confederate relic; either could go, and the book would know what it knows.
U2 · Music
8.7 · Tier IV
The frame is compelled at both ends: “Zoo Station” announces arrival in a hostile world, and “Love Is Blindness” closes in the dark the songs between have walked into. “Until the End of the World” stands fourth and names betrayal as the subject, and the songs after it carry it. The subtractive test bites once, at “Tryin’ to Throw Your Arms Around the World”, a drunk man’s dawn the record could lose. “Who’s Gonna Ride Your Wild Horses” restates the dangerous lover of other songs, a soft spot, but it carries the slide from betrayal into obsession that “So Cruel” completes. That song and “Ultraviolet” hold their ideas a little long.
Gustave Eiffel · Architecture
8.7 · Tier IV
Judged on structure, purpose and site. The purpose is height, a thousand feet for the centenary, and to be climbed; granted that, almost everything is compelled. The legs splay because a tall structure is overturned by wind, and the curve of their edges answers the wind’s action, so the silhouette is a diagram of the force it resists. The lattice is open because a solid face would catch the wind; the members diminish as the load does; the stages come where the legs gather and stiffen one another. What yields: the arches between the legs, drawn for the eye more than for load; the first stage’s ornament, much of which later hands took away without loss; and the purpose itself, a chosen round number, so that the tower is compelled from a premise that was not.
Alfred Hitchcock · Film
8.7 · Tier IV
The subtractive test finds almost nothing loose. The forty thousand dollars, the patrolman and the trade at the car lot seem to promise a crime film, and they are required because they are a decoy: the film needs the audience invested in a story it is about to drown, and Marion’s flight is spent on that investment. Even the newspaper hiding the money, tossed into the trunk by Norman unknowing, bears weight, since the money sinks with her. What holds the axis is the courthouse, where the psychiatrist states in clinical prose what the cellar has already shown: the one place the parts are permitted rather than compelled, a few minutes in a film of about 109, after which the cell takes the film back at once.
Anonymous · Architecture
8.7 · Tier IV
The subtractive test bites hardly anywhere in the body of the church. Take away the transept, as the makers did, and nothing is lost: the five aisles run unbroken from the west wall to the double ambulatory, compelled by the idea of one undivided space. The stepped section is required twice over, by light, since each tier lights the one inside it, and by structure, since each tier braces the next and lets the flyers be short and steep. The lower church is required by the site. What yields is the west front, where five portals, unequal towers and a giant buttress pier read as accumulated, and the nave chapels, which are ordered additions, not consequences.
Gian Lorenzo Bernini · Visual art
8.7 · Tier IV
Judged on the group as it stands. Daphne cannot go, and no part of her can: the roots, the rising bark, the leafing hands and the still human face together are the event, a change that has to be readable from foot to crown. Apollo cannot go: the pursuit is the cause, and his hand at her side, touching flesh already turning to bark, is the hinge of the story. The laurel trunk behind her is the transformation and the support at once, the best kind of necessity a sculptor can find. What yields: Apollo’s drapery, a swirl that is a support and a sign of speed but could take another shape without loss; the quiver strap; the rock and the base, permitted rather than compelled. Almost nothing is idle, and the idle parts are the ones marble demanded.
Rembrandt van Rijn · Visual art
8.7 · Tier IV
Judged figure by figure, and there are only two, joined at the hands. Remove the man’s right hand and the picture loses its event; remove her fingertips on it and the gesture becomes taking rather than giving, and the meaning goes. His left arm round her shoulder is the second embrace, the protective one, required to make the first tender. The averted gazes are required: had the two looked at each other, or at us, it would be courtship or display. The gold sleeve and the red dress are the two halves of the light. What yields is the setting: the dark architecture and the foliage at the left are required as darkness and as nothing particular, the lower right is summary, and the width beyond the figures is permitted more than compelled.
J. M. W. Turner · Visual art
8.7 · Tier IV
Judged on the configuration, which is few things: a vortex, a hull, a mast, a signal, a break of light. Take away the hull and the vortex has no centre and no victim; it becomes weather, a study, and the human stake goes. Take away the mast and its pennant and nothing rises against the spiral: the one vertical among curves is how the eye knows the boat is still upright. Take away the signal and the boat no longer speaks. Take away the break of light and the vortex has no outside. The scale is compelled: smaller and the spiral would read as ornament, larger and the hull would be lost. What yields is the reach of the field at its edges and lower left, permitted rather than required.
Richard Strauss · Music
8.7 · Tier IV
Strauss’s first decision is subtractive: he cut Wilde’s play himself and set the rest as prose, with no librettist and no verse between. The act is a chain. Narraboth looks at Salome; Salome hears the voice from the cistern; Narraboth’s longing lets her have the prophet brought up; the prophet’s refusal makes the demand; Herodes’s oath makes it payable; the dance pays the oath. Each link holds. The subtractive test finds give in three places: the quintet of the Jews halts the action, and the Nazarenes’ report of miracles halts it again; Herodes’s catalogue of what he will give instead runs past its point, though that is its point; and the Dance is the most separable music in the work, often played alone and losing little.
Led Zeppelin · Music
8.7 · Tier IV
Eight tracks in about forty-two minutes, and the record stands on two required pillars. Stairway to Heaven must end side one: the riff, the rock and roll and the folk duet before it are gathered into its climb. When the Levee Breaks must end side two, the record’s heaviest weight placed last. The Battle of Evermore is required as the bridge from electric to acoustic and the place the myth first speaks, and Black Dog earns its opening, voice and riff in call and response setting the band’s terms. Inside the long tracks little is idle: each section of Stairway turns, and Levee’s length is its weight. The test bites on Four Sticks and Misty Mountain Hop, and on Rock and Roll, an homage.
Franz Schubert · Music
8.7 · Tier IV
The subtractive test finds resistance at the joints and give in the spans. The Adagio’s F minor middle section cannot go: without it the return of E major is merely a da capo, and with it the return is altered and shadowed. The Trio cannot go: the slow D flat chorale inside the Presto is the work’s second semitone turn, and without it the Scherzo is a hunt with no halt. The first movement’s theme for two cellos in E flat is the work’s emotional source. Length is not charged; repetition the argument does not require is. The first movement’s transitions restate by design, and the Finale’s popular theme returns more often than its material needs. Below Op. 131 at 9.3 for that give.
Radiohead · Music
8.7 · Tier IV
Ten tracks in fifty minutes, and no song outstays its idea. The fifth track, an instrumental of processed guitar that ends just short of the record’s midpoint, survives the subtractive test: it follows the one song about not being there by removing the voice, and the disappearance becomes literal instead of sung. The sixth is the track a hostile listener would cut, the nearest thing to the previous record, though the middle would lose its ironic floor. What holds the score down lies outside any track: the sessions yielded a second album, so the selection was one of several possible, and the silence before the coda is convention, not requirement.
Molière · Literature
8.6 · Tier IV
The subtractive test finds very little, and it must look hard, because the play has almost no plot to carry: every scene has to earn its place by what it shows, and nearly all do. The opening debate sets the law. The sonnet scene puts Alceste’s principle to its first test, on a stranger, and wins him an enemy. The portraits show the salon at its pleasure and Célimène at her art, so that her letters in the last act are recognised as the same art turned on her suitors. The duel with Arsinoé shows the prude and the coquette trading in one coin, and the lost lawsuit and the letters bring the world’s two verdicts down on Alceste together. The test bites in two places: Du Bois’s farce of a forgotten paper in the fourth act, which serves the timing more than the meaning, and the marquis’s display of themselves in the third, which repeats what the portraits showed.
Bruce Springsteen · Music
8.6 · Tier IV
Ten songs in about forty-one minutes, and the subtractive test finds very little to take. Nebraska must open: the killer’s flat account sets the record’s question, what is left when the bonds that hold a man have gone. Atlantic City and Johnny 99 give the question an economic cause. Highway Patrolman is the centre, weighing the bond of blood against the law and letting both stand. My Father’s House and Reason to Believe are the required end, the family and faith tested last. State Trooper repeats one figure for its whole length, and the repetition is the dread, not slack. The test bites lightly in the middle of side two, where Used Cars and Open All Night could go with some loss.
Ivan Turgenev · Literature
8.6 · Tier IV
The test is subtractive, and the plan is the argument. Maryino sets the fathers against the son and his friend; Nikolskoe tests Bazarov’s creed against love; the parents’ house tests it against filial love and the land; the return to Maryino brings the duel, which is the old world’s last answer; the death tests it against the body. Each station is required, and each is short. The fathers are paired, and the pairing bears weight: Nikolai, who yields, plays the cello and reads Pushkin; Pavel, who resists, lives by his “принсипы” (his Frenchified principles). What the test can take is small. Kukshina and Sitnikov make their point in their first scene and repeat it; the governor’s ball is thin; Pavel’s past with Princess R. arrives as a block of exposition, though the ring with the sphinx and Fenichka’s likeness to the princess repay it. Perhaps a twentieth of a short book is permitted rather than compelled.
Gunnar Asplund and Sigurd Lewerentz · Architecture
8.6 · Tier IV
Judged on purpose, site and structure. The landscape resists the subtractive test almost everywhere. Approach, long wall, open slope, path, cross, hill and forest edge are few elements, and each does one thing in the funeral’s passage: take away the cross and the slope has no measure; take away the grove and the path has no end above the chapels; take away the open ground and the forest has nothing to close round. The crematorium is compelled by its use, three chapels of three sizes and a common loggia for several funerals at once, each needing privacy. What yields is the campaign: hut, temple and crematorium share one ground, and the Resurrection Chapel’s angled portico reads as a decision made, not one required. The burial woodland is required as a whole and ordinary in its parts.
Mikhail Lermontov · Literature
8.6 · Tier IV
The subtractive test is hard to pass against this book, because each tale answers a question the others leave open. Remove “Bela” and Pechorin has no witness who loved him. Remove “Maksim Maksimych” and there is no moment where the man is seen with no story attached, offering two fingers to the old officer who ran to meet him, and no hand-off of the notebooks. Remove “Taman” and the journal opens on the Pechorin of the spas, not on the man who wrecks a smugglers’ trade for no reason. Remove “The Fatalist” and the book ends on society instead of on the question whether anything is willed. What the test finds is in “Princess Mary”: spa-society scenes, the balls and the well-side chatter, that say twice what they say once, and a Grushnitsky intrigue that repeats its turn of ridicule more than the design needs. A twentieth of the whole, perhaps; the rest is required.
Le Corbusier · Architecture
8.6 · Tier IV
Judged on plan, section and structure, under purpose and site. Take away the pilotis and the car cannot pass under the house, the ground floor cannot recede, and the main floor loses its height above the wet grass and its view. Take away the curve of the hall and the car’s path has no form. Take away the ramp and the house is three stacked floors, not one route. Take away the terrace and the living room is a room, not half of an outdoor one. Nothing is applied. What resists the test: the programme was fitted to a doctrine more than the doctrine to it; the site compels little, and four equal fronts answer no one direction of it; and the grid gives way round the ramp, a compromise rather than a necessity.
Anton Chekhov · Literature
8.6 · Tier IV
The subtractive test finds little to take. The tour of the first chapter must come first: it shows the ward before the doctor sees it as his own, so that the close returns to a room the reader has already entered. Gromov’s history must precede Ragin’s, because the madman’s fear of being locked up for nothing is the fate that will befall the sane man, and the order makes the fear prophetic. The dialogues are the hinge, the one place the doctor’s philosophy is tested by someone who suffers. The charge falls on the middle of the descent: the journey to Moscow, Petersburg and Warsaw ruins Ragin’s money and his peace, as it must, but runs longer than its work, and some of the postmaster’s talk could go with little loss.
J. M. W. Turner · Visual art
8.6 · Tier IV
Subtract and see. Take away the hare and the engine runs against nothing: the picture loses its one measure of how fast a living thing can go, and its open question, whether the hare escapes or is overrun. Take away the ploughman and the old pace of the land, a furrow walked at a horse’s speed, is gone from the right. Take away the old road bridge and the boat and the railway has nothing to be newer than. The diagonal of the track is required: it is the one line in the canvas that holds, and it is the speed. What yields is the weather. Large passages of cloud and rain could be laid otherwise without loss, and the figures on the left bank are notes rather than structure.
Paul Cézanne · Visual art
8.6 · Tier IV
The subtractive test, put to this canvas. Remove the dark band of near trees and the plain loses its measure: the band is the ground the painter stands on, and it makes the plain read as distance without one receding line. Remove the plain and the mountain floats; its weight is given by the long horizontal of patches it rises out of. Remove the sky’s patches and the mountain becomes a silhouette against a backdrop, which is what the late manner refuses. Within the canvas very little is idle. What gives: the plain’s patches could be disposed otherwise without loss, a count rather than a structure; and the subject was painted many times, so that this configuration is one answer among several, necessary to its moment and not to the problem.
Jean Renoir · Film
8.6 · Tier IV
Run the subtractive test movement by movement, and the three places resist it. The opening is required: Maréchal, the mechanic made officer, at a bar with a record, and Boëldieu with his monocle set the class line before either is captured; in Rauffenstein’s mess a German officer cuts the wounded Maréchal’s meat, and the line that crosses nations is set. Hallbach is the commons, and its tunnel is never used: that waste is the point, the war’s indifference to effort. Wintersborn is the aristocrats’ room, the farm the people’s, and Boëldieu’s death frees the two who could not be his friends. What gives is in the first camp: the revue’s preparations, Cartier’s comedy and some barrack exchanges are episodic and could be shortened without loss.
Sandro Botticelli · Visual art
8.6 · Tier IV
Judged figure by figure, by subtraction. Venus cannot go: she is the event. The winds cannot go: they are the arrival, the force that moves her from the sea toward land, and their tangled pair of bodies is the counterweight to her stillness. The attendant cannot go: the mantle she holds out is the other half of the action, the goddess about to be clothed and received, and the picture holds the instant before. The shell is the vehicle and the sign of the birth. Wind, goddess, shore: the three parts are what an arrival in progress requires. What yields is at the edges: the falling roses, which decorate more than they carry; the inlet and the grove, which locate the shore without adding to the argument; and a sea that is nearly a schema.
J. M. W. Turner · Visual art
8.6 · Tier IV
Judged on the composition, since the canvas has no words but its title and the lines beneath it. Take away the tug and the picture is a ghost ship at sunset, a mood with no agent. Take away the sun and the funeral has no day to end; take away the moon and the left half loses its counter-light, and the picture becomes a single blaze. The five principal elements bear weight against each other: high pale masts against the low black funnel, setting sun against new moon, dissolving hull against hard silhouette, and the river doubling every opposition. Necessity is high at the core and holds far toward the edges. What yields is the margin: the minor marks on the water could be shifted or lost at little cost.
Andrea Palladio · Architecture
8.6 · Tier IV
Judged on plan, section and structure under purpose and site. The three parts are compelled by three users: the nave for the people, the tribune for the state’s annual ceremony, the choir for the friars, who must be present and apart. Take away the screen and the friars are either in the people’s church or walled off from it; take away the tribune and the procession has nowhere to arrive. The steps are required, lifting the church above the water’s edge and making arrival an ascent, and the linked chapels keep the nave one hall for the procession. What resists is the exterior: a front whose temple fronts answer the section rather than build it, plain brick flanks, and two turrets that serve the skyline more than the building.
Robert Schumann · Music
8.6 · Tier IV
The subtractive test meets resistance at the frame and the hinges. Remove no. 1 and the cycle loses the open question it exists to answer; remove no. 16 and the postlude has nothing to bury. No. 13 cannot go: it is where the dream turns into knowledge. Nos. 7 and 9 are the two faces of the wedding, denial and spectacle. But the test finds give, and the strongest evidence is Schumann’s own hand: he removed four songs before publication and the cycle closed over the gap. A cycle that can lose a fifth of itself to its maker has parts chosen rather than compelled. Nos. 3, 4 and 5 say one happiness three ways; no. 14 repeats the dream of no. 13 in a lighter key.
Peter Zumthor · Architecture
8.6 · Tier IV
Judged on structure, purpose and site. The composite wall is compelled: the stone of the valley laid as structure, so that the building is made of the mountain it is cut into. The section is compelled: half sunk in the slope and grassed over, the bath kept warm in the ground and open only to the valley. The roof slabs, parted by lines of light, give the only top light. The small rooms are required by bathing as a passage through heat, cold, scent and sound: take away the hot bath or the cold bath and the round breaks. What resists: the placing of the blocks is one of many the system allows, and a block could move or go without the whole falling; some hold rooms any plan would hold; and the joining to the hotel is an inheritance of the site, not a choice of the form.
José Clemente Orozco · Visual art
8.6 · Tier IV
Judged on the configuration of the dome. The burning figure cannot go: he is the work, set at the one point every line of the chapel leads the eye to. The ring of figures beneath him cannot go either: without them there is no measure of rise and no earth for the fire to leave, and the dome becomes an emblem rather than an event. The colour is necessary in the strict sense: fire alone carries heat in a ceiling of grey and earth, and a second warm motif would split the summit. What yields to subtraction is detail within the ring, whose number and posture could vary without loss; Orozco had already made the argument with one figure, at Pomona in 1930. The scale is compelled by the vault, not permitted by it.
Claude Monet · Visual art
8.6 · Tier IV
Judged on the configuration. Take away a composition and its oval opens: the enclosure, which is the premise of the work, needs all four walls of each room. Take away Soleil couchant and the first room’s day has no end. Take away the second room and the first still stands as a room, but the cycle loses its turn from open water to the bank, from the day’s course into the shade of the willows. Removal fails at every wall, and the scale is the surround’s, which no smaller field could make. What is permitted rather than compelled is length: a field of water has no internal measure, and each composition was fitted to the wall the rooms allowed.
David Fincher · Film
8.6 · Tier IV
Judged on the theatrical cut. The length is compelled by the subject, which is attrition: a case that eats twenty-two years must be felt to eat them, and the viewer pays out time as the men pay out careers. The subtractive test finds almost no slack. The abduction of Kathleen Johns looks like a detour and is required, since the case cannot even say which crimes are its own. Bob Vaughn’s basement, a dead end, is required for the same reason: the investigation is mostly dead ends. What gives: Graysmith’s marriage is stated in a few scenes rather than built, Melanie is there to object and leave, Avery’s decline is dropped rather than closed, and the late montage compresses what duration earned.
Mamluk, under Sultan an-Nasir Hasan · Architecture
8.6 · Tier IV
The programme compels the plan. Four schools of law need four teaching spaces and four lodgings; a congregational mosque needs a qibla hall; a funerary foundation needs a tomb; one court gathers them, and the cruciform answers every need with one figure. The madrasas fill exactly the squares left between the arms, so nothing in the plan is idle. The site compels the rest: the portal turned to the street, the mausoleum pushed toward the square and the Citadel, and the vestibule and bent passage reconciling the two alignments. What yields to the subtractive test is the scale. The iwans and the portal are larger than any use requires, permitted by a sultan’s purse as much as compelled.
Krzysztof Kieślowski · Film
8.6 · Tier IV
The scheme compels ten films, and the subtractive test, put to the cycle, finds each required. Without I the cycle loses its argument against the idol of calculation; without X it ends in tragedy rather than laughter. Inside the films there is little fat: V gives its murder and its hanging equal, unbearable duration, because each requires the other. Three things give. The mapping of films to commandments is loose — III could stand under adultery as easily as under the Sabbath, and VI is about watching more than adultery — so part of the necessity is given by the number rather than the argument. III’s night search repeats its stations beyond need, and IV turns on a reversal that is a device more than a necessity.
Arcade Fire · Music
8.6 · Tier IV
Ten tracks, and nearly every one passes the subtractive test. Tunnels must open: it sets the record’s world, children making their own life under snow while the parents’ world fails, and its slow build into the full band is the record’s method in small. Wake Up is the centre of force and could not go. In the Backseat must close: after nine tracks of gathering, a single voice asks to be carried rather than to drive. Haïti, which looks like a detour into one family’s history, is required, the one place where loss is historical rather than domestic. The test bites twice, and lightly: Crown of Love restates the record’s longing more than it advances it, and 7 Kettles is the frame’s softest panel.
W. G. Sebald · Literature
8.6 · Tier IV
The book is made of digressions, and the test is whether they are required. Most are, though not by plot: the star-shaped fortresses of Antwerp, which grew more vulnerable the more they were fortified; the nocturnal animals in the Antwerp zoo with their watching eyes; the waiting room of the city’s station; Austerlitz’s lifelong study of the architecture of the capitalist age. Each is the same knowledge, that the structures of order hold their own catastrophe, approached from outside before the life itself is approached, and the life is the one subject the man has spent his career avoiding. Remove them and the repression has no form. What holds the axis lower is a share that is permitted: the moths and Uncle Alphonso at Andromeda Lodge run longer than their part in the design, the journey to Marienbad with Marie de Verneuil is drawn out, and the meditation on time at the Greenwich observatory could be shorter without loss.
Paul Thomas Anderson · Film
8.6 · Tier IV
Run the subtractive test part by part. The wordless prologue is required: it shows the man as body and labour before he has a voice, and the dead worker’s son taken there is the origin of the family the rest of the film spends. The Sunday plot, the blowout and the baptism are each load-bearing, because each turns one drive on a different bond, and the 1927 epilogue is required in kind, since the son must be disowned and the prophet killed for the argument to close. No part could go. What gives is length, and that holds the axis here: the Henry episode, a test of whether blood can reach him, runs long, the Standard Oil meetings and the pipeline negotiations carry the business argument at more length than its weight, and the epilogue’s pitch is permitted rather than compelled.
Chandela builders · Architecture
8.6 · Tier IV
Run the subtractive test from the stair. The sequence is compelled by the rite: a threshold, two halls of growing size and darkness where the congregation gathers, a narrow vestibule, the dark cell of the god, and the ambulatory for walking round it. Nothing in it can go without breaking the passage from outer to inner. The roofs are compelled by the governing idea: each rises over the space it covers, and the spire stands where the sanctum is. The balconies are required twice, as the only light and air within and as the arms of the cross. What yields is quantity: some 870 figures and tier upon tier of mouldings, whose number is permitted, not compelled.
Knut Hamsun · Literature
8.5 · Tier IV
The book is built of episodes, which invites the subtractive test, and most episodes pass it, because each is a step in one descent and one psychology: the waistcoat pawned, the shavings chewed in the street, the long lie told to an old man on a bench, the night in the police cell where the narrator, under a false name, refuses the free meal ticket out of shame, the bone begged from a butcher, gnawed and vomited. The repetition of the cycle across four parts is the argument: the mind learns nothing and falls the same way. What the test finds is in the fourth part, the long stay in a boarding house where the narration slackens into incident, and in one or two passages on Ylajali that repeat what the first already showed.
Frank Lloyd Wright · Architecture
8.5 · Tier IV
Judged on plan, structure, purpose and site. The corner piers carry the roof, hold the stairs and carry the air: take them away and the room needs columns, the galleries need stairs elsewhere and the walls need windows. The busy street compels the light from above, the blank walls shutting out its noise; it compels the side entrance, and the entrance compels the cloister beneath the galleries. A congregation gathered to hear one speaker compels the galleries; the double purpose of worship and service compels the joining hall. What yields to the subtractive test: the cast ornament of the exterior capitals and much of the wood-strip pattern within; an interior of Unity House ordered more than required; and the four like faces of the block, for which an economy of building is a builder’s reason, not the room’s.
Ludwig Mies van der Rohe · Architecture
8.5 · Tier IV
Judged on structure, purpose and site, the subtractive test finds almost nothing to remove: eight columns, two planes, a core, glass, two steps of terrace. Take away the columns and nothing holds the planes. Take away the height and the floor lies in the flood and the meadow comes up to the glass. Take away the core and the services have nowhere to go but the walls, which would end the open room. Take away the lower terrace and the ascent is a ladder. Nothing is applied. What resists: the necessity is the idea’s more than the dwelling’s. Glass on four sides is not required by a weekend in the country and served it badly, and the offset of the terrace is ordered by composition, not compelled by use.
Built for Qabus ibn Wushmgir · Architecture
8.5 · Tier IV
Run the subtractive test and the building gives back almost nothing to take: no range of windows, no portal screen, no colour, no applied order. The core is the room, the shell is the monument, the cone closes it, the two bands carry the name. The flanges are the one part that invites the question, and they answer it: they stiffen a tall thin shell and save brick against a solid drum of the same reach, and they are the building’s whole means of catching light. The purpose compels the height, a tomb meant to be a ruler’s name on an open steppe. What holds it below the Pantheon’s 9.0 is the inside: one empty cylinder, its use not shaped by the form.
Henri Labrouste · Architecture
8.5 · Tier IV
Run the subtractive test and little is idle. The two storeys answer the programme: stacks and treasures below, where light and the risk of fire matter least; readers above, where the light is. The length of the reading room and its double vault come from the need to range books along the walls and seat readers under even light, and the central iron spine is the least material that will span the room twice without filling it. Even the façade’s chief ornament is the shelf list made public: each panel names what stands behind it. What could go without loss is small: some of the vestibule’s painted and sculpted programme, its busts among it, is a grace, and the festooned detail outside is a register of style.
Joni Mitchell · Music
8.5 · Tier IV
Ten songs in about thirty-six minutes, and the subtractive test finds little in the songs to take. Inside each, the arrangement has been cut to what carries the voice: four songs are voice and piano alone, one is voice and guitar alone, and where others play they add one colour, not a band. The title song is three minutes of piano and voice with no chorus; Little Green is a ballad of verses with nothing beyond the guitar. The test bites at the lighter edge. Carey is a holiday song on a Greek island and All I Want an opening whose list of wishes runs long; either could go at less loss than any piano song, and This Flight Tonight is the slightest writing on side two. But the lighter songs are the freedom the heavier ones count the cost of.
Tawaraya Sōtatsu · Visual art
8.5 · Tier IV
Apply the subtractive test and almost nothing yields. There are two figures, two clouds and a field. Remove either god and the other has nothing to answer: the work is the confrontation across the gap. Remove the clouds and the gods stand in nothing, for the dark pooled ink is the only weight that lets the gold read as sky. Remove the gold and the void becomes a background rather than the weather itself. The cropping is required too: it pushes the figures inward, as if just arrived. What can be argued against is the fluttering drapery and the swing of the wind bag, fuller than bare need. Held below the top band because so few elements make necessity easier to hold than in a crowded room such as Las Meninas, at 9.0 on this axis.
Rembrandt van Rijn · Visual art
8.5 · Tier IV
Subtract, part by part. The face cannot go: it is the picture’s one fully built thing, and its argument. The cap cannot go: it is the one white and the brightest mass, crowning the face as the light’s second source. The robe is the dark ground the face stands out of, and its breadth is the figure’s weight. The tools cannot go, though barely painted: without them this is an old man, with them it is the painter, and their half-made state is the claim. Without the circles the wall is a void. What yields is little: the hand at the hip hardly registers, and the red under the robe could be another colour.
Ludwig Mies van der Rohe · Architecture
8.5 · Tier IV
The subtractive test finds almost nothing to remove. Take away a girder and the roof falls; take away a pair of columns and the span fails; take away the base and the hall sits on the street with its basement windows at the walk; take away the partitions and the room has no scale for the body. The service shafts are the least a building with heat and drains must admit. The scale is compelled by the argument: a school as one room, every year in sight of every other, needs a span of this order. What holds the figure: the girders above the roof are the thesis made visible, not a requirement of the span, and the one room carries costs in noise and heat the school did not compel.
Billy Wilder · Film
8.5 · Tier IV
Judged on structure and on the screenplay’s economy. Run the subtractive test and nearly every element is a gear. The anklet on the staircase is the hook; the exchange about a speed limit at the door sets the terms of the affair as a negotiation; Keyes’s lecture on the statistics of suicide puts the threat into the machine before the machine is built. The car that will not start, the crutches, the observation platform, the witness from Medford, Lola’s suspicion and Nino Zachetti each close a door. The frame gives the ending away at the start, so every part must be required by the trap, not by suspense. What gives: the Lola and Zachetti strand is plot machinery, the first wife’s murder arrives by report rather than in a scene, and Keyes’s comic bouts with Norton outlast their work.
Marilynne Robinson · Literature
8.5 · Tier IV
The subtractive test finds a short book that resists it. Each loss prepares the next custody: the grandfather’s train sliding from the bridge into the lake, the mother’s car driven into the same water, the grandmother’s quiet death, the great-aunts’ retreat to Spokane, then Sylvie. Remove the great-aunts and the comedy that shows what ordinary custody looks like is gone; remove Lucille’s defection to her teacher and Ruth’s choice has nothing to be chosen against; remove the night on the lake and the abandoned homestead and the crossing at the end has no rehearsal. The scale is compelled: a book about what is kept and what is lost keeps very little itself. Charged: the middle round of truancy and walks along the shore repeats more often than the argument needs, and some of Ruth’s meditations restate in a second figure what the first already carried.
R.E.M. · Music
8.5 · Tier IV
Twelve songs of three to four and a half minutes, and inside the songs almost nothing can go. Peter Buck’s figures are short and repeated, Mike Mills’s bass carries a second melody, and each song ends when its figure is spent; nothing is there for display. Radio Free Europe must open, the one song with a single’s drive. Perfect Circle must close the first side, its slow piano and guitar the still centre the side has been moving toward, and West of the Fields is a fit last word, an open close. Held off the top across the middle: 9-9, its voice garbled on purpose, could go with little lost, We Walk’s charm is local, and the songs share one mode closely enough that the order could shift without loss.
Artemisia Gentileschi · Visual art
8.5 · Tier IV
Judged on the configuration, by subtraction. Remove the maid and the killing becomes a solo feat, and what the picture knows, that this takes two bodies, is gone. Remove Holofernes’ arm pushing up against her chest and his resistance becomes a corpse’s: the struggle is in that fist. Remove Judith’s left hand, gripping his hair and pressing his head into the mattress, and the stroke has no anvil. Three pairs of arms converge on one point, the neck, and each bears load. The blood, thrown in jets, is the instant’s clock. What gives is at the margin: the enlarged dark field above is atmosphere, not argument, and the bracelet and the coverlet’s pattern could be other without loss. The near life size is compelled.
Louis Kahn · Architecture
8.5 · Tier IV
Judged on purpose, structure and site, the three rings pass the subtractive test because each answers one need of a library. Readers need light, so they sit at the outer wall, each carrel at its own window. Books need protection from light and a strong floor, so they stand in the concrete ring between. A library needs a place where the community of readers meets the whole collection, so the centre is a hall from which every floor of books is seen. The brick piers thin as their load thins; nothing in the outer wall is applied. What yields: the hall is larger than any purpose requires, the cross beams are deeper than their roof asks, the hidden entrance answers a principle rather than a use, and the screen above the roof is ordered, not compelled.
George Bähr · Architecture
8.5 · Tier IV
Subtract any element and the purpose answers back. The galleries stand where the congregation must see and hear the pulpit; the piers stand where the galleries need support; the pulpit stands before the altar and under the organ because the Lutheran service is Word, Sacrament and song in one act. The corner towers carry the stairs the galleries require and steady the base of the dome. The dome is the part a hostile reader calls surplus to a parish: but it is the roof the central room calls for, and its civic charge is part of the commission. Stone where timber might have served is the most assembled choice, and it cost the piers.
Talk Talk · Music
8.5 · Tier IV
Six tracks in forty-one minutes, and very little could be removed without loss. The Rainbow must open, because its first minutes of near-silence, scattered tones and a single trumpet teach the listener how to hear the rest. Eden and Desire complete side one’s arc from stillness to eruption. I Believe in You is the centre of the second side, and Wealth must close, a hymn on organ ending in quiet. The test bites lightly twice. Inheritance, the least distinct track, restates side one’s method in small, and the opening minutes of The Rainbow, though required, run longer than their teaching needs. Much of what a hostile listener would cut is the silence that makes the rest audible.
Cormac McCarthy · Literature
8.5 · Tier IV
The test is subtractive, and it finds very little to take. The book is made of its necessities: the cart, the pistol with its last cartridges, the search for food, the road. Remove the cellar of captives and the man’s fear loses its proof; remove the bunker and the book loses its one abundance, the test of whether the good may still be enjoyed; remove the thief and the son’s mercy never outgoes the father’s; remove Ely and the theology goes unspoken; remove the memories of the mother and the man goes on living against no argument. The scale is compelled: a short book for a world with almost nothing left in it. Charged: the middle repeats its round of house, search, tins and sleep more often than the argument needs, and some of the man’s dreams do the same work twice.
Dionysus Flambouras · Literature
8.5 · Tier IV
The subtractive test finds most of the book required. Seventeen of the eighteen stories carry a fact the rest depend on, and their returns are placed: a crate found under snow behind a wheel comes back as CHECK UNDER SKID on a receiving report, a line drawn through fourteen comes back through CROMTON and through INEDIBLE, and a rag pocketed on a kill floor wipes a shovel at a grave. Ten sentences of four words or more recur verbatim in forty thousand, most of them ritual, the tool roll unpacked and packed in the same words. The exception is Caribou Rouge, one hockey game the next story keeps as a nickname and a pair of gloves; it could go. Lesser slack sits in the sparring rounds of Palestra Vittoria and in the second morning of Bloom, which fills a case the next story fills again.
Frida Kahlo · Visual art
8.4 · Tier IV
Judged on the configuration, element by element. Remove either Frida and there is a self-portrait, not a division: the work is the pair. Remove the joined hands and the two are a mirror image; with them, one self keeps the other company. Remove the vessel and the hearts are emblems with no circulation. Remove the miniature and the blood has no source; remove the clamp and the bleeding is fatal or unstated, where with it she is her own surgeon; remove the blood on the white skirt and the cost is unpaid. What gives is at the edges: the bench is a support, not an argument, and another storm would serve as well. The near square and the life size are compelled by the confrontation; smaller, this would be an ex-voto.
Edvard Munch · Visual art
8.4 · Tier IV
The test is subtractive, and the canvas gives almost nothing to take. Remove the woman and the picture becomes a portrait of a sick girl, a genre subject of the 1880s, which Krohg had painted; it is her bowed, faceless head that makes the girl the one who consoles. Remove the pillow and the profile loses the pale field that makes the face a light going out. Remove the curtain and the gaze has nowhere to rest. The joined hands dissolve almost to nothing, and that is required: the one contact in the room is where the paint gives way. The near square is compelled. What yields is at the right margin, where the props of the sickroom are true but replaceable: a count, not a structure, and the reason the figure stays below The Starry Night’s 8.9.
Andrea del Verrocchio · Visual art
8.4 · Tier IV
Taken figure by figure, the subtractive test finds almost nothing to remove. The raised left foreleg, free of any support, is the stride and the threat at once; the three planted legs carry the whole weight in a triangle the eye reads as balance under strain. The rider’s stance in the stirrups cannot go: it turns a seated portrait into a man rising to strike. The twist of the torso against the horse, the head over the shoulder, the baton: each is required by one proposition, will mastering force. The pedestal is required too, since the walled square lets the group be seen only against the sky. What yields is the decoration of harness, saddle cloth and frieze, and the length of the pedestal’s columns.
Francis Ford Coppola · Film
8.4 · Tier IV
The subtractive test meets resistance almost everywhere. The square is required, since every later scene is a rehearing of it. The landlady’s key and Amy’s questions establish a man who cannot bear to be entered, and the price of it. The convention looks like a digression and is not: Moran’s bragging names the past job Harry has confessed, and the pen Harry is handed there bugs his own party, the first proof that the listener is heard. Meredith’s theft carries the tapes to the client without his consent, so his refusal becomes futile. What gives: the convention runs longer than its work, its salesmanship repeating its point; the dream is a risk only partly earned; and the long wait at the hotel wall is slower than the dread it builds.
Henri Rousseau · Visual art
8.4 · Tier IV
The subtractive test finds almost nothing to remove. Take away the lion and the canvas is a woman asleep in a desert, a picture of fatigue; take away the woman and it is a lion under the moon, a menagerie scene. The work is the pair: the threat bent over the defenceless and arrested. The mandolin and the jar make her a wanderer and a musician and not merely a body, her whole life laid beside her, and the strings answer the stripes of her robe. The moon is the light the scene requires and the cold that makes it night. The empty sand is required too: no footprints, so no event in time. What gives: the few stars and the exact drawing of the hills. The large scale is earned; at this size the figures are close to life and the silence has room.
Alvar Aalto · Architecture
8.4 · Tier IV
Judged on plan, section and structure under purpose and site. Its purpose was a regimen, sun, air, rest, quiet and cleanliness, and the building resists the subtractive test more than most modern buildings of its decade. Remove the southern orientation of the patient wing and the cure has no light. Remove the stacked open terraces and the rest cure moves into rooms. Remove the corridor on the north and the rooms lose their sun. Remove the splaying of the wings and kitchen, dining hall and patients sit in one mass, sharing noise, smell and shadow: the angles are compelled by sun and separation, not by composition. What yields: some composed play at the hub and the entrance canopy, angles freer than strict need requires, and later hospital additions assembled rather than compelled.
Joel Coen and Ethan Coen · Film
8.4 · Tier IV
Judged on structure and on the screenplay’s economy, and in 98 minutes almost nothing is idle. Jerry’s scheme generates every strand: the money he owes GMAC on vehicles that do not exist, the father-in-law who will not lend, the kidnappers hired through Shep Proudfoot, and the car given in part payment that puts dealer plates on a car seen at the highway killings. The plates are the thread Marge pulls. The fight over the ransom sends the money into the snow by a fence, and Carl’s death leaves it there; the woodchipper is the end the road compels. Held below the top by the Mike Yanagita scene, which pays but runs longer than its payment, and by the hotel-room interludes with the escorts, which pad the kidnappers’ road.
Diego Velázquez · Visual art
8.4 · Tier IV
Judged figure by figure, the canvas resists subtraction. Venus cannot go, nor can her turning away: the premise is a body offered and a face withheld. Cupid cannot go: he is the hand that holds the mirror, and without him the reflection would be her own act, a vanity, not something shown to us. The mirror cannot go: it is the one place her face exists. The grey satin is the cool dark that makes the flesh warm, and the white sheet is the step between them. The scale is compelled, life size, so that the body is a body in the room. What gives is at the margin: the crimson curtain and the ribbons, permitted rather than compelled.
Vincent van Gogh · Visual art
8.4 · Tier IV
The subtractive test finds almost nothing to take. The picture has four elements and each bears weight. Remove the sky’s weight and the field is merely sunny. Remove the crows and the dread has no agent and the sky no depth: their diminishing size is the only measure of distance up there. The central path is the argument. It comes to the viewer and stops in the wheat, leading nowhere, and the two side paths, running out of the frame, make the middle one a choice rather than a road. The green verges are needed to set the red track burning. What yields is the count and placing of the crows, where a bird more or less changes little, and the two paler patches of cloud, which loosen the sky without clearly earning their place. The necessity is that of a few strong elements, not of many parts bound together.
Alfred Hitchcock · Film
8.4 · Tier IV
Judged on structure. The subtractive test meets resistance through most of the film. The opening pan does the exposition with objects alone: the thermometer, the sleeping man, the cast, a smashed camera, the photograph of the racing crash that broke the leg, a negative and its printed cover. Each window across the yard is a version of the question Jeff will not answer about Lisa: the newlyweds, Miss Torso, Miss Lonelyhearts, the songwriter, the couple with the dog, the Thorwalds. Remove one and the argument about marriage loses a term. The flower bed, the jewellery, the knife and saw, the trunk and the ring are each planted and paid. The give is real and is weighed in full: the two arguments between Jeff and Lisa state one case twice, and Doyle’s second visit is procedure the film does not need.
Denis Villeneuve · Film
8.4 · Tier IV
Judged on the theatrical cut, the core resists the subtractive test. The prologue is required twice: first as grief, then at the close as foreknowledge, and nothing in it is idle once the second reading arrives. The sessions in the shell are required, because the audience must learn the logograms as Louise does, ring by ring, before it can be asked to read time as she comes to. The name Hannah, the kangaroo anecdote on the limits of translation and the word read as “weapon” each pay out later. What gives is the thriller machinery around the core, the soldiers’ bomb and the news montages, which supply pressure a leaner film could supply otherwise; and Ian is thinner than his share of the running time.
Television · Music
8.4 · Tier IV
Eight songs in about forty-six minutes, and the subtractive test finds little slack. Inside the songs almost nothing is idle: each guitar line is required by the other, and the riffs of See No Evil and Friction are built as interlocking parts that collapse if one is taken away. The title track’s length is compelled rather than permitted: its long instrumental passage climbs by stages to a climax and a return to the verse, and no stage could go without the climax losing its ground. See No Evil must open, the method stated at speed, and Torn Curtain is the compelled end, the record’s dread given room. The test bites lightly twice, and that holds the figure off the top: Guiding Light, a ballad, softens the second side without turning it, and Prove It restates the record’s manner more than it extends it.
Jonathan Glazer · Film
8.4 · Tier IV
The method is repetition, so the subtractive test is run against it: one more afternoon in the garden is not padding if it adds a sound, an object or a decision, and most do. The fur coat brings the plunder into the house; the engineers bring industry; the river brings the camp into the children’s bodies; the mother’s visit tests the household against an ordinary eye, which cannot stay. The cut to the museum is required, the one place the film shows what the wall hid. What gives: a second tour of the garden does one job twice, and the red screen states a horror the sound had already carried.
Interpol · Music
8.4 · Tier IV
Eleven tracks, and the subtractive test finds the frame required. Untitled must open: a wash of guitar fading in, a threshold rather than a song, which sets the record’s distance before a word is clear. NYC is the record’s centre and the source of its title. PDA is required as the place where the restraint breaks into its long instrumental coda; Stella as the record’s deepest descent; Leif Erikson as the quiet close. Each carries a part of the argument no other track carries, and the long songs in particular could lose nothing of their length without losing their release. The test bites in the second half: Hands Away is a slight interlude, Roland sits outside the record’s manner, Say Hello to the Angels is energy the record would survive losing, and Obstacle 2 answers Obstacle 1 more weakly than the pairing promises.
Pieter Bruegel the Elder · Visual art
8.4 · Tier IV
Judged figure by figure, since the panel has no words. The bride cannot go: she is the reason for the feast and its one still point, the only figure framed. The door-tray cannot go: it is the event of the picture, food arriving, and its carriers turn the diagonal of the table back across the foreground. The beer-pourer and the child at the lower left close the near corner and carry the appetite down to the floor. The piper who looks at the food rather than playing is the joke and the truth in one head. The gentleman and the friar at the right are the outside looking in. What yields: parts of the crowd along the far side and at the door are fungible, and the grain wall is required in kind, not in extent.
Dorothea Lange · Visual art
8.4 · Tier IV
Judged on the frame and on the series, which lets the subtractive test be run on the maker’s own evidence. The wider exposures of the same visit hold more: the tent, an elder daughter, a rocking chair, the open ground. Each time Lange came closer she took something out, and this frame is what was left. Take away the raised hand and the face is a portrait of fatigue; with it, the face is thinking, about the next day. Take away the turned children and the mother is one sitter among four; turned, they leave her the only face, and their weight is on her. Take away the infant and the hand loses its reason not to drop. What yields a little is the tonal detail of the tent fabric and the sleeve, which could be other without loss.
Ptolemaic builders · Architecture
8.4 · Tier IV
Run the subtractive test. The building is a machine for one act, the daily and festal approach of the king, in practice his priests, to the god, and almost nothing fails it. From the pylon inward each space is smaller, darker and higher in floor than the last: the open court, the screened half light of the outer hypostyle, the dimmer inner hall, the offering hall, the vestibule, the sanctuary in near darkness. Remove a stage and the gradient the cult required breaks. The corridor inside the enclosure wall is the boundary of purity; the stairways serve the New Year rite on the roof; the side chapels house the gods who shared the house. What yields is extent, not order: the chapels round the sanctuary multiply by enumeration, and the court’s colonnade is ample beyond what any one rite needs.
Edward Hopper · Visual art
8.3 · Tier IV
Judged on the configuration. Remove the street and the dark buildings opposite and the light has nothing to stand against: the diner becomes an interior, and the subject, a lit room seen from the dark, goes. Remove the lone man and the counter holds a couple and a worker, a scene of company; he is the measure of solitude, and his back is the one figure turned from us. Remove the counterman and nobody works or looks. Remove the couple’s nearly touching hands and their relation is undecided in another way. The missing door is required: the viewer is shut out by it. The glass running out of frame at the right and the street at the left make the scene a fragment of a city, not a stage. What gives is the inventory: the urns are a fine passage, not an argument, and the blinds and the sign could be otherwise.
Tadao Ando · Architecture
8.3 · Tier IV
Judged on structure, purpose and site. The subtractive test finds very little to take away: three bays, one court, one bridge, one stair, four rooms, and a street wall with only a door. The court looks like the gratuitous element, the one a sensible client would remove, and it is the reason for everything else. On a plot walled in along both its long sides it is the house’s only source of light and air, so the blind front and the windowless party walls are compelled by it, and it in turn is compelled by the site. The proportion of thirds is drawn out of the plot, not imposed on it. What resists: the house states a few ideas in a few parts, and the necessity of a small thing is easier to win than that of a large one.
Thutmose (attributed) · Visual art
8.3 · Tier IV
Subtract, part by part. The crown cannot go: its tall flat mass, tilted back, is the counterweight the long forward neck needs, and the silhouette is that balance. The neck cannot go: it carries the head out into space and gives the bust its poise. The collar is the base that stops the form and turns a head into an image. The paint cannot go: the crown’s blue, the gold band and the skin’s warm tone are half the object. The one eye is the hard case, a gap in an image built on symmetry, a state of the making the work does not need. What yields is little: the flat cut at the back, a model’s convenience.
Joseph Strauss, Charles Ellis, Leon Moisseiff and Irving Morrow · Architecture
8.3 · Tier IV
Judged on purpose, structure and site. A suspension bridge is the art in which the subtractive test bites hardest, and this one passes it almost everywhere. The strait was too deep and its current too strong for many piers, so the span had to be long; a long span over a shipping channel had to hang; the hanging span compelled two towers, two cables and two anchorages, and the height of the towers follows from the sag of the cable and the clearance shipping required. The arch over Fort Point is compelled by the decision to keep the fort, and that decision is right. Little can be removed without loss. Held below the top because the necessity is the type’s more than this work’s: much of it would be required of any bridge on this site.
Damien Hirst · Visual art
8.2 · Tier IV
Judged on the configuration. Very little can be removed. Take away the liquid and it is a carcass; take away the glass and it is a specimen on a slab, with no barrier between the living and the dead and no display; take away the title and the work loses its proposition and becomes a natural-history exhibit. The scale is compelled: the shark has to be large enough to threaten the viewer’s body, and the tank long enough to let it seem to swim. What gives is substitution, not removal. The three bays are a design choice the work could do without, and the animal itself has been substituted once, by the artist, who held that the work continued. A work that survives the replacement of its central element has shown that the element was required as a kind, not as itself. Necessity is high, and of a narrow kind.
Hellenistic (Roman marble copy) · Visual art
8.2 · Tier IV
The subtractive test on one figure and its few attributes. Nothing in the composition is idle. The bowed head carries the dying. The right arm, locked straight, is the last thing holding him up, so that the whole figure becomes a span of time measured by one arm’s strength. The wound is small and exact and the blood a few drops: enough to make the event certain, no more. Without the torque, the clumped hair and the moustache the work loses its argument, that this is the foe. The broken trumpet is an army’s voice gone silent; the sword is laid down, not dropped; the shield is his last ground. What yields is the scatter on the base, the belt and the length of the sword, permitted rather than compelled. Held below the top because a single figure resists subtraction easily.
Jean-Pierre Melville · Film
8.2 · Tier IV
The subtractive test finds little to take. The opening, which a hostile editor would cut first, is the premise: a man whose life is a room, a bird and a cigarette. Each procedure is required by what follows. The keys tried one by one on the stolen car show that Jef has method and nothing else; the garage, the gloves and the alibis are what the line-up takes apart; the wound on the bridge brings the dressing at the basin, the same method turned on his own body; the bird is the only witness to the bugged room. The ending pays the whole. What gives: the police procedure in the middle runs longer than its information, and the pressure on Jane repeats a point already made.
David Fincher · Film
8.2 · Tier IV
Judged on structure, and the subtractive test meets resistance almost everywhere. The prologue is required: Erica’s verdict on Mark is the wound the rest of the film answers, and the refresh at the end closes it. The two depositions are required, one for each betrayal, the twins’ charge of theft and Eduardo’s of friendship; neither could carry the other. Facemash is required, since the site that ranks women is the seed of the one that ranks everyone. The Summers scene shows the old order refusing to defend its own; the restaurant where Erica rebuffs Mark sends the network to other schools. What gives: Christy Lee’s jealousy and the burnt scarf are stock, and Henley, though it earns its place, is a set piece a sterner film would have halved.
Christopher Nolan · Film
8.2 · Tier IV
Judged on structure, and the film is lean: the subtractive test fails across its spine, because each strand carries what no other can. The Mole gives the trapped army and its repeated failed escapes, the hospital ship, the minesweeper, the beached trawler. The Sea gives the civilians and the cost of going. The Air gives the cover that makes the evacuation possible and the one man who chooses to stay. The shivering soldier is required twice: he is the army’s trauma on the little boat, and his blow kills George, the price of the rescue. What gives lies at the edges: the trawler repeats the minesweeper’s lesson at length, Collins’s ditching spends time, and two officers on the mole explain.
Mark Rothko · Visual art
8.2 · Tier IV
Judged part by part: a ground, two rectangles and the edges between them. Take away the upper dark block and the weight pressing down the field goes, and with it the tension against the warm ground. Take away the lower block and the dark floats unanswered, with no second interval to measure it. Take away the ground between and around them and the rectangles become a flag or a wall; its breathing at every edge makes them hover. The scale is compelled: smaller, the painting is a design. What yields is proportion: the heights of the blocks and the margins could shift by a hand’s breadth, as the many canvases in the format show they did. Necessity of kind is total; of exact measure, not.
Greek colonists of Poseidonia · Architecture
8.2 · Tier IV
Judged on structure, purpose and site. The Doric order is a grammar that resists subtraction: column, capital, architrave, a frieze of triglyphs over every column and every intercolumniation, cornice and gable, each member answering the one beneath it and the timber house above it. Here the order is carried through with almost no surplus, and with no programme of sculpture. The interior is compelled as well: a cella this wide could not be spanned in stone, so two rows divide it, and two storeys let slender upper columns reach the roof without crowding the room. The house faces east to its altar. What yields: the weight of the order exceeds what the load needs. It is meaning, not necessity, and the type was given rather than found.
Georges de La Tour · Visual art
8.2 · Tier IV
Judged object by object, the canvas resists subtraction almost everywhere. The woman cannot go, nor the skull: the picture is the pairing of her head and the skull at two heights, the living face lit and the dead one in her lap, and the hand on the skull joins them. The hand under the chin is the act, thought held still. The flame is the light, the clock and the soul in one, and its smoke is the one movement in the room. Through the glass the oil is seen being used up. The darkness is the room and the penitent’s night. What yields is the devotional furniture of the table, the iconography’s inventory, some of which could go without loss. The other versions are a further charge: the canvas is necessary as a form more than as the only form.
Tang builders · Architecture
8.2 · Tier IV
Run the subtractive test on the frame and almost nothing in it is idle. Every member is structural, and every structural member is shown. The brackets are not ornament applied to the eaves but the means of carrying a heavy tiled roof far out beyond the wall, and their size answers the load. The inner ring of columns exists because the sanctuary exists: it frames the platform and carries the ceiling over it, so that the plan is the purpose drawn in posts. The terrace answers the slope. What yields: the outer aisle is wider than the purpose strictly needs, the later doors and windows are not compelled, and a front of seven bays is chosen for rank as much as for use.
Egyptian (New Kingdom) · Visual art
8.2 · Tier IV
The subtractive test, part by part. Take away the gold and the claim goes: gold was the flesh of the gods, and the face is gold because the king has become one. Take away the lapis of the brows and eyes and the face loses its second divine material. Take away the vulture and the cobra and the king no longer holds the two lands, nor their guard at his brow. Take away the beard and he is no longer Osiris. Take away the collar and the text on the back and the head loses its armour. Almost nothing is idle, and the scale is that of a head laid on a head. What yields is the source: the parts are required because the funerary programme required them. The work earns its parts; it did not find them.
Egyptian (Old Kingdom) · Visual art
8.1 · Tier IV
The subtractive test, part by part. Take away the papyrus and the man is merely seated; take away the poised right hand and he is reading, not about to write; take away the lifted head and the eyes and he is at work rather than waiting on a word. Each part carries the one instant the statue holds, attention before dictation. The soft chest and the slight paunch are not ornament either: they are the sedentary body of the office, and they make the man particular. Nothing could go without loss, and nothing is added. What holds the axis below 9 is that the type was given: the scribe’s pose was a formula of the workshop, so the necessity lies in the realisation more than in the conception.
Vladimir Shukhov · Architecture
8.1 · Tier IV
The subtractive test, applied to the lattice, finds almost nothing idle. Each straight member carries load; the rings hold the members at their spacing and resist buckling; the narrowing of each section answers the load diminishing upward and the wind, which passes through an open lattice rather than against a skin. Remove a ring and the section loses its stiffness; remove one family of members and the surface is no longer doubly curved. There is no cladding, ornament or room. The scale was compelled twice: by purpose, since an antenna must be high, and by scarcity, which cut it. What resists the test: a guyed or trussed mast would also stand, so the hyperboloid is the best answer, not the only one.
Francisco de Zurbarán · Visual art
8.1 · Tier IV
The subtractive test is almost unanswerable, because there is almost nothing to subtract. The lamb is the work. Without the cord the animal is resting, not offered, and the picture becomes a pastoral study. The ledge lifts the animal off the ground into the place of an altar or a butcher’s slab, and the ambiguity between the two is the argument. The black ground removes every place and every hour. The light from the left models each lock of fleece and leaves the far side in shadow, which is what makes the animal a body. What yields is small: the exact extent of the ledge at the right, and some of the dark field above, required in kind but not in measure.
Tulunid, under Ahmad ibn Tulun · Architecture
8.1 · Tier IV
The purpose is the Friday congregation of a whole city, and the plan is compelled by it. The open court takes the overflow and the ablution; the shade runs five aisles deep on the qibla side, where the rows stand, and two deep elsewhere; every bay is a place of prayer turned to one wall. The brick piers are compelled by material and by the refusal of reused columns, thick enough to carry arch and roof without ties. The ziyadas pass the subtractive test: they hold street and market off the sanctuary. What yields: a size beyond any congregation the city could steadily fill, a spiral that is rhetoric more than call, and a frieze and cresting surplus to use, though not to meaning.
Johannes Vermeer · Visual art
8.1 · Tier IV
Take something away and ask. Remove the turban’s falling end and the head loses its counterweight: the drop behind her answers the tilt of the face and the turn of the shoulder. Remove the earring and the line from eye to shoulder loses its fixed point, for the drop is a second eye, the brightest light below the face, hanging in the shadow of the neck. Remove the collar’s white and the jacket is a mass with no edge to turn against; remove the dark and the head has nowhere to come from. What yields: the broadly treated jacket, and the yellow at the turban’s top, an accent more than a requirement. Held below Broadway Boogie Woogie’s 8.7 because the test is easier with four elements than with forty.
Mimar Hayruddin · Architecture
8.0 · Tier IV
Judged on purpose, structure and site, the subtractive test finds almost nothing to take. The purpose is one crossing at one place, where the Neretva runs in a gorge between rock banks, and the rock gives the abutments. A pier in that channel would stand in the river’s full force, so the site compels a single span; the single span compels the arch’s height; the height compels the roadway’s climb; and the gradient requires the stepped paving. The parapets are as low as safety allows. Nothing is ornament: no carved spandrel, no statuary. What yields, slightly, is the height, which exceeds what a crossing strictly needs; but that is the margin of a stone arch of its date, and it is scored as necessity.
John Singer Sargent · Visual art
8.0 · Tier IV
The test is subtractive, and the canvas has almost nothing to subtract: one figure, one table, one ground. The table is required, since it gives the right arm its backward twist, and that twist turns a standing woman into a figure under tension, held between display and withdrawal. The fan is required as the one relaxed thing, the counterweight at the left hand. The crescent is the only sign in the picture and names what she is being made into. The ground is space for the silhouette, and the silhouette is the picture. What yields is the lower half: the long fall of black skirt is permitted by the format more than compelled by what the picture says. Here the sparseness is the argument.
Roman · Architecture
7.9 · Tier III
The subtractive test finds almost nothing to remove. The arcade exists because a channel must keep its fall while the ground drops away, and every height in the elevation is the distance between that level line and the ground. Where the ground is shallow one tier suffices; where it deepens at the Azoguejo a second is set under the first, since a single arch of that height would not stand in dry stone. The piers taper because the load diminishes upward; the projecting courses mark the stages of the build and stiffen the pier. The bend follows the ground. What yields is small: the attic panel and its lost inscription, which carry no water, and the niches later set in it. So little meaning is asked of the parts that the figure stays below the highest.
Muqi · Visual art
7.8 · Tier III
Judged fruit by fruit, since the subtractive test is almost literal here. Take away the darkest fruit and the sheet loses its weight and its anchor; the eye has nothing to rest on. Take away the fruit in outline and it loses its other pole, the thing nearly unpainted, and becomes a gradation of greys with no vanishing end. Take away an intermediate fruit and the interval changes, for the rhythm is in the spacing as much as in the tone. The empty paper cannot go: it is the space the fruits stand in and the light they stand against. What is permitted is the number: six is not demonstrably necessary, and so small a field makes necessity easier to reach.
Samuel Barber · Music
7.8 · Tier III
The subtractive test finds very little to take. There is one line and one arch, and every stage of the climb is a step the climax needs: a statement, a restatement in another voice, a rise in register, a tightening of the harmony, the summit, the silence. Remove the silence and the climax becomes an ending; remove the shortened return and the work stops at its scream; remove the open close and it consoles, which it must not. The test bites in the climb, which proceeds by sequence, the same stepwise shape restated higher: one wave of it could go with a loss of weight but not of argument. Eight minutes are easy to keep necessary, and the brevity is not credited.
Leo Tolstoy · Literature
9.4 · Tier V
Judged on the work, and on the Russian in part. Length is not a cost, and the spine is compelled. Every thread the first book leaves open is paid: the icon returns on Andrew’s chest at Austerlitz, the son is born as the wife dies, the Anatole match comes back as Natasha’s ruin. The scenes and the essays need each other: the essay on causes cites Rostov, who “charged the French because he could not restrain his wish for a gallop across a level field” (X.I). What holds the axis lowest of the twelve is the argument told again: the case against the historians, restated through Book XV and in both Epilogues, with the Masonic ritual and the Berg evenings, five or six per cent of the whole.
Herman Melville · Literature
9.4 · Tier V
A quarter of the body advances no event, yet most of it is put to work. The ordinary hunt is licensed inside the plot: Ahab “must still in a good degree continue true to the natural, nominal purpose of the Pequod’s voyage” (ch. 46). The lecture on the line (ch. 60) kills Ahab, the whale’s divided vision (ch. 74) decides the second day’s tactics, and the drugged whales of ch. 87 come back. What holds the axis at 8.5 is a removable fringe of about 9,000 words (chs. 25, 56, 62, 63, 83, 101 and the Sleet burlesque of ch. 35), Bulkington raised and buried, the leg back-filled out of place, and a book that twice admits it repeats itself.
Anonymous (the Yahwist and the other sources) · Literature
9.3 · Tier V
The book is short for what it holds, and its narratives are pared to the bone: the binding of Isaac is nineteen verses (22:1 to 19), Cain and Abel eight (4:1 to 8). The repetitions mostly work. The three stories of a wife passed off as a sister (12, 20, 26) put the promise in danger at each generation, and Judah and Tamar (38), which seems to interrupt Joseph’s story, is required by it: Judah’s “She hath been more righteous than I” (38:26) is the change that lets him offer himself for Benjamin in 44. What holds the axis lowest of the twelve is the archive: the chiefs and kings of Esau’s line through chapter 36, and a flood told in two strands, a pair of every kind (6:19) and seven pairs of the clean (7:2).
Leo Tolstoy · Literature
9.3 · Tier V
Length is not a cost; the question is whether the parts are required, and the spine passes the test. Remove Levin and Anna’s story loses its measure: the two marriages are read against each other, and the phrases of her last ride, “the meaning of life” and “the struggle for existence” (VII.30), are the phrases he argues his way out of in VIII.12. Remove the Oblonskys and the strands do not touch. What holds the axis lowest of the twelve is about a twentieth of the whole that says at length what could be said briefly: Sviazhsky’s farming argument (III.26–28), the provincial elections (VI.27–31) and the war argument at the bee-house (VIII.15–16), which is the author’s polemic more than Levin’s.
George Orwell · Literature
9.0 · Tier V
The test is subtractive, and the spine passes it. Everything in the book bends to Room 101: the diary is the first crime, the coral paperweight and the room above Charrington’s shop are the bait, O’Brien’s flat is the trap, and each is required by the end it serves. The rhymes are planted to be called in: “Oranges and lemons” gives Charrington’s shop its last line, and “the place where there is no darkness”, dreamt in Part One, is the lit cell of the Ministry of Love. Even the Goldstein extracts are required, since O’Brien will say he helped to write the book: the tract becomes evidence that the Party knows the truth about itself and holds it in doublethink. What holds the axis below 9.0 is exposition in excess of need. The extracts run long and restate what Part One has shown, and Part One’s tour of the Ministry, the canteen and the slogans explains more than the drama asks. Perhaps a tenth could go; the cost lies in the length of these passages, not in their presence.
Bob Dylan · Music
8.9 · Tier IV
Nine tracks in about fifty-one minutes, and the subtractive test finds four that cannot go. “Like a Rolling Stone” opens the argument, a woman cast out of a guarded world; “Desolation Row” closes it, a whole street of the cast out; “Ballad of a Thin Man” gives it from the other side, from the man who cannot see; the title track gives it a place. The eleven minutes of the closer are compelled by its procession, and length is not charged. The give is small and specific. “From a Buick 6” is a serviceable blues the rest does not need, and “Tombstone Blues” and “Desolation Row” each carry a verse that could go, so the slack sits inside songs as well as between them.
Jorge Luis Borges · Literature
8.9 · Tier IV
Inside the stories the subtractive test finds almost nothing. Borges builds them backwards from their turns: in “Emma Zunz”, “La otra muerte” and “Deutsches Requiem” every circumstance is a premise of the end, and “La casa de Asterión” is two pages in which no sentence could go without the last line losing its force. The book as a whole is less compelled. Its order is felt but loose: “El inmortal” must open, since its claim that one man is all men is the key to every later identity of opposites, and “El Aleph” must close. Between them, “Abenjacán el Bojarí” and “El hombre en el umbral” are lesser variations on devices the book has already used, and “Los dos reyes y los dos laberintos” is an emblem the labyrinth stories make redundant. Remove any of the three and the book knows nearly the same. That holds the axis at the foot of the eleven.
Bertolt Brecht · Literature
8.9 · Tier IV
The chronicle form invites the subtractive test, since the scenes are episodes rather than links in a causal chain, and most of them pass it. Each child is taken by a scene of its own, Eilif in the second and eighth, Swiss Cheese in the third, Kattrin in the sixth and eleventh, and each death is foretold in the first, when Courage lets the slips with the black cross fall to every one of her own children. The fourth scene, where she teaches a young soldier to swallow his anger and then withdraws her own complaint, is the play’s theory acted out. What could go: the tenth scene, a song heard from a farmhouse, a mood more than a step; the Chaplain’s longer turns, which say twice what the action shows; and the Cook’s offer, which runs long before it arrives. These hold it lowest of the eleven gated and floored axes.
Alexander Pushkin · Literature
8.9 · Tier IV
No great narrative poem invites the subtractive test more openly, because it shows its removables. The stanzas on the little feet of the first chapter, the album verses, the bad roads, the literary quarrels of the day and the invocations of the muse are the book’s charm, and some of them are plainly permitted rather than compelled; Pushkin himself omitted stanzas and printed their numbers, and the sequence survived the loss. The story would not notice them gone. The book would: the digressions are its second action, the narrator’s life running beside the hero’s and ageing across the years of writing, and without that warm voice Onegin’s coldness has nothing to be measured against and the close has no one to speak it; cut them and Onegin becomes a Byronic tale. The spine is lean and every turn of it is required: the refusal in the garden, the duel, the reversal at the ball. What holds the axis here, the lowest of the twelve but one, is the matter that is merely delightful: topical chatter in the first, third and fourth chapters, of its day and removable without loss, and a design trimmed and rearranged rather than compelled from the start, as the numbered gaps and the Journey moved to an appendix show.
Raphael · Visual art
8.9 · Tier IV
Judged figure by figure. Christ cannot go: he is the light of the whole upper zone. Moses and Elijah, drawn into his orbit, make the event the Transfiguration and not an ascension. The three apostles thrown on the rock are the human response at the top, blinded where those below are only blind. The boy cannot go: his rolled eyes and rigid arms make the second centre, the possessed body against the glorified one. The father and the apostle pointing upward are the hinges between the zones; the kneeling woman is a still axis between two agitated groups. What yields: the two deacon saints at the summit’s left edge, who could go without loss, and the back ranks of both lower crowds.
T. S. Eliot · Literature
8.9 · Tier IV
The plan of five movements in four poems makes the subtractive test unusually sharp, since every movement answers to its counterparts in three other poems. Remove the rose garden of Burnt Norton I and the close of Little Gidding, which returns to it, has no source; remove the turn of East Coker II, “That was a way of putting it”, and the poem loses its argument that every form is provisional. Most of the work resists. What holds the axis is real and locatable: The Dry Salvages repeats in its long lyric and its meditations what Burnt Norton said more tightly, its fifth movement opens on a catalogue, and “O dark dark dark” in East Coker III runs on past its effect. A tenth of the whole could go with loss of pattern but little loss of matter.
Charles Dickens · Literature
8.9 · Tier IV
The subtractive test goes harder against this book than against any other long Dickens. Every major strand is called in by one secret: the convict on the marshes (chapter 1) is the benefactor; Jaggers, who brings the expectations (chapter 18), is Miss Havisham’s lawyer and keeps Estella’s mother as his housekeeper; Compeyson, the second convict, is the man who jilted Miss Havisham. Orlick, who strikes Mrs Joe down with the convict’s leg-iron (chapter 16), returns at the limekiln (chapter 53). Wemmick’s two lives are the book’s argument about the self that money divides. What could go: Wopsle’s Hamlet (chapter 31) and his stage career, the Pocket household at Hammersmith and some of Pumblechook’s business, perhaps a twentieth of the whole.
Insular · Visual art
8.9 · Tier IV
Judged on the book’s structure and the relation of its decoration to its text. The great pages stand where the text requires them: at the openings of the four Gospels, at the Chi-Rho where Christ enters history, and at the Passion, where decorated text pages mark the hymn and the crucifixion. Remove any one and the book loses a hinge of its argument; the canon tables are required by its work as a harmonised Gospel. What resists the test is the profusion. The animals in the line ends and the men pulling each other’s beards are ordered and alive, but most could be thinned without loss. That every letter of the holy text deserves honour is their case, and it carries the axis this far; the uncorrected errors in the text hold it here.
Arnold Schoenberg · Music
8.8 · Tier IV
The subtractive test is put twenty-one times, and it finds more give than in a through-composed work. Schoenberg chose these poems from fifty, and a selection could have been otherwise: Colombine and Valse de Chopin restate the moonlit languor that Mondestrunken has already set, and Serenade, Pierrot bowing his viola on Cassander’s bald head, adds less than Gemeinheit had. But the frame resists. Each part of seven ends on a number that changes state: the sick moon over a flute alone, the verses as crosses, the old scent of fairy-tale time. Within numbers the compression is extreme: Galgenlied is gone in seconds, and nothing in it could be shorter. The rondel’s returns are form, not padding.
Jean-Luc Godard · Film
8.8 · Tier IV
The spine is one line: a man kills a policeman, waits in Paris for money and a woman, is betrayed by her and dies. Take out the killing on the road and nothing follows; take out the hotel room and the betrayal has no weight; take out the Bogart still and the last gesture means nothing. The travel agency is the hinge of the waiting: the money is in a crossed cheque only Berruti can cash, which is why Michel stays in Paris. Orly gives the film its motto and holds on Patricia’s face before the betrayal. What can go is scattered: the lavatory robbery, the car-dealer business, some exchanges in the hotel room. Looseness is the manner; the test asks only what is required.
Ambrogio Lorenzetti · Visual art
8.8 · Tier IV
Taken wall against wall, the programme is compelled. Each effect requires its cause, and the cause would be an emblem without the effect: the north wall alone is a treatise, the east wall alone a view of a prosperous town, and together they argue that this city is what this government produces; the west wall runs the same argument backwards. Within the allegory the parts are tight, the cord from Justice’s scales through Concord to the citizens and up to the Commune drawn as one line. What yields is density. Several of the virtues about the Commune and the vices about Tyranny could go without loss, Magnanimity beside Temperance and the doubled armed figures below among them, and the verse cartouches restate what the image already shows.
The Clash · Music
8.8 · Tier IV
Nineteen songs in about sixty-five minutes, none long, and most are required. London Calling must open, the alarm the rest of the record answers. Clampdown and Death or Glory carry the argument of conscription and compromise; The Guns of Brixton gives the threat of the title a street and a voice; Spanish Bombs gives it a history. The double album is additive by design, and its plenty is part of its claim: a band that would play the whole city’s music has to play a great deal of it. The subtractive test still bites. Koka Kola is a sketch, I’m Not Down and Four Horsemen restate defiance in a lighter key, Lover’s Rock is a joke at length, and Train in Vain stands outside the order.
Kenji Mizoguchi · Film
8.8 · Tier IV
The main strand resists subtraction. The kiln fired during the raid shows the potter’s greed and his art at once; the crossing of the lake, with the dying boatman’s warning, is why Miyagi is sent back to her death; the market is where Wakasa finds him; the mansion is the dream the war’s money buys; Miyagi’s death on the road is the price, shown before the homecoming so that the viewer knows what Genjūrō does not. The two strands answer each other: one man wants wealth, the other rank, and each wife pays with her body. What gives is the execution of Tōbei’s strand: the stolen general’s head, the troop of retainers and the meeting in the brothel come by coincidence and at speed, and his reform is a few minutes long. The parts are required; one of them is made thinly.
The Beach Boys · Music
8.8 · Tier IV
Thirteen tracks in about thirty-six minutes, and no song outstays its idea by length. The frame is compelled: Wouldn’t It Be Nice must open, the wish for adulthood the record will spend, and Caroline, No must close, the mourning of the innocence that wish was spending. God Only Knows, Here Today and I Just Wasn’t Made for These Times are required by the passage from devotion to doubt, and Let’s Go Away for Awhile gives once, without words, the escape the songs ask for. The test bites only at the margins. Sloop John B was recorded before the album was conceived, though its wish to go home is not foreign here; the title instrumental restates the sixth track more slightly; That’s Not Me is soft.
The Velvet Underground · Music
8.8 · Tier IV
Eleven tracks in about forty-nine minutes, and the long songs earn their length from inside. “Heroin” needs its seven minutes, because its tempo is its argument. The length of “European Son” is the most open to question, and it is required: the second side runs from the rush of “Heroin” through two short songs and the viola’s shriek into dissolution, and a short ending would make the dissolution a gesture. “Sunday Morning”, added last, lays the soft surface over the dread the record keeps. The test bites twice, on about seven minutes: “There She Goes Again” rests on a borrowed riff, and “Run Run Run” is a sketch.
Steven Spielberg · Film
8.8 · Tier IV
The subtractive test passes most of the film’s length, and length is not charged. The long first hour, Schindler at his business, is required: the claim is that a profiteer became a rescuer, so the profiteer must be seen enjoying himself, and the papers that save lives are the factory’s own paperwork. Nothing in the liquidation can go. Goeth’s scenes with Helen Hirsch show power as intimacy, and are needed. What gives falls at the end. Schindler’s breakdown states in words what the red coat, the list and the diamonds have already shown, and could go with gain. The shower scene’s feint toward the gas is permitted by the plot, not compelled by the argument.
Sultan Muhammad · Visual art
8.8 · Tier IV
The subtractive test bites on a painting of profusion. The core cannot go: Gayumars enthroned at the apex, his son and grandson beside him, the arc of courtiers turned toward him, the mountain that lifts him and the beasts lying quiet among them. That is the argument, a world ordered around its first sovereign, and the crowding is argued too, since the first age is an age of plenty and the profusion is what the reign holds. But a viewer who lost a third of the faces in the rocks, a pair of the grazing animals or several courtiers at the ends of the arc would lose nothing the painting needs. The rock grotesques are a Turkman workshop habit carried in, not a requirement of the subject. Necessity is real at the centre and loose at the edges.
Hugo van der Goes · Visual art
8.7 · Tier IV
Judged part by part, and the centre holds. The child on the bare ground cannot go: the panel is a ring drawn round an emptiness, and he is its point. The Virgin, Joseph and the kneeling angels close the ring; the three shepherds break into it from the right, and their arrival is the picture’s one movement. The still life cannot go: wheat, jar and glass stand at the lip of the panel between the viewer and the child, a second altar under the first. The single patten at the left tells the viewer that the ground is holy. The wings carry the donors into the same winter and continue the road to the stable. What yields is in the background: small narrative episodes, part of the building, and several hovering angels that could go without loss.
Ingmar Bergman · Film
8.7 · Tier IV
A short feature, and its spine resists subtraction. Take out the prologue and the break at the glass loses its frame; take out the letter and the glass has no motive; take out the doubled monologue and the composite face is a trick. Applied strictly, the subtractive test still finds give for so short a film. The radio drama and parts of the hospital exposition are serviceable rather than required. The blood scene states as a figure what the son monologue has already said in speech. The Warsaw photograph repeats the work of the Saigon footage. The prologue’s catalogue is ordered by association, not necessity. The structure is compelled; more of its parts are chosen than its brevity suggests.
Robert Bresson · Film
8.7 · Tier IV
A picaresque is additive by nature, and one could imagine a station more or a station less; run the subtractive test scene by scene and the film resists it in the main and gives in places. Each keeping is a vice the donkey bears, pride in the father, cruelty and lust in Gérard, drunkenness in Arnold, avarice in the grain merchant, and each is joined to Marie’s line, so that removing one breaks a crossing as well as a station. The ellipses have already done the cutting. The give is real and counts: the middle third carries more plot than the film will explain, the gendarme, Arnold’s suspicion, the inheritance, and the circus, one of its summits, is a station that could be lifted out without breaking a thread.
Built for Fujiwara no Yorimichi · Architecture
8.7 · Tier IV
Run the subtractive test. The pond cannot go: the hall is meant to be seen across water, and without it the building is a pavilion on a lawn. The orientation cannot go: the hall faces east so that the worshipper on the east bank looks west, toward Amida’s land, with the evening sun behind the image. The opening in the door lattice cannot go; it gives the face across the pond. The wings are the hard case. Their upper storey cannot be entered and they shelter nothing, idle under use and required under purpose, since without them the paradise palace is a single hall. What holds the axis is the tail corridor, which could go with little loss.
Claude Lanzmann · Film
8.7 · Tier IV
Judged on structure, and the length is the first question. The film’s method is accumulation: the trains are returned to again and again, the grass at Treblinka is crossed many times, and the arrival at the ramp is told by a guard, a survivor, a driver and a farmer. Most returns are required, because each witness stands at a different distance from the same act: remove Stier and the railway has no clerk, remove Gawkowski and it has no driver. What gives is real and counted in full. Travelling shots of track and landscape do the same work more often than the argument needs, and the second era’s Warsaw material, Hilberg on Czerniaków and Grassler’s evasions, runs longer than its yield.
Baldassare Longhena · Architecture
8.7 · Tier IV
Judged on plan, section and structure under purpose and site. The vow asked for a church to receive a city once a year, in procession, from the water, and the broad steps rising from the canal and the great arch of the entrance are compelled by that arrival. The octagon with its ambulatory is compelled by the crowd: a festival multitude can circle the centre while the six chapels keep their altars. The high drum and dome are compelled by the site, the one point in the city seen from the Bacino, the Giudecca and the Grand Canal, and the scrolled buttresses resolve the drum to the octagon below; without them a cylinder would sit on a polygon. What resists: the sanctuary is a second building, joined to the first by sequence rather than necessity, the campanili are small and almost vestigial, and some of the sculpture crowding the facades could go without loss.
Sandro Botticelli · Visual art
8.7 · Tier IV
Judged figure by figure. The right group is a chain: Zephyrus seizes, Chloris becomes, Flora is what she became, and remove any one and the metamorphosis, the picture’s one event, cannot be read. Venus cannot go: she is the still centre, and the arch of foliage is drawn round her. Cupid’s blind arrow, aimed at the middle Grace, is the hinge between the violence of the right half and the dance of the left. The Graces are the picture’s rhythm. What yields is at the left: Mercury, turned away, is required by any programme and slight to the eye. And the figures stand side by side, so the joins between groups are spacing, not action. Necessary at the centre, permitted at the edge.
Pontormo · Visual art
8.7 · Tier IV
Judged figure by figure. The ring cannot go: the figures form a vortex round an empty centre, and at that centre are hands, the Virgin’s reaching and a mourner’s withdrawing, holding nothing. Christ’s body cannot go, nor the two youths who bear it, the one in front crouched on his toes under a weight he seems not to feel. The Virgin is the second pole, larger than the rest, swooning toward the body she is drawn away from. The woman seen from behind in the foreground turns the viewer into one of the ring, and the bearded man at the right edge is the one figure who looks out. What yields is the upper tier: one or two of the heads crowded at the top could be taken without loss, permitted by the format more than compelled.
Franz Liszt · Music
8.7 · Tier IV
The large plan resists the subtractive test. Each of the four movement-functions also does sonata-form work: the slow section is the development’s first stage, and the fugato is development and scherzo at once and delivers the recapitulation, so none can be cut without breaking two forms. The opening scales are required by the end, which returns to them, and three motifs carry nearly everything. The give is in Liszt’s rhetoric: passages restated a step higher by sequence, sometimes twice, where once would argue as much; recitative-like links that stretch time; octave cascades that display a harmony already stated. A pianist’s cut of a few bars costs this work less than a cut of one bar costs Op. 131.
Zhang Zeduan · Visual art
8.7 · Tier IV
Judged at two levels, since the scroll has no words. At the level of the incident the subtractive test is generous: one porter fewer on the bank, one customer fewer at the wine shop, and nothing fails. At the level of the sequence it is strict, and the sequence is the work. The mist and bare willows must come before the thickening along the river; the river must build to the bridge, the bridge hand on to the gate, the gate open on the street. Without the countryside the city has no outside to grow from; without the bridge the river has no crisis; without the gate there is no threshold. The density gradient is the argument, and only many parts can carry density. The incident still yields, and holds the axis in the middle eights.
Giuseppe Verdi · Music
8.7 · Tier IV
Length is not charged: the liturgy sets the scale. The subtractive test meets resistance where the structure turns. The returns of the Dies irae are the spine: cut the one after the Confutatis and the plea for mercy no longer collapses back into terror. The Libera me, which brings back the storm and the opening Requiem aeternam, cannot be cut without leaving the first movement unanswered, and the unaccompanied Te decet hymnus is the first bare voice the end returns to. The test finds give in three places: the long Offertorio, whose Hostias can feel a set piece; the Liber scriptus, a fugue in 1874 and replaced whole in 1875; and the Sanctus, which could change places and lose little.
Gian Lorenzo Bernini · Architecture
8.6 · Tier IV
Judged on plan, structure, purpose and site, and the constraints were many: a crowd to be gathered where it can see the benediction loggia and the window of the papal apartments; an obelisk and a fountain already in place; Maderno’s façade, too wide and too low for the dome; the palace on the north; processions to be carried under cover. The oval holds the crowd within a narrow site and centres it on the obelisk; the trapezoid corrects the façade’s width in perspective; the corridors carry the procession up the rising ground. Take away the colonnade and the crowd stands in a forecourt with no edge. What yields: 140 saints where fewer would serve, four rows chosen for effect more than shelter, and two figures set in sequence rather than one compelled.
Ernest Hemingway · Literature
8.6 · Tier IV
The subtractive test finds little to cut in the second and third books. Burguete must stand: the fishing on the Irati with Bill and the Englishman Harris is the one stretch of the novel without Brett, and its peace is the measure of what Pamplona destroys. The fiesta must stand whole, since its seven days are the plot. The coda must stand: Jake alone at San Sebastián, swimming and recovering his order, then the telegram from Madrid, and the last taxi, which repeats the Paris taxi of the first book and closes the circle the second epigraph announces. What the test finds is in the first book. The opening chapters of Cohn’s history, Frances Clyne’s long tirade and the itineraries of bars and boulevards say at length what the book needs said briefly. The repetition of drink and talk is in part the design, a numbing ritual, but not all of it is required.
Le Corbusier · Architecture
8.6 · Tier IV
Judged on plan, section and structure, under purpose and site. Remove the level roof line and the house loses the one datum by which it meets a slope it refuses to terrace. Remove the pilotis and the slope must be cut. Remove the stacking, cells above, study at the entrance, common rooms below, the church last and lowest, and the day’s order is no longer the building’s. Remove the loggia and the cell is a room, not a hermit’s place before a landscape. What resists the test: the court, left as raw slope, can be crossed but not lived in; the routes climb and fall more than the life requires; and the oratory’s pyramid and some objects on the roof answer the eye more than the use.
Eugène Delacroix · Visual art
8.6 · Tier IV
Judged on the configuration. The pyramid cannot lose its apex or its base: take Liberty away and the picture is a street fight with no direction; take the dead away and the advance costs nothing and rises from nowhere. The wounded man in blue cannot go: his upturned face is the hinge between the dead and the living, the one figure who sees her. The flag cannot go: it is the vertical the whole field climbs to, and its colours are repeated below it. The test gives at the flanks. The boy and the man in the top hat carry the coalition of classes, but either could be moved or exchanged without collapsing the triangle, and the worker with the sabre states the same point a third time. The crowd behind and Notre-Dame are lightly stated. The scale is compelled: a contemporary event at the size of history painting is the claim.
Ornette Coleman · Music
8.6 · Tier IV
Six tracks in about thirty-eight minutes, and the subtractive test finds most of the record held. The heads are short and exact, and nothing is written that does not set the solos going. “Lonely Woman” cannot lose its fast drums or its slow horns; the work is the gap between them. “Peace”, the longest track, is the record’s long breath, and the sequence needs it between the two short pieces of side one and the turns of side two. The test bites twice. “Eventually” and “Chronology” are both fast pieces on angular unison heads, and one could go with less loss than any other track. And Cherry’s solos sometimes find less than Coleman’s and mark time inside the free length the form allows. Freedom of length is the argument, so the cost is light; it is still a cost.
Odo of Metz, under Charlemagne · Architecture
8.6 · Tier IV
Judged on structure, purpose and site. The octagon and its ring cannot be parted: the rising barrel vaults over the gallery are the buttresses of the octagon, so the storey that carries the king is also the storey that keeps the vault standing. The eight piers carry what the plan requires and no more. The westwork is compelled by use, giving the throne its place on the axis and the king his entrance from the palace side. What yields to the subtractive test: the columns in the upper arches are screens, required by meaning, Rome brought north, and not by structure; the octagon would stand without them. The Gothic choir answers a later use, pilgrimage to the shrines, but it is a second building joined to the axis, not compelled by the octagon.
Jan van Eyck · Visual art
8.6 · Tier IV
Judged figure by figure. Rolin cannot go: the picture is his, and his kneeling body, alone and unsponsored, is its claim. The Virgin and Child cannot go, nor the angel, whose crown makes her Queen of Heaven and gives the panel its one vertical motion. The loggia cannot go, because it sets the donor and the Virgin in one room and opens that room onto the world. The two small figures at the parapet are the hinge between near and far, the place where the viewer’s own looking enters the picture. What yields is the profusion of the distance: its houses, boats and passers on the bridge are permitted by the panel’s appetite for the visible rather than compelled by its argument. Little could be cut from the near half; more from the far.
Gillo Pontecorvo · Film
8.6 · Tier IV
A chronicle, and it resists the subtractive test more than chronicles usually do. Each phase produces the next: the police killings bring the rue de Thèbes bomb, that bomb brings the women’s bombs, the bombs bring the paratroopers, the strike gives Mathieu his map of the Casbah, the map gives him the pyramid, and the pyramid closes on Ali. The frame is required, since opening on the old man’s torture tells the viewer from the first minute what method will win. Ali’s conversion at the guillotine is required, his life being the thread. What gives: the purge of the Casbah makes its point twice, some raids repeat each other, and the coda is compelled by the thesis rather than by the plot.
Henri Matisse · Visual art
8.6 · Tier IV
Judged on the configuration. The red cannot go: it is the picture, and without it the canvas is a room with furniture in it, a cousin of The Pink Studio of the same year. The reserve lines cannot go: they are the only way the room survives the flood, and they carry the space with a minimum of means. The clock without hands cannot go: the one object that tells the time and does not, on the composition’s axis. The painter’s works cannot go as a class: they are the only colour the red allows. Where it gives: the ring of works is a count, not a structure, and one canvas or one sculpture could be removed with the argument whole; the crayons, the glass and the chair at the right are lighter than the rest. The scale is compelled: smaller, the red becomes a colour, not a space one stands before.
Richard Linklater · Film
8.6 · Tier IV
The subtractive test runs film by film and then across. Before Sunset resists it best: eighty minutes and a plane to catch, so that every walk, from the bookshop to the boat to the car to Celine’s stair, is spent against the clock and none can go without shortening the time they have. Before Midnight is required in its spine, the car, the hotel room and the café, and the quarrel needs the whole day before it. Across the three no film can go, since each is a term of one argument about time. What gives: the street actors, the palm reader and the poet in Before Sunrise, which add texture rather than meaning, and the lunch table in Greece.
Balthasar Neumann · Architecture
8.6 · Tier IV
Judged on plan, structure, purpose and site. The governing fact resists the subtractive test: the place of the vision is fixed, and the plan is compelled to it. The great oval exists to put that place at the centre; the Altar of Mercy stands there because it can stand nowhere else; the free arcade lets pilgrims circle it and light reach it; the western and choir ovals make the central one a centre on a long axis rather than a rotunda. What yields: the Latin cross outside, an inherited form that does not follow the ovals within, and the outer reaches of the stucco and fittings, more than the use compels. Necessity was found after the fact, in the repair of another man’s plan, which strengthens its claim.
Titian · Visual art
8.6 · Tier IV
Judged on the composition. The left half withstands the subtractive test: Ariadne, the departing sail, the empty sea and the ring of stars are each required, since together they state abandonment, the past and the destiny the god brings. Bacchus’s leap is the hinge of the whole and cannot go. The right half is where the question bites. The rout is a catalogue of the god’s attributes, the snake-girt satyr, the child with the calf’s head, the Silenus on his ass, the cymbal player, and its noise is needed against Ariadne’s solitude; but the calf’s leg waved above, or the dog, could go without the picture knowing less. The procession is required as a mass more than member by member.
J. M. Coetzee · Literature
8.6 · Tier IV
Subtract and see. The opening, with its economy of desire that Lurie believes he has solved, cannot go, for the whole book is the undoing of that solution. The affair with Melanie, the committee, the attack, the clinic, the visit to George and the opera are each required by the argument: each is a hearing at which Lurie is asked to account for himself and gives a different account. The book is short and its scenes are rationed. A hostile reader could take out some of the opera in its middle stretch, where the shift from Teresa young to Teresa aged is argued at length in Lurie’s head, and one or two of the later Cape Town scenes. These are small. The scale is compelled, though not every paragraph bears weight as in the tightest short novels.
José Saramago · Literature
8.6 · Tier IV
The test is subtractive, and the design resists it. The premise is one proposition worked through in order: a city goes blind, the state confines the first cases, the confinement becomes a tyranny within a tyranny, and the city outside, once all are blind, is a ruin that a few must learn to live in. Each stage is required by the last. The asylum is long, and its length is the argument: the filth, the hunger and the waiting must be endured in time before the women’s night with the ward of the gun can carry its weight. The dog of tears, the church and the writer in the first blind man’s flat each make one turn. What holds the axis is the narrator: some of the asides and proverbs, and some of the city’s middle passages, add commentary rather than necessity, and a few could go without the knowledge changing.
Joy Division · Music
8.6 · Tier IV
Nine tracks in about forty-four minutes, and the album was chosen rather than collected: the group kept its two best-known songs of the period, “Love Will Tear Us Apart” and “Atmosphere”, off it. The frame is required. “Atrocity Exhibition” opens by inviting the listener in to watch suffering staged; “Decades” closes on young men come home from a war. Between them side two descends in four long tracks to a funeral tempo, and none can go without breaking the descent. Within the songs nothing is ornamental. The test bites once, at “A Means to an End”, the plainest rock song on the record, which argues nothing the others do not.
Giovanni Pierluigi da Palestrina · Music
8.6 · Tier IV
The large plan is the rite’s: the Ordinary fixes the five movements and every clause, so the subtractive test must ask what the setting adds. In the Gloria and Credo it adds almost nothing idle. At about fifteen words a minute each phrase is said once and handed to the next group of voices, and the full six are held back until the text needs them. The widening to seven voices in the second Agnus Dei is the work’s one structural addition, and it is the close. The give lies in the melismatic movements: the Kyrie’s three sections and the Sanctus with its repeated Hosanna are spacious by convention, not by argument, and the Sanctus is the most separable stretch.
Pink Floyd · Music
8.6 · Tier IV
Ten tracks in about forty-three minutes, joined without a gap, and most pass the subtractive test. Speak to Me looks removable and is not: it compresses the record into its brief opening, and its heartbeat is the one the record ends on, so that without it Eclipse would close on nothing. On the Run is wordless and required, the one place the dread of motion is set with no voice to soften it. The Great Gig in the Sky carries death without a sung word and could sit nowhere else. The test bites at Any Colour You Like, a jam on the colours of Us and Them that the record would survive losing, and lightly at the reprise of Breathe inside Time, which restates more than it turns.
Robert Louis Stevenson · Literature
8.5 · Tier IV
The subtractive test finds very little to take. Each of the eight chapters told from outside is an incident that adds one fact to a false theory: the door and the cheque suggest blackmail, the will makes Hyde an heir, the Carew murder makes him a criminal, the letter whose hand matches Jekyll’s suggests forgery, and then come Lanyon’s collapse, the face at the window, and the last night, when the theory is that Hyde has murdered Jekyll. Every false theory is required, because the book’s knowledge is that a respectable reading of a respectable man reaches every explanation but the true one. Lanyon’s narrative is required because it gives the transformation to a witness before the man explains it. What holds the axis there is the middle of the statement, where Jekyll restates his theory of the double and the episode in Regent’s Park and the letters sent from a hotel run long: a paragraph or two of moral exposition could go with the knowledge unchanged.
Peter Paul Rubens · Visual art
8.5 · Tier IV
Run the subtractive test figure by figure in the centre, scene by scene across the triptych. The centre resists it. The weight begins with the two workmen at the top of the cross, one holding the sheet in his teeth because both his hands are taken; remove them and the body does not come down. Joseph of Arimathea and Nicodemus, on ladders, carry the middle of the fall. John, braced at the foot with one foot on a rung, takes the whole weight on his chest. The Virgin reaches without touching; the Magdalene receives the foot on her shoulder. Each figure is a station on the body’s path. The wings are required in argument but not in sight: the Visitation’s loggia, servant and architecture are permitted rather than compelled, and the hermit on the outer face is the programme’s weakest link.
Robert Smithson · Visual art
8.5 · Tier IV
Judged by subtraction on the coil and the site together. Take away the straight stem and the spiral floats out of reach, an island and not a jetty: the stem makes it a road that goes out and turns back on itself. Take away the closure at the centre and the coil becomes a hook, a gesture that ends. Take away the site and nothing is left, for the rock is the shore’s own basalt, the red is the north arm’s and the salt is the lake’s. There is no ornament and no secondary rank. What holds the axis is substitution: the length, the width and the number of turns are permitted rather than compelled, and the dumped edge obeys no law finer than rock as it falls. Compelled as a whole, permitted in its dimensions.
Billy Wilder · Film
8.5 · Tier IV
Judged on structure. The dead narrator is required: he is the film’s first fact and the authority for its tone. The house is required, and every room of it works: the organ, the screening room, the bridge table, the pool Norma had filled for him, the room with no locks. Max’s revelation, husband, director and author of the fan letters, is held back until it reorders everything. The visit to Paramount is required: the studio wants her car, not her. The Betty strand is required in kind, an honest script written by night against a kept life by day, but its length gives: Artie Green’s New Year party and the drugstore scenes run on genre rhythm and could lose a third, and the repossession men announce a fact already established.
Terrence Malick · Film
8.5 · Tier IV
Judged mainly on structure, with Holly’s narration as its verbal part. Much of the film resists the subtractive test, and the test also finds give. The dog is required: the father’s punishment is the first killing in the film, and it is his, so the second answers it. The burning house is where Holly’s account first fails to meet what is shown, and the film is built on that failure. The garden is required so that the rest is exile; the rich man’s house holds the one place Kit speaks to the world in his own words; the cairn is his last record. The give is real: the road is additive by nature, Cato’s farm or the rich man’s house could go with its beat moved elsewhere, and the men in the woods, shot from cover and barely seen, are incident, not event.
Salian builders, under Conrad II and Henry IV · Architecture
8.5 · Tier IV
Judged on structure, purpose and site, where the purpose is imperial memoria and episcopal worship. The crypt cannot go: it raises choir and altar over the relics and is the root of the burial place. The royal choir and the graves before it cannot go: they are what the church was enlarged to hold. The alternating piers of the second campaign cannot go, since every second one carries a vault. The length yields only in part: a nave of this length was wanted by an emperor rather than compelled by a liturgy, and the giant arches, built to frame a timber-roofed wall, survive as a rhythm the vault did not need. What holds the rest is that the size is the claim.
Pagan builders, under King Kyansittha · Architecture
8.5 · Tier IV
Run the subtractive test on the plan and very little yields. Four Buddhas of the four quarters require four niches; four niches require four faces; four faces require four porches. The cross is compelled by the programme, not chosen for symmetry. The solid core is required twice, as the masonry that carries the tower and as the wall the images stand in. The two corridors are required by the rite, the outer for the reliefs walked past in order, the inner for the images approached. The hidden openings are required by images that must be lit from above unseen. What yields: the corner stupas and towers on the terraces, and porches longer than access demands.
Kate Bush · Music
8.5 · Tier IV
Twelve tracks on two sides, and the subtractive test falls differently on each. Side two passes it almost whole: each of its seven parts is a stage the night requires, the drift into sleep in And Dream of Sheep, the body under the ice, the trial in Waking the Witch, the soul at home unseen, the future self pleading in Jig of Life, the view from above in Hello Earth, the morning. Remove one and the passage breaks. Side one is a set of songs, and the test bites there. Mother Stands for Comfort is the slightest, though its mother’s complicity is answered by the father and son of Cloudbusting, and The Big Sky’s long close is permitted rather than compelled.
Gerhard Richter · Visual art
8.5 · Tier IV
The subtractive test, canvas by canvas. Funeral cannot go: it is the only public image and the only ending. Youth Portrait cannot go: it is the one face before the story, and without it the cycle is a police file. Cell and Record Player cannot go: objects where bodies were, the questions the official finding left, set down without comment. Dead cannot lose a canvas: the head shrinking and fading from the first to the third is the argument, a face going out of reach as it is looked at. The three canvases of Confrontation, three moments of one turn of the head, hold for the same reason. What yields is the Arrest pair, two nearly identical, hard-to-read frames of one event where one might serve, and the second Man Shot Down, which adds less than the third Dead.
Reed and Stem, and Warren and Wetmore · Architecture
8.5 · Tier IV
Judged on purpose, structure and site. The governing parts are compelled, each by the one before: the smoke law forced electrification; electricity let the yard go underground; the buried yard let the air above it be sold, and the sale paid for the whole. The two levels, the loop tracks, the ramps and the roadway round the building all follow from moving a great volume of trains and people through one block without crossing flows. The concourse is sized to the crowd, and its central clock is the one point every route passes. What resists the test: the Coutan group, much of the applied ornament and the sheer height of the vault could go and the station would work as before. That a city's gate must speak as a gate defends much of it, not all.
Kenzo Tange · Architecture
8.5 · Tier IV
The subtractive test finds little idle. The masts are there because the cables need them; the anchors are there because the cables pull; the saddle of the roof is the curve of the hangers between ridge and rim, so the roof’s figure is its statics, not a shape drawn first and engineered after. The crescent plan follows from the same decision: two half-circles slid apart give a long axis for the cables, a free span for the pool and its stands, and an entrance at each tip without cutting the ring of seats. The small hall does the same with one mast and one cable. What yields: the sweep of the concrete at the tips and the projection of the anchors go further than the forces ask, toward the image, and the low podium is ordered rather than compelled.
Maya, under K'inich Janaab' Pakal and his son · Architecture
8.5 · Tier IV
The test is subtractive, and the building resists it well for a temple-pyramid, because the order of making is the argument. The crypt and the sarcophagus came first, the pyramid rose over them, the stair was left hollow and then sealed, and the temple at the top carried the text. Remove the stair and the tomb is a sealed cache with no relation to the temple; remove the conduit and the dead king is cut off from the rites above; remove the panels and the temple loses its reason, which is to set this king’s death in the dynasty’s time. What could go with least loss is the front stair and the temple shell, shared with the type: the parts unique to it are required, the parts shared are permitted.
The Rolling Stones · Music
8.5 · Tier IV
Ten tracks in about forty-six minutes, and the record stands on pillars that hold. Brown Sugar must open: it sets the record’s terms, appetite and swagger, in its first riff. Moonlight Mile must close, the long road home after the night the record has spent. Sister Morphine is required as the place the appetite comes due, Dead Flowers as its sardonic answer, and Wild Horses as the one undefended love song. The subtractive test finds give in three places: I Got the Blues adds a style rather than a turn, You Gotta Move is a faithful cover the record could lose, and the coda of Can’t You Hear Me Knocking is beautiful without being compelled.
Nirvana · Music
8.5 · Tier IV
Twelve tracks in about forty-one minutes, none over five, and nearly every one passes the subtractive test. Serve the Servants must open: it answers the previous record’s fame before anything else can be said. Heart-Shaped Box carries the governing image, Frances Farmer the one figure from history, and All Apologies the required end, the only place the record lays down its arms. Dumb is the rest the first assault needs. The test bites in three places, and lightly. Very Ape and tourette’s, under a tenth of the time together, repeat a jolt Scentless Apprentice has already delivered at more force, and Radio Friendly Unit Shifter stretches one grinding figure past its use. Those three hold the figure.
Henry Purcell · Music
8.5 · Tier IV
Compression is the work’s first law. A whole book of Virgil is told in about an hour, and most numbers last a minute or two. Aeneas proposes, Dido assents, the witches plot, a storm breaks the hunt, a false Mercury commands, he resolves to sail, she sends him away, she dies: nothing is told twice. The subtractive test meets resistance in Dido’s two grounds, the cave, the Spirit’s command, the parting and the Lament. It finds give in four places: “Oft she visits”, which foreshadows by allusion only; the sailors and the witches’ dance in Act III, spectacle the action does not need; the Triumphing Dance; and witches who hate Dido for no reason the text gives.
Jackson Pollock · Visual art
8.5 · Tier IV
The subtractive test meets unusual resistance, for there is no part in the ordinary sense: no figure to remove, no passage that serves another. What carries the work is density held evenly across the whole width, and a hole anywhere would be felt at once as a hole; at that level every square foot is required. The scale is compelled rather than permitted: the line is the trace of an arm and a walking body, and the field has to exceed the viewer’s reach for the viewer to be inside it. What holds the axis is the other face of the all-over: a field without hierarchy cannot show why it stops where it stops. The necessity is of texture, not of structure.
Jean-François Millet · Visual art
8.4 · Tier IV
Judged on the configuration. The three women cannot go, and none of the three can go singly: they are one movement in three phases, the left figure bent full and reaching, the middle one stooped at the moment of picking, the right one half risen with the gathered ears held behind her back. Take one and the cycle breaks into poses. The high horizon cannot go: it keeps the heads below the far field and seals the women in the stubble. The distant harvest cannot go, or there is nothing they are kept from. The rider cannot go: he is the one figure of authority, and he is small. What yields is the population of the middle distance, a count permitted rather than required, and the scale, which the argument does not compel.
Akkadian · Visual art
8.4 · Tier IV
Judged element by element. The king cannot go: he is the summit of the figure and of the argument, and his scale is the claim. The mountain cannot go: it is the slope the whole order climbs, and its cone answers the shape of the stone. The stars cannot go: they are the gods the king alone approaches. The defeated cannot go: the man at his feet with a spear through his neck, the one who pleads, the one falling backward down the slope are the price the ascent is paid in, and without them the picture is a procession. The tree places the event in the world. What yields is the number: the diagonal ranks are required, their count only permitted, and the repeated gestures among the lower defeated could thin without loss. The design is close to necessary, the filling less so.
Agnès Varda · Film
8.4 · Tier IV
The test is the clock. Each chapter takes a few minutes of a woman’s wait for a biopsy result, and almost every one moves her a step from object toward subject: the tarot sets the fear; the hat shop and the mirrors show her living as a thing looked at; José’s visit shows that the man who keeps her is absent even when present; the rehearsal breaks her when her own song becomes an accusation; then the wig comes off and the city, Dorothée and Antoine follow. Few chapters could go without loss. What could be shortened is the middle: the drive and the studio with Dorothée, and the projection booth, which carries its point a little longer than it needs. The taxi radio and the café chatter are texture rather than step.
Nicolas Poussin · Visual art
8.4 · Tier IV
Judged figure by figure. The tomb cannot go: it is the subject and the centre, and the four figures are placed only by their relation to it. The kneeling reader cannot go: his finger on the letters is the act of the picture, and his shadow is the one dark mark the stone receives. The pointing shepherd at the right cannot go: he turns the discovery from the stone to a living face, and his question is the hinge. The woman cannot go: she is the answer. The shepherd leaning on the tomb at the left gives most easily, since the group would stand without him, though not as a frame round the stone. The landscape is required as Arcadia but generic in its parts. Held a step below the top by those margins.
João Gilberto · Music
8.4 · Tier IV
Twelve short songs, and the subtractive test finds very little inside any of them. Each performance is the song once through, sometimes with a short return, and stops. “Chega de Saudade” states its minor lament and its major release and ends; “Desafinado” takes its long form once. Jobim gives the band a phrase where the voice breathes and nothing more. Across the sequence the test bites a little: “Hô-ba-la-lá” and “Bim Bom”, Gilberto’s own slight pieces, and the comic “Lobo Bobo” are three, and one could go without loss. They are the plain ground of the method, the beat with almost no song on it, as “Freddie Freeloader” is on Kind of Blue. A few string pads are permitted rather than compelled.
Clint Eastwood · Film
8.4 · Tier IV
Run the subtractive test and most parts are paid. The bounty begins in a fine of horses, a price set on a woman’s face as damage to property, and the plot follows from that valuation. Munny’s falls in the pig mud and from his horse set up the ruined gunman the ending will contradict. English Bob looks like a digression and is required: his beating, and Beauchamp’s change of loyalty, set out the law of the town and the making of legends before Munny enters it. The fever puts Munny on the floor so that Delilah’s visit can happen. What gives: the ride north is long, the Kid’s boasting is laid on more than once, and some business with the deputies is filler.
Luis Barragán · Architecture
8.4 · Tier IV
Judged on plan, section and use. The subtractive test bites hard because the house is made of very few things: walls, openings, light, a handful of materials. Remove the dim vestibule and the hall’s light from above loses its force; the house is a sequence of compression and release, and each compression is required by the release that follows. Remove the blind street wall and the house’s whole proposition, withdrawal from the city, is lost. Remove the cantilevered stair and the library loses its one vertical gesture. Remove the terrace walls and the roof becomes a view over Tacubaya. What resists: the service floor, some bedroom arrangements and parts of the studio answer a household’s needs rather than the argument, and the objects set in place are chosen, not required.
Zhang Yimou · Film
8.4 · Tier IV
Run the subtractive test and the film resists it more than most. The four seasons are the plot: arrival, rivalry, catastrophe, replacement. Each ritual is set up and then turned. The lantern call becomes Songlian’s ambition, then her fraud, then the black covers that seal her house. The foot massage, its small hammers and bells heard across the courtyard, is first a pleasure, then a token of standing, then a sound the others are made to hear. Yan’er’s hidden lanterns pay off in the snow; Meishan’s opera on the roof pays off in the room on the roof. What gives: the autumn has more scheming than the design needs, the effigy, the doctor and the haircut being three moves of one kind, and the repeated lantern call is sometimes only repetition.
U2 · Music
8.4 · Tier IV
Ten tracks in about forty-two minutes, and the subtractive test finds one cut. Elvis Presley and America, over six minutes and the longest track, is a vocal that sounds found rather than written, its words half-formed over a backing that drifts, and the record would lose nothing it argues without it. The other nine bear weight. Bad needs every bar of its six minutes, because the song is the climb. MLK needs its brevity. And 4th of July, two minutes with no voice, opens the second side by removing the singer, and so makes the record’s method literal. What holds the figure here is the size of the cut, about a seventh of the running time, and two soft spots: Wire and Indian Summer Sky are riffs more than songs, though each holds its place in the sequence.
Mexica · Visual art
8.4 · Tier IV
Tested ring by ring. The central face cannot go: the whole disc turns on it, and its knife tongue and clawed hands holding hearts state the price of the sun’s motion. The sign 4 Movement cannot go: it is the present age, and its arms are the only place the four dead ages are held. Remove the day ring and the disc loses the count of days that turns inside the count of ages; remove the serpents and the cosmos has no boundary and no carrier; remove 13 Reed and it loses its anchor in a named year. Each ring is a different scale of time, and each is needed for the claim that all scales are one. What yields: the quincunx and ray bands are partly ornamental filling, required in kind but not in number, and the edge may be unfinished.
Otto Wagner · Architecture
8.4 · Tier IV
Run the subtractive test and the hall resists it. The glass vault is there because the room at the heart of a deep block must be lit from above; the glass floor is there because the rooms beneath need the same light; the aluminium outlets stand free because the heating must reach the floor of a glass-roofed room, and they are shaped as the thing they are. The bolts state how a thin skin hangs on a frame. The plan, a block wrapped round its hall, is compelled by the institution: thousands of small transactions at counters, clerks behind them, offices above. What holds the axis at 8.5 is the outside: the cornice figures, the canopy and the attic are emphasis chosen, and the long office fronts could be shorter or longer without loss.
Prince and the Revolution · Music
8.4 · Tier IV
Nine tracks in about forty-four minutes, and the subtractive test finds little to cut. Let’s Go Crazy must open: its spoken sermon sets the record’s terms, the afterlife and the party in one breath, and its guitar runs the record up to speed. The Beautiful Ones is the first turn inward, a ballad that ends in a scream. When Doves Cry opens the second side as the plainest statement of the record’s wound, and Purple Rain must close it; Darling Nikki is the profane pole the sacred one answers, and Computer Blue keeps its place as the bridge from love to obsession. The test bites twice, lightly: Take Me with U, a bright duet, carries the film’s romance more than the record’s argument, and Baby I’m a Star’s length is the stage’s. Two soft tracks, neither idle.
Liao builders · Architecture
8.4 · Tier IV
Run the subtractive test on structure, purpose and site, and little can be taken. The two rings of columns are the tower. The concealed storeys cannot go: braced on the diagonal, each is a stiff ring between bracketed storeys that flex, and that alternation is how a timber tower of some 67 m stands in a country where the earth moves. The brackets carry the eaves out over the platform and give the joints their yield. Purpose compels the sequence of images, a realm to a storey; the open plain compels the height. What resists is display: a repertory of bracket forms beyond what load requires, and balconies that serve the view more than the images.
Denis Johnson · Literature
8.4 · Tier IV
The test is subtractive, and it finds little to take. Each story is one episode pressed to its turn, and the order is an argument: a wreck, the long middle of addiction and complicity, a recovery that is small and not innocent. “Car Crash While Hitchhiking” must open, because its narrator’s claim to foreknowledge and its closing address set the terms on which every later story is told; “Beverly Home” must close, because it answers that address. “Work” and “Emergency” carry the book’s double law, that grace and harm arrive together. What holds the axis is the middle: “The Other Man” and “Happy Hour” are slighter than their neighbours, and either could go with the knowledge little changed.
Dionysus Flambouras · Literature
8.4 · Tier IV
Little here is not action, speech, road or record, and the scene carries almost no slack. The ten dated entries are as spare as the prose they answer, and each moves a plot the characters cannot see: a neighbour’s call credited, a careless answer that puts a yard owner on file, a day with no entries because it was spent at Randolph’s. What the mother knows still arrives in the order she can bear: “There is more later. Not now.” The negation that weighed on the earlier reading has been cut back, “did not” now 137 times and the acceptance 27. What the subtractive test still finds is the middle, where the son’s story is carried in long reported speech across two sections, and the courtesies that close each stop, thank you and drive careful, repeated past their use.
Dionysus Flambouras · Literature
8.4 · Tier IV
The register makes slack hard to hide and the collection carries little of it: nearly every story stops on an object, a sound or a single line of speech, and The Shutdown closes on a man keeping one hand on a cake box at the first corner rather than on any verdict. What remains is restatement. The Map escalates through more recalculations than its law needs, its screenshots and zones repeating one turn, and The Record states its condition in short sentences that say the same thing several ways: it did not require recall, it did not improve with use, it did not degrade with neglect. The Replacement, the longest story at about 2,500 words, advances by increments a reader has already taken. Most of the book is required; a few pages in three stories are only permitted.
Jasper Johns · Visual art
8.4 · Tier IV
The subtractive test returns an odd answer, and the oddity is the work. Nothing in the design can be removed, because nothing in the design was chosen: take away a stripe or a row of stars and it is no longer the flag, and the work requires that it be the flag exactly. The painter’s choices lie in the support, the edges and the skin, and these too are required. Set the image within a margin and it becomes a picture of a flag; make the surface smooth and it becomes a flag. Where it gives is the skin: any other newspaper would serve under the wax, and the stroke is local and interchangeable, a texture rather than a sequence of necessary acts. Compelled as a whole, permitted in its parts.
Chris Marker · Film
8.3 · Tier IV
Judged on 28 minutes, and the spine resists subtraction. The prologue holds the whole plot folded: the face, the jetty, a man falling. The war is told in a few photographs of ruined Paris because the film needs the condition, not the history. The camp is required, since it makes the man an instrument and sends him; the meetings with the woman are why he can travel and what he loses; the museum is time made into a place; the end closes the beginning. What gives is real for so short a film. The journey to the future, its people and the power unit they hand over, is a plot device the film hurries through and could shorten without losing a fact the loop needs, and the experiments in the camp repeat their effect.
Edgar Degas · Visual art
8.3 · Tier IV
The subtractive test on a figure with few parts and none idle. The raised chin cannot go: it is the whole attitude, a child presenting herself and refusing at once, and with the nearly closed eyes it makes the face offered and withdrawn together. The clasped hands cannot go: they draw the shoulders back and push the narrow chest forward, the posture of the class and of inspection in one. The turned-out fourth position cannot go: it is her labour, standing at rest. The real hair and cloth cannot go: without them she is a statuette of a dancer, with them a specimen of a girl. What gives a little: the slippers and the base carry less, and the ribbon is an accent the bronzes show can be changed without loss.
Nick Drake · Music
8.3 · Tier IV
Eleven tracks in about twenty-eight minutes, and the record is built to resist the subtractive test. Every song is voice and guitar with no introduction, solo or coda beyond what the figure needs. Road and Harvest Breed end almost as soon as they are stated, and the brevity is the argument: a speaker who will not say more than he can. The one addition, the piano phrase in the title song, is required, since it lets the record open on a second colour before closing to the bare form. The test bites twice. Horn, a single guitar line between songs, could go with small loss, and Free Ride and Which Will sit close in manner. Necessity is easier to keep in so small a form, and that holds it below Kind of Blue at 8.6.
Eladio Dieste · Architecture
8.3 · Tier IV
Judged on structure, purpose and material. Subtract any part of the nave and it fails or falls. The wave in the walls is not a decoration of a box: it is what lets a wall one brick thick stand and carry a vaulted roof with no buttress and no column. The double curvature of the roof is what lets a brick vault one unit thick cross the nave. The wave grows from nothing at the floor to its full height at the eaves because the wall is a ruled surface between a line and a curve, and wall meets roof where the wave is deepest. The material was chosen because it was local and cheap and laid by masons the town had. What yields: the tower and the sunken baptistery are less compelled than the nave, and the choir loft is ordinary.
Evelyn Waugh · Literature
8.3 · Tier IV
Ask what could be removed, and little can. The staged divorce at Brighton, Tony’s weekend with Milly and her child Winnie to give the evidence of adultery the law then needed, looks like a comic set piece and is load-bearing: there his decency is made to perform its own humiliation, and there he first refuses Brenda’s family, declining the alimony that would force the sale of Hetton. The death of the child is placed exactly at the hinge. The forest chapters, often called a break, are compelled by Hetton: Tony seeks the City because his Gothic house has failed him. The interleaving of London scenes into the expedition is the one place a reader might ask whether the alternation is needed; it is, for it keeps Brenda’s slide into poverty and Beaver’s departure for America in the same frame as Tony’s fever.
Arvo Pärt · Music
8.3 · Tier IV
The subtractive test meets the rule. In Silentium nothing can be removed: the voices are drawn from one line, and to take one out would break the proportion that brings the music down to its last silence. The voice held to the triad cannot lose a note without the melodic voice losing its partner. The two movements need each other: play without silence is a showpiece, silence without play is a meditation with nothing it has come from. The test finds give in Ludus. Its sections are additive, and one fewer would cost scale, not argument; the closing cadenza is the most separable stretch, a display the process permits rather than compels. A short work passes the test more easily, and that is not credited as a virtue.
Joseon builders · Architecture
8.3 · Tier IV
Run the subtractive test. The chambers cannot go: each is a reign, and their number is the dynasty’s count. The terrace cannot go: it is the floor of the rite, the open ground on which the officiants stand before the spirits, and its emptiness is what the long hall faces. The wings cannot go: they close the court, so that the rite is held inside the shrine and not before it. The three-strip path carries a rank in its section. The scale is compelled, not permitted: the hall is as long as it is because there were that many kings. What could be removed lies at the margins: the lesser halls serve the rite but not the form, and they hold the axis short of the top.
Michael Haneke · Film
8.3 · Tier IV
Judged on the one version, and it is lean: the subtractive test meets resistance almost everywhere. The opening long take is required, since it teaches the viewer that the film’s own image may be the watcher’s tape. The drawings are required, carrying the buried accusation before Georges admits there is one. The visit to the mother is required, because her vague memory is where the past has gone soft. Pierrot’s night away turns a threat into the family’s crisis, and Georges’s answer, the arrest of Majid and his son on no evidence, reenacts the childhood denunciation. What gives: the dinner-party anecdote and Anne’s friendship with Pierre restate the mistrust without moving it, and the talk-show set makes its point once and returns to it.
Hellenistic · Visual art
8.3 · Tier IV
Judged on structure alone. The subtractive test finds the parts required. The ship cannot go: without it the figure is a Nike on a pillar, as at Olympia, and the arrival has nowhere to happen. The wings cannot go: flung back and up against the body’s forward pitch, they are the brake, and the stance reads as landing only because of them. The drapery is the wind made visible, and nearly every fold is a vector. What yields is in two places: the himation rolled at the hips and bunched between the legs, cut in channels deeper than the wind requires because the drill and the light reward them; and the ship’s oar-boxes, required by the type of ship rather than by this one.
Unknown (English or French) · Visual art
8.3 · Tier IV
Taken element by element, the object resists subtraction to an unusual degree for its size. The king cannot go: the work exists for his kneeling. Each saint is a title to rule: Edmund, the martyred king of the East Angles; Edward, the royal saint of Westminster and the king’s chosen patron; John, who points to the Lamb. Remove one and a claim goes. The Child cannot go, since the whole exchange is his blessing; the banner cannot go, since it is what passes across the hinge. The angels in the king’s livery are the boldest element and the argument requires them. What yields is their number, whether eleven for a reason or a crowd to fill a field, and the flowers and trees are permitted ornament.
Portishead · Music
8.3 · Tier IV
Eleven tracks in about forty-nine minutes, and the subtractive test mostly fails to find a cut. Silence must open: its spoken Portuguese introduction, its pounding drums and its end cut off mid-phrase announce a record that will not let a song finish. The Rip is required as the one place the old tenderness is let in and then turned to machinery; Deep Water, ninety seconds of ukulele and close harmony, is required as the breath between the two most punishing tracks. Machine Gun and Threads are the spine. The test bites twice: Magic Doors restates the record’s mode without a turn of its own, and Small’s long organ middle extends a mood more than it advances one.
Oscar Wilde · Literature
8.3 · Tier IV
The subtractive test, put to the plot, finds almost nothing loose. Every invention of the first act is spent by the third: Bunbury is exploded; Ernest is killed, mourned and then found to be real; the cigarette case inscribed from little Cecily opens the whole country plot; the handbag scorned in the first act is the recognition token of the last. The cucumber sandwiches and the muffins are one joke placed twice, so that appetite replaces feeling at the two worst moments. The cut from four acts to three removed a whole scene and tightened the play. The charge is the epigram, detachable by nature: many single lines could go without the structure noticing, and some of the wit is permitted by the form rather than compelled by it.
Jean-Auguste-Dominique Ingres · Visual art
8.2 · Tier IV
The subtractive test gives almost nothing. The figure is the picture, and the picture is one line: from the turban down the long back, over the hip, along the thigh to the folded foot. Remove the turned head and the gaze, and the nude becomes a body seen without seeing back; the gaze is the event. Remove the fan, and the right hand has nothing to lower, and the one vertical accent in the lower half goes. The blue silk and the curtain are the cold against which the pale skin is set; the curtain closes the right edge as the turban closes the left. What yields are the props of the Orient at the lower right, permitted rather than compelled, and the fur and fringe, a little more inventory than argument. The long canvas is compelled by the long body.
Peter Zumthor · Architecture
8.2 · Tier IV
Judged by the subtractive test. The opening at the top cannot go: it is the only light and the only opening to heaven, and the rain on the lead depends on it. The lead floor cannot go: it receives rain and light and gathers both into a shallow pool. The burnt wall cannot go: it is the memory of the tent and the fire, and the reason the room is dark. The glass stoppers cannot go: they are the necessary holes of the making, turned into the only lights in the wall. The angled passage cannot go. The test bites on the outside: the pentagonal prism and its bands are a fine sign in the field, but the room would keep almost all it says inside a plainer shell. Held below the top because the work is small, and smallness makes necessity easier to keep.
Deerhunter · Music
8.2 · Tier IV
Eleven tracks in about forty-six minutes, and the subtractive test finds no padding. Earthquake must open: it wakes the record into its haze, the past entered as a slow dream. Desire Lines is the centre, the one place the record breaks into open motion, and its coda is required as release. Helicopter is the record’s darkest story and its clearest song. He Would Have Laughed must close, an elegy that lets the record end on a person rather than a mood. Revival and Coronado give the record its brief brightness. The test bites at Sailing, which drifts on almost nothing and restates Earthquake’s mood more thinly, and lightly at Memory Boy and Fountain Stairs, which pass without changing the record’s course. The frame and the centre are compelled; three tracks are slighter than the rest.
Paul Thomas Anderson · Film
8.2 · Tier IV
The film is a series of tests of a household’s rules, and most scenes are required by that design. The breakfast order is the first measure of appetite and the first exchange of power. The measuring scene makes Alma an object of the House before she is a person in it. The asparagus dinner shows that tenderness offered on her terms is an act of war in his house. The first poisoning is the hinge, and its fever gives the cause of the pattern. What gives: Barbara Rose’s wedding runs past its use, the New Year’s ball repeats a reconciliation the fever carries better, and some scenes of the House at work are atmosphere, not turn.
Edgar Degas · Visual art
8.2 · Tier IV
The subtractive test, part by part. The empty tables cannot go: they are the distance the picture is about, and they push the couple up and right into the corner where they sit. The mirror cannot go: it doubles the two heads as blurred shadows and closes the room behind them, so that they are walled before and behind. The glass cannot go: it is the title and the woman’s whole occupation. The man’s cropping cannot go: it makes him turned away, half outside her evening. What could be lost is small: the newspaper on its stick and the objects on the near table serve the café’s truth and anchor the zigzag more than they carry meaning, and a little of the floor at the lower edge reads as reach. The economy is strict, and it is the economy of a small subject.
James McNeill Whistler · Visual art
8.1 · Tier IV
Judged by subtraction, and the canvas resists it. Remove the curtain and the figure drifts left into nothing: it is the counterweight to the long black mass of the dress and the stop for her gaze. Remove the framed print and the upper right is a void; its small dark rectangle answers the head across the wall. Remove the footstool and the dress has no base; the stool is what makes the seated body a horizontal block. Remove the dado and the planes lose the line that ties them. The whites of cap, cuffs and handkerchief are the points by which the eye crosses the black. What holds it short of the top is the count: necessity is easier won in five parts than in a crowded field, and the print’s image is not required, only its rectangle.
Rachel Whiteread · Visual art
8.1 · Tier IV
The work is one operation applied to one thing: fill the space, then remove the walls. Each part of the result is set by the house and not by the artist. The fireplaces, the window bays, the stair and the marks of the switches are there because the house had them, and none could be absent without falsifying the cast. Take away the site and the work becomes an object in a gallery, a large Ghost; take away the fact that this was the last house of its terrace and it loses its witness; take away the public ground and it loses the dispute through which it spoke. Even its brevity reads as required: a monument to an erased house, itself erased. What yields is the choice of this house over another, which circumstance made.
Gerhard Richter · Visual art
8.1 · Tier IV
The subtractive test, element by element, and there are few elements, which is part of the claim. Remove the grey and she turns toward nothing in particular, toward a wall: the canvas becomes a snapshot of a child looking round, and its second subject, painting and its blank, goes. Remove the jacket’s pattern and the body loses its warmth and its one assertion of colour, and the figure sinks into the ground. Turn the head to us and the painting becomes the portrait it refuses. The drawn-back hair, showing the nape and the line of the cheek, is the hinge of the turn. What yields: the proportion of grey to figure could shift a little, and the ornament of the pattern is a given of the photograph, not a choice.
Damien Hirst · Visual art
8.0 · Tier IV
The subtractive test, part by part. Take away the box and nothing is born: the head rots for an empty room. Take away the head and the flies hatch and die with no feeding, no breeding and no rot; the cycle loses its centre. Take away the killer and death comes only by age, slow and unseen, and the one sudden, mechanical and audible death is gone. Take away the partition and the crossing from the room of birth to the room of death, the one event the case stages, is lost. Take away the glass and the viewer is inside. What could go is maintenance, the keeper’s, not the argument’s. Held below the top because the parts are generic by design: any head, any killer of the pattern would serve.
Jasper Johns · Visual art
8.0 · Tier IV
The parts are few, and each is tested. The flag cannot go: it is the given design that takes composition away from the painter, and so it is the premise. The edge-to-edge fit cannot go: give the flag a field around it, as in Flag on Orange Field, and it becomes a picture of a flag. Three is required: one flag is Flag, two make a pair or an echo, and three make a progression, with a direction that points out of the wall at the viewer. The wax is required, since it keeps the hand inside a design that needs none. What gives: a fourth step would extend the argument, not break it, so three is a minimum rather than an exact sum; and within each field almost nothing is decided, which limits what the test can find.
Bridget Riley · Visual art
7.8 · Tier III
The subtractive test hardly finds a purchase. The panel has one element, the black and white unit, and one operation, its narrowing across the width. Every column is a step in that progression, and to remove one is to break the rate, which is the whole content. The two values cannot be reduced, and colour would turn a perceptual event into a pattern of hues. The short widening after the fold is required: without it the surface would simply recede to an edge; with it the eye finds a crease and a return. What holds the axis below the top is the kind of necessity: a rule’s, generated rather than searched for, so that a slightly different rate would make a slightly different painting of equal claim.
Cao Xueqin · Literature
9.3 · Tier V
Length is not a cost; the question is whether the parts are required. The argument of the eighty chapters is the life of a household in the season before its fall, and the plenitude is that argument: the birthdays, feasts, prescriptions, rents and quarrels over a funeral allowance are what will be lost, and the fifth chapter has already said so. Episodes that look detachable bear weight: Jia Rui’s death by the mirror (ch. 11, 12), the You sisters (ch. 66, 69), Liu Laolao’s outside eye. What holds the axis lowest of the twelve is matter the novel could lose, about a tenth of the eighty: drinking games quoted whole (ch. 40, 62, 63), poetry sessions that repeat one pattern of composition, ranking and teasing, and the servants’ quarrels of ch. 58–61, all of one shape.
Augustine of Hippo · Literature
9.2 · Tier V
The narrative books pass the subtractive test as few autobiographies do, because they are ruthless in selection. The father’s death is a clause (III.4.7), the son a few sentences, whole years gone, while one theft of pears is given seven chapters, since the book needs a sin with no motive but itself. The death of the friend, the dismissal of the companion, Ponticianus’s story and the garden are each required by the argument about the divided will. What holds the axis lowest of the twelve is the last three books. Their place is argued and they belong; but much of the twelfth book’s weighing of rival readings and the thirteenth’s allegory of the firmament could be shortened without loss, and the catalogue of temptations in the tenth (X.30 to 39) runs long.
Charles Baudelaire · Literature
9.1 · Tier V
The subtractive test on a body of 126 poems has two parts: does the sequence require its sections, and does each section require its poems. The sections pass. Take away “Tableaux parisiens” and the book loses the city, where its spleen is given a world; take away “La Mort” and “Bénédiction” has no answer. The poems do not all pass. “Le Vin” is the weakest section: “L’Âme du vin” and “Le Vin des chiffonniers” are good, “Le Vin du solitaire” and “Le Vin des amants” slight. Poems such as “Le Mauvais Moine”, “La Muse vénale”, “Bohémiens en voyage”, “Châtiment de l’orgueil” and “Le Flambeau vivant” could go without the book noticing: perhaps an eighth to a sixth of the whole. The design is required; not every poem in it is.
Jonathan Swift · Literature
9.0 · Tier V
The four voyages are required, and in their order: man seen from above, then from below, then as an intellect cut loose from use, then as an animal measured against a reason he does not have. Remove one and the argument loses a term; reorder them and the last voyage’s verdict arrives unprepared. Within the first, second and fourth parts very little is idle: the inventory of the pockets, the fire put out, the King of Brobdingnag’s questions, the Houyhnhnm master’s cross-examination all carry the argument. What holds the axis down is the third part, a miscellany of the flying island, the Academy of Lagado, the sorcerers’ island, the immortals and a stop in Japan, joined by travel rather than necessity: Balnibarbi or Glubbdubdrib could go without loss to the whole.
Michelangelo · Architecture
9.0 · Tier V
Run the subtractive test on Michelangelo’s core and it resists. He reached it by subtraction, cutting away Sangallo’s ambulatories, and what is left is load: four piers for one dome, four arms to buttress them, one giant order to bind the mass. Take away an arm and the dome loses its bracing; take away the drum’s paired columns and it loses its spurs. Run it on the building as built and it yields. Maderno’s three bays were compelled by purpose, not by the design, which closed without them. What holds the axis here: the façade’s width was set for towers that do not stand, and the colossal putti, the medallions on the nave piers and much of the marble are ordered rather than required.
Ralph Ellison · Literature
9.0 · Tier V
The test is subtractive, and it bites. The frame is required: the Prologue’s cellar and its riddling sermon on the “Blackness of Blackness” set the terms on which every episode is a lesson the narrator already knows. The Southern chapters are required in sequence, the battle royal, Trueblood, the Golden Day, Bledsoe’s letters, each a script the narrator is handed. Liberty Paints and the factory hospital are the hinge. What holds the axis at the foot of the twelve: the novel’s law is that the narrator is used and betrayed, and in the Brotherhood chapters it is shown more times than the knowledge needs. The committee scenes, the speeches and the scene with Sybil run past their turn, and perhaps a tenth of the book is permitted rather than compelled. The repetition is in part the argument, that the condition is a structure met everywhere, but the Brotherhood makes it more often than the argument requires.
Imhotep, under Djoser · Architecture
8.9 · Tier IV
The subtractive test bites less than one expects. The dummy chapels are not filler: each solid building is a station of the jubilee, built so that the king’s ka could keep performing it, and the Houses of the North and South state the two lands he rules. Wall, gate, colonnade and court are the sequence the rite requires. Two things hold the figure down. The pyramid was reached by accretion, a mastaba enlarged and then overbuilt twice, so its final form was arrived at rather than compelled, and the rectangular base records the revisions. And the long rows of identical chapels and the doubled burial carry a repetition a terser complex could shed.
Plato · Literature
8.9 · Tier IV
Subtract and see what goes, and most of what looks loose is required. Lysias’s speech must be given whole, because the second half takes it apart (262d to 264e) for having no beginning, middle or end, its parts as interchangeable as the lines of the epigram on Midas (264d). Socrates’ first speech must be given and must be wrong, because the palinode is its recantation, and the two are reread (265a to 266b) as the left and right hands of one division of madness. The cicadas, which read as ornament, are the drowsiness the conversation has to resist. What holds the axis down is about a tenth of the whole that could go: the catalogue of handbook terms and their inventors (266d to 267d), satire at a length the argument does not need; the programme of matching speech to soul (271a to 272b), stated more than once; and a stretch of assent that carries no weight.
Francisco Goya · Visual art
8.9 · Tier IV
Judged plate by plate, and the series resists subtraction less than a single canvas does; that is its cost. Plate 1 cannot go: the kneeling man, arms out in darkness, is the presentiment the whole argues out. The chains of plates cannot go as wholes, because the series argues by accumulation and by the dry reply of one caption to the last: “Esto es peor” (37) after the mutilated body, “Yo lo vi” (44) as the witness’s oath. The famine group cannot go, nor plates 79 and 80. What yields is in the middle: ten or a dozen plates of reprisal and flight repeat their neighbours’ work, and a few animal satires of the last group are local and replaceable. Required in its shape, permitted in its count.
Gabriel García Márquez · Literature
8.9 · Tier IV
The repetition a careless reader takes for padding is the argument: the names return because the family cannot escape itself, and Úrsula, near the end of her life, feels that time is going round in a circle. A line that cannot remember is condemned to return, and the returns have to be felt as a weight, not reported. The spine is required: the founding marriage of cousins and the fear of the pig’s tail, the insomnia plague, the wars, the banana company, the massacre, the rain, the last incest and the child. What holds the axis lowest of the twelve is accretion within that spine. The long comedy of Aureliano Segundo between Fernanda and Petra Cotes, the raffles and the animals multiplying, the courtships of Pietro Crespi, the seventeen Aurelianos who arrive to be shot, and some of Fernanda’s grievance could be shortened or exchanged without the book knowing less. Perhaps a tenth of the whole is the narrator’s abundance rather than the book’s necessity. The episodic method permits additions; the end disciplines them only after the fact.
Rainer Maria Rilke · Literature
8.9 · Tier IV
The spine passes the subtractive test. The First sets the terms: the cry the angels will not hear, the lovers who cannot hold each other, the early dead. The Eighth gives the diagnosis, the Ninth the answer and the Tenth the descent; remove any of them and the arc from lament to praise breaks. The cycle answers itself across its length: the angels who cannot hear in the first lines are, in the Tenth’s first line, the angels whose assent the poet hopes for. Three things hold the axis down. The fifth place was filled twice, so a slot in the cycle could take another poem. The Third could go with little loss, and the Sixth gathers passages written over ten years. And the rhetoric sometimes says three times what it has achieved once, as in the Seventh’s repeated invocations.
W. B. Yeats · Literature
8.9 · Tier IV
The subtractive test, taken poem by poem and then on the book. Inside the major poems almost nothing can go: in “Sailing to Byzantium” each stanza makes one move, the country refused, the soul’s school, the prayer to the sages, the golden bird, and the last line, “Of what is past, or passing, or to come”, answers the first stanza’s “Whatever is begotten, born, and dies”. The order argues too, from Byzantium as the wish to the ghosts called to the table at the close. What holds the axis is what the great poems carry with them. Counted by poems, perhaps a sixth of the book is permitted rather than required: “Owen Aherne and His Dancers”, “The Three Monuments”, “Wisdom”, “The Fool by the Roadside” and “Fragments” could leave the book with its knowledge little changed, and inside “The Tower” the testament of the third part runs on past its point before “Now shall I make my soul”.
Virginia Woolf · Literature
8.9 · Tier IV
The subtractive test passes at the level of design and strains at the level of the paragraph. Remove the interludes and the soliloquies lose their measure of time: the sun’s one day is what makes six lives one span. Remove Percival and the six have no centre to circle and no death to fail to understand. Remove Bernard’s summing up and the book never turns from many voices to the one who tried to hold them. Each of the six is required, defined against the others: Louis’s accent against Neville’s ease, Rhoda’s facelessness against Jinny’s body, Susan’s earth against them all. What holds the axis down is density within the parts. The soliloquies restate their images, Louis’s chained beast, Rhoda’s puddle, Jinny’s dancing body, more often than each section needs, and the sixth and seventh sections circle without advancing as sharply as the first five. A tenth of the book could go without loss.
Gustave Flaubert · Literature
8.9 · Tier IV
The design is subtractive by temperament, and the repetitions are the argument. Frédéric’s oscillation among four women, Mme Arnoux, Rosanette, Mme Dambreuse and Louise Roque, is required, because each is a version of the same deferral priced in a different currency, and the book’s knowledge is in their equivalence. Arnoux’s businesses, the art paper, the faience works and the shady speculations, are required too, since they carry money through every relation. What fails the test is a margin of social machinery: the full roster of the Dambreuse salon, the Cisy duel and part of the club scenes of 1848 run past their point, and some of the dinners and promenades of the second part could go without a fact the ending needs. A life that does not progress makes the drift partly earned and partly cost, about a tenth of the whole.
Paul Cézanne · Visual art
8.8 · Tier IV
Judged on the configuration as it stands. The two trees cannot go: their lean makes the arch, and the arch is the picture. The gap at the centre cannot go: through it come the river, the far bank and the sky, and the triangle is built to open there. Below that the test gives. The fourteen bathers come from a repertoire the painter had used for thirty years, the strider, the kneeler, the one drying her hair, the one on her front, and the London canvas holds the same arch with fewer. Take one figure from either group and the triangle stands. The fruit and the dog are an enigma more than a requirement. The scale is compelled: this was to be the museum picture. The architecture is necessary, its population permitted, and the unfinished parts cannot be tested at all.
Albrecht Dürer · Visual art
8.8 · Tier IV
The subtractive test is hard to run on a plate whose subject is a heap of things unused. No class of object can go without loss. Take away the dog and the torpor loses its body; take away the scales, the hourglass and the bell and the stalled figure loses the measure of time running past her; take away the square and the plate loses its counter-charm, the square of Jupiter set against Saturn. The idle compasses are the hinge, and every tool on the floor repeats them. The members of each class give: the plane, the nails and the crucible could be other tools. Necessary in its argument, assembled in its inventory.
Virgil · Literature
8.8 · Tier IV
Read as a book, almost nothing can go. Remove the first poem and the book loses the dispossession every later poem is read against; remove the ninth and the answer to the first is lost; remove the tenth and the book has no close, no turn from pastoral, “surgamus”, let us rise (10.75). The fourth must be there for the sixth and tenth to read as they do. What holds the axis lowest but one is the contests. In the third and seventh poems the exchanges run in matched couplets or quatrains, and many could be dropped or reordered with the knowledge little changed; the catalogue of gifts in the second and the refrains of the eighth are similar. The frame needs a contest, not every stanza in it: perhaps a sixth of the lines are ornament.
Li Bai · Literature
8.8 · Tier IV
Subtract and see. At its height the body passes the test as few lyric bodies do. “Sitting Alone on Jingting Mountain” is twenty characters with none repeated: the birds go, the cloud goes, and what remains is “相看兩不厭，只有敬亭山”
(looking at each other, never tired of it: only Jingting Mountain). Take out a line and the emptying cannot happen. “Quiet Night Thought” turns on two motions, the head raised to the moon and lowered to home, and holds nothing else. The long songs are necessary differently: Jiang jin jiu is additive by design, the cup refilled, and its accumulation is its argument. What holds the axis lowest but one is the body as a whole: a thousand poems, among them many farewells, drinking poems and poems to patrons that repeat the figures of the best (the moon, the cup, the white hair, the drifting cloud) without needing to exist. The core is necessary; the body is not.
Pedro Calderón de la Barca · Literature
8.8 · Tier IV
The spine is subtractively tight. Remove the first jornada’s tower and the palace test has no meaning; remove the return to the tower and the third jornada’s restraint is unearned; remove Clotaldo’s recognition of the sword and Rosaura’s honour plot never touches the prince’s. The parts the play could most nearly lose come from the form, not the argument: the Astolfo and Estrella courtship of the first jornada, dynastic exposition with gallantry laid on; Rosaura’s long narrative to Segismundo in the third, which retells what the audience half knows; some of Clarín’s business before his death. The subplot is the main plot’s mirror and is carried as design, but not every scene of it is required, and that holds the axis at 8.4.
Stendhal · Literature
8.8 · Tier IV
The spine is required end to end: the sawmill, the tutor’s post, the seminary, the secretary’s desk, the shot, the cell. Each station is a rung, and the second book answers the first, two women, two ladders, two windows. Remove Besançon and Julien reaches Paris without the black coat that is the book’s title and argument. What holds the axis among the lowest is the middle of the second book: the secret note and the conspirators’ meeting, and the long campaign of love letters copied from Korasoff and sent to Mme de Fervaques, which make their point several times over. Against them the end is compressed almost to ellipsis: the shot, the trial and the execution take a fraction of the space the letters take. Necessity is high in the frame and lower in the middle.
Geoffrey Chaucer · Literature
8.8 · Tier IV
The spine passes the subtractive test. Remove Pandarus’s long work in Books II and III and the love has no world; remove the Trojan parliament that trades Criseyde for Antenor and the fall has no cause outside the lovers; remove the ten days on the walls in Book V and the betrayal is a report, not an experience. Against Boccaccio the scale is compelled: the added third makes Criseyde a mind and Pandarus a man. What holds the axis at its lowest is what could go. The courtship of Book II is one movement told three ways; Pandarus’s proverbs pile beyond their wit; the soliloquy on predestination outruns its scene; and the close stacks five endings where three would do.
Rashtrakuta, under Krishna I · Architecture
8.8 · Tier IV
Run the subtractive test, which the method answers in its own terms: every element is what was left, so nothing was added that could now be taken away. The court is compelled, since a temple freed from the rock needs the void that frees it. The plinth lifts the sanctum back toward the level of the hill the block was cut from, so worship climbs from the pit to the height. The bridges are compelled by freedom itself: once shrine and temple stand apart, the upper levels need a crossing, and it is left in the rock. What yields: courses, cornices, roof storeys and false pillars are required by the masonry model, not by the rock, and the periphery is ordered more than required.
Plato · Literature
8.8 · Tier IV
Subtract and see what goes. The three conversations are a ladder, and each rung is required: every interlocutor takes up the position the last was ashamed to hold. Gorgias will not say that the orator may be ignorant of justice; Polus says Gorgias was shamed into it (461b); Callicles says Polus was shamed in turn (482c to e), and states the doctrine naked. Take one away and the ladder breaks; the catalogue of Athenian statesmen (515c to 519d) is required too. What holds the axis below the dialogue’s other figures is length: the proof that punishment benefits the wrongdoer, run through the analogy of medicine two and three times (476a to 479e), and the second half of Socrates’ monologue, rehearsing conclusions (506c to 509c). A twentieth or more could go without loss of argument.
Anonymous · Architecture
8.8 · Tier IV
Judged on purpose, structure and site, and much is compelled by the rock. A church on the summit needs a level, so the crypts exist, as massive as the arms they carry; the Great Pillars are as thick as the choir above them demands. The Merveille is heavy below and light above because it hangs on a slope, and the street climbs because the rock does. What holds the axis lowest is the accretion itself: the classical west front could go without loss to what the building says, the truncated nave is a remnant rather than a requirement, and the lodgings and the fortified entrance are ordered by need, not by the governing idea. The parts are compelled; the sum is assembled.
Olivier Messiaen · Music
8.8 · Tier IV
The architecture resists the subtractive test. Eight is seven and eternity; two Angel movements frame the whole; a Praise closes each half; the Abîme alone is the centre of the first half and the unison of the trumpets the centre of the second. Remove the first movement and there is no time to end; remove the sixth and the seventh trumpet never sounds. The test finds give in three places. The Intermède is, by the composer’s own account, of more external character; the two Louanges existed before the quartet, for other instruments, so the plan was fitted to them; and the Fouillis alternates its blocks past what the argument needs. Length is not charged.
Tintoretto · Visual art
8.8 · Tier IV
Run the subtractive test figure by figure across a wall twelve metres wide. The centre resists it entirely: Christ on the raised cross, the ladder and the man reaching down with the sponge, the mourners at the foot, the one vertical the whole wall turns on. The thieves cannot go: one hauled upright on ropes, one still on the ground, they put the execution into time, three crosses at three stages of one act, and without them the centre is an icon rather than an event. The dicers stay, since the world’s indifference to what it is doing is half the meaning. What yields is the outer crowd: horsemen at the edges, onlookers in the middle distance, the far architecture, permitted by the width rather than compelled by the argument. The scale is compelled by the room; the population is not wholly.
Umayyad, under Abd al-Rahman I · Architecture
8.8 · Tier IV
Judged on plan and structure, under purpose and site. Within the module the parts are compelled. The reused columns were short, and the hall needed height and a roof carried on gutters; so a pier is set on each column, the lower horseshoe arch braces column to column, and the upper round arch carries the wall that bears the gutter. Take away either tier and the system fails. What resists is the hypostyle’s nature: a field of equal aisles is extensible by design, and three of the four campaigns are that extension. A growing congregation compelled the growth, but the form permits the scale rather than argues it; and the last eight aisles, forced east by the river, push the mihrab off the centre of the hall.
Wolfgang Amadeus Mozart · Music
8.8 · Tier IV
The two paths require each other. Tamino seeks wisdom through trial; Papageno, given the same trials, wants a wife, wine and sleep, fails them, and is rewarded anyway. Cut either and the other is left a thesis. The trials are required by the love: Tamino’s silence, which Pamina takes for indifference, produces “Ach, ich fühl’s”, and her despair produces the Boys’ rescue in the second finale. The overture’s three chords return before the trials as the work’s signal. What holds the axis here is give. Act II is a chain of episodes: the priests’ duet against women, the Ladies’ second quintet, Monostatos’s second attempt on Pamina, the old woman who is Papagena, and dialogue the tradition cuts with little loss. Necessity is strongest in the two finales.
Sophocles · Literature
8.8 · Tier IV
The first three fifths are as tight as anything in Greek drama. Every scene closes a door on Ajax: Athena’s display ends his honour, the opened tent ends his concealment, Tecmessa’s plea ends his last argument for living, the son takes the shield and with it the future, and the speech on time ends the chorus’s watch. Nothing can be lifted out. The test bites in the last part. The burial quarrel is required, since the play asks what a man like this is owed and only his enemies can put the question. But it is put twice: Menelaus and then Agamemnon make the same case in the same terms, and Teucer answers both in kind. One of the two scenes could be compressed without the argument losing a step.
Anonymous (Neolithic and Bronze Age) · Architecture
8.8 · Tier IV
Run the subtractive test on the sarsen monument and almost nothing yields. Take away the lintels and the circle is a ring of posts; with them it is one raised horizon, closed on itself. Take away the horseshoe and the axis has no frame and no direction; close its mouth and the north-east, where the midsummer sun rises and the Avenue arrives, is not singled out. The site compels the line: the Avenue begins on chalk ridges that lie on the solstitial axis. What yields is the whole across fifteen centuries: bluestones set, taken up and reset, Aubrey Holes, Station Stones and outlying stones from different conceptions, and no recorded use to show each part required.
Johann Sebastian Bach · Music
8.8 · Tier IV
The subtractive test cuts two ways. At the level of the plan nothing can go: the book’s claim is every key, so the loss of any pair breaks it, and the order, each tonic once, major before minor, rising by semitone, admits no substitute. At the level of the pieces much could be exchanged without loss to the whole. A different E minor prelude or F major fugue would serve the plan as well, and several preludes began as shorter teaching pieces for Wilhelm Friedemann Bach and were enlarged to fill their places. Within the pieces necessity is high, and the economy of the C major fugue is strict. But the plan requires a piece in each slot, not this piece.
Thomas Mann · Literature
8.8 · Tier IV
Length is not a cost; the question is whether the parts are required, and most are. The decline needs four generations to be shown as a decline rather than a misfortune, and its pace is the slow pace of a family’s time: dinners, christenings, funerals and entries in the family book. Tony’s two failed marriages, to Grünlich and to Permaneder, are required twice over, as comedy and as the firm’s losses, since each costs the family a dowry and its name. Against the figure: the middle of the book is generous with set pieces that repeat a point already made; the lesser relations, the Gerhardt ladies, the cousins at Tony’s table, Clothilde’s appetite, are kept on a running joke; Christian’s afflictions are returned to more often than the argument requires; and some of the business with Hagenström and the senate election could lose a third without loss. Necessity is high and not complete.
Rainer Maria Rilke · Literature
8.7 · Tier IV
In the best poems the subtractive test finds no line to remove. “Der Panther” is three quatrains: the bars, the circling, and the image that enters the heart and dies there; none can go. The Torso turns on its last half line, and everything before it is needed to make the statue look back. But the unit is the book, and the book was made by accumulation over six years, by a method that produced poems in series: go and look, then make the thing. In the second part above all, the courtly portraits, some of the biblical pieces and several of the Paris townscapes read as exercises of the method; a score of them could go, and the book would still know what it knows. The two Apollos and the closing Buddha give the whole an armature, not an argument that compels its scale.
Sylvia Plath · Literature
8.7 · Tier IV
Taken poem by poem, the subtractive test finds almost nothing to take. “Edge” in ten couplets has no idle line. “Lady Lazarus” moves from the joke of “I have done it again. / One year in every ten / I manage it” through the crowd to the closing threat, and every turn is load-bearing. “Morning Song” makes the birth, the estrangement and the waking to the cry in eighteen lines. Compression is the book’s strongest claim. What lowers the axis is the book as a book: assembled by another hand after the author’s death, its shape is partly an editor’s, and no whole can be said to require each part. Some pieces are slighter, “Years”, “Totem”, “The Munich Mannequins”, and the late poems return to the moon, the hook, red and white with lessening force.
Pyotr Ilyich Tchaikovsky · Music
8.7 · Tier IV
The large plan resists the subtractive test. The march must stand third, at full force, for the finale to answer it; remove it and the lament answers nothing. The waltz must be in five, a dance that cannot quite be danced, between storm and victory. The opening bassoon and the closing basses lie in the same dark register, and each requires the other. The give is in the surface. Tchaikovsky builds by sequence and repetition: the first movement’s development drives its material up by repeated steps, the march restates its theme many times with growing orchestration, and the recapitulation of the second theme is long for what it adds. Length is not charged; repetition the argument does not need is.
Samuel Beckett · Literature
8.7 · Tier IV
The plan is announced, and it is the whole of the book: Malone will pass the time before death by telling himself stories and then making an inventory, and when the plan is done he will be done. Every part answers to it. The present-state passages are needed because the dying is the plot; the stories, because they are how the dying is borne; their failures, because the failure of the stories is what the book discloses. The close is compelled. What holds the axis here is the Lambert stretch: its tedium is meant, and Malone says so, “What tedium”, but the joke of a narrator bored by his own fiction is made early, and the farm pages run past the point where it adds a turn, as do parts of Macmann on the bench. Perhaps a tenth of the book is permitted rather than compelled.
Béla Tarr · Film
8.7 · Tier IV
Judged on structure, since length is not in itself a cost, and the subtractive test bites less than seven hours suggest. The overlapping chapters are required: the bells Futaki hears at dawn, the Doctor’s watching, Estike at the bar window and the dance inside are one night seen from four places, and the claim that each life is seen and not helped depends on seeing it four times. Estike’s chapter is the hinge, without which the speech over her body has nothing to turn into money. The police office and the clerks are required to show what Irimiás is. What gives is inside the takes: the drunken tango and the accordion run past their point, and the walk into the wind is held beyond what it knows.
Georges Seurat · Visual art
8.7 · Tier IV
Judged on the configuration. The frame of the picture cannot go: the long diagonal of the shadow across the foreground, the light bank beyond it, the river at the left and the trees standing like columns. Certain figures are required. The couple in profile at the right are the picture’s façade, the bustle and the top hat its emblems, the monkey their comment. The man lying at the left balances them and belongs to another class. The mother and the girl in white at the centre are the one frontal pair, the axis the crowd turns on. The woman fishing at the river’s edge answers the couple. Beyond these the test gives: in the middle distance figures could be moved or taken away and the composition would rebalance, as the studies show it did more than once. The scale is compelled, a museum picture of a public. The armature and a dozen figures are necessary; the population is permitted.
Aeschylus · Literature
8.7 · Tier IV
Remove any of the four movements and the play fails. The waiting is required because the audience knows what the elders do not; the Messenger, because the news must come as narrative, not as spectacle; Darius, because only the father can name the cause; and Xerxes must come at last, in rags, because the body of the king is where the defeat is finally received. That spine is iron. What holds the axis down are the catalogues: the parodos, the Messenger’s roll of the dead and the closing lament each list Persian names, and the list of kings in Darius’ scene repeats what the ode after it says better. The names are a dirge, and the roll is the defeat; but three rolls where two would serve, and a recited dynasty, leave the play more subtractable than the Oresteia. Some of it may be interpolation; the text is scored as transmitted.
Claudio Monteverdi · Music
8.7 · Tier IV
The subtractive test meets resistance at the centre and gives at the edges. The Messenger cannot be cut: Orfeo’s strophic joy in Act II exists so that “Ahi caso acerbo” can break it, and the wedding of Act I exists so that the loss has weight. “Possente spirto” is the myth’s act performed, the reason the opera exists. The give is in three places. Act I sets out the wedding beyond what the reversal needs. Act IV states the doubt that turns Orfeo in a few lines, so the decisive act is the thinnest. And Apollo’s descent can be removed, as the libretto printed at Mantua in 1607 shows: an ending that could be exchanged was not compelled.
Wassily Kandinsky · Visual art
8.7 · Tier IV
The subtractive test, on a surface of dozens of incidents. At the level of the whole it resists. Take away the dark, black-contoured ovoid a little left of centre, with its hot red-violet core, and nothing is left for the lines to be flung from: the field breaks in two. Take away the heavy dark lines across the left half and the swirl has no armature; take away the broad pale passages and the whole is mud. The long course of studies shows the large arrangement found, tested and fixed. What holds the axis is the parts: a hatched patch, a floating curl or a small disc could each be another of its kind without loss, and the crowding at the right edge reads as permitted rather than compelled.
Henry James · Literature
8.7 · Tier IV
The spine is required. Ralph’s request that his father enrich Isabel is the hinge of the whole: the fortune that should let her live as her imagination asks is what makes her prey, so the bequest, Madame Merle and Osmond are one mechanism and none can be lifted out. The suitors are needed too, since her refusals of Warburton and Goodwood define the freedom she then spends. What holds the axis is what could go without loss: part of the comedy of Henrietta Stackpole and Mr Bantling, which recurs past the point where it does work, in Henrietta’s European tour and the Paris chapters; some of the slow early Albany and London passages; and Ned Rosier’s courtship of Pansy, necessary in its consequence and long in its telling. None is idle in kind, but there is more of them than the argument compels.
Christopher Wren · Architecture
8.7 · Tier IV
Judged on structure, purpose and site. The dome is compelled at every layer: the inner shell is proportioned for the interior, the outer for the city, and the brick cone between them does the work neither shell can do, carrying the lantern’s weight to the drum. Light, structure and image are solved together. The broad crossing is compelled by the wish to gather a congregation under the dome. What yields: the upper storey of the side walls is a screen with nothing behind it but buttresses, required by appearance and not by structure or use. And the Latin-cross nave, compelled by the clergy’s demand for processional liturgy, meets the great central dome as two ideas reconciled rather than one.
Virginia Woolf · Literature
8.7 · Tier IV
The test is subtractive, and the design survives it. Remove the pageant and the day has no mirror; remove the Olivers and the pageant has no audience for its last scene; remove the interval in the barn and the book loses its proof that the audience goes on acting when the play stops. Even the cesspool of the opening is required, since the book begins and ends on what lies under the old earth. What holds the axis at the foot of the twelve, with Pressure on Tradition, is the state of the text. Woolf did not finish revising it, and it shows: Isa’s fragments of verse recur more often than they yield, some of the overheard chatter runs past its point, and Mrs Manresa’s part repeats one note without turning it. A tenth or two of the book is said twice, and that is charged, not excused by the circumstances of the death.
Horace · Literature
8.7 · Tier IV
Within the single ode the subtractive test rarely finds a cut. The Pyrrha ode, “Quis multa gracilis te puer in rosa”
“What slender boy, among many roses” (1.5), sets boy, girl and rose in the order of the scene itself and ends on the votive tablet of the shipwrecked man; nothing in its sixteen lines is idle. Across the body the test bites more. The present against death returns in near variations (1.4, 1.9, 1.11, 2.3, 2.14, 4.7, 4.12); several occasional odes, welcomes, small hymns and invitations, could go with little lost; and Book 4’s panegyric for Drusus and Tiberius (4.4, 4.14) is of doubtful necessity to the body. The argued order of the books holds the figure up: the frame, the opening run of metres, the Roman cycle.
Michelangelo Antonioni · Film
8.7 · Tier IV
Judged on structure. The design is subtractive in spirit: the film takes away its own plot and asks what remains. Without the long island movement the disappearance is an incident, not a hole; without the hours on the rocks, the storm and the hut, Claudia’s guilt has no ground. Without the slow lapse of the Sicilian search the forgetting cannot happen, because forgetting takes duration, and the length is compelled by it. The Taormina night answers the island. What gives is in the middle: the Messina crowd round a starlet, Giulia and the boy painter at the villa, and the visit to Patrizia’s house make points the film makes elsewhere. Perhaps a tenth of the running time illustrates rather than enacts.
Bruce Springsteen · Music
8.7 · Tier IV
Eight songs in under forty minutes, and the frame is compelled. Thunder Road must open, an invitation on a porch to leave by morning. Born to Run must open side two as the same call at full volume. Jungleland must close, the night ending in a death in the street, and Meeting Across the River is required as its hush, the small deal before the large elegy. Backstreets closes side one as the friendship the run will break. The test bites in the short middle of each side. Night restates the title track’s race from work to the road, with less. She’s the One is a desire song the sequence would survive losing, and Tenth Avenue Freeze-Out is a party the record could spare. What would go is little, and the frame would hold.
Federico García Lorca · Literature
8.7 · Tier IV
Subtract and see. The strongest poems leave little to take. Romance sonámbulo cannot lose its refrain, “Verde que te quiero verde”
(Green, how I want you green), because the refrain is the only thing in the poem that does not move; everything else, the wounded smuggler, the old man’s house, the drowned girl on the cistern, is a broken narrative the refrain holds. Romance de la luna, luna is all necessity: the moon comes to the forge, the child warns her, the gypsies come back to find him dead, and the poem stops. The order of the book argues too. What holds the axis: the three archangel poems are ornamental and could each lose a stanza without loss, and the deliberate gaps of the Don Pedro poem are partly a manner. A short book in which three or four of eighteen poems are slighter stops in the low eights.
John Milton · Literature
8.7 · Tier IV
The oldest charge against the play is Samuel Johnson’s: it has a beginning and an end and no middle, since nothing between the first scene and the last hastens or delays the catastrophe. The charge is half right. The outward plot does not move. But the visitations are the action: Manoa offers ransom and ease, despair dressed as rest; Dalila offers love and the bed, the old fault; Harapha offers contempt, which Samson answers by staking his strength on God again, the first turn outward; the Officer brings a summons first refused and then obeyed. Remove any one and the regeneration loses a step. What holds the axis down is in the parts: choral moralising that runs past the action, and a Harapha scene longer than its work.
Lorenzo Ghiberti · Visual art
8.7 · Tier IV
The test is subtractive, panel by panel and then across the doors. The ten fields run from the Creation to Solomon as a line through sacred history, and none could go without a gap in it: the Fall, the fratricide, the Flood and the covenant, the sacrifice of Abraham, the brothers’ blessing, Joseph’s forgiveness, the Law, the conquest, the king and the temple. The ten squares themselves replace the twenty-eight small fields of the earlier doors, and that choice is the argument for necessity: fewer and larger, so that each can hold a world. What yields is inside the panels. Several compress three to six episodes into one field, Adam and Eve, Joseph, Joshua, and in the crowds of the later panels some groups could be lost without loss of meaning. The frame is a second programme the narrative does not require. Required in its line, permitted in its fill.
Virginia Woolf · Literature
8.6 · Tier IV
The subtractive test mostly fails to find slack. The thesis, that “a woman must have money and a room of her own if she is to write fiction” (ch. 1), is shown step by step: the turf she may not walk on, the library she may not enter without a Fellow or a letter, the two meals, Mrs Seton’s thirteen children, the aunt’s legacy of five hundred a year from a fall from a horse in Bombay. The meals are not ornament; “One cannot think well, love well, sleep well, if one has not dined well” (ch. 1) is the thesis in small. What could go without loss: some of the satire of the Museum catalogue, a run of the fourth chapter’s survey that lists more than it needs, and the passage of Mr A and Mr B, which makes one point twice.
Francisco Goya · Visual art
8.6 · Tier IV
Judged figure by figure. The sleeper cannot go: he is the subject and the hinge. The block cannot go: it carries the title as part of the image, the squared plinth on which reason has laid its head. The owl holding out the drawing tool cannot go: it is the turn of the plate, the night handing the sleeping artist his instrument, the point at which the monsters become the work. The lynx cannot go, the one creature awake and looking out, which binds the viewer into the scene; nor the darkness, where the creatures are made. What yields is count and mass: the bats are a swarm, permitted rather than required, and the swarm could be smaller or larger without loss.
Ernest Hemingway · Literature
8.6 · Tier IV
The subtractive test finds the spine required and the margins not. The Nick stories make an arc that cannot lose a member: birth and a suicide in “Indian Camp”, the father humbled in “The Doctor and the Doctor’s Wife”, love broken off in “The End of Something” and talked over in “The Three-Day Blow”, the road and violence in “The Battler”, the wound in interchapter VI, and the return in “Big Two-Hearted River”. The interchapters cannot be taken out without making a different book: they set the private stories inside a century. “Soldier’s Home” and “Cat in the Rain” are required as the other halves of the same return and the same marriage. What holds the axis is the slighter matter: “Mr. and Mrs. Elliot” is a sneer more than a story, “My Old Man” is a borrowed vernacular, and “Out of Season” could go with little lost. A book of this length is charged for three pieces that could be lost.
Fritz Lang · Film
8.6 · Tier IV
Run the subtractive test. Elsie’s sequence cannot go: it is the crime the film never shows. The panic in the streets, where an old man is nearly lynched for speaking to a child, sets the city’s condition. The double conference is the film’s argument in its structure. The beggars’ watch is how the city catches him; the whistle and the chalked letter are how; the office building is the trap; the court is the reckoning. What gives: the procedural montage of fingerprints, maps, raids and searched lodgings runs longer than the argument needs, and the raid on the underworld bar plays a scene of comedy twice. The coda before the judge states in words what the court has already shown.
Jørn Utzon · Architecture
8.6 · Tier IV
Judged on structure, purpose and site. The podium resists the subtractive test: it is the stair, the public ground and the whole back of house, so everything that would otherwise stand on the skyline goes underneath. The shells resist it more than their critics allow: each group rises to its highest shell over the stage, so the roof’s section follows the theatre’s and the stage tower is absorbed, not hidden. The site compels the rest, for a point in a harbour is seen from all sides and from above, and the roof is the façade. What yields: the halls are separate from the shells, with large voids between, so the form is compelled by site and section more than by the rooms; and the restaurant group is ordered rather than required.
Jacopo Barozzi da Vignola and Giacomo della Porta · Architecture
8.6 · Tier IV
Judged on plan, structure and use. The governing decision resists the subtractive test: take away the aisles and the congregation is one body before one altar and in earshot of one pulpit, which is what a church for a preaching order is for. The chapels are pushed to the edge and linked so that private devotion never crosses the nave; the transepts are drawn back inside the rectangle so that the crossing gathers light without breaking the room. What yields is in the later work: the two transept altars, Pozzo’s above all, are larger and richer than the plan requires, the nineteenth-century marble adds weight without sense, and the front’s doubled pediments and crowded pilasters could be thinned.
Marvin Gaye · Music
8.6 · Tier IV
Nine tracks in about thirty-five minutes, and the segues complicate the subtractive test: the record is built to be heard as one span a side, so a track slight alone is often a passage. The frame is compelled. The title song must open, its party voices setting the street before the voice enters; Inner City Blues must close, its last minute returning the opening theme. What’s Happening Brother, the veteran home and out of work, and Flyin’ High, the addict, are each required. The test bites twice. God Is Love, under two minutes, restates the title song as a creed and could go with little loss beyond a link; Right On, the longest track by far, is permitted more than compelled.
Juan Bautista de Toledo and Juan de Herrera · Architecture
8.6 · Tier IV
Judged on purpose, structure and site. The programme compels the plan: a basilica at the centre because the house exists for the office of the dead and the king’s prayer; the monastery beside it because monks sing that office day and night; the palace behind the apse because the king will live as near the altar as a layman may; the college because the house must teach; the crypt under the altar because the founder will lie there. Remove any one and the argument fails. What yields is the grid itself: the courts multiply beyond what each function needs, and the long south and west fronts repeat a bay that no purpose specifies to that length.
Joseph Conrad · Literature
8.6 · Tier IV
The subtractive test finds the domestic plot whole. The mother’s cab ride to the almshouse removes the last person between Winnie and Verloc and gives Stevie his scene with the cabman’s horse; Stevie’s stay with Michaelis makes the label sewn into his coat, and the label is how Chief Inspector Heat traces the body to the shop. Mr Vladimir’s commission sets the engine going, and the Professor has the last word. The test bites in the official world. The Assistant Commissioner’s visits to Sir Ethelred and the comedy of Toodles carry the state’s indifference, which is half the subject, but they run longer than the argument needs, and his motive, the protection of Michaelis and of his wife’s patroness, is a thin thread for so much weight. Winnie and Ossipon on the boat train are required, and dilated.
James Baldwin · Literature
8.6 · Tier IV
The test is subtractive, and the frame passes it. Remove Florence’s prayer and the book loses its witness: she alone holds Deborah’s letter, the proof that Royal was Gabriel’s son, and her threat to use it on the walk home turns the past into a weapon in the present. Remove Elizabeth’s prayer and John’s paternity, Richard’s arrest and death, and the reason Gabriel cannot love the boy all vanish. Remove “The Seventh Day” and the night has no ground. What holds the axis below the higher figures is Gabriel’s prayer, which in places repeats its turn, lust, repentance, the claim of election, more than its argument needs, and a few pages of Part One that set the church scene at length before the action.
Kurt Vonnegut · Literature
8.6 · Tier IV
The test is subtractive, and the book is compressed enough that little yields to it; much that looks removable bears load. The first chapter, the author’s confession of the years in which he failed to write about Dresden, must stay: it sets the terms on which every later scene is judged and gives the subtitle its meaning. The Tralfamadorian chapters must stay, since they supply the law of time the book both tests and suspects. The refrain is necessary in the strict sense: a death without “So it goes” would read as an exception. What could go with little loss is some of Billy’s life in Ilium, the Lions Club and parts of the Valencia material, the longer summaries of Kilgore Trout’s plots, and the party scene with Maggie White, which repeat a joke the book has already made. Perhaps a twentieth of the whole is permitted rather than compelled.
John Milton · Literature
8.6 · Tier IV
The poem is about the shortest Milton could make a trial of this kind: one encounter, two voices, a few days at the end of a fast. Nearly every part survives the subtractive test. Mary’s meditation and the disciples’ waiting in Book II are not ornament: they show the human world that waits on the trial without knowing it, and set the domestic scale to which the last line returns. Belial’s counsel of women, which Satan scorns, defines the tempter by what he knows will not work. The banquet, an addition to scripture, earns its place. What holds the axis down is the panoramas: the Parthian host in Book III and Rome in Book IV run on past a point made before the catalogue ends.
Gislebertus · Visual art
8.6 · Tier IV
Judged part by part. The Christ cannot go: everything in the field is measured from him, and his frontal stillness is the law the agitated halves answer. The scale cannot go: the judgment is a weighing, and the beam with an angel and a devil leaning on it is the hinge of the right half. The rising dead on the lintel cannot go, for they are the viewer, small, at the threshold, sorted already by which way they walk. The hands closing on the head cannot go; the terror is remembered by them. What yields lies in the upper left, where the ranks of apostles and the arcaded city are rhythmic filler, and in the repeated angels at the edges of the mandorla. The scale of the portal is compelled by the door; the density inside it is partly permitted.
Maya · Architecture
8.6 · Tier IV
Judged on purpose, structure and site. Little yields to the subtractive test. The square and its four stairs are the four quarters, with the summit as their centre; the nine terraces carry the year’s eighteen divisions only because the stair splits each one; the steps and the platform close the count of days. The temple door turns to the north stair, the one stair with serpent heads, so the single asymmetry is purpose. The structure is compelled too: rubble behind a veneer must be terraced to stand at this slope. What holds it from the top: much of the programme is count, which other arrangements could meet, and the calendar requires the terraces more than the use does; a solid mound with a small room on top asks less of necessity than a building that must hold people within.
Martin Scorsese · Film
8.6 · Tier IV
Judged on the structure and the cut. All eight movements are required, and the doubling makes them so: the courtship of Betsy is the failed approach that the rescue of Iris answers, and the rally is the act the massacre replaces. Much that looks removable is load-bearing. The passenger played by Scorsese, describing what a .44 Magnum would do to his wife, gives Travis his own violence in another man’s mouth, and the gun purchase follows. The Wizard’s talk of a man becoming his job is the one counsel Travis receives, and it is useless. What gives is weighed: the office comedy between Tom and Betsy runs past its function, the drivers’ café scenes repeat, and the diary sometimes says what the picture has shown.
Tibetan, under the Fifth Dalai Lama · Architecture
8.6 · Tier IV
Judged on purpose, structure and site. The mass is compelled by the hill: the palace does not stand on Marpo Ri so much as continue it, the battered walls taking up the slope of the rock and the storeys stepping back as the hill narrows. The batter is compelled by material and ground, walls of earth and stone thick at the foot in a seismic valley. The two-part plan is compelled by the purpose, the rule of a man at once head of state and incarnate lama. What yields to the subtractive test is the interior: the Red Palace is an aggregate of chapels, halls and shrines, many of which could go without loss, and its tomb chapels were added as the lineage required, not as the form did.
The Beatles · Music
8.6 · Tier IV
Two sides, two tests, and the record passes most of both. The long passage of side two, from “You Never Give Me Your Money” to “The End”, is built of fragments that could not stand alone and are required where they are: “Golden Slumbers” runs into “Carry That Weight”, which brings back the theme of “You Never Give Me Your Money”, and “The End” answers the whole with its single couplet. The fragments exist only as passage, so the part that most invites cutting resists it. “Here Comes the Sun” and “Because” open the side as morning and stillness. On side one, “Come Together”, “Something” and “I Want You” are required. What holds the figure: “Maxwell’s Silver Hammer” and “Octopus’s Garden” are passengers, and “Her Majesty” is a joke left on the tape.
Agesander, Athenodoros and Polydorus of Rhodes (attributed) · Visual art
8.6 · Tier IV
The subtractive test, part by part. The father cannot go: his torso is the work. The younger son, already bitten and sinking, cannot go: he is what the father fails to save, and the second serpent’s coil passes through him to the father. The serpents are the structure, not decoration; they bind three bodies into one block. What yields is the elder son. He stands at the right edge with his leg still being wound, his head turned to the father, half outside the action, and the group reads whole without him. The sons’ scale, adult bodies at two thirds of the father’s size, is a convention the eye accepts, not a necessity, and the altar is barely legible as an altar.
Otto Dix · Visual art
8.6 · Tier IV
Judged panel by panel, the structure resists subtraction. Take away the left wing and the war has no beginning: the dead of the centre are there with no account of how men came to them, and the march into the mist is the only image of the living whole. Take away the right wing and the work holds no act of a living man, no carrying out. Take away the predella and the cycle does not close: night, sleep and the grave in one image are the last word, set in the altar’s lowest place. The centre cannot go. What yields is inside the centre: its wreckage, entrails, wire and timber are part catalogue, and several of its corpses could be fewer without loss.
Don DeLillo · Literature
8.6 · Tier IV
The test is subtractive, and Part I looks most open to it: a run of set pieces, the most photographed barn in America, the Treadwells lost for days in the Mid-Village Mall, the German lessons, the double lecture on Hitler and Elvis. Each sets a law the later parts apply. The barn sets the law of mediated seeing that the toxic event turns on a death; the lecture sets the crowd and the mother as shields against dying, which Part III tests; the Treadwells lost in the mall are the first people lost inside consumption. The density is itself the argument, since the title names an ambience and the book must sound like one. Part II is required at every stage, and Part III carries out the law Part I states. What holds the axis is that a few episodes of Part I, and the length of Murray’s riffs, could go without the knowledge changing.
Luis Buñuel · Film
8.6 · Tier IV
A film built on repetition puts the subtractive test to the law before the members, and the law is required: a meal convened, a meal prevented, repeated until repetition becomes the meaning. That meaning needs its count. One failed dinner is an anecdote; a run of them is an argument, and the run escalates, from the calendar and a death to desire, the army, the police and the gunmen. The wrong night, the stage, Acosta at his refrigerator and the road as refrain are load-bearing. What holds the axis where it stands is that the give is confined to the told stories. The lieutenant’s ghost and the sergeant’s dream are heard by the guests rather than happening to them, and others could stand in their place, as The Phantom of Liberty (1974) went on to show; every interruption that happens to the six is a step in the escalation, and none could go.
R.E.M. · Music
8.6 · Tier IV
Twelve tracks in about forty-nine minutes, and ten of them pass the subtractive test. Drive must open: a dark, low song that sets the record’s light before the band breaks in. Try Not to Breathe, Everybody Hurts and Sweetness Follows are the core, three ways of facing an end, and Man on the Moon, Nightswimming and Find the River make the last turn, from doubt to memory to passage. The instrumental is a breath before Sweetness Follows and earns its two minutes. The test bites twice, at about a sixth of the running time: Star Me Kitten, the slightest song, goes without loss, and Ignoreland, a tirade in a muddier mix, goes with gain. The Sidewinder Sleeps Tonite and Monty Got a Raw Deal are lighter still.
My Bloody Valentine · Music
8.6 · Tier IV
Inside the sound, necessity is near total: take one layer out of To Here Knows When and it becomes another track, because its meaning is that the layers cannot be separated. Across the album the subtractive test finds something, and less than a first hearing suggests. Touched, under a minute of bent tone, is the hinge into To Here Knows When, and little would be lost without it. What You Want restates the attack and lead figure of Only Shallow and I Only Said without a law of its own, and Come in Alone is close kin to both. The frame holds, an assault at the start and a dance at the close. One removable track and two close variations are what hold the figure where it stands.
Franz Schubert · Music
8.6 · Tier IV
The subtractive test meets resistance in the first movement’s frame and in the Andante. The trill cannot go: it is the only event in seven bars of stillness, and it returns at the structural joints. The first-ending bars are the clearest case of necessity in the work: music written only to lead back into the repeat, carrying the trill at fortissimo, so that to cut the repeat is to cut music that exists nowhere else. The Andante is tight, and its return is required by the C sharp minor it left. The give is real elsewhere: the development’s sequences run on, the finale’s refrain returns more often than its argument needs, and the Scherzo, perfect and small, could be exchanged for another without the whole knowing it. Length is not charged; redundancy is.
Werner Herzog · Film
8.5 · Tier IV
The subtractive test bites less than one expects of a film made so loosely. Each station is a stage of one subtraction: the column is split, the party loses a raft, the leader is deposed, the puppet emperor dies, the women go, the horses go, the men go. Remove the coronation and the film loses its account of legitimacy; remove the man in the canoe and it loses its one face of the people being conquered; remove the ship in the tree and it loses the sign that the delirium is shared. What gives: the drift of the middle third repeats its effect more than it advances it, two or three skirmishes on the bank do the same work, and the trial of Ursúa runs longer than its point needs.
Graham Greene · Literature
8.5 · Tier IV
The test is subtractive, and the spine resists it. A hunted priest, a lieutenant who hunts him, a betrayer, a border, a return, a death: none of this can go. The chapters of onlookers look removable and are not. Mr Tench the dentist, who opens the book and closes the execution, is the godless world in which the priest dies without witnesses who understand it. The Fellows on their banana station give Coral, the child who hides the priest and asks him the one practical question about faith he cannot answer. The pious mother reading the life of the boy martyr Juan supplies the false hagiography against which the true death is measured. What holds the axis below the top: the Fellows marriage is sketched more than it needs, Mrs Fellows a figure of comic dread repeated rather than deepened, and the stay with the Lehrs runs a little long for what it adds.
Giorgione · Visual art
8.5 · Tier IV
The subtractive test on a picture whose subject is unknown. The storm cannot go: it is the event that binds the field and the one moment of time in a still scene, and the first witness named the picture by it. The woman and child cannot go, nor the man: the picture is the gap between them, with the stream running down the middle. The town is the world the storm falls on. The broken columns are the hard case, the most insistent sign and the least explained; the plinth could be taken away without the composition failing, though the meaning would thin. What holds the axis well below the top is the figure opposite the mother, which the painter is reported to have changed during the making: necessary at the level of the field, provisional at the level of its people.
Ife · Visual art
8.5 · Tier IV
Put to a single head, the subtractive test finds almost nothing to remove. There is no narrative, no attribute and no ornament that is not structural: the face, the lids, the striations, the holes along the hairline that held hair, a veil or a crown of beads. Each head states the person and the office at once, and in the striated Wunmonije heads and the Obalufon mask the economy is absolute. The caution is the unit. The body is not a designed sequence but an assemblage of related castings, gathered by a building trench and by palace keeping, and asked of the body the test has an honest answer: one head could go, with loss of range but not of argument. That holds the figure in the eights, level with Laocoön and the Riace Bronzes at 8.4.
T. S. Eliot · Literature
8.5 · Tier IV
The subtractive test bites less than one would expect from a poem some of whose parts were first published apart. The repetitions that look like padding are the argument: “Because I do not hope to turn again” (I), turned over line after line, is a will that cannot will its turn, circling. The third section cannot be cut, nor the fourth, nor the close of the sixth, which answers the first. What can be questioned is the second: the leopards and the singing bones are among the best things in the poem, but the section first stood alone, and its place in the argument is made by assembly as much as by necessity. And the fifth section’s long run on the word goes on a few lines past its point. Idle nowhere; compelled not in every stretch.
Ludwig Mies van der Rohe · Architecture
8.5 · Tier IV
Judged on plan, structure, purpose and site, the subtractive test bites hard. Take away the plaza and the shaft cannot rise straight under the zoning it was built under, and it loses the distance from which it is read whole. Take away the pools and the axis has no measure; take away the blinds held to three positions and the face breaks into a thousand private decisions. The lobby, glazed and floored with the plaza’s granite, is required by the plaza. What yields is the famous detail: the bronze I-sections carry nothing, required by the building’s argument but not by its structure. The rear spine and wings are compelled by floor area more than by the law of the front, and an office floor compels almost nothing.
Frank Lloyd Wright · Architecture
8.5 · Tier IV
Judged on purpose, structure and site. The lot compels the plan: long, narrow and on a corner, it lays the house’s length along 58th Street with the service block behind. Privacy in a city compels the section: the living floor raised a storey and walled by parapets and planters, so that from within one looks out over the street and from the pavement sees roofs and shadow, not rooms. The eaves are required by the glass under them. Take away the chimney mass and the living floor loses its only division and its centre. What resists the test: the cantilevers run beyond what shade requires, a statement of the horizontal on a lot with no prairie; the hidden entrance is a choice the site permits, not one it demands; and the prows are figure as much as use.
Andrea Palladio · Architecture
8.5 · Tier IV
Judged on purpose, structure and site. Each part is required by one of three users. The nave and aisles take the lay congregation; the domed crossing and the broad presbytery give the state its room, so that the doge’s annual visit has a place before the altar; the screen of columns lets the monks sing in their own choir behind the altar while they stay seen and heard, and a Benedictine community at the hours requires the long choir. Vaults lit high above aisles require the thermal windows. Outside, the site requires the front: a church seen across open water must address the city. What resists the subtractive test: the front’s giant pedestals, raised higher than the interior asks, read as a means of making the order fit; and the choir runs longer than the view through the screen needs.
Kamāl ud-Dīn Behzād · Visual art
8.5 · Tier IV
Judged on the building, because the building is the work. The palace cannot be reduced: its closed doors are the trap, its rising stair is the pursuit, its stacked chambers are the depth of the enclosure Yusuf has been led into. Take away the stair and there is no flight; open one door and there is no miracle to come. The two figures cannot go, and their placement high in the structure, far from the ground door, is the plot. What yields is the ornament’s extent. The tile patterns, gilded friezes and panels of the façade are each made to the same perfection, and some could be simplified without loss; the courtly profusion is required by a palace built to seduce only up to a point.
Karl Friedrich Schinkel · Architecture
8.5 · Tier IV
Judged on purpose, structure and site. The long front is compelled by the site: a building facing a palace across a square could not answer with a temple front without claiming the palace’s centre, so it answers with a stoa, as long as the square’s north side asks. The two courts are compelled by light, since a deep block of galleries needs light on both faces. The rotunda is compelled by sequence, one room between the city and the collections. Take away the stair hall and the museum loses its one point of return to the city. What resists the test: the attic exists to hide the dome, a decision of decorum rather than need; the painting galleries needed screen walls the plan had not provided for; and eighteen columns are more than any use of the portico requires.
Luis Buñuel · Film
8.5 · Tier IV
Subtract, and the film mostly resists. The first movement cannot go: Don Jaime’s fetish, the drugging and the hanging bind Viridiana to the estate by guilt and turn her vocation outward into charity. The feast cannot go, since it is the reckoning the charity was built for. The small episodes bear weight too. Viridiana recoils from the cow’s teat, the body she refuses; she lays ashes in her uncle’s bed in her sleep, penance and death foretold; Rita skips with the rope beneath the tree. The give is in Jorge’s world. Lucía is a sketch who leaves when the film no longer needs her, and the dog, exact as an argument, is detachable as a parable.
Guru Arjan; rebuilt and gilded under Maharaja Ranjit Singh · Architecture
8.5 · Tier IV
Run the subtractive test on the ensemble, where it bites hardest, and the ensemble resists. Take away the pool and the shrine is a pavilion among buildings: the water is what separates the sanctuary from the town while leaving it in full view. Take away the causeway and there is no approach; double it and the single path to the word is lost. The four doors are compelled by the claim that the house is open on every side, the descent from the town by the same claim turned to humility, and the book at the centre is the reason for the whole. What yields is above the ground floor: the upper storeys, the kiosks and the dome are a crown of rank and devotion more than a requirement of use.
Carol Reed · Film
8.5 · Tier IV
Run the subtractive test and the spine holds. The first funeral is required by the last. The porter’s account of a third man is the hinge of the investigation, and his murder turns inquiry into danger. The penicillin evidence must come before the doorway, so that the most charming entrance in the film is that of a man known to have harmed children. The wheel is where the friendship is tested and refused; Anna’s refusal of Holly’s bargain prepares the last shot. What gives is the comedy. The lecture and its questions about James Joyce, the parrot that bites Holly and the taxi ride he takes for an abduction each make one point, that Holly is out of his depth. The tone needs some of it, not all.
Rembrandt van Rijn · Visual art
8.5 · Tier IV
Judged on structure alone. The two officers cannot go: the order passing from captain to lieutenant is the event. The musket drill cannot go: loading, firing and clearing make a company in motion. The girl in gold carries the emblem into the light; the flag, the drum and the arch give the march its sound and its doorway. What yields is the rear. The heads massed under the gateway, some no more than a face between two hats, are there because their owners belonged to the company and paid; a third could be thinned with no loss of argument. The portrait contract, not the action, compels them. The trimming is not counted.
David Bowie · Music
8.5 · Tier IV
Eleven tracks in about thirty-eight minutes, and the fragmentary method changes the subtractive test: the songs are cut short by design, so brevity is not slack. Speed of Life must open, an instrumental that sets the record going before any voice is ready. Sound and Vision is the hinge of side one, a song about waiting to speak that delays its own vocal. A New Career in a New Town is the bridge the two sides require; Warszawa is the record’s centre of gravity, and Subterraneans its compelled end. The test bites twice. What in the World is the busiest and least necessary of the songs, and Weeping Wall restates side two’s mode in a thinner palette. One soft track on each side holds the figure.
Carlo Scarpa · Architecture
8.5 · Tier IV
Judged on plan, route and surface, under purpose and site. In the plan almost nothing can go. The propylaeum is the only way in from the village dead, and its two circles make the first statement of the pair. The fork divides the place for contemplation, the water, from the place of burial, the arch. The arcosolium is the couple’s only roof, its low span the size of an act of sheltering. The chapel stands apart in water because it serves the rite on other terms. On the surface the test bites: the stepped moulding recurs at every edge, and part of the quantity of inlay, pin and fitting is a manner that could be thinned without a felt loss.
Max Beckmann · Visual art
8.5 · Tier IV
The test is subtractive, and the triptych answers it first in its frame. Take away either wing and the centre loses what it departs from: the boat becomes a regatta. Take away the centre and the wings are a chamber of horrors with no outside. The three panels are required by one another, and that requirement is the work’s argument. The centre is bare and close to necessity: king, queen, child, hooded figure, net, sea. Inside the wings the test gives somewhat. The crowding is meaning, no room and no exit, but particular figures and props could be altered or one removed and the room would stand with less evidence rather than broken. The wings’ symbolism is partly additive, a private lexicon laid in piece by piece.
Pierre Chareau and Bernard Bijvoet · Architecture
8.5 · Tier IV
Judged on purpose, structure and site. The site compels the founding fact: the tenant of the top floor would not leave, so the house had to be a frame slid beneath an existing storey, and a frame of slender steel is the answer that leaves room below. A courtyard in a dense quarter, overlooked on all sides, compels the glass block: light without sight. The double programme compels the screens and the double stairs. Take away the pivoting screen at the foot of the main stair and the doctor’s patients walk into the family’s salon. What resists the test: cranked ventilators, swinging cupboards and fitted devices multiply past what the programme requires. The core is compelled; a margin of the fitting is permitted rather than required.
Talk Talk · Music
8.5 · Tier IV
Six pieces in about forty-three minutes, and the subtractive test is hard to apply, because what a hostile listener would remove is mostly silence, and the silence bears weight. Myrrhman must open: the record begins in room hiss and a hesitant guitar, and the sound has to be found before it can be used. Ascension Day must follow as the one violent piece, and its hard cut is the hinge of the whole. After the Flood and New Grass, the storm and the calm, each require the other, and Runeii drains the sound back toward the silence it came from. Little is idle. The test bites at Taphead, whose long quiet opening is permitted rather than compelled, and lightly in the middle of After the Flood.
Senenmut (attributed), under Hatshepsut · Architecture
8.5 · Tier IV
Judged on purpose, structure and site. The terraces are compelled by the cliff: a building that climbs into a bay of rock must step, and each step needs a retaining wall. The porticoes give those walls depth and shade and carry the reliefs; the ramps carry the procession, which is the building’s use, to the only place the axis can end, the sanctuary cut into the mountain. Cult and site require the side chapels: Hathor is the goddess of the western mountain, Anubis of the necropolis. What yields is repetition: the lower portico answers the middle in kind, and a bay more or fewer would cost little. The relief walls are required politically more than architecturally. Held below the Pantheon’s single compelled room, at 9.0.
Johann Sebastian Bach · Music
8.5 · Tier IV
The set resists the subtractive test at its largest scale. Remove the fifth suite and the work loses its one retuning and the one darkness held through a whole suite; remove the sixth and the rising plan loses the new instrument it points toward. Within each suite the six places are required: the Prelude sets the key on an instrument that cannot sustain a chord, and the dances then test it in different metres. Single movements resist, the fifth suite’s Sarabande and the fourth suite’s Prelude among them. The give is in three places: the second Menuet or Bourrée could often go with little loss, repeats double many dances, and the number six is a convention Bach shared with his solo violin works, not one the argument compels.
Johann Sebastian Bach · Music
8.5 · Tier IV
Inside each concerto the subtractive test meets resistance. The first movement of No. 3 is one figure passed among nine parts, and none could go; the opening canon of No. 6 is its whole argument; the harpsichord’s cadenza in No. 5 is the point of the concerto and not an ornament on it. The test finds give in three places. The order, two in F, two in G, then D and B flat, is a collection’s order: remove a concerto and the set is smaller, not broken. No. 1’s dances could go with less loss than any other stretch. And the two chords of No. 3’s Adagio are either the purest necessity in the set or a space left empty.
Akira Kurosawa · Film
8.5 · Tier IV
Most of the 162 minutes is required. The hunt and the three arrows set the whole argument in the first reel: a father who thinks unity can be bequeathed, a son who breaks the bundle over his knee to show that it can be broken. The two refusals are each needed, a humiliation by rank at the First Castle and a closed gate at the Second. The siege is the turn and cannot be cut, and Kaede’s revenge alone shows that the old king made the world that destroys him. The give is real and recurs: the neighbouring armies watch from the hills at length for a pay-off quickly disposed of; several of Kyoami’s songs repeat a point already made; and the last movement stacks its deaths at a pace that lets one or two feel scheduled.
Dmitri Shostakovich · Music
8.5 · Tier IV
The large plan is compelled by what the work has to say: a public symphony that must end in affirmation, with grief allowed only in the middle. Remove the Largo and the finale’s triumph has nothing to answer; remove the finale and the Largo has no public to mourn beneath. The first movement grows from its opening canon and its long violin line, and the march of its development is that line made mechanical, which the argument needs. The test finds give in three places: the scherzo, bound to the rest by tone more than argument; the finale’s slow central section, long for what it carries; and the finale’s first march, which restates its tune more than it develops it. The coda’s repeated note is not give: the repetition is the point.
Dionysus Flambouras · Literature
8.5 · Tier IV
Measured, and the subtractive test finds less slack than the length suggests. Almost every part plants what a later part spends: the crossing reader that logs two names in another jurisdiction becomes evidence in a plea; the own goal credited to the last man to touch it closes in a police statement seven parts on; twenty-four dollars hidden in a furnace at nine returns as a confession and a payment. Proportion is the charge. Three parts carry more than two-thirds of seventy-three thousand words, and the opening sustains its monstrous voice for nearly twelve thousand, past the point at which its indictment is complete: the butter and the Geisha3000, and the imagined night raid on the Applebees’ hamper, could go without loss. In the last part the confessions at the table say aloud some of what the book has already shown, Abelard’s call and Randolph’s delay among them. One sentence recurs three times, by design. The cap clears with room; the top of the band does not.
H. G. Wells · Literature
8.4 · Tier IV
The subtractive test finds little to take, and what it finds is in the middle. The frame cannot go: the first dinner, where the fourth dimension is argued and a model sent into time, is both the premise and the trial of belief the whole book stages, and the second, where the Traveller comes in lame and filthy and wants mutton before he talks, makes the tale testimony. The last departure, with a camera and a knapsack, is required to leave the tale unproved. Within the tale, the Traveller’s successive theories of 802,701 are the design, not repetition, since each corrects the last. What could be thinned: some Weena passages, which repeat one note of tenderness, and the long middle of the Palace of Green Porcelain, which is partly inventory. Thinning, not cutting.
Giorgio de Chirico · Visual art
8.4 · Tier IV
Judged element by element, the canvas is nearly irreducible. Take away the girl and the street is only empty, a stage set; she is the only motion in it, the life that runs toward what the street holds. Take away the shadow and her run has no end and no threat: the shadow is the picture’s event, and it is made of absence. Take away the van and the second absence goes, an empty container with its doors open. Take away either arcade and the contradiction of space that makes the street unsafe disappears. What yields is degree, not part: the length of the lit arcade, the height of the sky. And the canvas belongs to a run of piazzas built from the same parts, which tells against compulsion in its vocabulary.
Olmec · Visual art
8.4 · Tier IV
Judged head by head, then as a body. Each head passes the subtractive test as few sculptures do: there is no body to remove, no attribute held in a hand, no setting and no inscription. What remains is required. The face gives the person; the helmet gives the office and, by emblems that differ from head to head, the particular holder of it; the ear ornaments complete the regalia; the mass of the stone gives the permanence the face claims. Even the flattened, less worked backs are necessary, because they fix the single frontal meeting the heads demand. As a body the test is weaker: seventeen is the number that survived and was found, not a number an argument compels, and one head could be taken from the set without the set losing its law. Held below the high eights for that.
Oscar Niemeyer · Architecture
8.4 · Tier IV
Judged on structure, purpose and site. The governing gesture resists subtraction almost wholly: the sixteen columns are at once the structure, the frame of the walls and the image; the ring is what lets them stand; the glass only fills between them. Take away the descent and the nave cannot lie below ground; set the nave at grade and the bases of the columns become an obstacle and the entry a door like any other. Nothing in the crown is applied. What yields is purpose: a glass drum under the sun of the central plateau is a hothouse, and a round room of hard surfaces is a hard place to hear the liturgy. The form is compelled by its own figure more than by worship, climate or hearing, and the bell tower and the angels could go without loss to the governing idea.
Octavia E. Butler · Literature
8.4 · Tier IV
The book is lean, and each journey has a job. The river brings Rufus as a drowning child and teaches Dana the law of her passage; the fire brings the curtains set alight by the boy and the first sight of a patrol and a whipped man; the long middle carries Kevin with her and strands him for five years; the last cycle, of Alice, Isaac and Rufus, ends in the rope and the final return. Very little could be cut without losing a fact the argument needs. What holds the axis below the high eights: the interludes in Los Angeles are thin and partly mark time, and the pattern of the journeys, danger, summons, danger, return, is repeated in the middle chapters more than it is developed. Kevin’s five years pass offstage, which is economical, but his return is told more than it is made necessary. The parts are required; a few of their joints are convenient.
T. S. Eliot · Literature
8.4 · Tier IV
The subtractive test finds very little to take. A poem that names its condition as “Paralysed force, gesture without motion” cannot carry slack, and almost none of it does. The five parts are a sequence of decreasing capacity: a chorus that can still describe itself, a single voice that can still fear and hide, a land of stone images where a kiss becomes a prayer to broken stone, a gathering by a river where sight itself has gone, and a last part where speech breaks. Each does what only it can. What holds the axis is the poem’s origin as an assembly: the third part, carried over from earlier fragments, is the slightest of the five and shares the work of the second, and the poem would lose least without it.
Built for Bishop Bernard de Castanet · Architecture
8.4 · Tier IV
Run the subtractive test on the shell and it holds almost wholly. The buttresses cannot go: drawn inside the wall, they are the chapels’ dividing walls and the vault’s support, and outside they are the towers of the rampart. There are no aisles to remove; there never were. The tower is the keep the fortress needs and the city’s mark. The brick was compelled by the place, a plain of clay without good freestone. What resists the test is what the building’s life added: galleries that cut the chapels’ height for a use the first plan did not ask, a porch whose necessity is ceremonial at most, and a choir that refills the single room the plan made single.
Caspar David Friedrich · Visual art
8.4 · Tier IV
Judged on the configuration. Remove the man and the canvas is a fine view of fog among peaks, one of a type. Remove the fog and the near rock joins the far mountains by the continuous ground of an ordinary landscape, so that the gulf he stands above goes. Remove the dark outcrop and he has nowhere to stand, and the near world of solid dark matter against the far world of pale dissolution is lost. Those three are required, and the scale is compelled: under a square metre and upright, it keeps the figure large enough to bar the view. What gives is the inventory of the middle and far distance. The spurs breaking the fog are a count, not a structure, and the great mass at the right is placed for balance more than for need.
Talking Heads · Music
8.4 · Tier IV
Eight tracks in about forty minutes, and the subtractive test finds little to cut but finds slack. Born Under Punches must open: it sets the method, a self heard as a machine of interlocking parts. Once in a Lifetime must open side two, the one place the record states its condition plainly. Listening Wind is required as the only view from outside, and The Overload as the end of the groove, where the ecstasy is shown its cost. The test bites twice. Crosseyed and Painless and The Great Curve run in one mode, fast and dense, and the second adds height more than a turn. Houses in Motion, the track a hostile listener would cut, restates Born Under Punches at a lower heat. One soft track and one doubled mode.
Kazuo Ishiguro · Literature
8.4 · Tier IV
The subtractive test finds little to take from the spine. Each part is required. Hailsham must come first, because the reader must learn the children’s world before learning what it is for, and must learn it as they did, in fragments. The Cottages must come between, because there the rumour of deferral takes hold and Ruth’s “possible” is sought and lost. The third part must close, because only there are the donations seen and the rumour tested against Madame and Miss Emily. The small episodes carry weight later: the lost tape, the pencil case, Tommy’s tantrums, the Gallery. What the test finds is in the middle: some of the Cottages chapters circle the friendship’s quarrels longer than they add a turn, and Kathy’s habit of deferring what she will tell sometimes delays without deepening. Perhaps a tenth of the book is permitted rather than compelled.
Frank Capra · Film
8.4 · Tier IV
Run the subtractive test and nearly every episode returns later as a debt. The boy who pulls his brother from the ice loses the hearing in one ear, which keeps him from the war, and Harry lives to save a transport; the boy struck in Gower’s back room stops a poisoning, and in Pottersville Gower is a broken man out of prison; the honeymoon money paid out in the run on the bank founds Bailey Park, which without George is a cemetery. The third act takes each scene away and shows the loss: the structure enacts the test. What gives: the heavenly frame runs long in exposition, Ernie and Bert and Violet are thinner than they look, and the pool at the dance is lengthened for its gag. The spine is necessary; some of its flesh is permitted.
Ludwig Mies van der Rohe · Architecture
8.4 · Tier IV
Judged on plan, section and structure, under purpose and site, much passes the subtractive test. The slope compels the section: the house turns a closed, low face to the street and opens its full height to the garden, so that the private rooms are entered at the top and the public room lies below them, nearer the land. Take away the free columns and the room becomes rooms; take away the onyx plane and library and sitting area have no boundary but furniture; take away the sinking glass and the garden stays a picture. What resists: the bedroom floor is a row of closed rooms off a terrace, ordered more than compelled; onyx, ebony, chrome and silk were chosen for rank and beauty; and the house is larger and grander than one family’s programme asked. The purpose included display, and a part can serve display and still be replaceable by a cheaper means.
Sandro Botticelli · Visual art
8.4 · Tier IV
Taken register by register, the parts are required. The ring of angels is the heaven the inscription promises and cannot go. The embraces below are the reconciliation that the devils’ flight makes visible; take them away and the end of time has no event in it, only an announcement. The Virgin at her outsized scale is the axis on which the three registers hang. The two processions, led by angels toward the Child, are the human approach and balance each other across the shed; the roof angels join earth to heaven. What yields: the processions make one statement twice, with variation, the olive branches and crowns are multiplied for emphasis more than argument, and some rock and landscape fill the edges.
The Smashing Pumpkins · Music
8.4 · Tier IV
Thirteen tracks in about sixty-two minutes, and the subtractive test bites more than once. Cherub Rock must open: the drum roll and the guitars building one layer at a time announce the method. Disarm is required, the one place the wall is set aside and the wound named. Soma is the long centre, Luna the compelled lullaby of an end, and Today and Mayonaise carry the record’s two faces, bright sound over a dark meaning and a tender melody lifted on the wall. What holds the figure is what the record could lose: a long passage of vamp in Silverfuck’s nearly nine minutes, Hummer’s drifting coda, one of Quiet and Rocket, which run in one mode with Geek U.S.A., and Sweet Sweet, a fragment that neither ends nor turns.
William Blake · Visual art
8.3 · Tier IV
Taken element by element the sheet resists subtraction. The compasses cannot go: they are the act the picture accuses and the point where his attention ends. The diagram cannot go: it is the one made thing in the image and the reason his back is bent. The rock cannot go: its coloured, teeming growth is what he turns from, and without it the figure is a nude study. The dark ground cannot go: it surrounds and drowns him. The fold of the body, head, arm and leg brought into one closed loop down to the scroll, is the argument made into a pose. What yields is texture: the growths on the rock were printed by a chance process, not placed one by one, and some of the anatomy is a repertoire Blake used elsewhere.
Gandharan · Visual art
8.3 · Tier IV
Judged on the parts, which are few. The body cannot go: it is the subject and the argument, every rib a year of the six. The posture cannot go: the meditative seat, symmetrical and upright, is the discipline that has done this to the body, and it holds the wasted frame like a scaffold. The face cannot go: the sunk eyes and the composed mouth carry the second meaning, that the mind is untouched while the flesh is spent. The robe is required by contrast: its full, regular folds over the legs are the only abundance in the work. The halo is required to name him. What yields is the base, permitted by the cult object’s function rather than compelled by the image, and some of the drapery’s quantity, which is workshop formula. Little is idle.
Hayao Miyazaki · Film
8.3 · Tier IV
The test is subtractive, and the spine resists it. The soot sprites are the hinge of belief: the father’s laugh in the bath drives them out, and tells the children that this house admits spirits and this adult will not mock them. The hospital visit plants the fear the telegram releases. The rain at the bus stop is the meeting the film turns on, and the seeds given for the umbrella become the night growth of the tree. The scale is compelled: a short film for a child’s span, with nothing padded. What holds the figure is the middle: the washing at the stream, Granny’s garden, Kanta’s mother at the door are texture more than load, and a tighter film would survive the loss of one or two.
Bruce Graham and Fazlur Khan (Skidmore, Owings and Merrill) · Architecture
8.3 · Tier IV
Judged on purpose, structure and site, the subtractive test finds very little to take away. The taper is compelled by the stacked uses: the deep floors at the foot suit parking, shops and offices, the shallower floors above suit apartments, whose rooms need daylight within a few metres, and the narrowing top suits the observatory and the masts. The taper also does structural work, drawing the mass in toward the top and stiffening the tower against the wind. The diagonals are compelled by wind load at this height, and the economy of the building depends on them. What weakens the claim: the masts add a use, not a form, and in the apartments the diagonals cross some windows.
Wes Anderson · Film
8.3 · Tier IV
The subtractive test finds the spine load-bearing. The prologue’s catalogue of prodigies is required: every adult failure in the present is measured against a success the film has already shown, Chas’s finance, Margot’s play, Richie’s tennis. Royal’s false cancer is the engine that returns him to the house, and its exposure is what makes him earn a place by other means. Chas’s grief for his wife, played as a fire drill and a tracksuit, pays out in his last exchange with his father, and the cemetery is prepared by Buckley’s death and the dog bought from the fireman. What gives: Raleigh’s study of Dudley, the Dalmatian mice, part of Eli’s line and Pagoda’s past are ornament the design permits rather than requires.
Walter De Maria · Visual art
8.3 · Tier IV
Judged by subtraction on the system. Take away the stay and the work becomes a view of poles at noon, when the thin steel all but disappears; the work exists at dawn and dusk and under weather, so the duration is required. Take away the level plane of the tips and the land’s relief is measured against nothing. Take away the isolation and the field becomes a sight among sights; De Maria made isolation essential, and the site was chosen for it. The scale is compelled: the field must exceed the eye. What holds the axis is the count: 16 by 25 is the output of the mile and the kilometre, and a grid of 15 by 24 would know almost the same thing.
William Gaddis · Literature
8.3 · Tier IV
The test is subtractive, and it mostly fails to find anything idle. One house, one season, a handful of voices: the unities are the condition of the book, since its subject is what reaches a woman who cannot leave and is never listened to. Every telephone call carries a fact of the plot that the reader must catch in passing; drop one and a thread breaks. Two things hold the axis where it stands. Repetition is the method: Paul’s harangues about money, lawyers and the ministry return with small variations, and some returns make the reader feel the weight rather than add knowledge. And McCandless’s long late speech against the fundamentalists and the people who run them says at length what the action has already shown.
Alice Munro · Literature
8.3 · Tier IV
The test is subtractive, and it is put twice. Inside the stories it finds almost nothing to cut, though they look digressive. In the title story every movement serves the turn: the furniture shipped west, the forged letters, the girls’ spite, Johanna’s train to a Saskatchewan town and the sick man she finds there, the late glimpse of Edith learning what came of the hoax. Remove one and the reversal, malice producing a marriage, does not hold. In “The Bear Came Over the Mountain” Grant’s old affairs with students are required by an ending that needs a husband with something to be forgiven. Across the book the test bites: the nine were not composed as a sequence, and the slighter stories restate a situation the others carry, a woman weighing a marriage against a life not taken.
The Smile · Music
8.3 · Tier IV
Thirteen tracks in about fifty-three minutes, and the important parts are required. The opening is necessary: The Same sets a pulse and an appeal before the band enters, and the trio’s arrival on The Opposite answers it, the two titles named as a pair. You Will Never Work in Television Again is the one fast, loud strike and earns its place early. Skrting on the Surface is the close the record needs, a release kept back until the end. The test finds give in the middle. Pana-vision and Speech Bubbles share a slow, string-lit manner, and Thin Thing and A Hairdryer are both studies in a knotted guitar figure, so that one of each pair does less than the other; Open the Floodgates and Waving a White Flag are textures more than turns.
Anselm Kiefer · Visual art
8.2 · Tier IV
The subtractive test on four elements: the ground, the straw, the black and the name. Take away the straw and the golden hair becomes yellow paint; the work loses its one material fact, a thing that is gold and burnable at once. Take away the black and the hair is only gold: the poem’s turn from the golden to the ashen goes, and the canvas becomes a harvest. Take away the name and the straw is a field, not a woman. Each is required, and nothing is added to them. What yields is extent and count: the field could hold more strands or fewer, run wider or narrower, because it is a field repeated rather than a structure articulated, and the ground between the strands is worked rather than compelled.
Ilya Repin · Visual art
8.2 · Tier IV
Judged figure by figure. The leader at the head of the line cannot go: the gang’s weight lands first on his chest, and his face, lifted and calm, is the picture’s intelligence. The boy in the middle cannot go: he is the one figure not yet bent, and the frieze turns on him. The last man, head hanging, nearly dropping out of the line, cannot go: he is where the gang ends and the load begins. The barge cannot go, nor the steamer’s smoke, which makes the men an anachronism already being superseded. What yields is in the middle of the file, two or three men whose types repeat rather than add, and the empty bank at the right. The width is compelled: the line must be long to be a line.
James Brown · Music
8.2 · Tier IV
Eight bands in a little over half an hour, and the subtractive test finds little to take. Fats Gonder’s introduction must open: it builds the star before the star sings and tells the listener this is a show, not a set of songs. The four short songs come at speed, about two minutes each, and the speed is the argument: the show will not let the room rest. “Lost Someone” must follow, the long slow plea that turns the rush into a sermon; the medley must close the singing; “Night Train” must close the record, the band playing the singer off. The test bites twice. “Think” and “I Don’t Mind” do the same work, and one could go with small loss; inside the medley, two or three songs are glimpses more than parts.
Brinkman and Van der Vlugt · Architecture
8.2 · Tier IV
The subtractive test is hard on a factory, and this one passes it closely. The plan follows the movement of goods: raw material arriving by water and rail, carried up and worked through the floors, packed and sent across the bridges to dispatch. The bridges, which most visitors take for the signature, are the shortest path between production and shipping, set at the angle the site forces. The slab is cantilevered because the front had to be free of columns for continuous light; the capital flares because the slab had to span without beams to block light and services. The three blocks step because three products were made. What holds the axis at 8.4: the curved office and the rooftop tearoom are chosen as much as compelled.
Rainer Werner Fassbinder · Film
8.2 · Tier IV
Run the subtractive test and the film resists it almost everywhere. About ninety-three minutes carry a courtship, a marriage, a town’s punishment and its relenting, an estrangement and a reconciliation, and nearly every scene is one term of a pattern the film needs twice. The dance in the bar opens the story and closes it; the staring on the stairs returns as friendliness on the same stairs; the grocer who refuses Ali comes back needing Emmi’s custom; Bruno’s kick into the television is paid by his request for a babysitter. What gives: the stretch at Barbara’s flat and the repeated refusals of couscous make one point more than once, and the doctor says aloud what the hospital image already carries.
Barry Jenkins · Film
8.2 · Tier IV
The subtractive test finds little idle. The triptych is the argument: take any chapter away and the film loses one of the three selves whose discontinuity is its subject. In the first, the swimming lesson, the dinner at which the boy asks what a word means and then whether Juan sells drugs, and Paula’s silent scream in a pink-lit hallway each bear weight: the father found, the word named, the father unmasked as the source of the mother’s ruin. In the second, the night on the beach and the beating Kevin is made to deliver are two halves of one betrayal, and the chair is the hinge into the third self. What gives: Terrel is a schematic bully, and the rehab visit states what the film had shown.
Greek (Classical) · Visual art
8.2 · Tier IV
Judged figure by figure, then as a pair. Within each body the subtractive test finds almost nothing to remove. The weight on the right leg, the left knee released, the hips tilted against the shoulders and the head turned hard aside are one decision carried through the whole: take away the turn of the head and the body is a stance, not an act of attention. The veins over the hands and feet, the deep curls of A’s hair and beard, the parted lips are required by the claim that this bronze is alive. What yields is the pair. The two may not have been made together and may stand a generation apart; they share a room because they shared a seabed. The pairing gives the work its most legible meaning and is also its least necessary element.
The National · Music
8.2 · Tier IV
Across twelve songs the subtractive test mostly fails to find a cut, and where it bites it takes little. Fake Empire must open: the record’s public frame, a night of willed play beside an empire nobody looks at, is set there alone. Gospel must close, quiet, the frame turned inward. Slow Show is the hinge, the one song that names the wish to go home, and Apartment Story and Start a War are its two faces, the shelter and the threat to it. Ada earns its place as the release the close needs. What holds the figure is the second half, where Guest Room and Racing Like a Pro restate what Apartment Story and Brainy have found, in the same tempo and grain: one song’s give, spread across two.
Maqsud Kashani (named in the inscription) · Visual art
8.2 · Tier IV
The test is asked of the elements, not of every repeat, since a medallion carpet is a system of mirrored repetition. The medallion cannot go: everything is laid out on it. The sixteen pendants cannot go: they turn a shape into a radiance. The lamps cannot go. They are the one thing that turns ornament into a place, a sanctuary lit from the centre, and their unequal size gives the field a direction. The inscription cannot go: it names the carpet’s position, a threshold offered by a servant. The corner quarters follow from the field. What yields is the density of the floral scroll, which is ground rather than argument, and the scale, set by a room, not by the design.
James Cameron · Film
8.1 · Tier IV
The plot is a single pursuit, and the subtractive test finds very little to remove, because nearly every object is planted to be paid. The phone book orders the killings and lets the police see the pattern. Ginger’s Walkman keeps her deaf to the killing in the next room. The answering machine gives the machine its quarry’s location, and the mother’s voice it later counterfeits closes the trap. The photograph Reese has carried for years is made in the last scene; the dog that marks the machine in the future marks it again at the motel. The police comedy is the disbelieving world the machine destroys. What gives: the Tech Noir sequence and the second chase repeat the first escape’s shape, and the freeway chase adds one phase more than the design needs.
Built for Bishop Bernward · Architecture
8.1 · Tier IV
Run the subtractive test and very little comes away. The module governs: each crossing a square under four equal arches, the nave laid off in the same unit, so that no bay is longer or shorter than the scheme requires. The piers stand where the squares meet, and the rhythm of the arcade is the plan stated in elevation. Both ends are compelled, the west by the founder’s crypt and tomb, the east by the high altar and the monks’ office; the towers carry the stairs to the galleries and the bells. What resists is the doubling itself, which one choir could have served, and four stair towers taller than their stairs require.
Henri Cartier-Bresson · Visual art
8.1 · Tier IV
The subtractive test bites hard. Remove the leaping man and nothing is left but a flooded yard. Remove his reflection and the leap loses its counterweight: a figure over water rather than a figure meeting his double at a point not yet touched. Remove the posters and the rhyme of man and dancer goes, and with it the wit that makes the leap a performance. Remove the ladder and he leaps from nowhere. Remove the gap between heel and water and he steps in a puddle; the picture hangs on a few centimetres of air. The crop is itself subtraction. What yields is the background, the buildings and part of the debris, and the second figure, which the picture tolerates as much as it requires.
Han Gan · Visual art
8.1 · Tier IV
Judged element by element, and there are only three. Take away the post and the horse is merely lively: the drama is the pull of a living body against a fixed vertical, and without the vertical there is no resistance and no subject. Take away the tether and the post is a stake beside a horse; the short, taut line between them is the hinge. Take away the turned head and the rolled eye and the struggle becomes a pose. Even the white of the paper is required, since the white horse is made of the ground itself, contained by line. What yields is the lower and rear body, where the hindquarters do less work than the forequarters. The scale is compelled: one animal, at one moment, close.
Félix Candela · Architecture
8.1 · Tier IV
Judged on structure, purpose and site. The shell resists the subtractive test almost absolutely. Remove a segment and the vault is no longer in equilibrium; remove the groin ribs and the load has nowhere to go; thicken the shell and the form loses the point of itself. Even the oblique cut of the edges is required, for it is what lets each edge stand free without a beam, and the eight identical segments are the logic of the intersecting hypars, not repetition for ornament. The site compels part of the rest: a restaurant at the water among flower gardens, opening on all sides. What yields is the purpose. The room needs a roof, not this vault, and kitchen, service and enclosure are fitted in rather than generated. The structure is compelled; the restaurant is permitted.
Antonio Canova · Visual art
8.1 · Tier IV
The subtractive test on two figures and a rock. Take away the wings and the crossing loses one of its arms: the group is the meeting of his rising wings with their two reclining bodies, and the wings alone lift it off the stone. Take away her raised arms and the ring that holds the two faces is gone. Close the gap between the faces and the work becomes a kiss, an event done, rather than the instant before revival. The small vessel by the rock could almost go, but it names the cause of the sleep and so the story. The scale is right, a little under life. What gives is the rock and the drapery, which could be otherwise and lose almost nothing.
Vladimir-Suzdal builders, under Andrey Bogolyubsky · Architecture
8.1 · Tier IV
Run the subtractive test on the church as it stands, and almost nothing can go. The three-bay facade is the four-pier plan written on the outside: each zakomara answers a vault inside, each pilaster a pier. The arcade belt divides the wall where the gallery once met it, so that even the belt is a trace of use. The mound is required: without it the church stands in the flood; with it the flood becomes its setting. What holds the axis short is scale and loss. A small votive church’s parts are compelled by a narrower argument than a cathedral’s, and the present compactness is partly the compactness of the lost gallery.
Hadhrami builders · Architecture
8.1 · Tier IV
Run the subtractive test, and almost nothing stands idle. The mound is required by the flood: the city stands above the water of the wadi. The wall and gate are required by a valley of feuding tribes and raiders. The height is required by both at once: inside a defended perimeter on a limited rise, a growing clan builds up and not out, and the tower lets one family hold storage, livestock, reception and private life on one plot. The narrow streets are required by the sun, the towers shading one another and the lanes; the mud by the place. What could go is little: lime trim, some decorated doors and windows, later accretions. Held short of the top because the necessity is a settlement’s, not a single argued work’s, and some houses could go without loss to the whole.
Claude Monet · Visual art
8.1 · Tier IV
Judged subtractively on a field with very few parts. Remove the sun and the canvas is a grey morning with no event. Remove the reflection and the sun hangs in the sky instead of joining sky to water, which is the whole incident. Remove the near boat and nothing measures scale or distance, and nothing human stands in the light; the two smaller boats are the recession, and the eye walks back on them to the port. The port, chimneys and cranes in the haze, makes this a working harbour of its decade and not a sunrise anywhere. The speed is compelled by the subject, minutes of light, and the small size by the speed. What gives: the left side, a scumble of structures and smoke that could hold more or less without loss, and the third boat, which could go.
Court of Benin · Visual art
8.1 · Tier IV
The subtractive test bites hard on an object this compressed. Remove the crown and the face is a woman’s face; the crown of small European heads and mudfish makes her the mother of a king whose wealth and divinity come from the sea. Remove the mudfish and the Portuguese become mere foreigners, history without cosmology; remove the Portuguese and the mudfish are Olokun’s sign without the trade that made Esigie’s Benin rich. Remove the iron and the face loses its marks of rank and its watchfulness. Remove the loops and it is a sculpture, not a pendant. Nothing is idle. What yields is the repetition: the crown and the lower band repeat their units, and one more or one fewer would not change the meaning. Level with Fountain at 8.4.
Henri Matisse · Visual art
8.1 · Tier IV
Judged plane by plane, since the work is made of separate parts. Take away a sheet of the spiral and the turn breaks: the snail is nothing but its rotation, and each plane is a step of it. Take away the green centre and the whorl has no origin. Take away the orange border and the field loses its edge and its counter-rhythm, straight strips against the turn within, and the spiral floats on an unmeasured white. Take away the white and the colours touch, and the intervals that make the rotation read as growth are gone. The scale is compelled too. What yields is detail: the ragged corners of single sheets, and the exact hue of some middle planes, which could have settled elsewhere.
George Stubbs · Visual art
8.0 · Tier IV
The test is subtractive, and the picture was made by subtraction. Everything the genre supplied has gone: rider, groom, saddle, landscape, the distant house, the racecourse post, the dog. What is left cannot lose anything further. Take away the twisted neck and the horse is a specimen; take away the white of the eye and the rearing is a display rather than a fear or a fury; take away the plain ground and he is in a place, which is to say in a genre. The scale is compelled: at half size it would be a sporting picture. Held below the top for one reason: the ground, though it is the picture’s decision, is a field of near emptiness, and emptiness is the least demanding of necessities to hold.
Marcel Duchamp · Visual art
8.0 · Tier IV
Judged on the parts, which are few, and on the test of substitution, which this work invites more than any other. Remove the signature and the urinal has no author and no year: it is plumbing in a hall, not a submission. Remove the turn onto its back and it is a fixture again, its use restored. Remove the title and the inversion goes: what receives no longer pours. Remove the act of submission, to a show that promised to refuse nothing, and the object makes no test. Each part is required, and there is nothing else. What gives is the object itself: any urinal of the pattern would serve, and the work has proved it, surviving the loss of its object and its replacement three times, once by a copy made by hand.
Grant Wood · Visual art
8.0 · Tier IV
Judged by subtraction, and little yields. The fork cannot go: it is the man’s office and the picture’s rhyme. The window cannot go: it gives the title its word and sets the church’s pointed arch inside a farmhouse. The woman’s step back behind his shoulder is the whole relation of the two figures, and her averted eyes are the only movement off the frontal axis. The loose curl at her neck is the one undisciplined line in a disciplined picture and is required for that reason. The spire answers the window; the porch plants give her a domain as the barn gives him one. What yields: the round trees, stage furniture, and some of the repeated prong, where rhyme becomes a game. Below Broadway Boogie Woogie at 8.7, level with Fountain at 8.4.
Anonymous · Visual art
8.0 · Tier IV
The subtractive test is severe on an object eleven centimetres high, and the figure mostly passes it. Remove the face and nothing goes, because there is none: the carver has already subtracted it, and that subtraction is the work’s first decision. What remains is what the carver judged required: breasts, belly, navel, vulva, thighs, the head as a mass of patterned rows, the bracelets. Each volume leans on the next, the breasts on the belly, the belly on the thighs, so that removing one leaves its neighbour unsupported. The arms are the weakest part, thin and laid flat, nearly a relief, permitted more than compelled; the bracelets are ornament the body would not miss, though they mark a person adorned. The absent feet are a choice the work needs.
Norman Rockwell · Visual art
8.0 · Tier IV
Judged by subtraction, almost nothing yields. The child is the subject and the only face. The marshals cannot go: the picture is about protection by a state that has no face, and they must be four, two before her and two behind, so that she is enclosed and still walks alone between them. Restore their heads and the law becomes four men; remove them and she is a child on a pavement. The wall carries the mob: the slur, the letters and the tomato are the whole crowd reduced to three marks. The white dress is required against the stained plaster. What yields: the things in her hands are particular rather than compelled, and the wall states its hatred twice, in a word and in initials.
Pablo Picasso · Visual art
8.0 · Tier IV
Judged on the configuration, part by part. The guitar cannot go: it is the man’s one possession, the one warm area of the field, and the centre his whole body bends round. Raise the head and the picture becomes a portrait of a beggar rather than a figure absorbed in his own act. Unfold the body, stand him up or stretch his legs, and the cramped upright that says there is no room for him goes. The blue cannot go either. The scale is compelled: smaller, the pathos becomes illustration; larger, the frame stops pressing on him. What gives is at the margin: the ground is a field, not a structure, and the line behind him could sit higher or lower; the crossed bare foot reads as studio arrangement.
Johannes Vermeer · Visual art
8.0 · Tier IV
Judged element by element, the canvas resists subtraction to an unusual degree for its size. The façade is the subject and cannot go, and its cropping at the top is the decision that turns a building into a face. The woman in the doorway is the house inhabited, and her lowered head sets the quiet. The children are the one action, the one place where time is spent rather than kept. The woman in the yard is the picture’s second room and the house’s labour; without her the passage is a hole. The right-hand passage gives the street its depth and its dark. What yields: the vine is partly ornament, the sky’s extent is permitted rather than compelled, and the right-hand building’s upper storey is less required than the rest. Nothing is idle; not every inch is pressed.
David Mackenzie · Film
8.0 · Tier IV
The film is lean, and its plants pay. The reverse mortgage and the oil under the mother’s land are the motive and the end: the brothers rob the bank to pay the bank with its own money, and the trust that keeps the oil for Toby’s sons is administered by that bank. Each procedure is the plan made visible and sets up a later scene: only Texas Midland branches, only small loose bills, the takings laundered at a casino. Tanner’s prison years and the father he killed are given in a few lines and pay on the ridge. The two waitresses look like digressions and carry the film’s world. What gives: the Rangers’ ribbing returns more often than it needs to, and the cattle drive before the grass fire nearly stands free.
Jane Campion · Film
8.0 · Tier IV
The subtractive test finds very little idle, because the film is built as a trap whose parts are planted in plain view. Peter’s paper flowers, the rabbit he catches and opens on his bed, the gloves he puts on to cut the hide from a cow dead in a gully, Rose giving Phil’s hides away to a trader, Phil’s torn hand, the rawhide rope Phil braids for the boy: each looks like character or incident and each is a piece of the killing. Phil’s refusal of hides from anyone, set early, is what lets him take Peter’s. Even the dog in the hills is the hinge of the bond that kills him. What gives: the Governor’s dinner and the parents’ visit run a little long, and Rose’s drinking goes on past what the plot needs.
Peter of Illyria, under Pope Celestine I · Architecture
7.9 · Tier III
The subtractive test finds almost nothing to take. The plan is the plan of an assembly that faces one way: an oblong hall, a path between two rows of columns, an apse to close it. The aisles carry the crowd and the procession; the arcades give the nave its pace; the clerestory, set high above the colonnades, lights the room, and is as large as the timber roof and the brick wall allow. Nothing ornaments without also ordering: the opus sectile band marks the springing of the clerestory wall and binds the arches into one line. What holds the axis below the top is that the parts answer a purpose the Constantinian basilicas had already solved, so the necessity is the type’s as much as this building’s. The side chapels and the reassembled schola are minor and do not dilute it.
A. M. Cassandre · Visual art
7.9 · Tier III
Judged element by element, the sheet resists subtraction almost everywhere. Take away the birds and the ship has no size: they are the one unit by which the hull becomes colossal, placed at the bow, where the eye arrives. Take away the band of sea and the hull floats in a void and loses its thrust from the water. Take away the lettering and the poster loses its office, which is to name a ship and a route; and the lettering is set as a plinth, so that the hull stands on the name. The upper works are already reduced to a few planes. What yields is small: the route line and the line’s name are required by the commission rather than by the image, and in the versions they vary without loss.
Vilhelm Hammershøi · Visual art
7.8 · Tier III
Judged element by element, the canvas resists subtraction. Take away the patch of sunlight and the picture loses the subject its title names: the room exists to receive it. Take away the woman and it becomes one of the painter’s empty rooms, a different and in some ways purer work; this one is built on the relation between a turned back and a falling light she does not look at. Take away the doors and wall panels and the room loses the measured rectangles that the bright patch on the floor repeats in light. Nearly nothing is idle; the reduction is the method. What yields is the exact furniture and the extent of floor and wall, permitted by the room as found, and the many variants show placement varied rather than single.
Stanley Kubrick · Film
9.1 · Tier V
Judged on structure, since image and sound carry the meaning. The four parts are required: the argument is the sequence ape, man, machine, what comes after man. Much that looks removable resists removal. The banality of the Floyd section — sandwiches on the moonbus, the zero-gravity toilet, small talk with the Soviet scientists — and Poole watching his parents’ birthday message without expression make the men flat, so that HAL can be the one who feels. What holds the axis lowest is the film’s own history: its maker cut it in the days after the premiere, so that version carried removable matter, and the release still holds stretches whose length is permitted rather than compelled — the full waltz of the docking, the moonbus passage, the second pod’s approach.
Claudio Monteverdi · Music
9.1 · Tier V
Length is not charged. Inside each number the subtractive test finds almost nothing to take: the Sonata’s eleven statements, the three voices meeting on one note in Duo Seraphim, the echo that must answer, the ten voices of Nisi Dominus on one chant. Across the whole it finds a design: the feast’s psalms in order, the concertos rising from one voice to six, the instruments returning at the end. But the give is the composer’s own. The print offers two Magnificats, ritornellos it does not require, and concertos fit for chapels or princes’ chambers; an editor removed them and a Vespers remained, performed and recorded. A work whose author supplies its alternatives has a necessity of the parts weaker than its necessity of the whole, and that holds the axis here. The chant beneath nine numbers is the one thing nothing could remove.
Friedrich Hölderlin · Literature
9.0 · Tier V
The severe case is that a body which includes drafts cannot claim its parts are required, because some of them are not settled. “Der Einzige” survives in three versions, “Mnemosyne” in three, “Patmos” in a fair copy and later reworkings; “Wie wenn am Feiertage” breaks off into prose. Even a finished hymn digresses: the long narrative of Christ and the disciples in “Patmos” can read as a set piece. The finished poems are made under a law of measure few lyric bodies match: “Brod und Wein” moves in three triads from night over the city to the gods’ departure to the poet’s vigil, and “Der Rhein” turns at its middle strophe. But the unit is the drafts too, and the subtractive test cannot be passed by a text its author had not decided. That holds the axis lowest of the twelve.
Hieronymus Bosch · Visual art
9.0 · Tier V
The subtractive test gives two answers at two scales. At the scale of the structure nothing can go. Without the closed exterior the opening has no beginning; without the left wing the centre has no origin, without the right no consequence; and each shutter is half the centre’s width, so that closed they cover exactly what they hide. What holds the axis at 8.3 is the scale of the incident. The man bent double with flowers growing from his rear, the couple in the mussel shell, the crowd under a giant blackberry: many such groups could be exchanged or removed and the centre would say the same. Plenitude earns the swarm, not any one group.
Attar · Literature
8.9 · Tier IV
The spine passes the subtractive test. Remove the excuses and the journey has no cost, since each bird names one attachment the Way must strip: the nightingale’s rose, the parrot’s longing for the water of life, the peacock’s lost paradise, the duck’s water, the partridge’s jewels, the humā’s royal shadow, the hawk’s place on the king’s wrist, the owl’s treasure in the ruins, the finch’s plea of weakness. Remove the valleys and the end is unearned; remove Shaykh Ṣanʿān and the poem loses its proof that the Way can cost faith itself. What holds the axis here, the lowest of the twelve, is the middle: the questions put to the hoopoe are answered by stacked anecdotes, several to a question, and some could be lost or exchanged without loss. The compression of the Persian couplet is beyond this reading, and is not charged.
Aeschylus · Literature
8.9 · Tier IV
The architecture is a sequence of visitors to a man who cannot move, and most of it is required. The binding must be shown by two agents, one brutal and one pitying, because the play’s question, force against sympathy, is put there before Prometheus speaks. The gifts must stand at the centre: they are what he is punished for. Io must come, the second victim of the same power, whose line leads to the future he alone knows. Hermes must close, because the secret is what Zeus wants. What holds the axis lowest of the twelve: the Oceanus scene, a comic interlude of over a hundred lines whose argument the chorus has already made, and the long Io geography, catalogues of peoples and rivers beyond what the knowledge needs.
Fyodor Dostoevsky · Literature
8.9 · Tier IV
Subtract and see. Take out Stepan Trofimovich’s long introduction and the book loses its thesis, that the liberal idealists of the 1840s fathered the nihilists of the 1860s: Pyotr is his son by blood, and the whole circle is his by descent. Take out the fête of Part Three and the town’s collapse has no stage; take out Marie’s return and the birth, and Shatov’s murder loses its weight. The spine passes. What holds the axis lowest of the twelve is that the plan changed in the writing, from a pamphlet against Nechaevism to a tragedy centred on Stavrogin, and it shows. Much of Part One’s comedy runs longer than the argument needs; Karmazinov’s reading at the fête is a settling of scores with Turgenev, carried at length; the meeting “with our people” and Lebyadkin’s verses repeat their points; and with “At Tikhon’s” withdrawn, parts of Part Two point at a centre the published book does not hold.
Modest Mussorgsky · Music
8.9 · Tier IV
The chronicle form invites the subtractive test, and the spine resists it. The prologue’s forced acclamation is required, because Kromy answers it with the same crowd unleashed. Pimen’s cell names the murdered child and creates the Pretender in one scene. The Kremlin scene with the clock is the centre, and the death needs it. What holds the axis lowest is give in three places. The Polish act, written in answer to the directorate, holds two scenes whose intrigue the rest of the opera barely uses, and its love duet could go with little loss. The nursery songs are genre pieces. The inn, though the escape happens there, is longer than its action.
Anonymous · Literature
8.9 · Tier IV
The spine of the first eleven tablets is compelled at almost every joint. Enkidu is made because the king oppresses Uruk, and made human through Shamhat so that he can meet him; the friendship seeks fame in the Cedar Forest; the insult to Ishtar, which reads like a comic interlude, brings the Bull of Heaven, the Bull brings the gods’ sentence, and the sentence is Enkidu’s death, which drives every step of the ninth to the eleventh tablets. The Flood is not a digression but the answer: Uta-napishti’s immortality was a grant never to be repeated. The sleep and the snake close the last doors. The darkness under the mountain, counted out double-hour by double-hour, is the time the journey takes; and the tripled speech, in which three hosts ask why his cheeks are hollow and he answers each in the same lines, carries a man repeating his grief. Two things hold the axis lowest of the twelve. Tablet XII, a twelfth of the series, is added after the ring of the first and eleventh tablets has closed and reopens the work on another premise, bringing back a dead man; nothing before it requires it. And the formulas run long: the five dreams on the road to the forest repeat their stages almost word for word, and messages spoken once are spoken again whole on delivery.
William Shakespeare · Literature
8.9 · Tier IV
The play is lean by the standard of the canon: nine scenes, one afternoon, and almost no matter that does not mirror the main action. The three conspiracies are required. Antonio and Sebastian’s plot against Alonso in 2.1 replays the usurpation of Milan in the present tense; the clowns’ plot in 3.2 replays it as farce, Caliban offering his island to a drunken butler. Ferdinand’s logs in 3.1 answer Caliban’s in 2.2. What holds the axis lowest of the twelve is what a production can cut without the play noticing: the court banter of 2.1, some of the clowning in 2.2 and 4.1, and the stasis of the long exposition in 1.2. Perhaps a tenth of the whole is slack.
Nikolai Gogol · Literature
8.9 · Tier IV
The itinerary passes the subtractive test. Each of the five landowners is a different relation to things: Manilov’s sentiment without an object, Korobochka’s hoarding fear, Nozdryov’s lying energy, Sobakevich’s solid greed, Plyushkin’s decay. Each bargain varies the one transaction, and take one away and the scale of the town’s dead is less. Chapter 7 gathers them on paper; chapters 8 to 10 are the reverse, the town turning a purchase into rumour. What holds the axis lowest of the twelve is what can go: the rumour chapters multiply versions past the point of need, and the Tale of Captain Kopeikin, though it is the one place the state’s cruelty to the living is shown, is set in a mannered frame the book does not need. And the scale is partly permitted rather than compelled: the volume is the first of a design never realised, and chapter 11 supplies at the end the history a plan required.
William Faulkner · Literature
8.9 · Tier IV
The great bones are required. Remove Lena and the book loses the frame by which Christmas’s thirty-three years are seen as one passage among others on a road that does not stop; remove the seven chapters of his past and his walk through Jefferson is a crime report. Byron Bunch carries news from one story to the other, and Hightower’s house is where the two meet, at a birth and at a death. What holds the axis lowest of the twelve is matter told twice or at length beyond its need: the Burden family history that Joanna recites in a block in chapter 11, the biography of Percy Grimm that opens chapter 19, and the grandfather’s cavalry raid, told in chapter 3 and told again at length in chapter 20. None is idle; none is compelled at its length.
Thomas Mann · Literature
8.9 · Tier IV
The subtractive test is the hardest this book faces, and a severe reader finds much to cut: the later disputations of Naphta and Settembrini repeat their positions more than they advance them; “Humaniora” and “Forschungen” are essays in anatomy and biology lodged in the narrative; Krokowski’s lectures, the séance, the gramophone’s catalogue, the meals and the rest cures all run long. More is required than that reader allows. The repetition is the subject: a novel about time dissolving in routine must make the reader live the routine, and the thermometer, the five meals and the two rest cures are the clock of the enchantment. Each long set piece carries a turn the book cannot spare. The carnival night is the one night of eros, “Schnee” the one vision; the séance brings back Joachim in the uniform of a war he did not live to fight, and the gramophone ends on the song Hans sings under fire. The narrator’s own defence, “Nur das Ausführliche ist wahrhaft unterhaltend”
“Only the thorough is truly entertaining” (“Vorsatz”), is a joke and a plea, not a proof. What holds the axis lowest of the twelve is real redundancy in the middle of the debates and the essay chapters: a book about tedium need not be tedious wherever it is long.
Alessandro Manzoni · Literature
8.9 · Tier IV
The spine is required and its joints are timed. Two words of threat to a coward (ch. 1) start every later life: the failed surprise wedding and the failed abduction on one night (ch. 8) part the lovers, and the parting sends Lucia to Monza, Gertrude’s history to the reader, Renzo to the riot and the riot to his exile. The Innominato is built over two chapters (20 to 21) because his conversion is the hinge, and Federigo’s life (22) because the conversion needs a man worth converting to. The plague must come, since only a catastrophe that spares no one can untie a knot the law could not. What holds the axis lowest of the twelve, and below Anna Karenina’s 8.5, is the history: chapter 28 and much of 31 and 32 argue as essays, and Don Ferrante’s library (27) is satire a scene could carry in a page.
Thomas Mann · Literature
8.9 · Tier IV
The subtractive test finds real excess, and the book half admits it: Zeitblom’s apologies for his digressions do not make them necessary. The Munich society chapters, the Rodde salon, the Schlaginhaufen evenings and the Kridwiss circle, run past the point their thesis is made; the courtship of Marie Godeau by proxy through Rudi Schwerdtfeger, lifted knowingly from Shakespeare, is machinery; Ines Rodde’s shooting of Rudi on the tram is melodrama the plot needs more than the design does; and the long descriptions of the imagined compositions repeat their method. Against that, almost nothing is idle at the level of design. Jonathan Leverkühn’s experiments, the osmotic growths that imitate life and the leaf butterfly, prefigure the music’s dead imitation of life; Kretschmar’s lectures set out the end of art before Adrian has written a note; the Schweigestill farm at Pfeiffering repeats the Buchel farm, so that Adrian ends where he began. The scale itself is compelled by the double time and is not charged. What holds the axis lowest of the twelve is what could go without loss: the Kridwiss stretches, the proxy courtship, the repetition in the descriptions. Required in its parts, overlong in its stretches.
Sophocles · Literature
8.9 · Tier IV
The spine is a man who arrives as a polluted beggar and leaves as a power the gods summon, and each visitor is a step in the change. Ismene brings the oracle that makes his body valuable; Theseus receives him; Creon tries to take him by force and Athens refuses; Polynices asks and is cursed. Remove Theseus and the gift has no recipient; remove Polynices and the new power is never used. What holds the axis at the foot of the twelve, level with The Encompassed, is the length and where it goes: Ismene’s exposition of the oracles is heavy; the argument with Creon goes back over the old guilt at a length the first defence had already covered; the seizure, the rescue and the battle ode run the suppliant mechanism in full. About a tenth could go with little loss.
Honoré de Balzac · Literature
8.8 · Tier IV
The test is subtractive, and the spine passes it. Remove Vautrin and Rastignac’s education has no tempter, so the choice at the end is no choice; remove Mme de Beauséant and nothing shows the aristocracy throwing away its own as the daughters throw away their father; remove Goriot and the education has no price. The long opening description of the pension looks removable and is not: the house is the book’s first proposition, that a milieu shapes and reveals its people. What holds the axis lowest of the twelve is contrivance and repetition. The Taillefer duel, arranged off stage to make Victorine an heiress, is a mechanism; Goriot’s protestations of love recur past the point where each adds; and the narrator’s generalisations about Paris and about women restate what the scenes have shown.
Euripides · Literature
8.8 · Tier IV
The play has almost no plot: from the moment the herald allots the women nothing can be reversed, and each episode is another loss. The subtractive test still finds most of it required, because the losses come in order: the future, in Cassandra, who will die with Agamemnon; the marriage-bed and the hope of a line, in Andromache given to Neoptolemus; the line itself, in Astyanax thrown from the walls; the last claim to justice, in the trial of Helen, which Hecuba wins and loses at once; and the city. Remove one and the descent loses a step. Held down by the Helen debate, detachable as the others are not, the second ode’s mythic excursus, and the prologue’s promise of the fleet’s wreck, never taken up within the play.
Franz Kafka · Literature
8.8 · Tier IV
The test is subtractive. The title story fails it entirely: the dead horse, the pigsty that has stood unused for years, the groom who bites Rosa’s cheek, the two horses, the boy’s wound, the singing children, the naked ride home; remove any one and the logic of the dream breaks, because every detail is both cause and charge in the doctor’s guilt. Vor dem Gesetz and Eine kaiserliche Botschaft are as tight as any prose in the language. The order is argued: the book opens on Bucephalus, the war horse become a lawyer in an age with no Alexander, and closes on an ape reporting how he became a man, and the dedication to the father stands over the family man and the eleven sons. What holds the axis is the book as a book: three slight pieces, the visit to a mine, the next village and the fratricide, could leave it with what it knows little changed, and Elf Söhne is more catalogue than necessity.
W. B. Yeats · Literature
8.8 · Tier IV
The subtractive test, taken on the poems and then on the book. The great poems pass it inside themselves: no stanza of “Byzantium” could go without the poem losing a stage of its purgation, and “A Dialogue of Self and Soul” needs both the Soul’s ascetic half and the Self’s long reply, since the reply is earned only against the refusal. The book has a governing need too: the tower and its stair are the place every voice speaks from, and the two song sequences answer the high style with the body. What holds the axis is the rest. “Statistics”, “Three Movements”, “Spilt Milk”, “The Results of Thought” and “Oil and Blood” are notes rather than parts, and in “Words for Music Perhaps” the Tom the Lunatic group and some of the lighter songs repeat what the Crazy Jane poems have already won.
David Lynch · Film
8.8 · Tier IV
Judged on the whole as released, with the pilot’s remains inside it. The dream’s stations are required: Winkie’s, the audition, the set, the apartment at Sierra Bonita and Club Silencio are each the repaired form of a fact the waking half will show plain. Most of the television pilot kept in the film is converted rather than carried: the Castigliane brothers become the dreamer’s account of why the part was not hers, the hitman’s botched job over a black book her wish that the man she paid were a fool, Adam Kesher’s wife, the pool man and the paint in the jewellery box her revenge on the director who took her lover. What remains is vestige, present because a series once needed it: Mr Roque behind his glass and his chain of telephones, the detectives who never return, Louise Bonner at the door. The give is real but narrow, and it holds the figure here.
Joseph Conrad · Literature
8.8 · Tier IV
Most of the book is required by its argument. The broken chronology is not ornament: the reader learns that the Occidental Republic exists before learning what it cost, so its causes arrive as a reckoning. Decoud’s isolation on the Great Isabel, Hirsch’s death under Sotillo, Monygham’s history under Guzman Bento’s priest-inquisitor, Teresa Viola dying unshriven because Nostromo will not fetch the priest: each is load-bearing, a case of a man or woman bound to an idea or a thing. The subtractive test bites in two places, and they hold the axis lowest of the twelve. Captain Mitchell’s tour serves the irony of official history but runs long and repeats what the reader has seen. And the last chapters, Nostromo’s secret courtship of Giselle while he is engaged to Linda, and Giorgio Viola’s shot in the dark, are compelled by the treasure plot but carried by a melodrama the book elsewhere avoids; much of that triangle could be cut without loss to what the novel knows.
Hector Berlioz · Music
8.8 · Tier IV
The large plan resists the subtractive test. Remove the march and the dream has no crime to answer; remove the finale and the crime has no damnation; remove the Scène aux champs and the turn from love to dread has no hinge, for the field is where doubt enters and the thunder answers. The idée fixe binds every movement to the plan. The test finds give in the parts. Three main melodies were made for other works: the Largo’s romance, the idée fixe from the cantata Herminie, and the march from Les francs-juges, which takes the theme only in its last bars. The waltz is a dance with the beloved sewn into it. Length is not charged; the loose joins are.
The Beatles · Music
8.8 · Tier IV
Thirteen tracks in about forty minutes, run together as one show, and the core is compelled. The frame must open and must return, A Day in the Life must follow the farewell, and She’s Leaving Home, Lucy in the Sky with Diamonds and Within You Without You each carry a part of what the record knows: the family, the dream the closer wakes from, and the one law of life set against the show’s bustle. The test bites at Lovely Rita and Fixing a Hole, about an eighth of the running time, and softens at two more. Two songs from the same sessions were issued as a single and left off: the order was a selection, not a necessity.
Wolfgang Amadeus Mozart · Music
8.8 · Tier IV
Apply the subtractive test to the sequence and almost nothing yields. The Rex tremendae is very short and every bar carries, its dotted majesty drawn down to “salva me, fons pietatis”
“save me, fount of mercy”. The Confutatis cannot lose either half: the men’s curse and the women’s plea are one thought, and the descent of “Oro supplex” is the hinge into the Lacrimosa. The test bites in the completion. Süssmayr’s Hosanna fugato is conventional, his Benedictus graceful but discursive, the Hosanna’s return adds little, and Maunder’s later completion leaves out the Sanctus and Benedictus with the work still standing. The liturgy compels those sections, not this music for them. The Communion’s return of the opening is required: the work must end where it began.
Anonymous · Literature
8.8 · Tier IV
The spine passes the subtractive test. Remove the prologue and Hallgerðr arrives without Hrútr’s sentence on her eyes. Remove Gunnarr’s story and Njáll’s counsel has no proof; the feud of the two wives, servant for servant, is the small engine the whole saga runs on. Remove the conversion and Höskuldr’s death has no meaning; remove the great lawsuit and the argument that law must hold the land goes unmade. What holds the axis lowest of the twelve: the genealogies that introduce each figure, a convention more than a necessity; long runs of procedure after the burning that repeat their point; and the Irish chapters, which carry more of their source than the saga needs. About a tenth could go with little loss.
Machado de Assis · Literature
8.8 · Tier IV
The book’s law is caprice, and caprice is hard to test by subtraction: a digression on a fly, a chapter on the reader’s defects, a chapter of dots each seem removable one at a time, and taken singly perhaps a tenth of the chapters could go without losing a fact or a turn. But the volubility is what the book exposes, so the removable chapters are also its evidence. What is strictly required is large: the death and the plaster that caused it, the delirium, the three loves, the political failure, Quincas Borba’s system, and the last chapter’s ledger, which needs everything before it. Held below the top because the joke on form sometimes runs as joke only, and a hostile reader can name chapters the book would not miss.
Pieter Bruegel the Elder · Visual art
8.8 · Tier IV
Judged by subtraction, episode by episode. Death on the lean horse with the scythe cannot go: he is the engine of the whole sweep. The trap cannot go, the great box with its cross, the one place everything moves toward. The king at the lower left cannot go, his hourglass held up to him and his gold taken, because the argument is that rank buys nothing; nor the lovers at the lower right, the one unaware pair, the counterweight to the panic. The burning sea and the scorched horizon make the triumph total. What yields is the method’s own cost. Many single episodes, a gibbet, one more skeleton at work, one more victim in the middle ground, could go without loss: their law is “and also this”. The plenitude is compelled; most of its members are not.
Edgar Allan Poe · Literature
8.7 · Tier IV
Poe made subtraction a doctrine: the tale-writer conceives “a certain unique or single effect” and admits no word that does not serve it, and the best tales obey. “The Tell-Tale Heart” is one confession pressed to one sound, and nothing can go. “The Cask of Amontillado” spends every line of its walk into the catacombs on the irony of Fortunato’s name, his motley, his cough and the joke about the trowel, so that the last bricks are compelled. In “Usher” even the long reading of the “Mad Trist” is required. What holds the axis well below what those tales earn is the body: the comic tales and hoaxes could go with little loss, and some arabesques are padded with learning that is decor.
Nathaniel Hawthorne · Literature
8.7 · Tier IV
The romance proper is among the most economical novels of its century: four figures, one town, one sign. Three scaffold scenes are the load-bearing beams, in chapters II, XII and XXIII of twenty-four, and almost every chapter between them turns one relation of the triangle. Take out the forest meeting (XVI to XIX) and the last scaffold has no cause; take out Pearl and the letter has no living answer, since she is “the scarlet letter endowed with life” (VII). Two charges stand. The chapters on the leech and his patient (IX to XI) restate one situation at more length than the turn requires, and the narrator glosses what the scene has already shown. The larger charge is the frame: “The Custom-House” is required for what it does, the found manuscript, the inherited guilt and the theory of romance, but not at its length, and the portraits of the old inspectors are a comic essay the romance could lose.
Bob Dylan · Music
8.7 · Tier IV
Eleven tracks in about forty-seven minutes, and the subtractive test parts the sides. Side two resists it entirely: four long songs, each a station of one leave-taking, Mr. Tambourine Man’s surrender, Gates of Eden’s vision, It’s Alright, Ma’s indictment and Baby Blue’s farewell, and none could go without a gap. On side one Subterranean Homesick Blues and Maggie’s Farm set the refusal, and the two love songs set a private faith against it (“speaks like silence”); all four are required, and so is the 115th Dream, the record’s one built myth. The test bites at Outlaw Blues and On the Road Again, slight blues in one comic mode, and at the Dream’s joke, which runs past its turn.
Charlotte Brontë · Literature
8.7 · Tier IV
The five stations are each required, and the test finds it. Gateshead gives the child’s rage and the red-room; Lowood gives Helen Burns’s doctrine of endurance, which Jane must outgrow and cannot discard; Thornfield gives passion; Marsh End gives its counter, St John’s cold vocation; Ferndean answers both. Remove Marsh End and the return is a surrender; with it, it is a choice made after refusing a second absorption. What holds the axis lowest of the twelve is what the test does cut: the Ingram house-party runs long, with charades and drawing-room satire beyond what the jealousy needs; the gypsy disguise is a device; and the chain that brings a starving Jane to the one door on the moor that holds her own cousins, and then the legacy from Madeira, is assembled rather than compelled.
Émile Zola · Literature
8.7 · Tier IV
The spine is compelled: hunger forces the strike, the strike forces the march, the march forces the troops, the shooting forces the sabotage, and the flood forces the last descent. The subtractive test finds the joints. Remove the Grégoires and the chain loses its other end: their brioche at breakfast in the second part against the Maheus’ empty bread box is the argument in two rooms, and Cécile strangled by old Bonnemort in the sixth is the chain closing. Remove Souvarine and the flood has no cause. What holds the axis lowest of the twelve: the Hennebeau household is given more than the argument needs, Deneulin’s ruin is told at a length its function does not require, and the beast, the wind and the red vision repeat past the point where the image is fixed. A tenth or so of the book is permitted, not compelled.
Henry Fielding · Literature
8.7 · Tier IV
The subtractive test finds a plot that resists it more than almost any long novel in English. Bridget’s sudden tenderness for the foundling, Jenny Jones’s confession, the lawyer Dowling’s errand and the message from the deathbed that Blifil keeps back are laid in the first books and paid in the last; the woman Tom saves from Northerton and takes to the inn at Upton is the Jenny Jones of Book I, and the near catastrophe of Book XVIII turns on it. The three movements are required: the country makes the expulsion, the road tests the hero, London tries him and the town. What holds the axis is the licence Fielding claims for a “new province of writing” (II.1). The Man of the Hill’s history makes at length a point the book could make in a chapter; Mrs Fitzpatrick’s narrative restates Sophia’s danger; the gypsies and the puppet-show are excursions. Perhaps a tenth of the book is permitted, not compelled.
Georges Bizet · Music
8.7 · Tier IV
The spine is short and every link pays. The flower thrown in Act I binds José; the arrest gives Carmen the bargain of the Seguidilla; the bargain sends him to prison; his release brings him to the tavern; the bugles test him and Zuniga’s return forces the desertion; the outlaw is one she tires of; and the bullring is where she has gone to Escamillo. What holds the axis here is the genre. The street boys, the smugglers’ quintet and ensembles, the vendors and the procession could go without loss to the drama, and Micaëla’s aria stops the third act for a portrait. The dialogue carries plot the music need not mark, which is why every theatre cuts it differently.
Johann Wolfgang von Goethe · Literature
8.7 · Tier IV
The spine passes the subtractive test. The conversation on chemistry cannot go: it names the law every later chapter obeys. The child cannot go: conceived in a night when Eduard and Charlotte each embrace the other while imagining the absent beloved, he is born with Ottilie’s eyes and the Captain’s features, and his drowning is the price of that night. Mittler cannot go: his name means mediator, and he parts what he touches. What holds the axis at 8.3 is the estate business and the pace of the second part. The paths, the moss hut, the new house on the hill and the reshaping of the ponds are thematic, but given at more length than the theme needs; Luciane’s visit runs long; some of Ottilie’s maxims would sit as well in another book. About a tenth could be shorter without loss.
Rainer Maria Rilke · Literature
8.7 · Tier IV
The frame sonnets are required, and the book could not lose them: I.1, the tree rising in the ear; I.3, what song is; I.5, no monument but the rose; I.26, the god torn and scattered; II.29, the close. The order is not arbitrary: Orpheus enters in the first line and the poet’s farewell speaks in the last. Between the frame, the subtractive test bites more often than it does in the Duino Elegies. The fruit sonnet of I.13 and the two machine sonnets are drawn to the theme rather than compelled by it, and several sonnets in the middle of Part II could change places or go without the arc breaking, because the arc is one of recurrence and not of progress. Much of the interior is a garland, not a chain.
Simone Martini · Visual art
8.7 · Tier IV
Judged part by part. The central scene resists subtraction nearly everywhere. Gabriel cannot go, nor his olive branch and crown; the words cannot go, for they are the event; the vase of lilies cannot go, set exactly in the gap between the two figures where the meeting does not yet happen; the dove at the apex completes the vertical. The Virgin’s recoil, her mantle drawn to her throat and her thumb in the book, is the picture’s reason. What yields is at the edges. The two saints are patrons required by the altar, not by the Annunciation: removed, the scene would lose a civic frame, not a meaning. The roundels are conventional furniture. A central field of near necessity inside a format the argument permits rather than compels holds the axis here, the lowest but one.
David Lynch · Film
8.7 · Tier IV
Judged on structure, since the dialogue is deliberately flat and works by tone. The spine is a descent and a return, and its main parts resist subtraction. Take out the opening montage and the ending’s mirror means nothing; take out the closet and the film has no point of view; take out the joyride and “You’re like me” has no ground. The case is needed as well: the ear opens the descent, and the detective in the yellow jacket binds the father’s world of police to Frank’s. What yields to the test is particular machinery: a drug ring the film barely explains, Mike’s chase, Aunt Barbara’s comedy, and a climax solved by a radio trick and a pistol.
Gustave Courbet · Visual art
8.7 · Tier IV
The frieze is necessary as a mass: what the picture says depends on a whole town standing at one level, and the number of figures is the argument, not padding. The grave cannot go, nor the crucifix, the one vertical against the sky, nor the gravedigger, the only figure attending to the dead rather than to the occasion, nor the dog, which looks away as the town looks everywhere but into the grave. Below that the subtractive test gives. Within the mass of women at the right two or three heads could be lost without loss; the men in black between mayor and women are as fungible; the double row behind the clergy thickens more than it articulates. The fungibility is partly the point, a crowd in which each is individual and none singular, but a method of accumulation cannot claim the necessity of a picture from which nothing can be removed.
The Jimi Hendrix Experience · Music
8.7 · Tier IV
Eleven tracks in about forty minutes, and the frame and the core are required. Foxy Lady must open, the sound announced in its first sustained, swelling note; Are You Experienced? must close, the invitation the whole record has prepared, its backward tapes the threshold. Third Stone from the Sun is required as the one long passage where the guitar leaves song behind, Red House as the blues the record grows from, and Manic Depression and I Don’t Live Today as the two places where the sound carries a condition. Fire is slight but drives. The test bites at Can You See Me and Remember, two short rhythm and blues songs a lesser band could have made, and at Love or Confusion, whose swirl restates Manic Depression with less force: three short tracks of eleven.
William of Sens and William the Englishman; nave by Henry Yevele · Architecture
8.7 · Tier IV
Run the subtractive test. Much is compelled. The crypt carries the raised eastern arm; the steps up through the screen divide a lay nave from a monks’ choir; the ambulatory round the Trinity Chapel exists because pilgrims had to circle the shrine without crossing the office; the Martyrdom is where it is because the murder was there. Even the inward pinch of the choir is compelled, by the decision to keep the chapels the fire had spared. What resists the test is accretion: two pairs of transepts, a cloister vaulted later, a tower added at the end, fittings and tombs that could go without loss to the plan. The parts are required by the history the building holds more than by one argument, a looser necessity than the Pantheon’s (9.3) or Sainte-Chapelle’s (8.8).
Anonymous · Architecture
8.7 · Tier IV
The subtractive test is severe on a stupa, and this one mostly passes it. Remove the dome and nothing is left to honour; remove the ground railing and nothing divides the walked world from the sacred path; remove the gates and the circuit has no threshold. The terrace with its double stair gives a second, raised round, and the railed square and parasols mark the axis at the summit. Each element answers a ritual act: approach, entry, circling, ascent, regard of the summit. What resists is quantity. The gates carry far more narrative than entry requires, and the plain railing proves the precinct can work without carving. That surplus is the teaching, but it was permitted by an economy of gift as much as compelled by the form.
Pallava · Visual art
8.7 · Tier IV
Judged by subtraction. The cleft cannot go: it is the river, the axis and the reason this face was chosen. The ascetic and Shiva cannot go, because the grace that answers penance is the event. The elephants cannot go: they are the mass of the earthly world on the right and the measure of scale. The cat cannot go: its parody of the ascetic is the work’s one argument made in miniature. The shrine with its sages anchors the human order on the left. What yields is the multitude itself. The flying couples, the ganas and the lesser beasts are an array whose number the size of the rock permits rather than compels; several could be removed and the convergence would still read. A congregation is additive by nature, and that holds the axis here.
Vasily Grossman · Literature
8.7 · Tier IV
Length is not a cost: the scale is compelled by the argument, that one law runs through every place the century put people, and that can be shown only by going to each place. Remove the German camp and Mostovskoy’s night with Liss, and the Soviet prison chapters lose their mirror; remove the gas chamber, and the Shtrum plot has no ground beneath the mother’s letter; remove Kazan, and the book loses the one man who capitulates without a gun to his head. The spine passes. What holds the axis lowest of the twelve is a real margin of the assembled: figures carried from the first book for continuity, Vera and the pilot Viktorov and Spiridonov at the power station, given chapters the design does not need; essay chapters that say directly what the scenes have shown; and Darensky’s Kalmyk interlude, beautiful and loose. A tenth or so of the book could go without loss of anything it needs.
Duccio di Buoninsegna · Visual art
8.7 · Tier IV
Judged part by part on the work as made. The back is compelled by its story: the Passion is a sequence the liturgy fixes, and the selection reads as its necessary beats, the Entry, the Supper, the Betrayal, the trials, the Crucifixion, the burial and the tomb, each a step the next requires. Peter’s Denial set below Christ before Annas makes one panel do the work of two in one instant. The front’s centre cannot go: the enthroned Virgin is the city’s petition and the inscription’s addressee. What holds the axis lowest of the twelve is the front’s choir: the ranks of angels and standing saints and the apostles in the arcades could be thinned by a third without loss of meaning, and some Ministry scenes are interchangeable with others the Gospels offer.
Albrecht Altdorfer · Visual art
8.7 · Tier IV
Judged by subtraction, since the panel has no text but its tablet. The large members cannot go: Alexander and Darius, the one point of decision in a mass that otherwise has none; the mass itself, whose numberlessness is the claim that history is made of multitudes swept along; the tablet, which states in words the reckoning the image cannot count; the curved earth, which puts the battle on the scale of the world; the sun and the moon, which make it a cosmic event. What yields is extent within the mass. The multitude is required, but not any given hundred of it, and a battle of half the figures would say the same; the town and camp at the right, and some distant ranges, are rich rather than needed. A battle crowd is additive by nature, and that holds the axis at 8.3.
Nasrid, under Yusuf I and Muhammad V · Architecture
8.7 · Tier IV
Judged on plan, structure and site. Within each palace the parts are compelled. Take away the pool and the Comares Tower loses its approach and its double; take away the bent passage and the court is entered on its axis, which only the throne should command; take away the low windows of the Hall of the Ambassadors and the room loses the view over the Darro that sets it at the cliff’s edge. Take away a pavilion of the Lions and the cross-axis is lopsided. Three things resist. The two palaces meet at a right angle by a passage no plan required. Pattern is extensible: a band of stucco could run a panel longer without loss. And the domes are hung, not compelled by load.
Anton Bruckner · Music
8.7 · Tier IV
The subtractive test meets resistance at the structural joints. Remove the quiet end of the first movement and the Adagio’s D flat has nothing to answer; remove the Scherzo’s insistence and the trio’s A flat has no weight to lift; the coda requires every movement, since it is built from their themes. But the test finds give, and the work’s own history shows it. Between 1887 and 1890 Bruckner replaced a whole trio and rewrote the Adagio’s climax; an editor spliced 1887 bars back in without the joins showing; the Finale was long played with cuts. Inside the movements a period is stated, halted and restated a step higher: much of this is structure, some of it habit. Length is not charged. The repetitions are.
Fyodor Dostoevsky · Literature
8.6 · Tier IV
The test is harder here than in a novel, because the book is built by accumulation: portraits, institutions, feasts, a hospital, animals, an escape. Much is required. The first chapters must establish the place before anything in it can mean. The Christmas feast and the theatricals are the two days on which the convicts are, for a while, free men, and the book’s argument about freedom needs them; the hospital is where the floggings are seen from the far side, on backs brought in from the line. What holds the axis lowest of the twelve is what could go without loss: some of the cataloguing of types in the seventh and eighth chapters of the first part, which repeats a point already made; the goat Vaska, closer to anecdote than the eagle beside him; and stretches of generalisation on punishment and on the Russian people that restate what the scenes have shown. The book is necessary in its spine and loose in its middle.
Thomas Jefferson · Architecture
8.6 · Tier IV
Judged on plan and use under purpose and site. Most of the plan is compelled by a programme written before it was drawn: one house per school, so each professor lives over his own classroom; students lodged between, so teacher and taught share one row; a covered way, so the schools connect dry; a green, so the community has a common room under the sky; a library at the head, so learning has its centre. The serpentine walls are compelled by economy. What yields to the subtractive test: the ten different orders are a display for teaching, chosen to be various, not required by the pavilions; the library room is a Pantheon interior asked to hold books; and the student rooms are smaller than their use asked.
Toni Morrison · Literature
8.6 · Tier IV
The test is subtractive, and the book resists it in its spine and yields to it at the edges. The spine is made of necessities: Macon Dead’s rents and his creed of owning things; Pilate’s green sack and the bones in it; the gold that Macon and Milkman believe hangs in a cave; the children’s song that turns out to be the family’s history. Each pays out in the second part. Remove Hagar and Milkman’s selfishness has no cost; remove the Seven Days and Guitar’s love has nothing to betray it. This is the lowest of the twelve, and what holds it there is the edges: the first part is long before the quest begins, Milkman’s idle twenties repeat one fact several times, the Seven Days’ logic is explained more than once, and Corinthians’ affair with Porter could be shortened without loss. Perhaps a tenth of the book could go.
Le Corbusier · Architecture
8.6 · Tier IV
Judged on purpose, structure and site. The core resists the subtractive test. The interlocking duplex is why every family can have two aspects and a double-height room while a corridor is needed on only one level in three, and the interior streets are where the section puts them. The rack follows from the idea of dwellings as units set into a frame; the pilotis free the ground so the park passes under; the roof is the ground the slab took away. What holds the axis at 8.3: the shopping street at mid-height is a programmatic wager, not a necessity; the pilotis are far heavier than their load asks; and the narrowness of the flats is compelled by the section more than by dwelling.
Frank Lloyd Wright · Architecture
8.6 · Tier IV
Judged on purpose, structure and site. The large rotunda resists the subtractive test almost entirely: the ramp is floor, gallery, circulation and structure at once; the void is light, orientation and the building’s single room; the outward lean of the wall is the ramp’s own widening. Take any of these away and the others fail. The site compels less: the building turns from the grid of Fifth Avenue and answers the park by refusing the street wall. What yields is purpose. Paintings do not need a slope, a curved wall or a shallow bay, and the form is compelled by Wright’s idea of a museum more than by the art it shows. The tower of 1992, part of the one work, is a conventional stack of galleries and offices that the form did not call for.
Guarino Guarini · Architecture
8.6 · Tier IV
Run the subtractive test. The dome passes it best: take away one arch and the star, the open octagon at the centre and the view of the lantern fail together, because each arch is braced by the arches it crosses; take away the open webs and the light that is the building’s reason goes. The bowed bays are compelled by the dome, gathering the drum’s eight points down to the floor. The site compels the hidden exterior. What yields is below: the presbytery is a second centralised room that the liturgy permits but does not require, the screens and coloured marble multiply articulation past what the space asks, and the pendentive zone is a set of transitions rather than one necessary step.
Walker Evans · Visual art
8.6 · Tier IV
Judged on the sequence, since that is the unit. The two-part plan is compelled: the first part holds people among their images, the second the built country without them, and the argument is the passage from one to the other, the faces becoming facades. Inside each part the subtractive test bites at the hinges. Penny Picture Display, a wall of small identical portraits, is the book’s statement of its own method and cannot go; Alabama Tenant Farmer Wife, the one face held at full gravity, anchors the first part. Posters, cars, signboards and graves recur and bind plate to plate. What yields is the middle of each part, where a street view or a frame house could be exchanged for another from the same campaign without loss; the exhibition’s other order shows the order was not single.
Ernest Hemingway · Literature
8.6 · Tier IV
The spine is tight and the five books are each required: war, love, rout, flight and death, and the last undoes the escape the fourth achieved. Remove the third book and the separate peace is never earned; remove the fifth and the love story is a romance with a happy exit. The subtractive test bites in the second book. The Milan summer runs long: the horse races at San Siro with the fixed horses and the Meyerses, the café talk with Ettore Moretti and the American singers, the rounds of drinks and endearments in the hospital bed, which repeat a state rather than move it. The billiards at Stresa with Count Greffi could go. The Swiss winter is long by design, and passes the test better than Milan, because its quiet is what the last chapters take away. What holds the axis is about a tenth of the second book that says one thing several times.
Clifford Possum Tjapaltjarri · Visual art
8.6 · Tier IV
The subtractive test bites in two directions. Each roundel and each track stands for a named place and a named passage of a being across country: remove one and a site goes from the map, and the law says what is there. In that sense nothing is ornament. But the composition is a gathering. The canvas holds several Dreamings because the painter chose to hold them, and a map can take one more line or lose one at its edge without changing its claim. The dotted fields are required as ground, the country between sites, but their extent is set by the canvas and not by the argument.
Joseph Haydn · Music
8.6 · Tier IV
The six days give the work a spine no part can leave. Each day is announced from Genesis in recitative, enacted in the orchestra and answered in praise, and all six close on a number with chorus. Take out a day and the week is broken; take out the Chaos and the work loses its subject, which is the passage from it to light. The subtractive test still finds give. The pattern is repeated more than developed: trio and chorus follow in the same order in nos. 18 and 19 and again in nos. 27 and 28, and no. 28 repeats the words of no. 26. Gabriel’s two arias are separable, and Part III’s second duet is often shortened without loss. The scale is permitted by the schema more often than compelled by it.
J. M. W. Turner · Visual art
8.6 · Tier IV
Judged by subtraction. Take away the sun and the sea has no source: the light is the picture’s spine, and it falls straight onto the place of the drowning. Take away the ship and the deed has no agent; it is small, fleeing and already half lost, and that smallness is the verdict. Take away the leg and the chain and the canvas becomes a sunset storm, for the atrocity lives in a few strokes at the lower right, the most necessary on it. Take away the typhoon and the promised judgment is gone. What gives is the margin: the fish and sea creatures are permitted, not compelled, and could be halved without loss; the gulls are filler.
F. W. Murnau · Film
8.6 · Tier IV
Judged on structure, since the words are few. The spine is required: the marsh gives the plan, the boat gives the refusal, the city gives the second courtship, and the storm gives back to nature the murder the Man renounced, using the bulrushes the Woman from the City bound for him. In the city the church is required, since it is where the Man breaks, and so is the café, the lowest point. There the subtractive test bites. The photographer, the barber and his masher and above all the pig chase at Luna Park could be shortened without loss; the holiday trains of the opening are a frame the film could do without; and the storm is compressed to the point of abruptness.
The Smiths · Music
8.6 · Tier IV
Ten tracks in about thirty-seven minutes, most of them required by what the record says. The title track states the nation, “I Know It’s Over” and “Never Had No One Ever” the self, and “There Is a Light That Never Goes Out” the one way out the self can imagine. The comic songs are not decoration: “Frankly, Mr. Shankly” and “Cemetry Gates” carry the record’s second claim, that wit is the provincial’s only weapon. The subtractive test bites in two places. “Vicar in a Tutu” could go with little loss, its joke at the Church already made in the title track, and “Never Had No One Ever” says one thing at length.
Norman builders, under William II · Architecture
8.6 · Tier IV
Judged on purpose, structure and site. The building had four tasks at once: abbey church, cathedral, royal mausoleum and the king’s answer to the archbishop of Palermo. The plan carries all four: a long nave for the people and the monks’ liturgy, a broad Byzantine sanctuary for the clergy and the thrones, the king’s throne opposite the archbishop’s under the image of his coronation. The mosaics are not ornament added to a shell; every bay advances the history toward the apse. What yields to the subtractive test: an arcade of reused shafts of unequal stone, assembled rather than compelled; a timber roof, the cheapest answer to the span; the visible join of Latin body and Byzantine head; and later chapels and porticoes the purpose does not require.
Diego Rivera · Visual art
8.6 · Tier IV
Judged on the programme, wall by wall. The two main panels cannot go: the car exists only as the union of engine and body, and the court is the one place where both halves are seen at once. The giants above them cannot go, for they are where the metal comes from, the earth stood up as bodies. The infant in the bulb of a plant cannot go: it is the origin the cycle turns from. What yields lies in the margins, and it is what holds the axis among the two lowest of the twelve. The paired allegories of good and ill are needed as an argument but could be fewer; the grisaille predellas repeat in small what the main panels show; and the main panels are crowded past what their argument compels, with passages of machinery that fill rather than build.
Charles Mingus · Music
8.6 · Tier IV
The subtractive test bites more than it does on a record of tunes, because this one is sectional by design. Inside “Solo Dancer” the parts are required: the slow, heaving ensemble figure over Dannie Richmond’s tread, the brass growling against it, the alto rising out of the mass. Each dance of side one sets up the next, and the titles hold them to a plan of one, two, many. The give is on side two. Its eighteen and a half minutes return to themes of side one and pass through episodes, a flamenco interlude for guitar, a passage of piano near to solo, a reprise of the alto’s lament, whose order could change without loss, and parts sound like a ballet’s linking music. The return is partly the design, a dance coming back to its figures, so it is charged lightly.
David Lean · Film
8.6 · Tier IV
The prologue is required: a death and a memorial at which those who knew him cannot agree who he was make the whole film an answer to a question it will not answer. Part One is near to bare. The well, where Ali shoots the guide for drinking, sets the law of the desert; the return for Gasim makes Lawrence’s claim, and his execution of the same man, to stop a blood feud, is that claim’s cost. Aqaba is the summit and the Sinai its price, paid with Daud. Length is not charged; the crossings are compelled. Repetition is charged, and Part Two gives more: the train raids make one point twice, Bentley is needed for the legend but played at length, and the council in Damascus is shorter than its weight.
Frédéric Chopin · Music
8.6 · Tier IV
Inside each prelude the subtractive test finds almost nothing. No. 7 is two phrases of eight bars and nothing else; No. 9 says its piece in a few lines; the last phrase of No. 20, repeated softer, is the one repetition that could go, and it is the one that makes the piece a farewell. The longer preludes hold their length: the middle of No. 15 must swell for the A flat’s return to mean anything. The cost is at the level of the unit. The key cycle requires twenty-four pieces, but a scheme requires a key, not this prelude: No. 3, No. 5 or No. 23 could give way to another figure in the same key. And for a century the set was played in handfuls.
Achaemenid, under Darius I and Xerxes · Architecture
8.6 · Tier IV
Judged on plan, programme and site. Take away the terrace and the court stands on the plain like any town; take away the double stair and the ascent becomes a ramp, without its two turns; take away the Gate and arrival has no threshold and no guardians. Take away the stair reliefs and the Apadana loses the image of what it was for. Its thirty-six columns are fixed by the span a timber beam will carry. What resists the test is the terrace as a whole: separate buildings set side by side on a grid across three reigns, with no single axis. Two great halls stand side by side; the Hadish, the Harem and the lesser palaces could go without loss to the governing idea; the files of guards repeat for repetition’s sake.
Alejo Carpentier · Literature
8.5 · Tier IV
The subtractive test finds a spine that is required and a book with almost no fat in the paragraph. The first part sets the law: Macandal’s maiming in the cane mill, his poisoning, his metamorphoses and his burning show that the enslaved live in a world the masters cannot see. The second, Bouckman and the oath in the storm, then the flight to Santiago de Cuba, turns belief into history. Christophe’s kingdom is the argument, the freed become masters, and the fourth part closes the cycle with new masters again. Each part is required. The test bites in the episodes Ti Noël does not witness, Pauline Bonaparte’s island idyll above all and the exiled queen’s Rome: they carry the theme, but could be shortened with little lost.
Édouard Manet · Visual art
8.5 · Tier IV
Judged part by part, the core holds and the setting gives. The three foreground figures cannot go: clothed men and an unclothed woman are the proposition, and the triangle they make, taken from the river gods in Raimondi’s engraving, is the composition. The still life cannot go: the shed blue dress, the hat and the spilled fruit say that she was clothed and is now undressed, the difference between a nude and a naked woman. Her look cannot go. Below that the test yields. The woman in the stream is needed as the pastoral’s bather, but her scale and the backdrop she stands in are arguable; the boat and the bird could go with little loss; the wood is a stage flat. The scale is compelled: a Salon format given to an outing on purpose.
The Doors · Music
8.5 · Tier IV
Eleven tracks, and the test bites in the middle of each side. Break On Through must open: it states the record’s one wish, passage through a threshold, in under two and a half minutes over a bossa nova beat turned hard. Light My Fire must close side one and The End the record; each is where the short songs’ tension is let out into duration. The Crystal Ship and End of the Night are required as the two night-pieces, the quiet doors. The rest resist the test more than they first appear to. Twentieth Century Fox is a sharp, slight portrait, but it is the daylight world the record wants out of, and without it the doors would open from nowhere; Take It as It Comes restates the side’s urgency, and that urgency is what the long piece releases. I Looked at You, garage pop in the manner of the day, is the one track that could go with ease. The short songs are the room the doors are cut in, compelled by the passage rather than permitted beside it.
Eugenio Montale · Literature
8.5 · Tier IV
The title section is close to irreducible. “Spesso il male di vivere ho incontrato” is eight lines in two quatrains: three images of the evil of living, “il rivo strozzato che gorgoglia”, “l’incartocciarsi della foglia / riarsa”, “il cavallo stramazzato” (the choked stream that gurgles, the curling of the parched leaf, the fallen horse), then the counter-image of a divine Indifference; remove a line and the scale collapses. “Meriggiare pallido e assorto” walks four stanzas toward a final turn the whole poem was moving to. The book is less compelled. “Movimenti” carries softer, musical apprentice pieces, “Corno inglese” and “Minstrels”, which the book could lose and know nearly as much, and “Mediterraneo” restates its argument across more movements than it needs.
Robert Frost · Literature
8.5 · Tier IV
The test is subtractive, and the great poems pass it. Nothing in “Home Burial” could go, and the slow arrival of Silas’s death in “The Death of the Hired Man” is paced to the line. The frame is exact: “The Pasture” opens on an invitation into a farmer’s chores, each stanza ending “You come too”, and the book is that walk, into kitchens, onto porches, across a boundary wall; “Good Hours” closes on a walker outside the cottages the book has entered. What lowers the axis is the middle. “A Hundred Collars” and “The Generations of Men” are looser, the second a flirtation drawn out past its matter; “Blueberries” is a pleasant gossip; “The Housekeeper” repeats a household of failed bonds that other poems give with more pressure. Three or four poems could leave with small loss.
Louis Le Vau and André Le Nôtre · Architecture
8.5 · Tier IV
Judged on purpose, site and structure. The purpose was a minister’s seat of reception and display, and the parts answer it: a forecourt to receive, a bridge and moat to set the house apart, a vestibule opening straight onto the axis, an oval salon where the company is gathered and turned to the view, suites on either side for the master and for the king. The valley compels the garden: the house on the upper ground, the fall of the slope, the river made into the cross-canal, the far rise closing the view. What resists: the repeated basins and side groves could be thinned without loss, the service courts are not required by the idea, and the moat is an inherited sign, not a need.
Akira Kurosawa · Film
8.5 · Tier IV
Judged on structure, and the two movements resist the subtractive test as movements: the first is required so that the viewer holds what the mourners do not, the second so that the deed is seen only as others saw it. Most scenes within them are needed. The petition montage sets the cesspool that becomes the park; the pension talk overheard upstairs sends Watanabe out of his own house; the night with the novelist is the false road, which must be tried and fail before the clockwork rabbit gives the true one; the last morning at the office is the reckoning. What gives is repetition, and it recurs in every part. The night tour, through bars, a strip show and a dance hall, makes one discovery several times; the days with Toyo repeat their unease; and the wake states its turn, each mourner recalling a further episode and growing drunker, more often than the argument needs. The movements are compelled; the length inside them is in places only permitted.
Michelangelo Antonioni · Film
8.5 · Tier IV
Judged on structure. The prologue and the coda are each required, and together they are the argument: the film opens on a love ending in silence among objects and closes on a love failing to arrive, with the objects left. Between them the Borsa sequences are required, setting feeling beside money as two markets with the same weather: the minute of silence for a dead broker, then the roar; the crash that ruins Vittoria’s mother and that Piero handles as a working day. The drowned car is required: a man has died and Piero looks at the dents. What gives is in the middle: the masquerade at Marta’s flat and the flight to Verona are strong images loosely tied to the line, and Verona could go with little lost.
Charles Laughton · Film
8.5 · Tier IV
Most of the film is required, and what is planted pays. The doll holds the money from the first reel to the last, and Pearl cutting paper dolls from the bills is the most dangerous scene in the house. Ben’s arrest on the lawn, with John watching, is required by Powell’s arrest in Rachel’s yard, where John breaks and beats him with the doll: the film’s whole argument is that second arrest. The cell scene puts the money in the killer’s head; Willa’s revival gives him a congregation. What gives: the Spoons’ parlour runs longer than its point, Uncle Birdie’s turn leads nowhere and the film says so twice, Ruby’s errands state one idea several times, and the mob is broad and quick.
Margaret Atwood · Literature
8.5 · Tier IV
The subtractive test finds little that can go. The Ceremony is the hinge, and everything leans on it. The Red Centre gives the Aunts and their method; Moira gives the one act of escape; the narrator’s mother and Luke give the time before and its own small complicities; Ofglen and the Mayday network give the possibility of resistance and its cost; the Commander’s study gives the regime’s private hypocrisy; the Historical Notes give the afterlife of the testimony. The alternation of Night and day is structure, not padding. Charged on two counts: Jezebel’s depends on a convenience, the Commander taking Offred to the one club where Moira happens to be, whose history then arrives as a long recited story rather than a scene; and the Scrabble evenings repeat their turn after their point is made. Necessary in its architecture; a few joints show.
Stanley Kubrick · Film
8.5 · Tier IV
Judged on structure. The spine resists subtraction. The second day is required: Bill goes back in daylight to each place of the night and finds it emptied, explained or turned sordid, and without the retracing the night would stand as fact. The party is required, since Mandy, Ziegler and Szavost are planted there. But at 159 minutes the subtractive test finds give. The bald man in the street plays a dread the warning at the gate has already set; the second visit to Milich restates the first; the desk clerk is held for comedy past his information. The echoing line readings are partly the dream’s law and partly only length.
Burgundian Romanesque builders · Architecture
8.5 · Tier IV
Run the subtractive test along the axis. The narthex cannot go: a church that drew crowds on feast days needed a room where the multitude gathered, waited and was ordered, with tribunes above for further altars and a door through which the nave is first seen whole. The ten bays cannot become six without losing the measured approach that is the nave’s purpose; the repetition makes the pilgrim’s progress countable. The crypt is the reason for the whole. What resists the test is less the plan than its filling: the capitals are a profusion, many illegible from the floor and not compelled by use, and the Gothic choir answers a real need in a second idiom.
Frank Lloyd Wright · Architecture
8.5 · Tier IV
Judged on purpose, structure and site. In the Administration Building the subtractive test mostly fails to find a removable part. The columns are the roof, the structure and the light at once: take them away and the room needs beams, a ceiling and windows, and is a different room. The blank walls follow from a stated purpose, to turn a clerical workforce inward from an industrial street to one shared sky, and the carport makes the approach by car the threshold. What resists: the glass tubing was a choice of image over weather, and its leaks show it; the curves of the walls answer a style as well as a need; and the tower’s small, round-edged floors and single stair fit laboratories poorly. The first building is compelled; the second is more willed than required.
Prince · Music
8.5 · Tier IV
Sixteen tracks in about eighty minutes, and the subtractive test bites more often than on a single album, as it might on a record assembled from three abandoned projects. But it bites on tracks, not on the scale. The subject is a whole society in one year, from the title song’s news to the sacred, and the four sides are compelled by it: take a side away and the record loses an order of its claim, not a stretch of its running time. Some parts are required. The title track must open, a bare report on the year that sets the public frame; If I Was Your Girlfriend is the record’s centre and could not go; The Cross and Adore are the compelled close, faith and then devotion. Housequake, Strange Relationship and I Could Never Take the Place of Your Man each say a thing the others do not. The test finds slack in three places and length in a fourth: Hot Thing is a groove more than a song, It holds one idea for five minutes, U Got the Look is a duet single the record tolerates more than needs, and Play in the Sunshine makes the turn from report to escape at greater length than the turn requires. The range is compelled; a few of the tracks within it are permitted.
William Kentridge · Visual art
8.5 · Tier IV
The test is run on the film and on the cycle. Within the strongest films nothing idles. In Mine the plunger of Soho’s coffee pot goes down through the breakfast tray into the shafts and the bunks of the miners: take it away and the film loses the hinge between the owner’s morning and the labour under him. In Felix in Exile every drawing of a body on the veld, covered by paper, by survey marks and then by the earth, is required. The cycle is weaker on the test. Its films were made one at a time, without a plan, over fourteen years, and it gathers rather than resolves: the love triangle and the megaphone in Johannesburg and Sobriety, Obesity and Growing Old could go without loss to the arc, and Tide Table adds as much as it completes.
Bernardo Bertolucci · Film
8.5 · Tier IV
Judged on the film as released in 1970, without the dance of the blind. The frame makes the structure purposeful: every return to the past is summoned by the drive, and the drive is the act the past has prepared. What resists the subtractive test is the core: the memory of Lino, the confession, the professor’s study, the dance hall, the wood. Each is required, and the end of the frame pays all of it. The test bites elsewhere. The visit to the mother’s villa and the visit to the father in the asylum are each a set piece of decadence carrying one idea, and either could lose half its length. The radio studio and the long betrothal scene run on charm. The coda is necessary in idea and contrived in mechanism: Lino, believed dead, turns up the same night in the same street. The dance of the blind, where restored, adds a scene whose motif is already carried.
Thomas Pynchon · Literature
8.5 · Tier IV
The test is subtractive, and it finds the spine required and the ornament partly permitted. Each clue Oedipa follows is necessary: the post horn on the latrine wall, the play with its one line about Trystero, the stamps, the night walk, the editions of Wharfinger, the auction. The Courier’s Tragedy, long as its summary is, cannot go, since it is the only place the Tristero speaks with a history. What could go with little loss is part of the comic machinery: the full length of Strip Botticelli and of Metzger’s career as the child actor Baby Igor, the Paranoids’ songs, part of the Inamorati Anonymous story, and the more cartoonish turns of Dr Hilarius’s breakdown. Each of these carries the theme of signal and noise, so none is idle, but each runs past the point where it adds a turn. Perhaps a tenth of the whole is permitted rather than compelled.
Luchino Visconti · Film
8.5 · Tier IV
The film’s main decision is subtractive, and right. It ends at the ball and the walk home at dawn, drops the novel’s last two parts, and leaves the Prince’s death foreseen rather than shown. Most of what remains is required. The dead soldier in the garden brings the war inside the house in the first minutes. The falsified plebiscite and Don Ciccio’s confession on the hunt are the political argument in small. Angelica’s laugh at the Donnafugata dinner is the new class breaking into the old room. What gives: the Palermo street fighting runs longer than its function, which is to show Tancredi changing sides; the lovers’ wandering through the palace’s empty wings repeats its point; the journey to Donnafugata takes in more ceremony than it needs. These are long stretches of a long film, not idle parts, and they hold the figure where it is.
David Fincher · Film
8.5 · Tier IV
The film is built to be watched twice, and the second viewing makes much of the first required. The revelation in the hotel room turns apparent digression into evidence: the single frames that flash Tyler before he is introduced, the projectionist’s splices, the narrator’s refrain, “I know this because Tyler knows this.” The support groups are needed for Marla, and Marla for the split; the office and its recall formula are needed for the economy the film attacks. Even the voice-over’s riffs, on the catalogue and the organs of Jack, are the split self talking. The give is in the Project Mayhem montages, which run on episode by episode, and in the replay after the revelation, which explains what the film has just shown.
Hilary Mantel · Literature
8.5 · Tier IV
The subtractive test bites less than the length suggests. The Putney opening is required: the beaten boy who leaves is the source of the man who learns that violence can be managed, priced and deferred. The long Wolsey sequence, through the cardinal’s fall and death in 1530, is required, since Cromwell’s loyalty to a fallen master is the ethical ground the rest of the book tests. The deaths of Liz and of the daughters Anne and Grace are not episodes but the hollow the later ambition fills. What could go: some of the middle court business of 1531 to 1533, Austin Friars scenes that repeat their note, and recollections of Italy given more than once. Below the 8.5 of Anna Karenina.
Ancient Egyptian, under Ramesses II · Architecture
8.5 · Tier IV
Run the subtractive test. The Great Temple is subtractive in fact: every part is what was left when the rest was taken out of the hill, and almost nothing yields. The axis is compelled by the sun: its length, its narrowing and its fall in height from hall to sanctuary are what let the dawn reach the statues at the back on two mornings of the year. The colossi are the pylon, the façade is the cliff face, the pillars are the rock left to hold the roof. What yields is repetition: the king four times outside, eight times on the pillars and on every wall, permitted by power more than required by the argument. The side chambers are ancillary, and the Small Temple is joined to the larger by kinship, not compelled by it.
Dominikus Zimmermann · Architecture
8.5 · Tier IV
The plan is compelled by the purpose. A pilgrimage church takes crowds that arrive, circulate and kneel: the oval with its ring of paired piers gives one gathered room for the congregation and an ambulatory behind it for processions, and the long choir sets the figure at the end of the axis, far enough to be approached and high enough to be seen over a crowd. Tower and priests’ house serve the clergy and cost the pilgrim nothing. The subtractive test bites only on ornament. Less of the stucco can go than in most churches of the type, because it dissolves the line between pier and vault; still, a share of it is permitted rather than required.
Reginald Ely, John Wastell and others · Architecture
8.5 · Tier IV
Run the subtractive test. The aisleless vessel cannot be reduced: it is what a college of a provost, seventy scholars, chaplains, clerks and choristers needed for a sung office and a founder’s chantry, and Henry VI fixed its dimensions in writing before the walls rose. The buttresses cannot go, nor the chapels between their feet; the glass cannot go, since the wall is nearly all window; the screen cannot go, since it closes the choir for the college. What resists is the antechapel: heraldry carved over its lower walls at a density no use compels, against the founder’s wish for a plain church, and a length, half the building, more processional than liturgical.
Peter Paul Rubens · Visual art
8.5 · Tier IV
Run the subtractive test figure by figure. Most of the programme resists it, because each figure is one of the goods that war destroys and the argument is their sum. Europe cannot go: she is the loss named. Venus cannot go: without her pull there is no struggle, only a march. Alecto cannot go: she supplies the force that Venus fails against. The fallen at Mars’s feet, the lute, the mother, the architect, are the inventory of civil life, each a distinct good. What yields lies at the margins: Plague and Famine crowd the shadow at the right and barely read as separate ideas, the Cupids multiply a figure one would carry, and the trodden books and drawing repeat the lute.
Edward Yang · Film
8.5 · Tier IV
Three hours are compelled by the design. The argument is that five lives run the same course at different stages, and that can be shown only by letting each run. Remove NJ’s days with Sherry and Ting-Ting’s romance loses its rhyme; remove Yang-Yang and the film loses the one eye that looks at what others cannot see; remove the coma and no one is forced to speak. Ota is required, the honest man the partners betray. What gives is weighed. A-Di’s debts, his old girlfriend and the gas leak repeat the family’s concerns more broadly than they need; the partners’ meetings make one point several times; the machinery of the killing is thicker than its function. Perhaps a fifth of the length is permitted rather than compelled.
Gerhard of Cologne and successors; completed by Ernst Friedrich Zwirner · Architecture
8.5 · Tier IV
Run the subtractive test on the choir and almost nothing goes. The ambulatory and the seven radiating chapels exist to carry pilgrims round the Shrine of the Three Kings behind the high altar; the clerestory exists to light it; the flyers exist because the clerestory is glass. The five-aisled nave is compelled by a cathedral built for the crowds of the Magi’s cult and for German kings come from their crowning at Aachen. What resists is the west. No use compelled two towers of 157 metres, only a medieval claim and a later age’s will to fulfil it, and the front panels every surface in tracery, gable and pinnacle past what structure or liturgy needs. The tracery is the system, not ornament; the defence holds in part.
Jackson Pollock · Visual art
8.5 · Tier IV
Judged on the configuration, by layer and by breadth. Take away the black and there is no armature: the brown and white float without the long arcs that hold them, and the field has no large rhythm. Take away the white and the field goes dark and heavy, the fine web that lifts the darks gone. Take away a metre at either end and the rhythm of three or four thickenings loses a beat, and the margins, which show the format was in view, are cut. Removal fails at the layer and the breadth. What holds the axis is substitution: at the level of the skein any line could be another, the teal is accent, and the canvas was cut from a roll on which One, of nearly the same size, was painted the same season. Compelled as a whole, permitted in its parts.
Egyptian (Early Dynastic) · Visual art
8.4 · Tier IV
The subtractive test, register by register. The king cannot go on either face: he is the axis of each. The two crowns cannot go: the object’s argument is that one man wears both. The smiting group is the whole of one face’s statement, and the falcon on the papyrus land, holding a rope to a human head, is its gloss in image-writing, the god holding the conquered land as the king holds the enemy. The serpopards cannot go: their wound necks make the cosmetic well the sign of two joined powers. The bull is the king’s other body. What yields is at the margins: the standard-bearers and attendants are partly a list of office, adding rank rather than meaning, and the fallen men in the lowest band repeat what the main field has said.
Günter Behnisch and Frei Otto · Architecture
8.4 · Tier IV
Judged on purpose, structure and site. Nearly every member is in pure tension and every part does work: the masts take compression, the net takes tension, the edge cables gather it, the anchors return it to the ground. Remove a mast and a saddle falls; remove an edge cable and the net cannot be held. The form is found, not chosen: the surface is the shape the forces take. The site compels the rest, for the roofs run low over the paths and rise over the venues, answering Grzimek’s hills. What yields: the stadium roof covers one stand only, so the purpose of a roof over spectators is half met; the scale and translucency answer the image as well as shelter; and over hall and pool the net is a ceiling over enclosures with their own law.
Workshops of Qin Shi Huang · Visual art
8.4 · Tier IV
The subtractive test bites at two levels. Remove a figure and nothing is lost; remove a rank and little is. Remove number itself and the work ceases: an army is a multitude, and the argument of these pits is that the state could put an army under the earth. The scale is compelled, not permitted. Each pit is required: the massed infantry of the first, the mixed arms of the second, and the command of the third, without which the host has no head. The types, archer standing and kneeling, infantryman, charioteer, cavalryman, officer and general, are the army’s organisation and cannot be thinned without the order going false. What yields is the single body inside the mass, replaceable by design. That is the work’s meaning and its limit here, and it holds the figure below Las Meninas at 9.0, where each figure carries weight.
Kraftwerk · Music
8.4 · Tier IV
Seven tracks in about forty-three minutes, and repetition changes the subtractive test: in Europe Endless the length is the content, a continent run past a window with no arrival, and cut to four minutes it would become a song. Side two is the most necessary stretch on the record. The title track sets the train going, Metal on Metal is the same journey with the melody stripped off, Franz Schubert is the arrival in a softer light, and Endless Endless closes the circle. No piece can come out without breaking the line. The test bites on side one: The Hall of Mirrors is long for what it develops, and Showroom Dummies, its theme belonging to the argument, has a manner that could sit on another album.
Thomas Eakins · Visual art
8.4 · Tier IV
Judged figure by figure. Gross cannot go: he is the intellect of the scene and its light, and the turn of his head from the wound toward the room is the picture’s act. The patient cannot go, nor the hands at the incision: the retractors, the probe and the blood are the fact the painting will not soften. The cloth of anaesthetic names what the century had just made possible. The woman in black cannot go: she is the one figure who refuses to look, and without her the picture loses its cost. The clerk recording and the painter in the tiers make the clinic a place where seeing is turned into record. What yields is the field of students, required as a mass and permitted as individuals, and the figures in the doorway, which are atmosphere.
Hou Hsiao-hsien · Film
8.4 · Tier IV
About 157 minutes, and the subtractive test bites less than the length suggests. The four brothers are each required: the eldest, who holds the family business and dies in the quarrel with the Shanghainese; the second, lost in the Philippines and never seen, an absence the house carries; the third, back broken from Japanese service, arrested as a collaborator and sent home deranged; the youngest, deaf and mute, taken last. Remove one and the arithmetic of a family thinned by successive regimes fails. What holds the axis among the lowest: the gangster and smuggling business is drawn at greater length than its job requires, the intellectuals’ talk at table repeats its point, and some ellipses cost the viewer the thread and give nothing back.
Anthony Burgess · Literature
8.4 · Tier IV
The book is short and its plan is strict: three parts of seven, crime, cure and return, and the third part retraces the first point for point, so that each victim comes back with power over the boy who hurt him. Remove the old man with the library books in Part One and his return in Part Three has nothing to answer; remove the chaplain and the question of choice has no voice inside the prison. The parts are required by the argument, and the last chapter is required by Burgess’s argument as he wrote it. What holds the axis is the mechanism of Part Three: the coincidences that bring Alex to the library, to Dim and Billyboy in uniform, and to the one house in England where he will be recognised are a moral pattern laid over the plot rather than grown from it, and the conspirators around F. Alexander are thinly made.
Joseph Wright of Derby · Visual art
8.4 · Tier IV
Subtract figure by figure and most resist. The lecturer cannot go: his hand on the valve and his gaze out at the viewer are the question the picture puts. The bird cannot go; a pale shape at the apex, lit hardest, it is the victim and the centre. The girls are the felt response, the man with the watch the measured one, the brooding old man the reflective one, and the ring of attention is built from them as a chord from its notes. The boy at the window with the cage is the hinge of whether the bird returns. What yields: the young couple are a sentimental aside that thins the ring’s gravity, and the left side carries more people than its argument requires. Compelled in most places, assembled in a few.
Jean-Luc Godard · Film
8.4 · Tier IV
The subtractive test mostly fails to find slack. Twelve short tableaux, each a station of Nana’s descent: the café break with Paul, the record shop and the borrowed money, the keys refused by the concierge, the police station, the cinema and Dreyer’s Joan, the first client, Yvette and Raoul, the billiard hall, the young man and the Poe, the end in the street. The two long digressions a hostile cut would take, the talk with Brice Parain and the reading of “The Oval Portrait”, are the argument: the first says what her life has been without her saying it, the second names the film’s own act on its model before it kills her. What gives is the catechism of the trade, long and recited, carrying what could be shown in less; and one or two tableaux are thin.
Gunnar Asplund · Architecture
8.4 · Tier IV
Judged on plan, section and purpose. Take away the drum and the library has no centre: if the whole collection is to stand round the reader at once, the circle is the one figure that does it. Take away the dark stair and the entry is a corridor, not an ascent; take away the clerestory and the white upper wall has nothing to do. The dropping of the dome is the plainest evidence: a classical crown the purpose did not need was drawn and then removed. What resists the test is the ring round the core. The rooms of the block could be replanned without loss, the shops are a revenue device, the pool belongs to the street, and the closing wing takes its form from symmetry more than need.
Richard Linklater · Film
8.4 · Tier IV
At this scale the length is compelled: twelve years cannot be felt in ninety minutes, and an unmarked cut between years needs room on each side to land. The large movements resist subtraction. Take out the first marriage, to Bill, the professor who drinks, and the flight from his house, and the mother has no climb; take out the second, to a veteran of Iraq who drinks too, and the cycle is a single accident; take out the sold car and the father has not changed. What gives is at the level of the scene: the camping trips, the photography teacher’s lecture, the late talk of technology and freedom, the plumber’s return. Drift is the method, and the film pays for it here.
Kongo · Visual art
8.4 · Tier IV
Subtract part by part. The medicine pack cannot go: without it there is no nkisi, only a carving, and its mirror is the eye through which the force sees. The raised arm and its weapon cannot go, for this is a hunter poised to strike. The open mouth and the tense stance, hands on hips, knees bent and chin forward in the Mangaaka, are the alert of an enforcer. The nails as a mass cannot go: they are the record of what the figure was asked to do. But the test bites on the nail field itself. No single nail is required, the density is the sum of local cases rather than a composition, and on smaller figures the accretion can be cluttered and the bindings random. Necessary as a mechanism, partly assembled as a surface.
Arcade Fire · Music
8.4 · Tier IV
Sixteen tracks in about sixty-four minutes, and the spine of the record is required. The frame is: the title song opens the remembered suburb and its reprise closes it, the song returning broken. Suburban War is the account of how friends were divided, We Used to Wait the account of what has gone from time, and Sprawl I and Sprawl II the return to the old streets and the flight from them. Ready to Start sets the adult’s position. The length mirrors the subject’s sprawl. The test bites in places: Rococo and Modern Man restate the record’s distrust of the modern young in the same terms, Wasted Hours and Deep Blue say quietly what We Used to Wait says fully, and Month of May bursts with an argument Suburban War has already made.
George Miller · Film
8.4 · Tier IV
The subtractive test bites less than on most action films. The film is one pursuit whose two halves are the same road taken twice, and the turn is the argument, so neither half can go. Most planted things are paid: the blood bag clamped to Nux’s car carries Max into the chase and later into Furiosa’s veins; the gearstick lock and the kill switches pay on the return; the Keeper’s seeds are the film’s last word on what flight can save; the wife’s pregnancy is paid when Angharad falls. What gives: the night bog repeats work the canyon has done, the guitarist is held in shot beyond his use, and among the Vuvalini the film briefly idles.
Massive Attack · Music
8.4 · Tier IV
Eleven tracks in about sixty-three minutes, built on loops that grow by accretion, so that length is part of the method and not slack. Angel must open: a bass line alone, then a voice, then the guitar’s eruption, the record’s whole procedure in six minutes. Teardrop is the still centre the dread needs. Group Four, the longest, is the compelled climax, its length building a pressure it then releases, and (Exchange) is the compelled exhale, the instrumental of the middle returned as the lights come up. The test bites in the second half, and that holds the figure: Black Milk and the title track run in one mode, slow, close and dark, Man Next Door is the track least made from the record’s own matter, and a few loops are held past the point their pressure tells.
Jackson Pollock · Visual art
8.4 · Tier IV
The subtractive test meets an all-over field differently from a composed one. Take away the dark web and the field has no skeleton and no depth. Take away the pale and there is no mist, and the lavender of the name cannot form. Take away the aluminium and the surface loses the glint that keeps it shifting as the viewer moves. Each layer is indispensable. The scale is compelled: the field must be larger than the eye’s span at the distance the body stands, or it becomes a pattern seen whole. But at the level of the single skein the test is passed too easily: a given loop, here or a hand’s width over, could be otherwise without loss. Necessity of the whole, much less of the part.
Paul Thomas Anderson · Film
8.4 · Tier IV
Judged on structure. The prologue resists the subtractive test: the night at the border makes Lockjaw’s humiliation and his desire, and the robbery makes Perfidia’s crime and her betrayal, the premise of every later pursuit, since the second part is a man trying to erase a child who may be his. The forgotten code on the telephone is required: it shows how far Pat has fallen into Bob, and why he cannot reach his network when it counts. The paternity test is the hinge. What holds the axis here is the middle: the progress through Baktan Cross repeats its comic beat, the convent runs longer than its work, and the Christmas Adventurers are explained in more scenes than they need, so part of the length is earned by momentum rather than necessity.
Bernardo Rossellino, for Pius II · Architecture
8.3 · Tier IV
Judged on the ensemble, under its programme and its site. Four powers stand round one floor and each is required: the church at the head, the pope’s family palace on one flank, the bishop on the other, the commune facing the altar across the square. Take away the town hall and the square becomes a papal forecourt; take away the bishop’s palace and the splay that frames the cathedral has no second arm. The trapezoid is compelled by a ridge falling south to the valley and by what the patron wanted shown, the cathedral as terminus and the valley as its flanking ground. The scale is small and right. What holds the figure down: the palace’s street fronts are a borrowed elevation laid on a new site, the bishop’s palace is a refacing of what stood, and the work thins quickly beyond the square. The necessity is of the ensemble more than of every part.
John Huston · Film
8.3 · Tier IV
The subtractive test mostly fails to find slack. Tampico looks leisurely, but each scene loads the machine: Dobbs begging three times from the same man in a white suit sets his shame and his luck; McCormick cheating the two men of their wages teaches them that nobody pays what is owed; Howard’s talk in the flophouse gives the whole plot in advance, so that the rest is the working out of a known law. The shares, the hiding places, the quarrel over who guards the goods, Cody’s arrival and the vote on him: each is a step in one curve. Two parts are less required. The Indian village is needed to separate Howard from the others but is played longer and warmer than the curve asks, and the execution of the bandits in Durango is a coda before the coda.
Abbas Kiarostami · Film
8.3 · Tier IV
The subtractive test is passed by the frame: one man, one request, a refusal and an acceptance, the night, the waking. The repetitions are the content: the same road, the same hill, the same tree, the same offer reworded for each listener, and each listener tests a different ground for refusing, fear, law and life. Bagheri’s story needs the two refusals before it. What gives is in the middle. The opening approaches run long before the offer is made, and the seminarian’s scene is slack where the soldier’s was taut, its argument known before it is spoken. The coda is required by the design, though a viewer may feel the night’s darkness had already answered.
Akira Kurosawa · Film
8.3 · Tier IV
The adaptation is a work of subtraction. The Porter, the soliloquies and the whole line of Macduff are gone, and most of what is left is required: from the lord’s visit to the banquet the film is as compressed as any on this desk, each scene turning the next. The test bites twice, and in a film so stripped the excess shows. The messengers who gallop into the courtyard one after another, each reporting a turn of the rebellion to a seated council, run past what they have to tell; the point, that power here is news of violence received at a distance, is made by the third. And the ride in circles through the fog is the meaning, a man going round in a web, held at a length that passes from necessity into demonstration.
Luis Buñuel · Film
8.3 · Tier IV
Judged on structure, most of the film is required. The prologue gives the first fantasy in the film’s realist grammar before the viewer knows which grammar is in force, so every later scene carries the doubt. The ski resort is needed for Husson, the one person who sees her. The childhood flashbacks are needed and kept insufficient: they offer a cause and the film withholds the claim that they explain. Marcel, from outside the bourgeois contract, is needed to carry the double life into the flat and break it, and the prologue’s bells require the ending. The give is in the run of clients, where one episode, perhaps two, could go without loss to the argument, and in the last stretch, where the shooting and Marcel’s death are dispatched rather than built.
Auguste Rodin · Visual art
8.3 · Tier IV
The subtractive test on one body. The bowed head cannot go, nor the hand under the chin: they are the act. The crossed elbow cannot go: right arm to left thigh forces the trunk into a twist the eye has to travel round, and that strain is what separates this figure from every relaxed melancholy before it. The curled toes cannot go: thought reaches the ground through them. The rock cannot go; it is what the weight presses on. What gives is the enlargement itself. In the tympanum every part was compelled by a place, and the figure leaned because there was a pit below him. Set alone and enlarged, the lean is kept and its reason is gone, and the swollen musculature is more than the thought requires. Every part is required; the scale is permitted rather than compelled.
Correggio · Visual art
8.3 · Tier IV
Judged element by element, very little yields. Io cannot go, and the cloud cannot go. The half face in the cloud, where her own face turns up to it, is the hinge of the picture, the point where the god is and is not there. The hand at her waist cannot go: without it the cloud is weather, with it the cloud is a lover. The white drapery gathered under her gives the flesh its key and the composition its base, and the tall, narrow format is compelled, since it lets the cloud come down from above and close over a single body. What yields a little: the stag drinking at the lower right, a gloss the picture could lose at small cost, and the bank and foliage at the lower left, permitted more than required.
Édouard Manet · Visual art
8.3 · Tier IV
Judged on the configuration. The squad cannot go, nor its closeness: the muzzles almost touch the men they kill, and the range is the argument, killing done at arm’s length by men who do not look. The sergeant cannot go: apart and indifferent, preparing the shot that follows, he is the routine after the event, set at the right edge outside the volley. The wall cannot go: it shuts off the landscape of the Boston canvas, presses the action forward like a stage and turns the world into spectators. The smoke cannot go: it hides the victims’ faces, so the picture refuses the martyrdom it shows. What gives: the onlookers on the wall are too many and too summarily placed to be compelled one by one, the slope at the upper right is a permitted addition, and the third of the condemned is barely needed.
Giuseppe Terragni · Architecture
8.3 · Tier IV
Judged on plan, section, structure, purpose and site. Take away the half cube and the governing ratio goes, and with it the sense that every front is a cut through one solid. Take away the central hall and the building is an office block; the hall is the reason for the house, the place where the party gathered, and every office looks into it. Take away the glass doors and the claim that square and hall are one room is unmade. Take away the open grid and the frame no longer shows itself as the building’s law. What resists the test: the differences between the four fronts are composed rather than compelled, and the blank marble plane of the main front was made to carry an image, a part that waited on something outside the architecture.
Jackson Pollock · Visual art
8.3 · Tier IV
The subtractive test bites in two places. The poles: eight, at intervals uneven but not random, leaning in a sequence that reads from left to right as a measure. Take one away and the measure breaks; take all away and what remains is another painting, a field without a beat. The poles are required. The field is harder. A poured surface resists the removal of any one skein because no skein is a part, but that is not the same as each part being required: a hand’s width of the congested middle could be otherwise without loss, and the painter’s practice of cutting his edges after painting made the bounds chosen rather than compelled. Some passages, worked layer over layer, are thick and muddied in a way that reads as search. Required at the scale of the poles and their relation to the field; less so at the scale of the skein.
Alvar Aalto · Architecture
8.3 · Tier IV
Subtract and ask what goes. The raised court cannot go: it is the building’s argument, the public room of a village lifted off the ground so that the civic is entered by ascent. The shops beneath cannot go: they help carry the cost, and they are why the court sits on a plinth. The chamber cannot go, nor its place as the one tall volume, nor the dim stair that withholds it. The two stairs answer each other and both are required. What is less compelled is the residential range and parts of the office wing, needed by the programme but not by the idea, and the library range, placed more to close the court than for its own use. Nothing is built beyond what the argument needs.
Lina Bo Bardi · Architecture
8.3 · Tier IV
Judged on purpose, structure and site. The site sets most of the building. The strip that could not be built on forced the sports programme into two towers on either side of it, and the towers, stacked because the plot was small, forced the bridges: the most striking form on the site is compelled by drainage and land, not chosen for effect. The halls are kept because they could hold the gathering programme with almost nothing added. The unglazed openings answer air and light in a hot city. What holds the axis: the river and the hearth are gestures the purpose does not strictly need, the water tower is enlarged past its service, and some openings are free invention.
Gustav Klimt · Visual art
8.3 · Tier IV
Judged subtractively. Remove the edge of the meadow and the union is safe; with it the lovers stand at a brink, and the woman’s feet, curled at the edge, carry the risk the faces conceal. Remove the gold field and the couple stands in a room or a landscape, and the claim that love removes them from place goes. Remove the contrast of the two ornaments, rectangles on him and circles on her, and the one mass no longer holds two natures. Remove the hidden face and the turned, closed one, and the picture loses its question, rapture or withdrawal. These are required. What gives: the ornament within the robes is denser than the argument needs; the flecked field, the tendrils falling at her feet and the profusion of the meadow could be thinned with little loss, and the lower third of the square is padding.
Adolf Loos · Architecture
8.3 · Tier IV
Judged on plan, section and use, much passes the subtractive test. The Raumplan is itself a subtractive argument: each room is given the height and level its dignity and use require, so that the dining room is raised to overlook the hall, the lady’s room lifted above both to watch over them, and the service floor kept low and out of sight. Take away a change of level and a relation between rooms is lost, not only a step. The plain exterior follows from the position that the house owes the street nothing, and the windows fall where the rooms need light. What resists: the half levels outnumber what a family’s day requires, and some stairs serve the spatial argument more than the household; the marble and mahogany are chosen, not compelled; and the cube is compelled less by its site than by a position.
Louise Bourgeois · Visual art
8.3 · Tier IV
Judged by subtraction. Take away the sac and its eggs and the spider is only a spider: the mother goes, and with her the title and the reason the creature holds itself so high. Take away the height and the viewer is no longer beneath it; it becomes an object to look at rather than a body to stand under. Take away legs and the enclosure opens and the figure limps: the eight make both the anatomy and the room. There is little ornament; the ribbed and knuckled surface of the legs is the one elaboration, and it carries the sense of a thing worked by hand. What holds the axis is substitution: smaller spiders made from 1994 carry the same argument at other sizes, and the exact height, the spread and the modelling of each leg are permitted rather than compelled.
Ridley Scott · Film
8.3 · Tier IV
The subtractive test bites only at the edges. The long opening looks removable and is not: the empty corridors, the waking and the breakfast talk of bonus shares establish the crew as hired labour on a company haul, which is what the company’s order will later spend. Every stage is paid by a later one: the quarantine Ripley demands and Ash overrides; the acid blood that forbids killing the thing aboard; Mother’s hidden order; the cat, which takes Brett into the landing-leg bay and later forces Ripley back. The give is in the repetitions. The middle hunt runs one pattern three times, a man alone, a dark space, a cut; the cat is a plot hinge as much as a necessity; and Lambert’s death is the least determined of the sequence.
The White Stripes · Music
8.3 · Tier IV
Fourteen tracks in about fifty minutes, and the subtractive test finds a first half that holds. Seven Nation Army must open: it states the record’s method, one riff, a kick drum, a voice and an absent bass, and its stance. The Bacharach and David cover is required as the hinge, where the band shows what its method does to a song built for strings. Ball and Biscuit is required as the centre, the long blues the shorter songs abbreviate, and The Hardest Button to Button closes the strong run. The limit is the second half: Hypnotize adds nothing Black Math has not given, and The Air Near My Fingers and Girl, You Have No Faith in Medicine restate the riff-song in a lower key.
Steely Dan · Music
8.3 · Tier IV
Seven tracks in about forty minutes, and inside each the subtractive test finds almost nothing loose: the method was to cut every part that did not serve, take after take, player after player, and the arrangements show it. The bass, guitar and horn parts of Peg are as lean as a pop arrangement can be and still carry its harmony. The title track’s length is compelled: its verse, its instrumental passage, Shorter’s solo and Gadd’s drumming over the closing vamp are the escape the song describes, taken at the length escape requires. Deacon Blues needs its seven and a half minutes to make a dream feel like a life. The test bites once, on I Got the News, a busy funk of obscure innuendo whose loss the sequence would scarcely feel; Black Cow’s outro runs a little past its argument.
Steve Reich · Music
8.3 · Tier IV
The large plan resists the subtractive test. Eleven chords are laid down in the opening Pulses and each becomes a section, so no section can go without leaving a chord of the cycle unrealised, and the closing Pulses answer the opening. Within the sections the test finds give. The number of repetitions is cued in performance, not written, so a section’s length is permitted rather than compelled, and the work is not the same length twice. Several sections work their chord by the same means, a pattern built, a resultant doubled, a fade, and a listener could lose a minute of almost any of them without losing a step. The process is required; its duration is not.
Joseph Paxton · Architecture
8.3 · Tier IV
Judged on purpose, structure and site, and in Hyde Park the subtractive test finds little to take. The purpose was a vast covered hall, raised in months on a park lawn and removable after it: hence parts made to pattern, bolted and wedged rather than built; hence the module, compelled by the pane and by a gutter that drains and carries the glaziers. The hollow column that is also a drainpipe is the building’s character: each part answers two needs. The transept was compelled by the site, by elms the public would not let be felled. What yields is first the ornamental surplus, decorative arched ribs and finials, a small matter; and second Sydenham, where the building, freed from being temporary, was enlarged by choice rather than need, its parts permitted and not compelled.
Umberto Boccioni · Visual art
8.2 · Tier IV
The subtractive test is hard on this figure, and it mostly passes. The arms are already gone, and their absence is what lets the torso drive forward as one wedge. Take a flange from the rear calf and the trailing motion goes, for each flange is the wake of a limb. Take away the forward lean and the figure stands; take away the stride and it is a statue. The helmet of the head, with its ridge and its hollow, is the one place the figure faces its direction of travel, and it is required. What yields: the flanges on the front thigh and the back repeat a little, a third flare where two have made the point, and the two plinths are blunter than the figure and could be otherwise. Dense and nearly closed, held below the top by ornament in its own idiom.
David Fincher · Film
8.2 · Tier IV
The seven days and the seven sins make most of the film compulsory: each murder is a station, and the last two can only be done once the detectives are close. The scenes that look like rest are required. The dinner at the Millses’ apartment, the train shaking the walls, gives the marriage and the city their measure and gives Somerset and Tracy their bond. Tracy’s breakfast with Somerset, where she tells him she is pregnant and has not told her husband, is the hinge of the ending. The library is the film’s key. What gives: the library records bought from the FBI are a contrivance that hands the detectives the killer’s door, the raid on the sloth victim’s room repeats the tension of the find, and the chase through the tenement is genre business longer than its use.
Billy Wilder · Film
8.2 · Tier IV
Judged on structure, and the farce is built as a machine whose parts are paid. The massacre is required: it makes the drag a matter of life and death, not whim, and the same gangsters return to the Florida hotel to close the trap. The train is required: it sets both disguises and lets Sugar confide her rule about saxophone players, which Joe then exploits. Joe’s second disguise is required, because it doubles him and makes him learn from both sides what he does to her; Osgood is required as Daphne’s mirror of Junior. What gives: the upper-berth party runs past its point, hotel business slackens before the yacht, and the convention’s routines carry more gangster comedy than the design needs. Most of the length is compelled; some is only permitted.
Filippo Brunelleschi · Architecture
8.2 · Tier IV
A chapter is friars seated round a room, and the plan answers it: a hall laid across the axis of entry, so that the bench runs long and every seat faces the centre, with the altar and the presiding place in the scarsella on the axis. The two arms are compelled by the assembly and by the slot between church and convent that the room fills; the dome marks the one place every face turns to. Take away the grey order and the room stands, but its measure, which is its argument, is gone. What yields to the test: the order is applied, not structural, and crowds in the corners; and the chapter does not need the portico at all, whose closed, heavy attic is the part most easily removed in thought.
Radiohead · Music
8.2 · Tier IV
Twelve songs of about four minutes, and the subtractive test finds a required core. Planet Telex must open: a blur of reverberating piano and looped drums that gives the world as already damaged, its burden that “everything is broken”. Fake Plastic Trees is the centre, Just the engine, and Street Spirit the compelled end, a fade named in its title. My Iron Lung is required as the record’s argument with its own past, and the title track, High and Dry and (Nice Dream) hold their places by what they add. The test bites in the middle and late running: Bones restates the failing body, Sulk is a lesser Fake Plastic Trees, and Black Star and Bullet Proof..I Wish I Was could go with small loss.
Steven Spielberg · Film
8.2 · Tier IV
Run the subtractive test and the film resists it far more than its genre does. The screenplay cut the novel’s affair between Hooper and Ellen Brody and its Mafia hold on the mayor, and what remains is near to bone. Each attack moves the town one step: Chrissie’s body is passed off as a boating accident, Alex Kintner’s death on a crowded beach puts a bounty on the shark, the tiger shark gives the mayor his false ending, Ben Gardner’s boat gives Hooper his proof, and the estuary attack, with Brody’s son in the water, sends Brody to sea. At sea, every scene changes the balance among three men, one boat and one animal. What gives: the bounty hunters on the docks and the cardboard-fin hoax repeat work already done, the autopsy of the tiger shark runs long, and the dinner where Brody’s younger son mimics him, the film’s tenderest scene, could go without loss of structure.
Anselm Kiefer · Visual art
8.2 · Tier IV
Judged part by part. The arched pane cannot go: it is the source, the infinite named at the top, and the one element the case does not carry. The glass cannot go: it is at once the vessels and their breaking, and without the shards on the floor the work is a library. The lead cannot go: books that cannot be opened are what the work knows about its inheritance. The iron case cannot go: it holds and bears, the vessel’s armature. What yields is the wired labels, which name what the arrangement already shows and do a caption’s work; the number of books, which a longer run of shelving would not change; and the scatter on the floor, reset at each installation and so contingent by design.
Lee Chang-dong · Film
8.2 · Tier IV
Judged on the theatrical cut of 148 minutes. The subtractive test meets resistance in most of the film, because nearly every object is planted twice. The cheap pink watch Jong-su wins in a shop draw and gives Hae-mi turns up in Ben’s bathroom drawer among other women’s trinkets. The cat he feeds and never sees comes, in Ben’s car park, to the name he knows. The well she says he pulled her from is denied by her family and conceded by his mother. What gives is length in the third movement, and it gives more than a little: the dawn runs past the greenhouses repeat a compulsion already shown, and the mother’s two scenes restate an abandonment the film has made clear. The search carries the compulsion, but it is longer than the knowledge needs.
Jasper Johns · Visual art
8.2 · Tier IV
The test is subtractive, and the work has its own controls in the other targets of these years. Remove the faces and it is a target, the subject of Green Target and its siblings: a different work, saying less. Remove the target and four cast faces in a box are a reliquary with nothing to answer them. The cut below the eyes is required: with eyes the faces would look back, and the argument between a thing made to be looked at and figures who cannot look would go. The newsprint is required by a surface that needs a ground of matter, not of paint. What yields is number and the front. Nothing the work shows compels four rather than three or five, and the front is an option: closed, the box leaves mostly a target with a ledge.
Burnham and Root; south half by Holabird and Roche · Architecture
8.1 · Tier IV
Judged on purpose, structure and site, the north half almost defeats the subtractive test. The thickness of the wall is the load it carries; the flare at the foot is the wall gathering its weight into the ground, the flare at the top the wall finishing without a cornice to fall off; the bays are the office block’s demand for light and rentable floor, pushed outward from a narrow lot; the rounded corners are what moulded brick does when no stone dressing is wanted. What resists: the south half, whose heavier cornice and articulated base are taste, not compulsion, and whose steel frame no longer needs the massiveness its matched colour and height imitate; and the thick wall itself, a dying method chosen from economy and conservatism where the frame was available.
Bichitr · Visual art
8.1 · Tier IV
Judged element by element. The emperor cannot go, nor the shaikh: the act of the painting is the book passing from one to the other. The hierarchy below cannot go either. The Ottoman sultan, the English king and the painter descend the left edge in one stair of rank, and the argument, kings set below a holy man, needs exactly two foreign kings, one of Islam and one of Christendom, to be universal. The hourglass is the throne and the subject at once; the halo is the claim that this king is light. The painter is the lowest rung and the signature. What yields is at the edges: the putti above are partly decorative, and the carpet and its border are ornament the argument does not need.
Billy Wilder · Film
8.1 · Tier IV
Judged on structure and on the screenplay’s economy, which is the film’s chief glory. The subtractive test meets resistance almost everywhere, because nearly every object is planted and paid. The broken compact, returned to Sheldrake as lost property, comes back in Fran’s hand at the Christmas party and tells Baxter, and the viewer, whose woman she is. The key travels up the hierarchy, and its refusal is the act of the film. The neighbours’ belief that Baxter is a rake prepares the doctor at the bedside; the gin rummy of her recovery is the last scene’s game; the cork on New Year’s Eve pays the pills. What gives: the parade of borrowing executives repeats one joke too often, Baxter’s cold is stretched, and the bar pickup on Christmas Eve is longer than its work.
Denis Johnson · Literature
8.1 · Tier IV
The test is subtractive, and it finds little to take; the book is built so that it would. A whole life in a short book leaves no room for an idle scene. The attempt on the Chinese labourer in 1917 is required, because Grainier reads every later loss as its answer and the book neither confirms nor refutes him. The fire is the hinge of the life, and the decades after it are required because the book’s subject is what a man does with a loss he cannot speak. The wolf-girl closes the grief the fire opened, and the last page hands the era from Grainier to the reader. What holds the axis is the anecdotal middle: some stations of the working years and of old age are vivid episodes of a chronicle, and could be moved or lost with little changed.
Denis Villeneuve · Film
8.1 · Tier IV
Run the subtractive test and the film holds. The Chandler raid is required: the bodies in the walls are why Kate volunteers, and the shed bomb that kills two officers is the first instance of the film’s law, that what is found kills. The Juárez convoy teaches her, and us, what the operation is before anyone names it. The scenes of Silvio, which look like digressions, are the counterweight: the man killed on a roadside has a son, and the coda pays the thread. The tunnel gives the turn, and the signature closes it. What gives: Ted’s bar scene is engineered to endanger Kate and deliver a clue, and Graver’s explanations in the last third say aloud what the convoy and the tunnel showed.
Tarsila do Amaral · Visual art
8.1 · Tier IV
Subtract and see. Take away the cactus and the figure loses its double: the plant repeats the body’s swollen, rounded segments and roots it, so that man and plant obey one vegetable law; without it the figure is a distorted nude, not a creature of the earth. Take away the sun and the picture loses its heat and its one warm accent against the blue. Take away the small head and the work loses its thought, for the inversion of the body is the image. The green ground cannot go: the foot and hand press on it, and the weight is the meaning. Necessity among four elements is easier won than in a crowded field, and the pose of head on hand is a borrowed melancholy, less necessary than the distortion.
Felix Gonzalez-Torres · Visual art
8.1 · Tier IV
Judged on the conditions, since the work is a set of rules realised at each installation. Its parts are few, and the subtractive test finds each load-bearing. Take away the weight and the pile is a quantity of sweets, not a body: the number 175 makes it a portrait. Take away the permission to take and it is a Minimalist floor piece with a sad title; the diminishing is the dying. Take away the right to replenish and it is one death with no afterlife; take away the parenthesis and the weight belongs to no one. The corner, the bright wrappers and the endless supply each do work. What gives is the matter: any candy of roughly the right kind serves. Necessary as a structure, loose as an object.
Mark Rothko · Visual art
8.1 · Tier IV
Judged on the configuration. The subtractive test finds almost nothing to take away: a ground, a few rectangles, two governing colours. Take away a rectangle and the stack loses its weight on the axis and becomes another picture. Take away the margin of ground round the rectangles and they stop floating and become flat bands; the canvas no longer breathes at its edges. Take away the blue and the rust has nothing to press against. The size is compelled: smaller, the field would be an object on a wall, not a presence before the body. What yields is the choice among variants. The format allowed hundreds of dispositions, and that these proportions of this rust and this blue are required, rather than one good solution among many, cannot be shown.
Gustave Caillebotte · Visual art
8.1 · Tier IV
The subtractive test, element by element. The lamppost cannot go: it splits the canvas into two pictures, the near couple and the open square, and the split is the subject. The couple cannot go, nor the cut figure at the right edge whose umbrella is about to graze theirs; that near collision is the event. The wet cobbles cannot go, since their sheen alone carries the light and the rain. The prow of the wedge building cannot go: the recession runs to it. The scale is compelled, so that the viewer becomes one more walker. What yields is the population of the middle distance: a walker more or less, a carriage, a window. Necessary in its architecture, permitted in its middle ground.
Eileen Gray and Jean Badovici · Architecture
8.0 · Tier IV
Judged on use, structure and site. The subtractive test goes far. Take away the shutters that slide and fold, and the house cannot be closed to the sun and wind of the cape and opened to the sea by turns. Take away the built-in pieces, which hang, swivel and fold out, and the small rooms lose the several uses each is made to hold. Take away the screened entrance, which turns the visitor before the main room is seen, and the house loses its privacy. Almost every element answers what someone in the house would do, at what hour, in what light. Below the top: some furniture is designed object more than requirement, the stencilled words and nautical props can go without loss to use, and the murals are required by nothing.
Edward Hopper · Visual art
8.0 · Tier IV
Judged by subtraction. Remove the people and the picture would become another picture, but there are none to remove: the absence is the subject, and the hour compels it. Remove the barber’s pole and the hydrant and the pavement loses its only events, its only scale and its two long shadows, which are the picture’s clock. Remove the raking light and the facade goes flat and the hour goes with it. Remove the dark block at the upper right and the frieze loses its one interruption, the city pressing beyond the low row. Make the blinds uniform and the upper storey becomes a pattern, not a row of rooms. What yields is the number of bays: the row could run a bay longer or shorter with little loss.
Georgia O'Keeffe · Visual art
8.0 · Tier IV
The subtractive test finds almost nothing to remove, because almost nothing was admitted: no vase, no table, no setting, no second bloom. Take away the pale upper petals and the dark has nothing to fall from. Take away the black lower petals and the canvas loses its weight and its descent. Take away the cropping and the flower becomes a specimen on a ground, the convention the painting refuses. What yields is the inside of the parts: the exact curl of an upper petal or the spread of the lower ones could be otherwise without loss, and the other iris canvases of the same years show that the motif admitted variants. The economy is real, and the necessity is surer within the canvas’s edges than among its sisters.
Mark Rothko · Visual art
8.0 · Tier IV
Judged first within a canvas. Take away the margin and the fields run to the edge: the picture opens into a window and the horizon becomes a landscape, which the white band refuses by stating the edge of the object. Take away the edge between black and grey and the canvas is a monochrome. Take away the grey’s brushing and the lower field goes dead, and the black has nothing to weigh on. There are three elements, and each is structural. Judged then on the series, the subtractive test bites: a canvas could be removed and the series would know what it knew. The variations are of degree, and the count is permitted rather than compelled.
Robert Capa · Visual art
8.0 · Tier IV
Judged by subtraction on a single frame, where almost everything is required. Take away the sky and the man is a figure on ground, not a figure against nothing; the emptiness above him makes the fall a fall out of the world rather than onto it. Take away the slope and the fall has no angle to cross: the line of the hill and the line of the body cut each other, and that crossing is the instant. Take away the rifle leaving the hand and he could be stumbling. The civilian shirt and the cartridge pouches make him a militiaman, and the image needs that. What gives is the margin: the stubble at the bottom carries no weight, the image has been cropped differently in different printings without loss, and the companion frame shows the same instant could be made again.
Diane Arbus · Visual art
8.0 · Tier IV
The subtractive test runs quickly on two figures, and almost nothing yields. Take one twin and the work does not shrink, it vanishes: what it says is in the pair. Take the matching clothes and the likeness becomes resemblance; the dresses, collars, tights and headbands make two children one image and drive the eye to the faces, the one place where sameness fails. Take the frontal pose and the square and the comparison is spoiled. The hard, even light removes atmosphere so that nothing but the comparison is left. What yields: the pale ground and the cut at the shin are workable rather than compelled, and a frame from the same minutes with a different tilt of a head would be a lesser but recognisable version. Necessity is high, and of a small kind: one comparison, made exact.
Eddie Adams · Visual art
8.0 · Tier IV
The subtractive test, run on an instant no one composed at leisure. Take away the general’s outstretched arm and there is no act, only a prisoner in a street. Take away the prisoner’s face, the eyes narrowed and the mouth pulled at the moment the bullet enters, and the image becomes a threat, not a killing; the whole work stands on that fraction of a second, which no frame before or after holds. Take away the soldier wincing at the left and the act has no witness inside the picture. Take away the street and the killing loses its place. What yields is the periphery: the buildings, the soldiers behind, the width of the frame. The necessity is the event’s more than an order the maker found.
Wes Anderson · Film
8.0 · Tier IV
The subtractive test finds a lean film and a compelled one. The clubs montage is not a decoration: it states the disease, a boy who has made a self from activities, and every later loss is subtraction from that list. The aquarium is required, since Max’s gift to Rosemary is the act that expels him, and its ruin on the baseball diamond sends him to Grover Cleveland. Bert the barber is required by Max’s lie about his father, and the barbershop is where Max goes to ground. Dirk carries the word that starts the war; Margaret Yang, dismissed and recovered, is the plot’s answer to Rosemary. What gives: three beats of the war could be two, Magnus is thinner than his screen time, and Blume’s marriage ends largely offstage.
Tiwa builders · Architecture
8.0 · Tier IV
Judged on structure, purpose and site, and almost nothing yields to the subtractive test. The room is as wide as a viga can span; the wall is as thick as earth needs to carry storeys; the setback of each storey is what lets a mud wall rise, and it gives the household above its terrace, its work floor and its street. The ladder and the roof hatch were what defence and winter required. The split into two houses is the stream’s doing, and the stream is the water. Even the plastering is not ornament but the condition of an earth wall’s survival. What holds the axis: the necessity is a type’s, met well over centuries, not a single designed argument; and a cellular aggregate is additive by nature, so that a room more or less would not be missed.
Canaletto · Visual art
8.0 · Tier IV
Subtract and see what fails. Take away the shadowed yard and the canvas becomes a clean view of a church across water, the commodity the painter later made in number; the yard is what turns the view into a statement about who makes the city. Take away the far bank in sun and the yard is a genre scene with no horizon of meaning. Take away the washing and the women at the doors and the stone loses its human scale. The shadow is not decoration: it divides the work of making from the made thing across the water. Very little is idle. What gives is at the margin: some of the staffage is additive, a boat or a figure more or fewer would change nothing the canvas knows, and the distant boats are filled in rather than required.
Mark Rothko · Visual art
8.0 · Tier IV
Judged on the configuration, which is a handful of fields. Take away the white band and the centre the title names goes, and with it the cool pause on which the warm fields above and below are balanced: the canvas becomes a warm field with nothing at its heart. Take away the field above or the field below and the stack becomes a pair, and the eye loses the rise by which it climbs and falls. The rose ground lets each field float; without it the fields would be blocks laid edge to edge. What yields is the colour of each part: the sibling canvases of 1949 to 1951 show the same structure in other keys, and this yellow, or this lavender, could have been otherwise without the format losing anything.
Renzo Piano · Architecture
8.0 · Tier IV
Judged on purpose, structure and site. Remove the leaves and the building loses the light it exists to give, and with it the reason for its section: the roof is light fitting, sunshade, structure and image at once. Remove the treasure house and the galleries must become a store, or the building must become large; the upper storey is what lets the ground floor stay small and its hangs few. Remove the veranda and the building stops belonging to its street; remove the grey cypress and it becomes an object on a lawn. Very little is applied. What holds the axis: the plan, a spine with rooms off it, could be cut or lengthened by a bay without loss. The necessity sits in the section, not the plan.
Hans Holbein the Younger · Visual art
8.0 · Tier IV
The subtractive test, element by element, in a field that holds very few. The face cannot go: it is the picture. The collar of SS cannot go: it is the one thing in the field that names whom this man serves, and it lies across the fur where the eye drops from the face. The red velvet sleeves cannot go: they are the one warm mass among black, fur and green, and they hold the lower half up to the head. The paper is the office, letters and business in one object. What yields is the curtain, needed as a ground but a convention carried from Basel, which another plain ground would serve almost as well; the hands, too, are placed more than needed. Little is idle, and little was at risk.
Michael Curtiz · Film
8.0 · Tier IV
Judged on structure. Run the subtractive test and most of the film resists it. The prologue makes the city a waiting room on a refugee trail before anyone speaks. The letters of transit are the one object that turns a love story into a choice about the war. Ugarte, Strasser, Ferrari and Renault are each required for a different price of passage: theft, force, trade and corruption. The Bulgarian couple are required, since the roulette is the scene where Rick first acts and rehearses the ending at small scale, and the flashback gives Ilsa’s leaving a cause the audience has seen. The give is in the margins: the elderly couple practising English, the pickpocket’s refrain, Sascha’s kisses and some of Carl’s business are pleasures of the studio ensemble, not parts the argument needs.
Joe Rosenthal · Visual art
7.9 · Tier III
The subtractive test is severe on this image, and it holds for most of the frame. Remove the man at the base of the pole and the pole floats. Remove the trailing figure at the left, whose hands only just reach it, and the group loses the sense of a lift still gathering. Remove the wind in the flag and the act is finished rather than happening. The pole’s diagonal is the whole architecture: every body is ranged along it or braced against it, and the empty sky is the space the flag is entering. What yields is the lower margin of rubble and splintered scrub, which carries place but could lose a third without loss. Necessity caught, not built, is still necessity in the object; it stands below Las Meninas at 9.0 and Broadway Boogie Woogie at 8.7 on this axis, whose necessity was composed.
Roy Lichtenstein · Visual art
7.9 · Tier III
The parts are few, and the subtractive test mostly fails to find slack. Remove the caption and the burst loses its speaker: the “I” who pressed the fire control is the only person in the painting, and the kill is narrated in his calm. Remove the word and the explosion is pictured but not heard, and the painting’s argument, that a death arrives as a sound printed in yellow, goes with it. Remove the split and attacker and target share a frame, as in the source; the join makes the shot cross an interval. The dots, contour and flat primaries are the code the painting is about. What yields is the cloud forms, some of the smoke and a plane generic by design. The cap clears with room.
Isambard Kingdom Brunel; completed by Hawkshaw and Barlow · Architecture
7.9 · Tier III
Run the subtractive test, and almost nothing comes away. The gorge is some 75 m deep and about 214 m wide at the chosen line, with ships passing below to the port of Bristol: no pier could stand in the river, so the span had to be one, and one span of that width in the 1830s had to hang. Each part follows. The towers lift the chains, the chains run back into the rock, the rods carry the deck, the girders keep the deck from moving under load and wind. The Leigh Woods abutment is there because the cliff on that side falls away below the level the Clifton tower takes from the rock. What could have been removed, the sphinxes, was never built: the money that stopped the work did the subtraction. Held below the top because the purpose was in part a prospect and a wager, the link to Leigh Woods never a road of first need, and because the towers’ massive portals carry more stone than the chains strictly ask.
Sesshū Tōyō · Visual art
7.9 · Tier III
Judged on the configuration, sheet and text together, the painting is a test of subtraction already performed: what remains when a landscape has been reduced to a few dozen acts of the brush. Without the dark accents the wash has no ground; without the pale mountain there is no distance. Take away the banner and its pole and the one vertical that tells the eye this is a place where people drink and live goes, and the wash becomes weather. The boat is the one thing in motion; the blank paper is mist, water and sky at once. What gives is in the middle passages of wash, where a stroke more or less would not be missed, and in the six added poems, honour permitted rather than compelled.
Egon Schiele · Visual art
7.8 · Tier III
The subtractive test is hard on this panel because so little is in it. Remove the plant and the head floats in a void with nothing to measure it against; the picture loses its one warm, round, living counterweight to the angular dark of the jacket. Fill the ground with a room or with ornament in Klimt’s manner and the isolation that is the picture’s meaning goes. The cut at the lower edge is required: it lets the jacket rise as a dark wedge, tips the figure, and makes the angle of the head read as tension rather than pose. What yields a little is the ground’s brushing, worked over more than its job needs in places, and the plant’s stems and leaf, drawn with an ornamental relish that is permitted rather than compelled.
Miguel de Cervantes · Literature
9.4 · Tier V
Judged partly on the Spanish. Length is not a cost; the question is whether the parts are required. The spine is compelled. Part II needs Part I as a printed book. Sancho’s one lie in II.X carries the second half, through Merlin’s lashes to the deathbed rumour that Dulcinea is disenchanted, and the death is required, certified so that no other author can raise him (II.LXXIV). What holds the axis lowest of the twelve the book itself names: the Curioso and the captive’s tale stand “apart from the story” (II.XLIV), 8.7 per cent of the novel. With Leandra, Clara’s open thread, the Trifaldi’s long farce and the lectures given twice, about a tenth could go.
Johann Wolfgang von Goethe · Literature
9.4 · Tier V
Judged on the work as one. The spine passes the subtractive test outright: the Lord’s wager (317) and Faust’s (1699–1702) are answered at the death and in the angels’ lines (11936–11937). Gretchen cannot go, because she is what the striving costs, and she returns as intercessor; Helen cannot go, because the present the wager names is first lived with her. What holds the axis at 8.2 is what the plan permits rather than compels: the Walpurgis Night’s Dream, a satire on the 1790s; a masquerade twice as long as its burden; a scene of freckle cures; the Classical Walpurgis Night’s catalogue of creatures; and most of Act IV, whose argument needs one scene. The plan compels the scale; the execution permits much of it.
Ovid · Literature
9.3 · Tier V
The test bites, because the method is accumulation. Within an episode the necessity is high: Narcissus (3.339 to 510) cannot lose a line without losing its mechanism, since Echo can return only final words; and the closing argument (15.165 to 258) needs everything before it as instances. What holds the axis lowest of the twelve is the method itself: a poem whose claim is totality makes its episodes exchangeable. The two battle set-pieces (5.1 to 235, 12.210 to 535) could go with little loss, the dogs named over Actaeon (3.206 to 225) are wit at length, Pythagoras’ dietary frame outruns his argument, and parts of the Italian sequence of Book XIV are thin. The scale is permitted by the method, not compelled by it.
Lucretius · Literature
9.0 · Tier V
The order of the poem is the order of the argument, and it cannot be shuffled. The mortality of the spirit cannot be argued in the third book before atoms and void are established in the first two, nor the images of the dead explained in the fourth before the spirit is shown mortal; the mortality of the world in the fifth rests on both. One axiom stands under all six: “nullam rem e nilo gigni divinitus umquam”
“nothing is ever born from nothing by divine power” (1.150). What holds the axis lowest of the twelve: the proofs of mortality pile up past need, the multiple causes of the sixth book run long, and the doublets and an unkept promise show a last revision missing.
Charles Dickens · Literature
9.0 · Tier V
The design states its question in chapter 16: “What connexion can there be” between Chesney Wold, the town house, the footman in powder and Jo with his broom; almost every household answers it. Mr Turveydrop is the parasitic parent beside Mrs Jellyby the absent one and Skimpole the child who will not be one, three forms of the neglect that Chancery is at scale. George and the Bagnets carry the plot to Tulkinghorn’s murder; Snagsby and Chadband carry Jo; the Smallweeds bring the will that ends the suit. What holds the axis lowest of the twelve is the slack that twenty numbers left: Boythorn, the repeated Bagnet routine, some of Chadband, the Turveydrop wedding comedy and the drawn out Woodcourt and Jarndyce resolution, near a tenth of the whole.
Paul the Apostle · Literature
8.9 · Tier IV
These are occasional letters, and much of them is business. Romans 16 is a list of greetings; 2 Corinthians 8 and 9 are two appeals for one collection; 1 Corinthians spends chapters on food offered to idols, head coverings and lawsuits; travel plans recur and are revised. A great deal could be removed and the core argument would stand. Yet the subtractive test must ask what the occasion is for, and the occasion is the form’s reason. Galatians is nearly all necessity, six chapters driving one claim from autobiography through Abraham to the life of the spirit, with no thanksgiving because none could be given; Philemon has not a spare clause; Romans 5 to 8 runs as one compelled sequence from Adam to the declaration that nothing can separate. What holds the axis lowest of the twelve: necessity is high in the cores and slack at the edges of a collection no one designed.
Franz Kafka · Literature
8.9 · Tier IV
The test is subtractive, and the spine passes it at every joint. K. claims to be the surveyor and a telephone call from the castle confirms him; he takes Frieda because she is Klamm’s mistress, and the taking costs him her; he accepts the post of school janitor because it binds him to the village; he chases Klamm through Momus and Erlanger and, given the one chance the book allows, sleeps through it at Bürgel’s bedside. Olga’s long narrative of Amalia and Sortini passes too: it is the book’s second centre, the story of those who said no to the castle, set against K.’s story of trying to get in. What holds the axis at the foot of the twelve is what fails the test in the middle and at the end: the assistants’ farce repeats its point, the schoolroom chapters and the landlady’s second interview go over ground already won, and Pepi’s long monologue reinterprets Frieda’s motives a third time. The manuscript was never revised, and its late chapters expand where a revision would have compressed.
Giacomo Leopardi · Literature
8.9 · Tier IV
Inside the great poems almost nothing can be taken away. L’infinito is fifteen lines and each turns the one before, and A Silvia is built so that each stanza is required by the next. The order of the book is an argument too: it moves from the civic to the inward to the cosmic, and La ginestra at the end answers All’Italia at the start, a civic poem again, now addressed to the human race. But the subtractive test bites on the body. A quarter of the forty-one could go and the book would lose little it does not say better elsewhere: the exhortations of Nelle nozze della sorella Paolina and A un vincitore nel pallone, the Inno ai patriarchi, the sentimental deathbed of Consalvo, Scherzo, Imitazione and the fragments. That slack quarter holds the axis lowest.
William Faulkner · Literature
8.9 · Tier IV
The subtractive test bites harder here than on Faulkner’s single-action novels, because the book was assembled and the joins show. “Pantaloon in Black” has no McCaslin in it beyond the land, and a reader can ask what it adds: it keeps its place as the one part that gives a Black man’s grief from inside and then from the white sheriff’s office, the book’s blindness in small. What holds the axis lowest of the twelve: in “The Fire and the Hearth” the gold hunt and the salesman’s divining machine run as farce longer than the part’s real matter requires, and the fourth section of “The Bear” goes round its argument more than once. The core sequence, ledger to wilderness to the tent to the coffin on the train, is required in every link.
Louis Le Vau, Jules Hardouin-Mansart and André Le Nôtre · Architecture
8.9 · Tier IV
Judged on plan, structure, purpose and site. Some parts resist the subtractive test absolutely. Take away the axis and nothing is left: the town’s avenues converge on it, the king’s bedroom sits on it from 1701, and terrace, Latona, Tapis Vert, Apollo and canal are strung along it to the horizon. Take away the Hall of Mirrors and the state loses its room of passage. What holds the axis lowest is the work’s own history: bosquets, the grotto and the Labyrinth removed, and the garden whole after each loss. The lodge was kept for piety, not need; the site, without water, compelled nothing; and the scale was permitted by a king’s will more than required by a purpose.
Hafez · Literature
8.9 · Tier IV
The subtractive test bites at two levels and gives two answers. At the level of the couplet the necessity is extreme: in the couplet of the trust that Heaven could not bear, which fell by lot on “mad me”, the whole claim rests on the lot and on the madness, and no word can go. At the level of the ghazal the test is weaker, and the manuscripts are the evidence: couplets move, appear and vanish between witnesses, which a strictly necessary order would not allow. The ghazal’s law is the unity of the radif and the mood, not of an argument. Across some five hundred ghazals some are near-repetitions and some occasional or panegyric, and that holds the axis at 8.2.
George Frideric Handel · Music
8.9 · Tier IV
The large plan is compelled: prophecy, the coming, the Passion, the rising, the gospel sent out and refused, God’s reign, the dead raised. No part could go, and inside the Passion, from “Behold the Lamb of God” to “He was cut off out of the land of the living”, every number is required. Length is not charged; separability is, and the subtractive test finds give. The ascension and Pentecost run of Part II, from “Unto which of the angels” to “Their sound is gone out”, is the work’s most separable stretch and the one most often cut. In Part III “If God be for us” restates an argument already won. And Handel substituted, shortened and transposed numbers for a decade: the work itself shows that several of its parts could change without loss to the whole.
Bob Dylan · Music
8.8 · Tier IV
Seventy-three minutes on four sides, and the subtractive test bites, though less than it first seems. The long songs are required: Visions of Johanna sets the record’s night, One of Us Must Know its reckoning, Stuck Inside of Mobile its trap, Sad Eyed Lady of the Lowlands its end. Rainy Day Women #12 & 35 is required as the frame, the carnival the hymn of side four answers. The blues numbers are the question. Pledging My Time, Leopard-Skin Pill-Box Hat and Obviously 5 Believers give the night its ground and its laughter, but any one could go with little loss, and Temporary Like Achilles restates the shut-out lover of the fourth track more slowly. That partial slack, not the length, holds the figure.
Anonymous · Literature
8.8 · Tier IV
The subtractive test bites harder than the poem’s admirers allow, and less than its early critics claimed. The digressions mostly earn their place: the Finnsburg lay sung in Heorot predicts the hall’s own fate, a marriage meant to end a feud ending in fire; Heremod set against Sigemund defines the king Beowulf must become; the Ingeld forecast does the same work for the Danes. What holds the axis lowest of the twelve is repetition. Beowulf’s report to Hygelac retells the Danish adventures at length, with new detail but much restatement, and the Swedish wars are told twice in the second part, by the narrator and again by the messenger. The second part’s scale is compelled; parts of the first are permitted.
Henry David Thoreau · Literature
8.8 · Tier IV
The spine is required: the account of what life costs, what one lives for, then the year itself from the bean field through the ponds and the winter to the thaw, then the turn outward in “Conclusion”. Remove the accounts and the ecstasy has no ledger to answer; remove “Spring” and the argument for renewal is only asserted. What holds the axis lowest of the twelve is the subtractive test inside the chapters: “Economy” makes its case several times over, with catalogues of clothing, shelter and fuel a tighter book would cut by a third; “Visitors” and parts of “The Village” are anecdote more than argument; and “Higher Laws” sermonises on diet and chastity at a length the book’s own method, fact first and then meaning, does not earn. The drafts grew by accretion, and some of what accreted is idle.
Francis Ford Coppola · Film
8.8 · Tier IV
Judged on structure and on the cut. From the hotel room to the last losses the subtractive test finds little: each station on the river takes something from the crew or from the viewer’s idea of the war, and each is a step further from the law that sent the boat. The tiger is brief and required; it gives Chef the rule the voyage breaks. The plantation sequence, left out of this cut, shows a film made by subtraction. What holds the axis lowest is the compound. The photojournalist’s patter runs long and repeats, and Willard’s days in the cage and Kurtz’s scenes in the dark are permitted their length rather than compelled to it. The voice-over at times states what the image has shown.
Don DeLillo · Literature
8.8 · Tier IV
The test is subtractive, and the scale is partly compelled. The reverse order needs its layers: to end on the night of the shooting in 1952, the book must pass down through every layer from 1992, and each layer carries a change in Nick, in Klara and in the country. The ball’s line of owners needs Marvin Lundy; the waste needs Fresh Kills and Kazakhstan; the bomb needs Matt, the bombers and Lenny Bruce’s sets of 1962, which carry the missile crisis as dread. What holds the axis lowest of the twelve is the matter the layers permit rather than require: the long scenes of Nick’s marriage and its affair in the first part, stretches of Klara’s art-world talk, the chapter of the Texas Highway Killer, which restates a law the book has already set, and the length of several set pieces in the last part. Perhaps a fifth of the whole could go with the knowledge little changed, and the prologue’s separate life shows that the parts can stand alone; but what could go lies inside layers the descent requires, and no layer of the descent could go.
Kalidasa · Literature
8.8 · Tier IV
The spine is tight and its turns are required. The curse in the interlude before the fourth act is the hinge: without it the rejection of the fifth act is a calculated denial, and the play would be another play. The ring, lost at a bathing place and found in a fish, is required to turn forgetting into memory; the son of the seventh act is required because the recognition must pass to the next generation and the dynasty. The farewell of the fourth act does nothing for the plot and is required by what the play knows: the cost of leaving a world. What holds the axis among the lowest of the twelve is slack in two places: the king’s lovesickness talked over with the jester in the second act, which delays more than it builds, and Mātali’s summons to fight Indra’s demons in the sixth, a device to carry the king to heaven rather than a necessity.
Ingmar Bergman · Film
8.8 · Tier IV
The subtractive test has been run by the maker. The theatrical version lifts out about two hours and the work stands: that is the plainest evidence on the desk that much of the unit can be removed without the work ceasing, and it is what holds the axis lowest. What the cut loses is not ornament. The long Christmas is the argument’s first term: at length the Ekdahl world is a counter-order against which the bishop’s bare house is measured; shortened, it is a setting. The prologue, five acts and epilogue are compelled, each act turning the world by a death, a marriage, a captivity, a rescue and a release. Carl and Lydia’s scenes and parts of the bishop’s household are the parts most easily spared.
William Blake · Literature
8.7 · Tier IV
Subtract and see. The opening three plates cannot go: the Argument, the plate of contraries and the voice of the Devil give the rest its law. The Proverbs of Hell are the book’s centre of gravity, and the Leviathan fancy its demonstration: when the Angel who showed Blake the abyss goes, the vision goes with him, and Blake sits “on a pleasant bank beside a river by moon light”, because “All that we saw was owing to your metaphysics”. What holds the axis down is the looseness of the anatomy. The five Memorable Fancies are of unequal necessity: the dinner with Isaiah and Ezekiel and the printing house in Hell overlap in what they claim; the attack on Swedenborg repeats the opening’s point at a lower heat; A Song of Liberty could be lifted off and read in places as a separate poem; and perhaps a fifth of the Proverbs are slack beside the rest.
Robert Frank · Visual art
8.7 · Tier IV
Judged on the sequence, which is where necessity lives in a book of photographs. The frame of the book cannot go: the flag over the hidden faces at Hoboken opens it, the wife and child waiting in the car on U.S. 90 close it, and between them the road is the argument. The flag that returns through it cannot go, nor can the rhymes it sets going: jukebox answering television, the covered car at Long Beach answering the blanketed dead beside U.S. 66, the funeral at St. Helena answering the crosses in Idaho. What holds the axis, with The Encompassed the lowest of the twelve, is the middle: Frank chose eighty-three from many thousands, and a bar or a street could often be exchanged for another of its kind without loss. The plan is necessary; the count is permitted.
Romanesque builders; Obradoiro facade by Fernando de Casas Novoa · Architecture
8.7 · Tier IV
Run the subtractive test on the Romanesque body and it holds. The aisles and the ambulatory carry the crowds round the tomb without crossing the choir’s liturgy; the galleries are buttress and space for pilgrims at once; the barrel vault is as heavy as the galleries can hold, and the missing clerestory is the price of that, not a whim. Crypt, altar and the stair behind it are where the plan converges, and nothing in the east end idles. The Obradoiro has a reason beyond display: it shields the Pórtico from the weather and lights it. What yields is the accretion: patrons’ chapels, the gilded crossing, the cloister, façades built to answer plazas. A compelled core inside an assembled shell.
Thomas Hardy · Literature
8.7 · Tier IV
Subtract and see. Take out the Chase and nothing follows; take out Talbothays and the confession has nothing to destroy; take out Flintcomb-Ash and Alec’s return, finding her where hunger and Angel’s silence have put her, has no ground. The seven phases are a sequence of consequences. What holds the axis lowest of the twelve is the machinery that delivers them: the letter of confession that slides beneath the carpet (XXXIII), the overheard talk of the Clare brothers, the boots taken from the hedge at Emminster (XLIV), Angel’s return days too late. Hardy means chance to be the law, but several of these feel placed rather than compelled; and stretches of authorial essay state what the action already shows.
Ingmar Bergman · Film
8.7 · Tier IV
Judged on the structure and on the speech, since the film argues aloud. The frame cannot give: the game is the plot, and each episode is a stretch of the respite it buys. The confession is required, where the knight says what he wants and gives his game away; so are the strawberries, on which the sparing at the board depends, and the burning, where he looks for the devil and finds a frightened child. What gives is the smith’s comedy, Plog’s lament and Lisa’s return running longer than the counterpoint needs, and the bear dance at the inn, which repeats what Raval has shown. The speech gives too, saying what the images have shown. That padding, in so short a film, holds the axis among the lowest.
Seljuk and later builders · Architecture
8.7 · Tier IV
The subtractive test bites on a building made by accretion. The core is compelled: the court as the open centre of a city’s congregation, the qibla iwan leading to the dome over the mihrab, the iwans fixing the four axes so that the court can be oriented and entered from any side, the hypostyle carrying most of the congregation under roof. Each answers Friday prayer, climate and the gathering of a city. But a hypostyle is additive by nature: bays could be taken away or added without loss, and some rooms serve the institution rather than the form. The north dome chamber is placed on the axis, yet its purpose is uncertain in the record and not plainly required.
Alan Moore and Eddie Campbell · Literature
8.7 · Tier IV
The test is what could go, and the answer is divided. The murder chapters cannot go, nor the carriage ride of the fourth chapter, nor Gull’s death in the fourteenth, nor the frame of the two old men on the shore, which sets the whole as what history made of a lie. The notes cannot go either: they show which panels are record and which invention, and the book’s claim about history depends on that seam being visible. The cost is in the middle. Moore’s method is to admit everything the record holds, and most of it is threaded on Gull’s design; but some is the historian’s pleasure in a fact found, a chapter or two of procedure reads as permitted rather than compelled, and a handful of historical figures appear as visits rather than as workings. That accretion holds the axis lowest of the twelve.
Andrei Tarkovsky · Film
8.7 · Tier IV
Judged on the structure of the film as released. The episodes are stations, and most are required by what follows: Kirill sets off the jester’s arrest and confesses it at the bell; Theophanes’ contempt is what Andrei answers when he refuses to paint terror; the blinding throws the paint at the wall; the raid is where he kills and falls silent; the bell ends the vow. The prologue looks detachable and is not. What holds the axis lowest is length permitted rather than compelled: the Theophanes episode runs long in argument, the Feast’s night does more than its function asks, and the raid accumulates cruelties past what its argument needs.
Andrei Tarkovsky · Film
8.7 · Tier IV
The test presses hard on a film of episodes joined by memory rather than plot, and the answer is mixed. The prologue is required: a stammerer cured to say that he can speak is the licence for a confession that could not be made until now. The fence and the stranger, the barn fire, the printing house and the earrings visit are required, each a stage of the mother’s life alone. The newsreel of Sivash is required, because it makes a private memory a nation’s. What holds the axis lowest: the Spanish household, joined to the rest really but thinly; the Pushkin reading, which states a thesis the film elsewhere shows; and an order of association under which some parts could have stood elsewhere.
John Donne · Literature
8.7 · Tier IV
In the core poems the subtractive test finds almost nothing to take. “The Flea” is three stanzas because the argument needs three acts: the plea, the plea to spare the flea, and the reversal after the killing that happens between the second stanza and the third. Take any one away and the poem has no action. The nine quatrains of the “Valediction” each advance the case, from the deaths of virtuous men to the compasses, and its last line closes the circle the argument draws: “And makes me end where I begun.” “The Canonization” moves stanza by stanza from rebuke to legend. What holds the axis is the body as a whole. It has no authorial order and so no argument of its own, and a tail of a dozen slighter conceits, “The Computation”, “Love’s Diet”, “The Paradox”, “Witchcraft by a Picture”, could go with the body little changed. Weighed toward the core, as the body is read, it stands at 8.2.
Giovanni Battista Piranesi · Visual art
8.7 · Tier IV
Judged on the set as sixteen, and the test bites unevenly. The title plate, VII, IX, X, XIV and XVI cannot go: between them they carry the cycle’s four ideas, the space without exit, the machine of unknown purpose, the figure lost in a void it did not build, and the law that built it. The two new plates, II and V, are required by the argument of 1761; without them the reworking adds darkness and not meaning. What yields is the middle of the set: several of the arch-and-stair plates, XI, XII and XV among them, restate one proposition at one pitch, and one could go without loss. The repetition is partly the point, for the prison is infinite because it keeps arriving.
Huang Gongwang · Visual art
8.7 · Tier IV
The subtractive test bites harder on a handscroll than on a single field, and the scroll’s own history has run it once. The fire of 1650 took the opening, and what remains still reads as the work: the beginning was not load-bearing. Inside the surviving scroll the alternation of hill and water is required. Each opening of water is where the eye breathes, and each massing is earned by the low bank before it; the central range cannot go, nor the last flat water that closes the journey. What yields is in the long middle passages of rounded hills and trees, where a stretch could be shortened by a third without the structure failing, and the method of making was additive. The journey is compelled; its exact length is permitted.
John Ford · Film
8.7 · Tier IV
Judged on structure. Run the subtractive test and the search resists it: the raid, the funeral, the eyes, Lucy’s death, the years, the captives at the fort, Scar’s tent, the will and the lift each carry a stage of Ethan’s descent and return. Mose Harper, who looks like comic furniture, is required: he brings word of Debbie, and his wish for a rocking chair answers Ethan’s wandering. What holds the axis lowest is the settlement’s comedy. Charlie McCorry’s courtship and the long wedding brawl do one job, the ordinary life of the place, several times over; the slapstick around Look runs long before her death turns it; some of Laurie’s scenes are delay. These are Ford’s habits as much as the story’s needs.
Stanley Kubrick · Film
8.7 · Tier IV
The second part resists subtraction. Each step of the fall is required by the step after it: the assault on Bullingdon at the recital, the courting of Lord Wendover for a peerage, Bryan’s birthday horse, the barn. The annuity of the last scene closes the account the opening duel opened. The first part is a picaresque, and the picaresque is an additive form: the highwaymen on the Dublin road, the interlude with Lischen and the Chevalier’s gaming tour could each be shortened without the film losing a thought. Kubrick binds them by repetition, each turning on a counterfeit identity, a stolen uniform or a borrowed name, so they rhyme rather than pile up. The slowness is compelled; the order of Part I’s fortunes is not.
Alexander Pushkin · Literature
8.6 · Tier IV
The test is subtraction, and the play half resists it. Its spine is a set of hinges: Shuisky’s cynicism over a staged election; Pimen’s cell, where Grigory hears the murdered tsarevich’s age and is born as a pretender; Boris’s monologue, “Достиг я высшей власти”
(I have attained the highest power), where the guilt is spoken; the inn, where the pretender crosses the border; the holy fool’s refusal, the death of Boris and the people’s silence. Take any of these out and the play falls. What holds the axis lowest of the twelve is that the play is episodic by design and some scenes are thin links: the forest, Sevsk, the Kraków scene of courtiers and a poet. The love plot at the fountain is its own small drama, permitted rather than compelled. Boris is offstage for long stretches; the play is about the throne, not the man, and that is design, but it loosens the necessity of each part.
Spike Lee · Film
8.6 · Tier IV
Judged on structure. The spine is a day of heat, and the parts that carry the pressure toward closing time are required: the Wall of Fame and Buggin’ Out’s demand; Radio Raheem’s box, carried through every scene he enters until its silencing is the trigger; Pino’s hatred of the block and Vito’s friendship with Mookie; Da Mayor’s rescue of a boy, which earns him the right to stand between the crowd and the pizzeria; the opened hydrant, which brings the police early; Smiley’s photograph, which ends on the burning wall. Most vignettes load a claim cashed at closing time. The method is accumulation, and it permits as well as compels: the corner men’s three scenes repeat one function, the scene with Tina is a pause, and the quarrel with Jade is paid only in part.
Daniel Libeskind · Architecture
8.6 · Tier IV
Judged on structure, purpose and site. The parts that carry the memorial argument resist the subtractive test almost wholly. Remove the voids and nothing in the building is absent, which is what it exists to say. Remove the underground entry and the Jewish history of Berlin gets a front door of its own, which the plan denies it. Remove one axis and one of three fates, continuity, exile or death, goes untold; remove the Tower or the Garden and the axes end in walls. What yields is the museum. The fold of the zigzag and the angle of the slashes are fixed by a private derivation that the visitor cannot read and the use does not require, and the galleries, cut by voids and slashes, fight every exhibition put in them.
T. S. Eliot · Literature
8.6 · Tier IV
“Prufrock” passes the subtractive test as few poems of its length do. Each verse paragraph is a stage in one evasion: the invitation that never names its question, the fog that “rubs its back upon the window-panes”, the rehearsal of the visit, the chain of things that would or would not have been worth while, the collapse into “No! I am not Prince Hamlet, nor was meant to be”, and the drowning. Even the refrain of the women who “come and go / Talking of Michelangelo” is the room’s indifference returning on him. What holds the axis is the volume. “Aunt Helen”, “Cousin Nancy”, “The Boston Evening Transcript” and “Conversation Galante” are well turned, but the book could lose any one of them and know nothing less; “Hysteria” is the slightest of all, and “Portrait of a Lady” has a loose middle. A single poem would stand higher; the book, with perhaps a quarter of its pages removable, stands here.
Stanley Kubrick · Film
8.6 · Tier IV
Judged on structure. The argument requires the three parts and most of their stations: the night of violence has to be enjoyed before it can be taken away, the prison chaplain has to make the case for choice before the treatment removes it, and the Ludovico sequence has to be watched as Alex watches it, eyes clamped. The second half’s return to each victim in order is required twice over, as justice and as proof that the cured man is defenceless. What could go is weighed in full: the fight with the Cat Lady, with its rocking sculpture and bust of Beethoven, runs on as stylised excess beyond its need; the sped-up threesome is a joke that proves nothing the Korova has not; the prison intake is comedy at length.
John Steinbeck · Literature
8.6 · Tier IV
The design passes the subtractive test and the execution fails it in places. The general chapters cannot go: without chapter 5, where the bank is “the monster”, chapter 7, the used car lot, and chapter 25, the destroyed fruit, the Joads are a family with bad luck rather than the instance of a mechanism, and each of the three movements is required. What could go is in the narrative: the long middle stay at the Weedpatch government camp, where the dance, the committee and the toilets run on past their point; Al’s girls and cars; Rose of Sharon’s fears for her baby, restated without development; Casy’s speeches, which say again what the general chapters have shown. Noah walks off down the Colorado, half a figure. That permitted middle holds the axis at 8.2, level with The Bottomless Well as the lowest of the twelve.
Paul Gauguin · Visual art
8.6 · Tier IV
Judged on the configuration. The two ends cannot go: the infant at the right and the old woman at the left are the first and last terms of the questions, and without either the frieze has no direction. The fruit picker at the centre cannot go: it divides the length, joins the ground to the top edge, and is the Eden the title asks about. The idol cannot go; it is the only answer the picture offers, and it is mute. Below those the test gives. The two walkers in purple and the turning figure are an episode the painter’s own account explains with difficulty; the cats and goats are fill; several figures come from the painter’s repertoire of the years before and return in the canvases after, which shows that they can move. The length is compelled by the reading as a sequence. The armature is necessary; perhaps a third of the population is permitted.
Willem de Kooning · Visual art
8.6 · Tier IV
Judged by subtraction, part by part. Take away the eyes and the canvas loses its address: the whole field is organised as a stare at the viewer. Take away the teeth and the figure loses its double nature, idol and advertisement in one grimace. Take away the breasts, set like two shields over the centre, and the mass that holds the figure frontal goes. Those parts are required. The surround is not. The ground of slashed pinks, yellows and blue-greens could be other slashes, the hands could be other hands, and the broken lower legs mark where the painter stopped more than where he had to. Two years of repainting show that many states could have been called the painting. Compelled at the core, permitted at the edges.
Gustave Courbet · Visual art
8.6 · Tier IV
Judged on the configuration. The centre cannot go: painter, landscape, nude, boy and cat are the argument, the maker at work on nature with the ideal at his back and innocence looking on. The two flanks cannot go as flanks, because the picture claims that the painter stands between the world that lives on death and the world that lives on life, and the claim needs both. Below that the test gives. Within the left group several types could leave without loss, and the crowd is crowded rather than built; within the right, the friends read as a list, and one or two, the art lovers and the lovers at the window, feel permitted. The upper half, a third of the surface, is compelled as room and dark but not shaped. Necessary in its architecture, assembled in its population.
Stanley Kubrick · Film
8.6 · Tier IV
Judged on structure. The spine resists the subtractive test: the interview sets the past and the hotel’s courtesy; the tour plants Room 237, the maze and the Gold Room; Hallorann names the shining and gives his warning; the narrowing title cards are the trap closing. The three central encounters, at the bar, in the red bathroom and at the storeroom door, are each required, and the last is the hinge where the hotel acts. But the film holds more than it needs, and Kubrick showed it by cutting it himself by about twenty-five minutes for Europe. The paediatrician explains what Wendy’s evasions already show; Hallorann’s journey back is long for a man killed in seconds; the lobby skeletons are a turn the film can lose. Necessary at the spine, permitted at the edges.
John Soane · Architecture
8.6 · Tier IV
The subtractive test bites harder here than at a building composed once, because the house accreted over thirty-two years and parts of it are set pieces. The Monk’s Parlour and its yard, with the joke tomb of a fictitious monk and of Mrs Soane’s dog, could be taken away and the house would still say what it says. Against that, the site compels a great deal: three narrow plots, a terrace front, a collection too large for any room. Every top light, borrowed view and mirror answers the problem of bringing daylight and depth into a deep, shut-in plot. The core is necessary; the periphery is assembled.
Ridley Scott · Film
8.6 · Tier IV
Judged on the Final Cut’s structure, and the spine resists subtraction. Holden’s test is required, since it gives the test, the replicants’ violence and the first sight of Leon in one scene. The Tyrell visit sets Rachael’s memories and the eye; Leon’s photographs lead to the snake scale and Zhora; Sebastian is the door to Tyrell and the human dying too fast, the replicants’ mirror; the chess game gets Batty upstairs; the last hunt turns hunter into hunted so that Batty’s mercy can land. The unicorn reverie and the origami answer each other. What gives: the Esper enhancement, beautiful and long, finds one face; Zhora’s chase is a set piece more than a step; Bryant’s briefing is exposition the world could carry; and Deckard’s story is thin enough that whole scenes keep him walking through design.
Assyrian court sculptors · Visual art
8.6 · Tier IV
Judged slab by slab and scene by scene. Some parts resist subtraction absolutely. The cage and its opening make the hunt an arena and the lion a released captive. The king’s close combat is the claim the cycle exists to make. The libation turns the killing into rite. The dying lions are where the cycle’s force lives: take away the lioness and it loses its centre of gravity. But a palace frieze is also a filling of wall, and much here is permitted rather than compelled: the ranks of the cordon, the repeated grooms and horses, the beaters, the spectators on the hill, the near identical lions carried away. The core is required; the extent, set by the rooms, is not.
Philip Roth · Literature
8.6 · Tier IV
The test is subtractive, and it bites at three places, hardest at the first. The frame is long: Zuckerman’s boyhood hero worship, the dinner at which the Swede talks of nothing but his three sons, and the reunion take most of the first part before the chronicle begins, and they are required, since the Swede’s blankness at dinner is the problem the whole imagining tries to solve. The lesson in how a glove is cut and sewn looks removable and is not: it is the pastoral of work, the craft on which the family’s decency rests. What holds the axis at the foot of the twelve is repetition. The Swede’s anguished questions recur across the second and third parts with diminishing return, Lou Levov’s tirades run past their point, and the dinner party restates guilts already established. Perhaps a tenth of the book could go without the knowledge changing.
Vladimir Nabokov · Literature
8.6 · Tier IV
The subtractive test is harder for this book than its finish suggests. The chapters were made as separate magazine pieces, each complete in itself; the tutors of chapter 8 or the Mayne Reid games of chapter 10 could go, and the book would close over the gap with little scar. That is what holds the axis at 8.2. What resists the test is the weaving the book names as its purpose: “The following of such thematic designs through one’s life should be, I think, the true purpose of autobiography”. The threads it lays (the matches, the colored glass, the father, the butterflies) bind the chapters more tightly than their origins promise, so that most are required by the design. A long book compelled in parts, permitted in others: between a collection and a novel.
Nabataean · Architecture
8.6 · Tier IV
Judged on purpose, structure and site, and necessity holds wherever the place commands it. Without the dam, the tunnel and the channels the approach drowns. The sequence from the Bab as-Siq through the cleft to al-Khazneh cannot lose a part, since the long dark passage is what the facade answers; ad-Deir needs its climb; the living city lies on the valley floor, ringed by the cliffs of the dead, with water threaded through both. The order of the basin is compelled. What holds the axis, level with The Swerve at the foot of the twelve, is the field below that order: hundreds of family facades lose little by subtraction one at a time, and the great fronts are compelled by display, not by the plain chambers behind them.
Stanisław Lem · Literature
8.5 · Tier IV
The book is built on a single compulsion: a man who has come to study a thing that cannot be studied is visited by the one person he cannot face, and every chapter turns between the two. The Harey chapters and the Solaristics chapters require each other: remove the library and the love story is a ghost story; remove Harey and the library is a satire on science with no stake in it. Gibarian’s death before Kelvin arrives, Berton’s report, the oxygen, the annihilator and the last landing are each needed. What holds the axis lowest of the eleven it shares with the summit conditions is the length of the library. The catalogue of symmetriads, asymmetriads and mimoids, and the century of rival schools, run longer than the argument needs; the book could be a tenth shorter without loss.
Venetian · Architecture
8.5 · Tier IV
Run the subtractive test on the section. The sovereign body was the whole patriciate, and the room that held it had to be one undivided hall of great span; it sits on top, where it can be widest and lit from both fronts, and its weight is why the top storey is a wall. Below, the arcade gives the square a covered walk at the seat of power and the loggia a gallery for the state’s ceremonies, and the windows fall where the rooms need them, not where symmetry wants them. What yields is much: the courtyard fronts could be other without loss, the interior sequence grew by accretion and by fire, and many canvases could go without the rooms saying less. The fronts are close to necessary; the whole is assembled.
Zora Neale Hurston · Literature
8.5 · Tier IV
The frame is required: the story exists because Janie comes back and tells it, and the last chapter returns to Pheoby so that the telling becomes the act the book is about. Each marriage is required by the next. Killicks’s mule and plough are the life Nanny chose; Starks’s store and lamp are the life Janie chose against it; Tea Cake is the life she chose for herself, and its price is paid in the flood. Even the mule’s mock funeral, a comic set piece, carries load. Subtraction still finds loose matter: the Mrs. Turner episode makes its point and is dropped; the trial is so compressed that the climactic speech is withheld; the beating on the muck takes a paragraph and leaves no mark on the form.
Umayyad, under al-Walid I · Architecture
8.5 · Tier IV
Judged on purpose, structure and site. The core is compelled. Congregational prayer in rows facing Mecca wants a hall wide along the qibla and shallow toward it, and the three long aisles give exactly that; the arcades on reused columns carry a timber roof at the span those columns allow. The courtyard is required as the overflow and gathering place of a Friday congregation in a Syrian climate, and the porticoes shade it. The transept is required by the mihrab and the ruler’s place before it. What yields to the subtractive test is real: the enclosure’s size and shape were given by the Roman temenos, a bay more or less of the hypostyle would not be missed, and the minarets, courtyard domes and shrines are accretions of use.
Leon Battista Alberti · Architecture
8.5 · Tier IV
Run the subtractive test on the nave. Take away the aisles, as Alberti did, and the crowd before the relic stands in one room; the chapels become what aisles were for, places of private devotion, and also the buttresses the vault needs, so use and structure are one fact. Take away the small chapels in the piers and the bays lose their rhythm and their hollowing, the mass removed where weight is not needed. One unit builds the whole and is required at every scale. What yields is at the joints: a front lower and narrower than its nave, mended by the ombrellone; a crossing and dome the nave does not compel in their present form; and later paint that could go without loss to the structure.
Public Enemy · Music
8.5 · Tier IV
Sixteen tracks, and the subtractive test finds a hard core and a loose margin. Bring the Noise must open the songs, as the manifesto; Don’t Believe the Hype must follow, turning it on the press that will receive it. Black Steel in the Hour of Chaos is the centre of gravity, and Night of the Living Baseheads, the one place the record turns its argument on its own community, could not go. Mind Terrorist and Security of the First World work as station breaks in a broadcast. The test bites three times: Cold Lampin’ with Flavor is a turn the argument could lose, Show ’Em Whatcha Got restates a mode, Prophets of Rage repeats Rebel Without a Pause at lower heat. Two strong tracks were made before the album was conceived as a whole. A tenth to an eighth is permitted rather than compelled.
Jules Hardouin-Mansart · Architecture
8.5 · Tier IV
Judged on plan, section and structure under purpose and site. The Greek cross with its four round chapels is required by the purpose first set: a centralised royal chapel, a room for the king that is a centre and not a nave, joined at its sanctuary to the soldiers’ church so that one altar serves king and army. The south front gives the king his own approach; the north opening gives the soldiers sight of the altar. The paired columns of the drum work as buttresses. What resists the subtractive test is the section’s display: the outer dome lifted far above the inner to be seen across Paris, a second painted dome there to be glimpsed through the first, trophies and gilding that are surplus. Display was the commission’s purpose, but a plainer two-shell church would have served worship.
Robert Altman · Film
8.5 · Tier IV
Judged on structure, since the talk is deliberately half-heard. The town is the argument, and every scene that builds it is required: the first poker game in Sheehan’s roofless saloon, the three women in tents, Mrs. Miller’s arrival and her ledger, the bathhouse, the widow taken into the trade. Without them the snow at the end would be a shootout and not a burial. The company men, the lawyer and the three killers each enter once and are not spared. What holds the figure down is the middle hour, which loosens: the birthday party, the bathing women, McCabe’s muttering in his room run on past their structural need, and several of the ensemble’s scenes are present because Altman let them happen, not because the finale asks for them.
Seamus Heaney · Literature
8.5 · Tier IV
The test is subtractive, and the stanza helps. The skinny quatrain leaves almost nothing idle in the line, and the best poems resist removal stanza by stanza: “Punishment”, “The Grauballe Man”, “Sunlight”, and “Strange Fruit”, a sonnet that cannot spare a word. The book yields more than its best poems. Part I repeats its central gesture, a preserved body, a tender gaze, a turn to the Ulster present, several times; “Bone Dreams”, “Come to the Bower”, “Ocean’s Love to Ireland” and “The Betrothal of Cavehill” could go with little loss, and “Viking Dublin: Trial Pieces” is long for its yield. In Part II “Freedman” and “The Unacknowledged Legislator’s Dream” are slight. “Hercules and Antaeus” is required: it closes the frame “Antaeus” opens. High in the parts, lower in the assembly.
Michael Powell and Emeric Pressburger · Film
8.5 · Tier IV
The spine survives the subtractive test. Julian’s stolen music is the first case of the film’s law, that the work devours its makers, and it brings him to Lermontov. Lermontov’s question at the party, why she wants to dance, is answered only by the last reel. Boronskaja’s marriage and dismissal is required: it shows in advance what marriage costs a dancer in this company and opens the role Vicky will fill. The ballet is required, and so is the death that repeats it. What gives is the middle: the company’s routine, the comedy of Ratov and Livy, the Riviera and the long courtship passages make their point more than once, and the turn to collapse rests on fewer events.
Hayao Miyazaki · Film
8.5 · Tier IV
Judged on structure. The spine is required. A curse taken in defence of a village sends a prince west to find its cause, and the cause is an iron ball fired from a town that is clearing a forest, so the wound in his arm is the film’s argument carried on a body. The raid on Irontown, with Ashitaka walking out through the gate with San while shot through, is required; so are Okkoto’s march and corruption, which repeat Nago’s fall at the scale of a clan, and the head’s return. What gives is the middle, and it holds the axis at its figure. The film crosses between town and forest more often than the argument needs. Lord Asano’s samurai at the gate, whom the plot drops, and the market’s long introduction of Jigo could go without loss of a fact; Kohroku’s comedy is relief, not law. At this length the scale is permitted more than compelled.
Luciano Laurana and Francesco di Giorgio Martini · Architecture
8.5 · Tier IV
Run the subtractive test on plan, section and site. Much is compelled. The ridge forced two faces: a civic front to the piazza and the cathedral, a ducal front to the valley, and the Torricini stand where the second meets the cliff, their towers carrying the stairs the loggias need. The courtyard is the hinge that gives one centre to a building absorbing older wings; the ramp and the stables are compelled by a court that rode. What holds the figure here is the plan itself: an agglomeration, irregular round the older blocks, with a piazza front never finished, and a good deal that could be otherwise without loss.
Andrea Palladio; scene by Vincenzo Scamozzi · Architecture
8.5 · Tier IV
The subtractive test is sharp here, and the building mostly resists it. Remove the colonnade crowning the cavea and the room loses the closure that makes it a Roman open theatre brought indoors; close the frons’s openings and the streets have no gate to be seen through; flatten the cavea and the shared sightline to the frons is lost. The half ellipse is compelled by the site, and Palladio made the compulsion into the plan. What yields: the frons is overfilled, tier on tier of statues and aedicules, much of it the Academy’s homage to itself, which could be thinned without loss; and the streets, necessary for the opening play, fix every later play in Thebes.
Kendrick Lamar · Music
8.5 · Tier IV
Sixteen tracks in about seventy-nine minutes, and the spine passes the subtractive test while the flesh does not entirely. Wesley’s Theory must open: it sets the pact of fame. u and i are required as a pair, the self-hatred and its answer. Alright and The Blacker the Berry are the record’s public poles, hope and a fury that names its own complicity, and Mortal Man is the record’s reason, the poem read whole to a dead man. How Much a Dollar Cost carries the theology. The test bites in the second half: Hood Politics, Complexion and You Ain’t Gotta Lie say what the record needs at a length it does not compel, and Institutionalized restates the opening at lower heat. Length is not charged; perhaps a sixth of it is permitted rather than required.
Built for Taira no Kiyomori · Architecture
8.5 · Tier IV
Run the subtractive test. The siting cannot go: the island was held sacred, by tradition, so the shrine was built not on its ground but on the strand between land and sea, and everything else follows. The corridors cannot go: on a tidal flat they are the only ground, and they bind the scattered halls into one passage. The gapped floor, the low height and the open platform facing the gate are required by the sea. The gate cannot go: it marks the threshold for those who came by boat. What holds the axis is the plan’s additive habit. The Heian residential manner is a set of halls joined by galleries; the Marōdo shrine, the Noh stage and the length of the west corridor could each be shorter or absent without the argument failing.
Charlie Chaplin · Film
8.5 · Tier IV
Judged on structure. The spine is a double misrecognition, and it is strictly built. The girl takes the Tramp for rich because she cannot see; the millionaire knows him as a friend only when drunk; and each blindness needs the other, since the money her eyes need can come only from the man who forgets where it came from. The eviction notice, the sweeping job and the fight are required: each is an honest attempt to earn what will finally be given, and each failure is why he must take the gift and be arrested. The ending is required by the first meeting. What gives is the set piece kept for itself: the swallowed whistle, the spaghetti and the streamer, the apache dance, the repeated business of the millionaire’s car. The boxing match is required in kind and longer than its work. The episodes are compelled in order and permitted in length.
Yasunari Kawabata · Literature
8.5 · Tier IV
The subtractive test is hard to answer against a book this spare: there is almost no exposition to cut, and the elisions do much of the work. What Komako was to Yukio, and whether she was ever his fiancée, is never settled, and must not be. Nearly every image recurs with work to do: the mirror, the cold hand, Yoko’s voice. But the book was not composed as one thing. It came out in episodes over twelve years, and Kawabata extended it twice after he had called it finished. The autumn section restates the lovers’ impasse it has already shown; the chijimi passage could be lifted with a loss of tone rather than of meaning; and the fire, the last part written, reads as a decision made late about a book that could have kept going. Necessity is high in the parts and lower in the whole.
Wang Ximeng · Visual art
8.5 · Tier IV
Judged on the sequence, and the test is harder here than on a single field, because the handscroll is additive: massif follows water follows massif. Some parts resist removal. The low shore at the opening and the low ground at the close are the frame of a journey and cannot go. The great central rise, the peaks at their highest and the blue at its most saturated, is the summit the whole is built toward; without it the rhythm has no crest. The long bridge with its pavilion, crossing open water between massifs, is a hinge. But in the middle reaches a range of hills and a hamlet could be dropped and the scroll would close around the gap, shorter and not less. The length is compelled in principle and permitted in detail.
Gabriel García Márquez · Literature
8.5 · Tier IV
The spine is required. Opening on the day of Urbino’s death and Florentino’s declaration, then going back half a century, makes the reader hold the end while the middle accumulates, so that the last chapter’s voyage is paid for by everything between. The suicide of Jeremiah de Saint-Amour is not ornament: an old man who chose death rather than age frames two old people who choose love in age. What holds the axis there is the catalogue at the centre. The middle chapters on Florentino’s affairs proceed by episode, the widow Nazaret, Ausencia Santander, Sara Noriega, Olimpia Zuleta, Leona Cassiani, and several could go without loss to the argument; some of Urbino’s civic chapters are period colour. The catalogue is partly the point, six hundred and twenty-two entries set against one fidelity, but the book’s scale is permitted more than compelled in its fourth and fifth chapters. Necessity is strong in the frame and the last chapter, looser in between.
Mirak Mirza Ghiyas, under Bega Begum and Akbar · Architecture
8.4 · Tier IV
Judged on structure, purpose and site, much is compelled. The site is compelled by the saint: the dynasty lays its first emperor in India within reach of Nizamuddin’s grace. The plinth is compelled twice, lifting the tomb to stand as the centre of the paradise and holding the real grave in the earth beneath the cenotaph. The double dome is compelled by two scales, a profile for the city and a chamber in proportion; one shell could not serve both. The ninefold plan is compelled by circumambulation. What resists the test is the repetition the type brings: four identical fronts on a site whose sides were unlike, upper rooms that serve little, kiosks as much sign as structure, and more plinth cells than the first burial needed.
Adam Lock and others · Architecture
8.4 · Tier IV
Run the subtractive test. Take away the scissor arches and the central tower falls: they are compelled in the plainest sense and govern the crossing so completely that the church cannot now be thought without them. The chapter house stair is required by a chapter house raised over its undercroft and by the route on to the vicars’ street; its worn treads are use made visible. The nave’s unbroken triforium is a choice the level elevation needs. What yields is accretion: the west front is a screen wider than the church it fronts, its towers later than its lower storeys; the cloisters are a fifteenth-century rebuilding; the eastern arm replaces an earlier one. Many parts are fitted rather than required.
Middle Byzantine builders · Architecture
8.4 · Tier IV
Judged on structure, purpose and site. The katholikon’s plan answers a need. A pilgrimage church round a saint’s tomb wants one broad, unbroken centre where a crowd can stand under the dome, and the octagon scheme gives exactly that: the dome springs from squinches over the corners of the square, the four columns of the ordinary cross-in-square are gone, and the naos is one space. Galleries, narthex and crypt each have their office: the place above, the threshold, the burial below. What yields to the subtractive test is the pair as a pair: two churches of two types, on any dating two campaigns, joined at a tomb the cult made sensible. Remove the smaller church and the katholikon loses its neighbour, not its reason.
Christopher Nolan · Film
8.4 · Tier IV
Judged on structure and on the screenplay’s economy, and most of it resists the subtractive test. The bank robbery is required: the crew kill one another on the Joker’s instruction, and that is his whole thesis, shown before he says a word. The pencil at the mob meeting, the coin, Gordon’s family and the two addresses are all planted and paid. The ferries are required, since they are the city’s answer to the thesis. The spine is compelled. What gives lies at the edges: the Hong Kong extraction does in a sequence what a scene could do, Reese’s threat to unmask Batman is raised once and dropped, Gordon’s faked death repeats a deception the film plays several times, and Two-Face’s arc is pressed into the last forty minutes.
Raymond Hood and the Associated Architects · Architecture
8.4 · Tier IV
Judged on purpose, plan and structure. The test bites hard at the heart. Take away the Channel Gardens and the sunken plaza and the tower stands on a street like any other; take away the axis and the plaza has nothing to face. The slab is compelled rather than chosen: its thinness, its setbacks and its height are what keeping office floors shallow and stacking elevator banks produce on that lot. The low pavilions on Fifth Avenue lower the street wall so the tower is seen across a gap, and make the entrance a passage rather than a door. The concourse and service levels are required by a complex that keeps its traffic below. What resists the test: the ring of secondary slabs, the International Building aside, could be rearranged without loss to the governing idea, and the Music Hall is required by the programme, not the plan.
Leo Tolstoy · Literature
8.4 · Tier IV
The subtractive test finds a core that cannot be touched. The frame conversation sets out the respectable positions so that Pozdnyshev can break them; the confession moves from the brothel of his youth to the honeymoon quarrels, the children, the doctors, the music and the dagger in one forced line; the close has the man who has argued for hours ask the narrator’s pardon. Every stage of the marriage prepares the killing, and the killing is the argument’s proof and its refutation. What can be removed lies inside the tirades: the passages on doctors, on contraception, on girls raised as bait and on the end of the race if chastity were general restate a thesis the action has made. Necessity is high in the plot and lower in the preaching.
Athenian (architect unrecorded) · Architecture
8.4 · Tier IV
Judged on structure, purpose and site. The building’s irregularity is its strongest evidence of necessity: nearly every departure from the temple type answers a fixed thing on the ground. The rock falls from east to west, so the east porch stands at the upper level and the north porch at the lower, its columns taller to reach their roof. The north porch reaches past the west wall toward the Pandroseion and its olive; the south porch stands at the place of Kekrops. Remove a porch and a sacred place loses its door or its marker. What yields is the joining: the west front and the south porch, scarcely an entrance, read as parts placed rather than one figure compelled, and the argued thesis of a larger plan cut short keeps the charge of compromise alive.
Paul Auster · Literature
8.4 · Tier IV
The test is subtractive, and the trilogy passes it in most of its parts. Ghosts passes almost entirely: a watcher, a watched man and a room, and nothing the fable does not need. City of Glass is nearly as tight: the wrong number, the assumed name, the case, the walks, the meeting with the writer called Auster and the disappearance are each a stage in the loss of a self, and Stillman’s theory of a fallen language, long as it is, is the case’s motive and must stay. The repetition is itself required: three versions of one story, each nearer its teller, are the argument, and none could go without the knowledge changing. What holds the axis is The Locked Room, whose middle, the years of marriage and obsession and the Paris journey, runs longer than its knowledge needs and is much of it told in summary.
Michael Cimino · Film
8.4 · Tier IV
Run the subtractive test and the part most often attacked resists it. The wedding, which looks like length, is the argument: the crowns, the wine that falls on the bride’s dress unseen, the soldier at the bar who answers every question with an obscenity, the dance at which Steven’s mother weeps. Without the hour in Clairton the cage and the return would have nothing to tear. The first hunt is required by the second, the cage by the Saigon den, the hospital by the funeral. What holds the axis lowest lies inside the movements: the drive to the mountains and the quarrel over boots run long, Saigon’s night streets are atmosphere more than step, and Michael’s return in 1975 rests on a descent of Nick’s shown only in fragments.
Metallica · Music
8.4 · Tier IV
Eight songs in about fifty-five minutes, and the subtractive test finds the parts mostly required. Battery must open, its terms set in the first minute as a classical-guitar figure gives way to the band. The title track is the centre and could sit nowhere else. Sanitarium is the one place the record turns inward, Disposable Heroes the public form of the same servitude, Orion the record’s breath, and Damage, Inc. its end in violence. The test bites twice: The Thing That Should Not Be restates its menace on one riff more than it develops it, and Leper Messiah’s middle is a change of riff more than a turn. Inside the long songs, sections repeat by the habit of the form.
Pearl Jam · Music
8.4 · Tier IV
Eleven songs in about fifty-three minutes, and the subtractive test finds a required first half and a frame that holds. Once must open, its killer’s voice rising out of the instrumental figure that begins the record; Alive is the centre, and Jeremy the public statement; Black is the one place the record turns from damage to love lost, and Release the close it needs, a son calling to a dead father, with the frame returning around it. The test bites on the second side, and that holds the figure. Oceans is a slight interlude, Porch is energy with little turn, Garden and Deep restate the brooding of the first half less specifically, and some of the long guitar codas run on from habit rather than need.
Hilma af Klint · Visual art
8.4 · Tier IV
Judged on the configuration, then within the panel. Take away Childhood and the life has no origin; take away Old Age and it has no close, and the turn from bloom to geometry, which is the cycle’s argument, goes with it. The four ages are compelled. The count within them is less so: adulthood’s four panels are the life’s fullness, and the weight is meant, but one of the four could go and the age would still read, which no pair allows. Within the panel the composition accretes, and many of its spirals, buds, rosettes, loops of script and small figures could be moved or removed without loss. The scale is compelled; the population of motifs is permitted.
Jakob Prandtauer · Architecture
8.4 · Tier IV
Judged on purpose, structure and site, and the site compels most of the plan. The rock is long and narrow, so the abbey is a line and not a quadrangle in a valley. The church stands where the rock ends, its front turned to the river; the Marble Hall and the library run out beside it and close on a terrace, with a curved gallery between them low enough for the church front to show over it from below. Raise the gallery and the church disappears from the river; take it away and the terrace loses its frame. Use compels the courts, choir, refectory and cells. What yields is the imperial suite and its long corridor, rooms for a court that seldom came, a repeated bay that could be shortened without loss to the argument.
Paul Valéry · Literature
8.4 · Tier IV
The test is subtractive, and the book answers it unevenly. In “Le Cimetière marin” almost nothing can go: the poem moves from the noon sea as pure being, through the self reflected in that stillness, to the dead, to the refutation of Zeno, to the wind and the turn to life, and each stanza is a step of that argument. “Ébauche d’un serpent” and “La Pythie” are long and could lose stanzas without the argument breaking; the serpent’s rhetoric turns back on itself more than once. The book is an arrangement rather than a sequence, and its slight pieces, “L’Insinuant” and “La Ceinture”, could go without loss to what it knows. A necessary centre and permitted edges.
Unknown court painters (Heian period) · Visual art
8.4 · Tier IV
Judged scene by scene, since the whole is gone. Within a scene, removal fails. In Kashiwagi III Genji holds the infant Kaoru, who is not his son: take away the women at the curtain’s edge and the court is no longer watching; take away the diagonal of the dais and Genji floats, where it is that diagonal that crowds him into his corner. In Minori the bent autumn grasses outside cannot go either. Each picture is one chosen moment set beside text excerpted for it, and the pairing is exact. What yields is the set: two or three scenes from one chapter sometimes repeat a single interior with little gain, the Yadorigi pair among them, and the choice of a quiet moment before or after the event is a convention as much as a necessity.
Alfonso Cuarón · Film
8.4 · Tier IV
Judged on structure and on the economy of the telling, and the subtractive test meets real resistance. The film is a chase with no subplot and no scene away from Theo, and its world is laid in the backgrounds of scenes doing other work: the bombed café, the caged refugees at the station, the Quietus advertisements, the burning cattle by the road. Julian’s early death turns a favour into a vocation; Jasper’s house is required, the last place of private life, whose loss is the cost of the journey. What gives: the Fishes’ plan to keep the child as a political flag is genre machinery, explained in an overheard conversation; the farmhouse escape, with a car that will not start, is suspense by formula; and parts of the exposition come in speeches that could be shorter.
Leos Carax · Film
8.4 · Tier IV
The subtractive test is where an episodic form is weakest, and the film meets it with a frame that is required: one day, one car, one dossier, so that each role is labour and the day is a life. Most appointments carry a separate part of the argument. The motion-capture session takes the image away from the actor’s labour; the father brings the role into the family, where the lie hurts; the double killed in the warehouse turns the roles on the man; the Samaritaine breaks the system with a real past; and the set pieces hold no idle shots. What gives: the beggar on the bridge is a sketch, the café killing repeats the warehouse in a lower key, and the order of the middle appointments is not compelled.
Ludwig Mies van der Rohe · Architecture
8.4 · Tier IV
Judged on plan, section and structure, under purpose and site. Subtract from the upper hall and nothing goes without loss: eight columns, one plate, the glass, two shafts, two stairs. The roof is not a covering on a box; the box is a lesser thing set back beneath it, and the corners fly, so that the plate is plainly carried at the points that carry it. As structure the building passes the subtractive test as few do. The charge falls on use. The same plate on the same perimeter columns was drawn for a rum company’s offices in Cuba and a private museum in Franconia before it was a national gallery, and the hall, glass on four sides, has never been a good room for pictures. The parts are required by what the building says, less by what it is for.
Maya · Visual art
8.4 · Tier IV
Judged on the cycle’s configuration. The three rooms are three movements of one argument: the heir presented to the nobility, the captives who underwrite him taken and arraigned, the court dancing and bleeding in thanks. Remove the middle room and the presentation has no price; remove the last and the battle has no issue in rite; remove the first and the violence has no object. Within the middle room the battle on three walls and the arraignment on the fourth cannot be separated: the mêlée produces the captives and the stepped platform sorts them. What yields is register filler: the long rank of nobles in white mantles, some attendants of the last room, the generic masks of the vault. The scale is compelled, though not in every figure.
Elias of Dereham and Nicholas of Ely (attributed); spire by Richard of Farleigh · Architecture
8.4 · Tier IV
Run the subtractive test. The main parts are compelled by use. The second transept gives the choir its own crossing and the altars of a large secular chapter their place; the low ambulatory and the Trinity Chapel give the daily Lady Mass its own room and the processions of the Use of Sarum a route round the east end; the chapter house is the seat of the chapter’s government, the cloister its processional and burial walk. The spire passes on site rather than use: in a flat meadow it marks church, close and town from miles off. What yields is repetition and display: ten identical bays that could be eight, a west front wider than the nave behind it, a cloister for a chapter with no monks.
Voltaire · Literature
8.4 · Tier IV
The subtractive test bites less than the episodic shape suggests. Every station is a case, and the cases are chosen to cover the field of evil: war in the Bulgarian village, nature at Lisbon, the Church at the auto-da-fé, lust and the body in the old woman’s story, empire in Paraguay and Surinam, the polite world in Paris, the state in the shooting of an admiral, wealth and taste in Pococurante, power in the six dethroned kings. Remove El Dorado and the book loses its proof that a good society is possible only where no one can reach it; remove Martin and Pangloss has no rival system. Where the test bites: the reunions, a joke fully made by the second, and the Paris chapter as Voltaire enlarged it in 1761, whose card table and literary quarrels could go. Perhaps a tenth is surplus.
Kenzo Tange · Architecture
8.3 · Tier IV
The subtractive test bites hardest on the plan, and the plan resists it. Set the museum on the ground and the axis is cut: the visitor arriving from Peace Boulevard faces a wall, not a line of sight to the ruin. Take away the cenotaph and the line loses its station, the place where the names of the dead are kept and the dome is framed. Take away the dome as terminus and the park is a civic garden with a museum in it. Each of the three is required by what the work has to say. What is not compelled is the museum’s body as a container: a long louvred box on pilotis whose exhibition floor is a neutral hall that could hold any collection. Necessity is high in the plan and ordinary in the building.
Romano-Egyptian painters · Visual art
8.3 · Tier IV
Judged at two scales. A single panel resists subtraction almost wholly: a face, the hair, the neck, the edge of a tunic or mantle, a necklace or a wreath, a dark or neutral ground. Nothing is narrative and nothing is setting; every element is the person or the sign of the person’s rank and care. The eyes, large and set slightly high, cannot go, nor the highlight on the nose and lower lip that makes the flesh. What could go is little: some jewellery painted to inventory rather than to see. At the scale of the body the test fails more often. A hundred more or fewer bearded men of the same type would change little of what the body says, and its size is permitted by burial and finding, not compelled by an argument.
Patti Smith · Music
8.3 · Tier IV
Eight tracks in about forty-three minutes, and the frame is compelled. Gloria has to open: the record begins by refusing a doctrine and then seizes a garage song of male desire, and every later track follows from that seizure. Land has to stand where it does, the climax of side two, and Elegie has to close, a hush after the frenzy. Birdland and Land, improvised at length, are the record’s reason for being. The subtractive test bites twice. Break It Up is the most conventional song here, its dream of a dead singer spent early, and Free Money says in four minutes what Gloria and Land say better. Birdland drifts in its middle before it rises. About a tenth of the record is permitted rather than required.
Federico Fellini · Film
8.3 · Tier IV
Judged on structure, with the small verbal part of the patter and the Fool’s speech. The spine survives the subtractive test. The sale on the beach is required by the beach at the end. The chain act, repeated in the same words in every square, measures a man who does not change. The sick child at the wedding prepares Gelsomina’s recognition of herself in the Fool; her flight shows she could leave, so the pebble speech has a choice to work on; the killing is the hinge, and without the abandonment the coda has nothing to answer. What gives is the middle: the circus stay and its company run long for what they do, the episode of Zampanò’s woman is a sketch, and several stations could be thinned without loss.
Walter Gropius · Architecture
8.3 · Tier IV
Judged on plan, section and structure, under purpose and site. At the level of the part, necessity is high. The workshops need even, abundant light and are given a wall of glass; the classrooms need daylight on desks and are given ribbon windows; each studio needs a private outside and is given a balcony; the two schools share a road and are joined over it by the office that ran them. Take away the bridge and the building is two schools; take away the hall, the canteen and the studios and the school is a factory. What resists the test is the whole: a pinwheel is additive, its arms could be longer, fewer or turned another way, and the flat, open site compels none of its asymmetry. The glass wall exceeds its use.
T. S. Eliot · Literature
8.3 · Tier IV
The subtractive test mostly fails to find slack. Remove the Tempters and Thomas’s last choice has nothing to be chosen against; remove the sermon and the play never says what a martyr is before it shows one; remove the Knights’ prose and the play ends in liturgy with no world left to accuse. The fourfold design is exact: three Tempters Thomas has foreseen, then a fourth he has not, who offers him martyrdom for its glory. What holds the axis is the choral writing of Part I and the opening of Part II, where the women’s dread is restated in catalogues of season and smell longer than the action asks, and the Priests, who are scarcely told apart and could be two.
David Markson · Literature
8.3 · Tier IV
The test is subtractive, and the book’s method is repetition, so the test asks which returns are required. Kate circles back to the same facts, names and corrections: a remembered painting, a figure from the Trojan War, a composer, the house down the beach that she burned, the son she lost. The return is the meaning. A mind alone can only re-order what it already holds, and each pass shifts a fact or exposes a confusion, so that the grief under the trivia surfaces by accumulation; remove the repetitions and the knowledge goes. Where the test bites is length: the cumulative effect is reached well before the end, and some stretches of the middle return without shifting anything. Necessity holds in the method and weakens in the measure.
Italo Calvino · Literature
8.3 · Tier IV
The test is subtractive, and it meets two kinds of necessity. The architecture compels the count: eleven series of five, entering and leaving in a staggered order that rises and falls across nine chapters, so that removing a city breaks a figure the book is built on. The frame is required outright: without Polo and Kublai the cities are prose poems; with them they are an argument about knowledge, power and description. The test bites on meaning. Within a series a city sometimes restates its neighbour’s paradox in a new image, several Cities and Desire and Thin Cities turning on the same reversal, and three or four cities could go without the book knowing less. Necessity is total in the form, and what the content could spare weighs as much as what the form forbids.
Michelangelo Antonioni · Film
8.3 · Tier IV
The subtractive test bites at the centre and slackens at the edges. The middle third is compelled: each enlargement requires the last, the eye moving from a woman’s glance to a fence to a hand and a gun, and the night visit to the park is required by what the prints could not settle. The frame is required too: the whiteface troupe opens and closes the film, and the tennis it mimes answers the question the prints raised. The guitar neck, fought for and dropped, tells the photograph’s fate again. What gives: the romp with the two girls outlasts its function, the party restates the club, and the Veruschka shoot and the models make one point twice. A tighter film of ninety minutes can be imagined.
Norman Foster (Foster and Partners) · Architecture
8.3 · Tier IV
Judged on plan, section and structure, under purpose and site, the building mostly resists the subtractive test. Remove the masts and trusses and the open floors, the free ground and the atrium go together: they are one decision. Remove the sunscoop and the atrium becomes a dark shaft. Remove the open concourse and the ascent by escalator loses its point. The flanking cores are compelled by the wish to clear the plan. What is not compelled is the scale of the structural expression. A suspension frame on this site was a choice, not a necessity; the open floors could have been had more cheaply, and the cost buys rhetoric as well as space. The roof cranes and the heavy bracing are partly emblem.
Thelonious Monk · Music
8.3 · Tier IV
Five tracks in about forty-three minutes, and the subtractive test finds give in one place. The title track resists it wholly: each chorus at its alternate tempo is required, because the form exists only in the change. “Pannonica” is a portrait in under nine minutes, and its celeste could not be removed without removing the person drawn. “I Surrender, Dear” is the record’s breath and its only view of Monk’s piano unaccompanied, load-bearing as a frame. “Bemsha Swing” closes on an old tune made new. The test bites on the blues: “Ba-lue Bolivar Ba-lues-are” runs thirteen and a half minutes, nearly a third of the record, and some of its long, uneven choruses could go with little loss. That length is permitted, not compelled.
Jørn Utzon · Architecture
8.3 · Tier IV
Judged on purpose, structure and site. The two lit corridors resist the subtractive test: they carry circulation and bring daylight into a deep plan, and they make the building’s rhythm and the first experience of entering. The vault resists it more: it is the instrument that turns a single high window into an even, falling light over the altar, and without it the room is a hall. The modular exterior follows from an additive method and a parish budget. What yields: the plainness outside is a choice the building could have made otherwise, the shed roofing and greenhouse glazing are a manner as much as a necessity, and the billows have more curves than the light alone requires.
Neil Young · Music
8.3 · Tier IV
Eleven tracks in about thirty-five minutes, and brevity changes the test: songs this short carry little slack inside them, and the question is what the record needs. After the Gold Rush is its centre and must be there. Southern Man is the one public song and the one long electric passage, and side one needs its weight. Birds and Don’t Let It Bring You Down carry the grief of side two, and Tell Me Why is the right opening, a plain question on acoustic guitars. The test bites on the two fragments that close the sides as sketches rather than endings, on Oh, Lonesome Me, which the record could lose, and on two good songs that restate rather than turn.
Jonathan Glazer · Film
8.3 · Tier IV
The film is built by repetition, and the repetitions are required: each lure is the same act shown again, so the audience learns the routine as she has, and its breach means something. The beach is required, since the infant left crying on the shingle measures what she is before she changes. The disfigured man is the hinge: she looks at her face in a mirror and lets him go, and the film turns on that one act. The flight north, the meal, the bed and the forest each go further into the body she wears. What gives is in the middle: the nightclub, the long drives and some of the Highland wandering run longer than their work, and the motorcyclist’s searches repeat what is known.
Medang (Mataram) builders · Architecture
8.3 · Tier IV
Run the subtractive test on the centre and little yields. Each great temple is answered by its mount across the court, Nandi facing Shiva, so the six are three pairs and none is spare. The four cellas of the Shiva temple are required by its cross plan and by the family of the god it sets at the quarters; base, body and roof are required by the tower’s reading as a mountain. The rows of the second court are required by the mandala: without them the centre is not a centre. What yields is the repetition inside them. Two hundred and twenty-four nearly identical shrines are ordered, not each compelled, and the apit, kelir and patok shrines are thinly motivated by use.
Wim Wenders · Film
8.3 · Tier IV
The subtractive test passes in the frame and gives in the middle. The desert walk, the silence and the refusal to fly are each paid later: the man who will not leave the ground is the man who, by his own account through the glass, once tied his wife to a stove with a bell on her ankle, and who still cannot stand where a family stands. The Super 8 film is required, the first image of Jane and the first time Hunter sees his parents as a couple, and nothing in the two booth scenes could go. What gives: the Los Angeles movement is long for what it moves; Walt and Anne’s claim on the boy is stated more than dramatised and dropped once the truck leaves; the man on the overpass is atmosphere.
Ogata Kōrin · Visual art
8.3 · Tier IV
Judged cluster by cluster and interval by interval. What carries the work is not any one plant but the spacing: the gold between the clusters is the water, the distance travelled and the rest in the music, and it is measured. Take away a cluster in the right screen and the band sags; take away the open gold of the left and the diagonal loses its run toward the edge. The pair is required: the right screen’s dense procession and the left screen’s thinning diagonal are the outbound way and the far shore. What yields is the logic of the repeated unit: a work built from a module concedes that a cluster could be added or removed with a change of rhythm but not of meaning.
Chaulukya, under Queen Udayamati · Architecture
8.3 · Tier IV
Judged on purpose, structure and site. The parts of the void are compelled. The descent exists because the water table falls with the season and the people must follow it; the length of the corridor is set by the depth of the water and the pitch of a stair someone carrying a full pot can climb. The pavilions across the corridor are not ornament: they are struts, propping the long retaining walls against the earth, and they are the landings where the climber rests. The shaft is where water is reached when the stair no longer reaches it. What yields to the subtractive test is the quantity of the programme: niche after niche of figures, many repeating type and pose. The structure is necessary; the surface is plentiful rather than required.
Roman · Visual art
8.3 · Tier IV
Judged figure by figure. The god and his consort cannot go: they are the centre the room turns on, and every mortal figure stands to one side or the other of them. The startled woman cannot go: she is the hinge, and her flight sets the tone of all that follows. The winged figure and the kneeling young woman cannot go: they are the ordeal and the reason for the fear. The satyr at the bowl, with the mask held above, is the one moment of seeing in the room, and the seated matron by the door frames the cycle as a life lived in this house. What yields is the company: the Silenus with the lyre and the young Pan with the kid, beautiful and partly decorative; an attendant at the sacrificial table; the bride’s toilette, which repeats in a calm key what the sequence has already done.
Leonard Cohen · Music
8.2 · Tier IV
Ten songs on two sides of five, and most resist the subtractive test, because each is a different station of one man’s dealings with women and with the sacred. Suzanne must open: it states the method, the beloved and the divine met in one harbour city. The Stranger Song and Master Song are the long portraits of rivalry and departure; Sisters of Mercy closes side one in shelter; So Long, Marianne opens side two in leave-taking, and Hey, That’s No Way to Say Goodbye answers it more briefly. The test bites on side two. Stories of the Street is the most diffuse of the ten; Teachers, a riddle-song, restates the seeker’s stance without adding to it; and the wordless coda of One of Us Cannot Be Wrong is added more than required.
Fela Kuti and Africa 70 · Music
8.2 · Tier IV
Two pieces, one to a side, and the subtractive test bites differently on each. Zombie is lean by its maker’s standard: the opening builds the groove in a fixed order, bass and guitars, then drums, then horns, and the vocal section is short and exact, one word and a set of drill commands, each needed because the drill is the argument. The long saxophone solo is the part a hostile listener would cut; it is the custom of the form more than the need of the song. Mr. Follow Follow is required in idea, since it turns the satire from the soldier to the civilian who follows. In execution its long instrumental stretches are permitted more than compelled, restating where they might develop. One lean side and one loose one hold the figure.
Gian Lorenzo Bernini · Visual art
8.2 · Tier IV
Judged figure by figure and mass by mass. Proserpina cannot go: she is the event, and her resistance, the hand pressing the god’s brow away, the head flung back, the open mouth, is the whole content. Pluto cannot go, and neither can his hand: the fingers sunk into her thigh are the one place where the theme becomes visible as matter. Cerberus is required twice, as the sign that the ground is already the threshold of the underworld and as the third support a striding group needs in marble. The drapery carries weight from her body to his and is made to read as movement. What yields: the crown and bident are attributes rather than argument, and the god’s spread of muscle is more than the action asks.
Muhammad ibn Mahmud Isfahani (attributed), under Timur · Architecture
8.2 · Tier IV
Judged on structure, purpose and site, the chamber yields little to the subtractive test: a square for the cenotaphs, opened in four recesses so that the dead lie at a centre gathered from four directions, with the crypt below holding the bodies on the same plan. The octagon outside is the geometry by which the square becomes a circle for the drum. What yields is the height. The tall drum and the outer shell are not required by the room, which the inner dome closes far below them; they answer another purpose, to raise the tomb’s sign over the city, and that purpose is real. But a part for display beside a part for the dead is two necessities joined, not one. The vestibule and gallery of the 1420s are ordered rather than compelled.
Franz Marc · Visual art
8.2 · Tier IV
The test is subtractive. Remove the deer and the picture loses its centre and its victim: it is the one creature whose whole body is given to the catastrophe, neck bent back into the path of the falling tree, and the diagonals converge on it. Remove the shafts of red and there is no event, only animals in a forest; the light is the blow. Remove the boars and the cataclysm has no breadth, no sense that it takes every kind. The large scale is compelled: the catastrophe must be bigger than the viewer. What yields is real. The left and right zones are crowded with faceted incident, and some subsidiary planes and animal fragments could be shifted or thinned without loss.
Neutral Milk Hotel · Music
8.2 · Tier IV
Forty minutes, and the subtractive test mostly fails to find a removable part. The King of Carrot Flowers must open: a childhood in a broken house, the home the rest of the record flies out of. The title song states the creed; Two-Headed Boy and its Part Two are the frame, and the closer cannot stand without the first. Holland, 1945 is the hinge where the dead girl is named by place and date. Oh Comely runs over eight minutes, and its length is its content. The test bites in three places: The Fool breathes but restates, the untitled instrumental is the most separable minute, and Communist Daughter is a strong image under-built, its drone coda longer than it needs. Three soft spots in eleven hold the figure, none of them filler.
Winslow Homer · Visual art
8.2 · Tier IV
Subtract element by element. The man cannot go: he is the picture. The broken mast and lost rudder cannot go: they are why he is here, helpless. The sharks are death close; the waterspout is death far; the ship is life far; the cane is the cargo, the trade and the reason for the voyage. Each peril stands at a different distance from him, so the four are a ring and not a pile. What yields is the evident accumulation itself, the charge made from the first showing that shark, storm and calamity are heaped up until the picture tips toward the illustrated story. The red flecks in the water are permitted rather than compelled. The ship, small and ambiguous, is the most necessary thing in the field: without it the picture is doom; with it, a question.
Ilkhanid, under Öljaitü · Architecture
8.2 · Tier IV
Run the subtractive test, and it bites less than the size leads one to expect. The octagon carries the dome directly, with no zone of transition made a show of. The walls are as thick as a brick dome of this span demands, and they are hollowed by bays and galleries wherever mass can be spared, so that the structure is lightened by its own rooms. The upper gallery is needed twice: it relieves the drum and gives the tomb its outward view across the plain. The eight minarets marked the octagon’s points and gathered the silhouette into a crown; their loss shows how much they were required. What yields: the mortuary hall, an annex the octagon does not need, and the second, painted campaign, laid over a scheme already complete.
Konstantin Melnikov · Architecture
8.2 · Tier IV
Judged on plan, section and structure, under purpose and site. Take away the lattice and the hexagon goes: the window is not cut into a wall but is a cell of the wall, so structure, fenestration and economy are one decision. Take away the intersection and the house is two silos; where the cylinders cut each other the stair and the passage between the halves fall. Take away the studio’s ring of windows and the room loses its reason, an even light from all round for the work. Very little is applied. What resists the test: the circle was chosen before the programme and the programme fitted to it; rooms in segments of circles take furniture poorly, the shared sleeping room is a doctrine as much as a need, and the small plot compels little.
New Order · Music
8.2 · Tier IV
Eight tracks in about forty-three minutes, and the test finds most of them required. Age of Consent must open: a high bass line carrying the melody announces the record’s sound before a word is sung. Your Silent Face is the centre and could not go. Leave Me Alone is the required end, the guitar band returning after the machines. The Village and 5 8 6 carry the turn to the sequencer that the record is about. The test bites at Ecstasy, a sequenced groove with little voice and little development, and at We All Stand, whose length is permitted rather than compelled; 5 8 6 runs its introduction longer than the argument needs.
Eero Saarinen · Architecture
8.2 · Tier IV
The subtractive test, applied to the figure, finds nothing to take. A weighted catenary is the line along which a self-bearing arch of tapering section stands in compression with least bending; the profile is the structure’s argument, not a drawing laid over it. Height equals span, the section tapers with the load, and the triangle gives three faces to the light and a stiff, hollow tube to stand in. Soften the taper or cut the height and the curve is no longer the shape of its own weight. What holds it lower is use. A memorial asks for no particular room; the interior is fitted to the form, not compelled by a programme, and the scale was chosen for a landmark. Necessary as a figure and a structure; permitted as a building.
Bong Joon-ho · Film
8.2 · Tier IV
Judged on the structure and the screenplay. Much of the film is required, and more than its loose manner suggests. The prologue’s culvert is paid by the epilogue. The trampled footprint and the tractor rolling over it hold the method of the whole inquiry in one image. The radio requests for Yoo Jae-ha’s “Sad Letter”, noticed by a woman officer, become the link to the third suspect. The bandage Seo sees on a schoolgirl’s back while she lives is how he knows her body. The three suspects escalate rather than repeat. What gives, and it gives more than a little: the bathhouse search and the shaman’s talisman are comic digressions that repeat what the interrogations show, Park’s girlfriend has scenes the film could lose, and Cho’s bar fight and wounded leg are laid out longer than they need.
Roman · Visual art
8.2 · Tier IV
Judged part by part. The raised arm cannot go: the statue is an act of address, and without it the figure is a model, not a ruler. The head cannot go, nor the Polykleitan body that carries the claim of a timeless order. The cuirass cannot go: it is where the world is placed on the body, the event at its centre, the sky above and the earth below as its frame, the mourning figures as its cost. The Cupid on the dolphin is both the support the marble needs and the claim of descent from Venus, necessity and meaning in one member, the best single stroke of economy in the work. What yields is the cloak, its heavy mass at the hips and the left arm permitted rather than compelled, and the doubling of divine witnesses on the breastplate, where one would carry the sense. Nothing is idle; some is ample.
Jonathan Demme · Film
8.2 · Tier IV
Judged on structure and on Ted Tally’s economy. The subtractive test mostly fails to find slack. The four interviews are a ladder: each costs Clarice Starling more of herself and buys a clue, the storage unit, the hint about coveting, the anagram names, the file returned with a touch of the finger. The moth found in the throat at the funeral home carries the plot to the Smithsonian and the theme to metamorphosis. The opening at Quantico, Starling among taller men in the lift, is required by everything after. What gives: her arrival at the killer’s own door is a coincidence covered by a plausible errand, not compelled; the Chilton subplot and the Senator’s televised plea run longer than the spine needs; the Memphis escape serves the ending’s freedom more than the rescue.
Michel Gondry · Film
8.2 · Tier IV
The subtractive test finds little to cut. The opening on the train to Montauk looks like a meeting and is the last act in disguise; once the erasure is understood, every detail of it is required, the skipped train, the unease of strangers, her question whether they have met. The clinic’s story pays at every turn: Patrick’s theft of Joel’s words shows a love without its memories as a script that fails, and Mary’s discovery of her own erasure sends the tapes that make the ending a choice. What gives is the middle of the outside line: the party on Joel’s sleeping body runs longer than its work, and Howard’s arrival restates an ethics already shown.
Inca, under Pachacuti and successors · Architecture
8.2 · Tier IV
Judged on structure, purpose and site. A terrace wall on a slope is compelled: it holds the hill and raises the platform, and three tiers step it down to the plain. The batter, the bonding of polygonal blocks and the absence of mortar are what a wall must have to stand through Cusco’s earthquakes, and it has. The saw-tooth plan is required by more than look: each salient lays the face of the next open to flanking view, and the short lengths buttress one another. What yields to the subtractive test is the size of the stones. A wall of hundred-tonne blocks stands no better than one of ten-tonne blocks; the giants are there to be seen, a purpose added to the wall, not compelled by it.
Mastodon · Music
8.2 · Tier IV
Most of the record resists removal. Blood and Thunder must open: it states the whale, the hunt and the riff language in under four minutes. I Am Ahab and Seabeast set hunter and hunted beside each other, the first a barking sprint, the second the record’s first slow, harmonised grief, and the contrast is structural. Hearts Alive is the compelled long form, the voyage the short songs have been circling, and Joseph Merrick its necessary exhalation. Eight songs in under thirty minutes is lean, and the necessity holds at both ends. The test gives in the middle: Island, Iron Tusk and Naked Burn are built from the same matter, and any one could go without the record losing a stage of its argument.
Guillermo del Toro · Film
8.2 · Tier IV
Judged on structure, and most of the parts are required twice, since each task mirrors something at the mill. The fig tree choked by a fat toad is the house Vidal occupies. The Pale Man’s laden table, the host seated at its head, is Vidal’s dinner for the priest and the local notables while the people ration bread. The mandrake keeps Carmen alive, and its burning is the mother’s choice of Vidal’s world over her daughter’s. The third task is the film’s question made literal. What gives: the toad announces the method more than it advances it; the fairies do work the Faun already does; some exposition says what the cross-cutting has shown; the guerrilla line has stretches a stricter film would compress.
Antonín Dvořák · Music
8.2 · Tier IV
The subtractive test meets resistance in the large plan and finds give in the joints. The cyclic returns make the movements need one another: the finale’s coda, which sets the first movement’s horn theme against its own, has nothing to gather if any earlier movement goes, and the Largo’s chorale stands where it does because it turns the first movement’s E toward D flat. The Largo’s C sharp minor episode, and the return of its theme broken off by silences, are the most compelled stretch. The give is real: the scherzo’s two trios could be shortened with little loss, the finale’s recalls are partly a roll-call, and the first movement’s exposition repeat is a convention.
Terry Gilliam · Film
8.2 · Tier IV
The loop is the argument for necessity. The dream of the airport, shown first as a child’s fragment, is the event the whole plot walks toward, and when it comes it is complete, with the boy watching. The planted things are paid: Railly’s voicemail, which the future mishears as the source; the photograph of a wounded soldier in 1917 who is Cole; the Cassandra lecture, which names the hero’s condition before he is believed; the tooth he pulls to escape the scientists’ tracking, answered when they find him anyway. The red herring is required, since the Army of the Twelve Monkeys must be the wrong answer for one quiet assistant with vials to fall like fate. What gives is the middle: Jeffrey’s dinner scene and the road section run long.
George Saunders · Literature
8.2 · Tier IV
The test is subtractive, and the strongest stories pass it within themselves. “Victory Lap” needs each of its three minds, the girl, the boy next door and the man who comes for her, because the rescue is the meeting of two trained consciousnesses with a third that has no training at all. “Tenth of December” needs both the boy’s fantasy and the dying man’s rehearsed speeches, because each rescue answers the other. “Sticks” is the book’s proof of compression: a father’s whole life, his love and its inarticulacy, told through a pole in the yard in one page. What holds the axis is the whole: “Exhortation” restates in miniature the corporate voice that other stories carry further, and the collection could lose a story or two with little changed.
Martin Amis · Literature
8.2 · Tier IV
The frame resists the subtractive test: every stage of the reversed life is required by what the reversal has to show. The American years come first because the reader must learn the backward law in ordinary life before it reaches Auschwitz. The New York hospital comes before the camp because there the law yields its first moral inversion: the doctor, seen backward, wounds the patients he treats, so that when the camp comes, where the doctor’s work was killing, the backward view will make it healing. The flight through Europe is the passage between them. Where the test bites is the comedy of the American part: the backward jokes recur after the reader has learned the law, and the affairs of Tod’s middle age run past the point where they add a turn. Perhaps a sixth of the book is permitted rather than compelled.
Ikeda Terumasa · Architecture
8.2 · Tier IV
Run the subtractive test, and much of the castle resists it because defence compels it. The approach turns and doubles back: take away a turn and the attacker’s route to the keep is shorter and less exposed to the walls above. The gates narrow in sequence; loopholes and stone-dropping bays stand where a path passes below. The white plaster is compelled, fireproofing timber against the fire that took most castles, and the stone base is required by the hill and the weight. What yields is in the keep: several of its stacked gables answer no room behind them, and its five roofs are as much a figure for the plain as a fighting position. The West Bailey is ordered, not compelled.
Alfonso Cuarón · Film
8.2 · Tier IV
Judged on structure and the cut, and the spine resists the subtractive test. The opening floor-washing gives the film its law of labour and water. The car squeezed into the narrow garage is Antonio’s presence before he leaves, and its later scraping is the household’s change. The martial-arts field puts Fermín’s discipline and Cleo’s steadiness in one image, and the massacre needs it. The stillbirth is the hinge, and the beach is its reversal. What gives: the New Year at the hacienda runs long, the forest fire is kept more for its image than for its argument, and some household beats, the dog’s mess and the children’s squabbles, make their point and are repeated.
Master Enrique and Juan Pérez · Architecture
8.2 · Tier IV
Run the subtractive test. The skeleton cannot lose a member: once the wall above the arcade has gone to glass, every pier, buttress and flyer is the structure, and the fabric’s own history shows how little margin it was given. The glazed triforium cannot go without breaking the continuous field of light that is the building’s purpose; the ambulatory and radiating chapels are the liturgy of a chapter made into plan. What resists: the plan is Reims’s, compelled by an inherited programme more than by this site; the detached west towers sit apart from the body; the choir enclosure in the nave cuts in two the long view the elevation was built to open; and the glass holds more figures than the floor can read.
Dashiell Hammett · Literature
8.2 · Tier IV
The plot is a machine with no idle wheel, and the subtractive test finds little to take. Archer’s death in the second chapter is the fact the last chapter answers, and every scene between moves the bird, the money or the frame. The one part that looks removable is the Flitcraft story Spade tells Brigid in the seventh chapter: a man walks out of his life when a beam falls near him and, years later, has rebuilt the same life elsewhere. It advances nothing, but it is the key to the book’s law and to the end, where Spade will not be a man who changes his life because a beam fell; without it the ending loses its warrant. Charged: Gutman’s history of the bird is exposition sized for the reader as much as for the drama, the inventory of clothes and furniture is partly habit, and a few middle chapters, the shuffling of Cairo and the police, would compress with little lost.
Moisei Ginzburg and Ignaty Milinis · Architecture
8.2 · Tier IV
Judged on plan, section and structure, under purpose and site. The section is the most compelled thing in the building. The type F exists because a corridor on every floor wastes a third of a block’s area; splitting the section so that one corridor serves three floors is economy turned into form, and the type K’s double-height room answers the same arithmetic for families. The bridge is required by the transitional idea: small kitchens in the flats, the dining room across the way. The columns free the garden slope, and the ribbon windows follow the frame. What resists the test: the communal block’s programme is lighter than its doctrine, the kindergarten was never built, and the penthouse on the roof is required by nothing in the scheme.
Cormac McCarthy · Literature
8.2 · Tier IV
The test is subtractive, and the frame resists it. The four phases are the argument’s shape: the ranch lost, a garden found, the prison, the return to a country that no longer holds the boy. Blevins is required throughout. A comic nuisance on the ride south, he is the debt the book pays: his horse and the shooting at Encantadora bring the arrest that ends the love, and his name follows John Grady into a Texas court. Alfonsa’s long history of the Revolution looks most removable and is not, since it gives the prohibition its reason and fate its argument. The confession to the judge is the book’s only verdict on the killing. What holds the axis is the last phase, where the search for the owner of Blevins’s horse adds incident more than turn, and stretches of riding and camp repeat the book’s lyric without advancing it.
Donald Judd · Visual art
8.2 · Tier IV
The subtractive test bites in two directions. Remove the sheds and the boxes become a warehouse of good objects; remove the glazing and the work loses the light that does half its making; remove the shared outer volume and the interior variation stops being legible as variation. Those parts are required. What is less required is the count. One hundred is a round number, not one the system exhausts: the interiors are inventions within a fixed envelope, not a set of permutations that closes at a hundred, and a hall of eighty or of a hundred and twenty would argue nearly the same thing. The rows must be long enough for repetition to become a field; the exact sum is permitted rather than compelled.
Henry Fuseli · Visual art
8.1 · Tier IV
Judged figure by figure, the picture resists subtraction at its core. The woman cannot go: she is the sleeper, and the throw of her body, head down and throat up, is the posture of a person possessed rather than resting. The incubus cannot go: it is the weight of the dream, sitting where the sleeper feels the pressure, and its outward look makes the viewer a witness. The horse cannot go: it is the mare of the night-mare, the word made a creature, entering through the curtain as the dream enters the room, and the curtain is required as the threshold it breaks. What gives is at the margin: the table, the bed’s furnishings, the dark at the right, some drapery permitted rather than compelled.
Henry Moore · Visual art
8.1 · Tier IV
The subtractive test, mass by mass, as carving invites, since the work was made by taking away. Take away the raised knees and the figure lies flat, and the land with her: the hills and the tension go together. Take away the void under the torso and the body closes into a lump; the opening is what makes the trunk an arch and lets light and landscape through. Take away the small head and the scale changes: a larger head makes a portrait of a woman lying down, the small one a body that is also terrain. The propping elbows lift the gaze toward the horizon. What yields is detail, the exact shaping of the breasts, the contour of a hollow, which could move without loss. Compelled in its parts, less so in its surfaces.
Vincent van Gogh · Visual art
8.1 · Tier IV
The subtractive test, put to the canvas figure by figure. Take away the lamp and the picture goes with it: it is the only light, and the picture is that light falling on these heads and hands and nowhere else. Take away the girl seen from behind and the table loses its dark centre, the lamp stops reading as a lamp, and the meal opens toward the viewer as if performed for someone. Take away the pair at the right and the meal loses its one exchange, a cup held out and filled. The near monochrome is compelled: earth painted on earth. What yields is the edge of the room, the beams and the rack at the upper left and the back wall, which are permitted rather than compelled.
Frida Kahlo · Visual art
8.1 · Tier IV
Subtract part by part. The column cannot go: it is the proposition, the spine made a ruin of architecture that still bears a head. The opened torso cannot go: without it the column is an attribute held, not a structure inside. The corset cannot go: the ruin stands only because it is strapped, the support external and medical. The face cannot go, for its composure against the tears is the second half of the meaning. The split plain answers the split body, and the white cloth turns a patient into a martyr. What yields is number: the nails are many, and their count and placing are permitted rather than compelled. Fewer would say the same. Otherwise the image is as tight as an emblem should be.
Vincent van Gogh · Visual art
8.1 · Tier IV
The subtractive test, put to the canvas. Take away the blue line where table meets wall and the two yellows fuse into one field: the vase floats and the picture loses its ground. Take away the wilting heads and the bare seed heads, hanging low at left and right and bald near the top, and the image becomes a bouquet at its peak, a decorative still life; the cycle from bloom to seed is what the arrangement says. Take away the signature and the vase loses the one blue mark at its centre that answers the line. What is permitted rather than compelled is the count, which a head more or less would barely change, and the format, a standard canvas the image did not require. Necessity is high in the scheme and looser in the inventory.
Toyo Ito · Architecture
8.1 · Tier IV
The subtractive test bites hard on the structure and lightly on the rest. Take away a tube and a column goes, and with it a shaft, a stair or a duct, and in some cases the light: each tube does three or four jobs at once, and the plates can be thin because the tubes are many. The double glass of the south face is compelled by the idea of a lit section open to the street. What the test does not compel is the fitting of each floor, meant to be changeable, or the varied faces to east, west and north, which are chosen rather than required. The looseness serves the programme, but much of what a visitor meets could be otherwise without loss. Compelled at the frame, permitted at the fill.
The Stooges · Music
8.1 · Tier IV
Seven tracks, and most resist removal. Down on the Street must open: a riff that sets the record’s pulse and a voice already half a howl. Dirt must close side one, because it is the first time the record slows, and its long smouldering vamp is what the side has been driving toward. L.A. Blues must end the record: the songs have been coming apart since 1970, and the last track is what is left when the song is gone. The test gives in two places. Loose is the most removable song, a third fast riff-song beside the first and third, doing what they do with less. The title track is long by vamp more than by need. The record is necessary in its arc more than in every minute.
Anselm Kiefer · Visual art
8.1 · Tier IV
The subtractive test on a single image, element by element. The perspective cannot go: it is the room’s purpose, a processional axis built to bring a visitor to the ruler, and the picture sets the viewer on it. The far door cannot go: it is where the axis ends, and nothing waits there. The skylight grid cannot go: it is the hall’s one source of light and the cage that closes it from above. The emptiness cannot go: a figure would make it a scene. The burned crust cannot go: without it the canvas records the hall and not its ruin. What yields is the surface at the margins, passages of crust and tear that read as Kiefer’s general handling more than as this room’s necessity.
Pablo Picasso · Visual art
8.1 · Tier IV
Judged figure by figure. The Harlequin cannot go: he heads the troupe, stands at the left edge in the strongest colour, and the hand he gives the girl is the one touch in the picture. The girl cannot go: she is the other end of that touch, and the only figure turned toward another. The fat jester in red is the weight of the central group and its one note of age and appetite. The two boys carry the troupe’s labour, the drum on the back. The woman seated at the right is the hinge: the group is defined by her distance. What could go: the second boy, a doubling of the youth, and the basket and the jug, props that could be other props.
Cormac McCarthy · Literature
8.1 · Tier IV
The test is subtractive, and the book is lean. Moss’s finding of the money in the first chapter sets every motion that follows, and the devices of the chase are each used and paid: the transponder in the case, the motel vents, the case hidden in the duct. Remove Chigurh’s scene at the gas station and the coin, and Carla Jean’s death has no ground; remove Bell’s monologues and the book is a chase with no one to measure it. Carson Wells is required, the rule of Chigurh shown on a professional, though his chapters are the most conventional in the book. What holds the axis is quantity, not kind: Bell’s lament is needed, but it runs longer than the need, and the hitchhiking girl Moss takes up near the end is thinner in necessity than in pathos, there to show his decency and to set the scene at the motel.
Eva Hesse · Visual art
8.1 · Tier IV
The subtractive test is put to a serial work, and it bites first at the count. Seven sheets or nine would know little less: the number belongs to the serial grammar Hesse shared with LeWitt and Judd, and is permitted rather than compelled. Everything else resists removal. Without the fibreglass the sheets go slack and lose the play of rigid and soft that each holds within itself; without the latex the cloth is drapery; without the cheesecloth there is no skin to coat. Hung flat on the wall the sheets are paintings; laid on the floor they are a heap. The drips, the ragged edges and the uneven saturation are evidence of the process the work is about. Only the count is loose.
Alfred Stieglitz · Visual art
8.1 · Tier IV
The subtractive test bites on almost everything. Take away the gangway and the picture loses its one decisive fact: the line that separates the two decks and the two classes, and the brightest shape in the frame. Take away the straw hat and the upper deck has no watcher, so the looking down goes out of the picture’s subject. Take away the funnel or mast at the upper left and the diagonals of the gangway and the stair have nothing to answer them. Take away the crowd below and the bridge divides nothing. What yields is at the edges, where figures are cut by the frame, and in parts of the crowd whose places could be exchanged without loss. A found image cannot have the closure of a composed one.
Buster Keaton · Film
8.1 · Tier IV
The economy is severe, and almost every element pays twice. The candy box with its price changed from one dollar to four comes back beside the rival’s gift as the measure of the boy’s poverty; the dollar in the sweepings sets his honesty against the rival’s theft before the watch is touched; the manual’s rule is played literally in the waking frame and redeemed in the dream; the screen he works behind in the first reel is the door he walks through in the second. The frame requires the dream, and the dream the last shot. What gives is the dream’s second half: the motorcycle ride and the car in the lake extend a chase whose stunts are additive, each a fresh astonishment rather than a needed step, and two or three could go without loss of meaning.
Ansel Adams · Visual art
8.1 · Tier IV
The subtractive test, band by band. Take away the moon and the picture is a dusk landscape with a lit cemetery: the axis between the cosmic light and the human dead is gone. Take away the lit crosses and the moon presides over a dark village with nothing to answer it; the crosses are the picture’s second light and its human term. Take away the snow range and its cloud and nothing carries the eye from village to sky, nothing says the same sun lights the far peaks and the near graves. Take away the black sky and the moon loses its solitude and scale. What yields: the dark middle ground could be cropped a little, and some of the necessity is the luck of a light found in a minute, not built.
The Cure · Music
8.1 · Tier IV
Eight tracks, and the frame is compelled. Alone has to open: a slow, massing prelude that delays the voice until the record has made its weather, then a first line that announces the end of singing. Endsong has to close, and its long wait before the voice is the end the opening promised. I Can Never Say Goodbye is the centre, placed sixth after the strife it answers, and And Nothing Is Forever is the vow the frame needs early. Drone:Nodrone, the busiest track, is the record’s hard edge, the dread the grief must pass through, and Warsong its bitterness; the two are a pair, and the pair is needed. The preludes are long by design. The test bites twice: A Fragile Thing is the most easily spared, and in And Nothing Is Forever the delay is habit more than argument.
Honoré Daumier · Visual art
8.0 · Tier IV
The subtractive test, figure by figure. The old woman cannot go: she is the axis of the picture, its stillness and its weight. The mother and infant cannot go: they put the beginning of life on the same bench as its end. The sleeping boy cannot go: he is the one figure who has given up the waiting, and his slump against the old woman is the only touch in the carriage. The rows behind cannot go either, and they are the key choice: without them the three are a genre group of the poor; seated behind them and facing out, they make the three part of a crowd that does not look at them. What yields is the crowd at the upper right, laid in rather than resolved, and some of the left wall: permitted margins, not idle parts.
Etruscan · Visual art
8.0 · Tier IV
Judged part by part. The two figures cannot be separated: the work is the pair, and either alone is a different object, a reclining banqueter, of which Etruria made many. The man’s arm about her shoulder cannot go: it is the bond made visible, the one gesture of possession and protection in the work. The raised hands cannot go: they are the speech of the banquet, an act of offering or anointing, and they turn two effigies into two persons doing something. The couch cannot go: it is the banquet, the bed and the container at once. What yields is below the waist. The legs under one cloth are summary, flattened and abruptly smaller than the torsos, permitted by the type more than compelled by the meaning; the cushions could be fewer without loss. Necessity runs high in the upper half and slackens below.
Gerhard Richter · Visual art
8.0 · Tier IV
Judged on the configuration. The elements are few, one figure, one stair, one ground and the soft passage of the brush over all three, and each is required. Remove the stair and the descent goes, and with it the answer to Duchamp the picture exists to give: a nude standing, not a nude coming down. Remove the blur and it becomes the sharp, posed academy nude it declines to be. Remove the colour and it rejoins the grey paintings of the year before, at the distance of a news picture rather than of a wife. The size is compelled: at the scale of a snapshot she would be a photograph again. What gives is the arrangement. The crop, the angle and the placing of the figure were set by the camera and accepted, not composed, and a step more or less would change nothing the picture knows.
Edward Weston · Visual art
8.0 · Tier IV
The subtractive test has little to work on: there is one thing in the picture. Take away the dark of the funnel and the pepper sits on a table, an object among objects, losing its isolation and the curved light that wraps it. Take away the long tonal scale and the ridges flatten into a vegetable. The frame is tight to the form, the lobes folded over one another, the stem at the upper left; a quarter turn would make a different picture. What holds the axis is the series itself. This is the thirtieth numbered pepper, and the others show the arrangement was found by trial among variants, not compelled. Exact in what it keeps; chosen rather than inevitable in the whole.
Denys Lasdun · Architecture
8.0 · Tier IV
Judged on purpose, structure and site, and the subtractive test bites hard here. The building mostly resists it. The fly towers are the purposes of two stages stood upright. The Olivier’s fan and its two tiers are compelled by the wish to hold a large audience inside one actor’s field of view; the Lyttelton is the proscenium house the repertoire required; the studio is the third mode of theatre the company needed. The strata are the foyer floors and terraces carried into the open, the circulation joining three houses made into the face, and they step toward the river and the bridge because the site has those two faces. What yields: the labyrinth of levels between the theatres, which a simpler plan could have resolved, and the long blind walls at the back.
Marcel Duchamp · Visual art
8.0 · Tier IV
Judged by the subtractive test, plane by plane. Remove the stair and the figure has no path: the descent, the title’s verb, could not be read. Remove the dotted arcs and the planes settle into a still Cubist pile; the arcs are few, and each carries the swing of a hip or a knee. Remove the lettered title and the canvas loses the word nude, the provocation the image cannot make alone, since no nude can be seen. Remove the browns and the planes separate into events of colour; the one tone is what lets the eye read one body. What yields is the count of states: three fewer at the top, where the early positions crowd and repeat, would lose nothing, and the dark band at lower right reads more as ground than as necessity.
John Huston · Film
8.0 · Tier IV
Run the subtractive test and very little gives. Archer’s death opens the case and binds Spade to it: the obligation to a killed partner is the first reason in the last speech, and it is set in the first minutes. Cairo’s search of the office, a tiny pistol in his hand, brings in a second bidder; Wilmer in the lobby makes a third party visible; Gutman’s first scene names the prize and his second explains it, so the legend arrives when Spade needs it and not before. Jacoby dying in the doorway is the most abrupt event in the film and is required: the bird must come from the sea, and it must cost a life to deliver. What gives is small: Iva Archer does little but set out Spade’s compromised position, and Dundy’s two visits make one point twice.
Athenian (architect unrecorded) · Architecture
8.0 · Tier IV
Judged on structure, purpose and site. The subtractive test finds little idle. A Doric peripteros binds column, triglyph and metope to one another and to the module, and here the system is carried through cleanly: thirteen columns on the flank to six on the front, the canonical doubling plus one. The building’s departures have purposes. The carved metopes that turn the corner on each flank and the porch frieze carried out across the colonnade mark the east end, the one that faces down over the Agora, and so serve the site; the deep east porch holds the approach. What keeps the figure from the upper band: the necessity is the order’s more than this building’s, required of every Doric temple of its decade.
Steven Spielberg · Film
8.0 · Tier IV
Judged on structure and on the screenplay’s economy, which is the film’s most praised virtue and earns the praise. Run the subtractive test through the first hour and it meets resistance at every turn. The prologue gives the hero’s method, his fear of snakes and his rival in eleven minutes; the lecture gives the Ark’s power and the staff; the headpiece burned into Toht’s palm gives the Nazis their wrong measure, so that they dig in the wrong place; the monkey and the dates pay at once; the sunbeam in the Map Room is the answer the whole Cairo stretch prepared. Every plant is paid. What gives is the second half: the passage by ship and submarine is filled rather than required, Jones’s crossing on the conning tower is left unexplained, and the stretch could lose half its length without loss.
Kara Walker · Visual art
8.0 · Tier IV
The parts are few and the subtractive test bites hard on most of them. Take away the site and the sphinx is a large sugar statue in a gallery, an allegory at a distance: the warehouse, its molasses-stained walls and the demolition the title names make the piece a homage on location. Take away the sugar and the white surface over the features of a Black woman stops being refined sugar, the whitened product of dark cane. Take away the boys and there is no time in the work: they soften and fall while the sphinx stays white, and their collapse is labour spent. Take away the title and the medieval subtlety is lost. What yields is the exact props the boys carry, and some detail of the posture.
Jordan Peele · Film
7.9 · Tier III
The subtractive test finds very little idle, because almost every object planted is paid. The deer struck on the road returns as Dean’s hatred of deer, as Chris’s guilt over his mother, and as the mounted head whose antlers kill Dean. The cotton bursting from the armchair Chris scratches at becomes the plugs that save him from the teacup. The phone’s flash, which unseats Andre, unseats Walter at the end. Rose’s refusal to give the officer Chris’s name, read first as loyalty, is read again as the removal of a record. Rod, who looks like comic relief, is the plot’s other half. What gives: the Coagula video explains what the film had already shown, Rod’s scenes repeat a beat, and Jim Hudson states the purpose aloud.
Philip Johnson · Architecture
7.9 · Tier III
Judged on plan, section and structure under purpose and site. The subtractive test finds almost nothing to remove: a frame, four planes of glass, a floor, one solid. Take away the cylinder and the room has no bath, no hearth and no anchor; take away the walnut block and the bed stands in the open; take away the corner columns and the box cannot close. Take away the Brick House and the Glass House cannot work at all: its guests and the closed half of its argument are there. The pair is necessary to each other, and that is the unit’s strength. What resists the test is purpose. A house for one man is a narrow demand; the parts are compelled by an idea of a house more than by the needs of one; the strict symmetry serves the diagram rather than any use; and the room is a dwelling only because another building does the dwelling it refuses.
Arnold Böcklin · Visual art
7.9 · Tier III
Judged element by element, very little is loose. The water cannot go: its stillness is the crossing and the silence, and a ripple would make it a voyage. The boat cannot go: without it the island is a view, with it the island is a destination. The white figure cannot go: it is the one light-bearing vertical in the lower half, and the only thing that faces where the viewer faces. The cypresses are the island’s interior; the cut doorways make it a necropolis rather than a crag. What yields: the coffin narrows a picture of dream toward a picture of a funeral; the masonry and landing are slightly over-described; the sky only darkens. Few parts, each necessary, but few: the distillation is close to an emblem.
Gerhard Richter · Visual art
7.9 · Tier III
Few parts, and the subtractive test bites on each. Take away the blur and the picture is a copied snapshot, a document of one soldier, and the distance it keeps from him goes. Take away the grey and the uniform takes its field colour and the scene its date and weather: a period piece, not a remembered one. Take away the title and he is any German soldier of the war; the word Onkel puts him in a family, and in the painter’s. Take away the pose of the family photograph and the picture loses its subject, the keepsake. What yields: the ground behind the figure and his exact placing in the field could alter a good deal without loss, and the method, applied across dozens of canvases from 1962 to 1966, shows that much here was given by the source rather than required by the work.
Mary Cassatt · Visual art
7.9 · Tier III
Judged element by element, the canvas resists subtraction more than most. The basin cannot go: it is the point on which the whole picture converges. The pitcher at the right cannot go without loss: it repeats the basin’s white and its curve, says where the water came from, and weighs the lower right against the chest at the upper left. The child’s hand on its own thigh is the one gesture of the child’s own; without it the child would be an object of care only. The stripes run down the lap to the foot and give the woman a body under the cloth. What yields is the outer pattern: the carpet’s figure and the chest’s painted flowers are permitted rather than compelled, the Japanese print’s vocabulary laid on as surface.
Hakka builders (Jiang clan) · Architecture
7.9 · Tier III
Judged on structure, purpose and site, the outer ring resists the subtractive test. The thick blind base is what defence asked of an earth wall; the openings begin high, where a ladder fails. The single gate is the fortress’s one weakness, made as small as the clan’s traffic allows. The equal rooms are the clan’s arithmetic, each household a slice of the ring, none favoured. The ring corridor is the only path round, and the hall at the centre is the reason the clan lives together. What yields is the middle: the second and third rings are less compelled, since a clan could live and worship in ring and hall alone, as clans did in single-ring buildings nearby.
Doris Salcedo · Visual art
7.9 · Tier III
Judged by subtraction, part by part. Take away the mesh and the crack is a fault, a geology; with the fence inside it the break shows what it is made of, and the border is in the foundation. Take away the progression from hairline to fissure and the work loses its time: the visitor entering at the west end sees nothing, then a scratch, then has to watch where he walks. Take away the length and it is an incident; the full run makes the division the building’s own. Take away the title and it is a wound with no language. The empty hall above is required too. What gives: the branching, and the exact length, which is the hall’s.
Agnes Martin · Visual art
7.9 · Tier III
The subtractive test is hard to run on a work built by one rule. Take away the gold and the painting is another of her grids in oil and pencil, a different work: the gold is required. Take away the grid and the field is a gilded panel, an object of decoration with no measure in it and nothing human in it: the grid is required. Paint the lines on instead of cutting them, and they would sit on the gold instead of opening it: the incision is required. What yields is the single unit. No individual line bears load, since the law is the even repetition, and a grid with a line or two more or fewer is easy to imagine without loss. Three parts, each indispensable; many lines, one decision repeated.
Andrew Wyeth · Visual art
7.9 · Tier III
The parts are few and nearly all required. Remove the figure and the field is a landscape with a house; remove the house and she reaches toward nothing; shorten the field and the distance, which is the whole matter of the picture, collapses. The high horizon is required: it pushes the house to the top edge and makes the field a slope she must climb. The turned head is required, since the picture is a direction of looking. What gives under subtraction is the cluster at the top: the barn and the lesser outbuildings could be fewer or placed otherwise without loss. The scale is compelled: a panel of about a square metre lets the grass be painted blade by blade and still be seen whole.
Albrecht Dürer · Visual art
7.9 · Tier III
The subtractive test finds little to take away, because almost nothing was put in: the animal, its shadow, the monogram and date, and the empty ground. Take away the shadow and the hare floats; it is the one thing that sets it on a floor and in a room. Take away the window in the eye and the creature loses its witness, the sign that it was seen by someone in a particular place. Take away the empty ground and the study becomes a picture with a setting, a different work. The hair is substance, not ornament: the coat is how the body, its weight and its alertness are known. What is permitted rather than compelled is the finish at the edges, where the fur of the haunch thins into the paper with less necessity than at the head.
Nam June Paik · Visual art
7.8 · Tier III
The subtractive test is the work’s own method, and it bites almost nowhere. Take away the camera and the figure watches a broadcast or a blank set, a gag about distraction, and the loop is gone. Take away the monitor and the camera records a statue for no one. Put any person or object in the Buddha’s place and the one necessary choice is lost: a figure whose whole iconography is contemplation, made to contemplate a screen that shows only itself. The figure’s stillness also makes the live image look like a still one, and that doubt is required. What gives is the exactness of the parts: any monitor of the period, any camera, and arguably any seated Buddha of that posture would serve, and the room and the distances are loose.
Damien Hirst · Visual art
7.8 · Tier III
The subtractive test, part by part. Remove the calf and the title loses its child; the work becomes an anatomical exhibit of a cow. Remove the cut and the animals are a natural-history display, whole and closed. Remove the gap and the viewer stands outside the body, not inside it. Remove the parting of the pairs and “Divided” loses its second sense; remove the title and the Madonna goes. The steel is the plainest that will hold the liquid. Nothing is idle. What holds it below the top: the four tanks are close to a diagram, the necessity is that of a single proposition, and the reported copy with new animals shows that the scheme is required more than these bodies.
Diébédo Francis Kéré · Architecture
7.8 · Tier III
Judged on plan, section and structure, under purpose, climate and means. Take away the raised roof and the earth walls take the rain and the sun, and the rooms become ovens like the tin-roofed concrete schools of the region. Take away the pierced earth ceiling and the warm air no longer rises out. Take away the oversail and the walls wash. Take away the open bays and the school loses its shaded outdoor rooms, where in that climate much teaching and waiting happens. The trusses are welded from bar because no crane could reach the site and bar could be bought and carried. Every part answers a constraint of climate, money, labour or material. What holds the figure below the high eights: the constraints are simple, and so is the building, a short argument fully compelled.
Man Ray · Visual art
7.8 · Tier III
The parts are few, and the subtractive test is short. Remove the two f-holes and what remains is a fine studio nude after Ingres, an homage and nothing more: the pun goes, and with it the work. Remove the turban and the citation of La Baigneuse Valpinçon weakens to a generic back; the turban makes the body Ingres’s before it is the photographer’s instrument. Remove the hidden arms and the outline breaks, since a violin has no arms. Remove the title and the second joke goes, the one that names this woman the photographer’s pastime. Each part bears load and nothing idles. What yields is the photograph beneath the marks: the light and tonality are good but could be other without loss, and the pose is borrowed, not compelled by the image’s own argument.
David Hockney · Visual art
7.8 · Tier III
The parts are few and almost all are required. Take away the splash and the picture is a photograph of property: the whole event of the canvas is that one irregular thing in a world of ruled edges. Take away the diving board and the splash has no cause and no direction; its diagonal is the only line in the field not parallel to an edge, and it points to the event. Take away the empty chair and the absent person has nowhere to have been: it is the one sign of a watcher, and it is empty too. Take away the bare border and the picture loses its claim to be an instant fixed, like a print. What yields is setting: the palms, the reflections in the glass and the exact proportion of terrace to pool could be drawn otherwise without the picture knowing less.
Jean-Honoré Fragonard · Visual art
7.8 · Tier III
Judged figure by figure, the canvas resists subtraction more than its genre leads one to expect. The woman is the light and the event. The lover cannot go: the picture is his view, and his raised arm and hat give it its direction. The older man cannot go: the swing must be pushed, and pushed by someone who does not see what the lover sees; that blindness is the joke and its edge. The slipper is the instant, the one thing in the air. The Cupid names the secret; the putti below look up as the lover does, so that even the stone takes part. What yields is the extent of the foliage: the bower is the frame, but its mass at the upper left and the edges is permitted rather than compelled, and some of the garden is ornament.
Interpol · Music
7.8 · Tier III
Ten tracks in forty-three minutes, and most of the record resists subtraction. Next Exit must open: a slow organ figure and a half-sung invitation out of town, the record announcing that it moves toward the light. Evil, Slow Hands and C’mere are the spine, each a short, hard song built on a bass line the song cannot lose without falling. Not Even Jail is the long climb the middle requires, and A Time to Be So Small the diminuendo the close requires. The test bites at two places only. Public Pervert spends its length on a mood Not Even Jail has just stated better, and Length of Love is the least distinct song, a mid-tempo rocker whose loss would cost little; Narc is good and restates Evil’s manner.
Élisabeth Vigée Le Brun · Visual art
7.7 · Tier III
The subtractive test finds very little to take. There are two figures, a seat implied, a fall of drapery and a plain ground. Remove the child and a society portrait remains; remove the mother and a child’s head has nowhere to rest. The interlocked arms are the picture: the child’s round the mother’s neck, the mother’s round the child’s body, one ring inside another, so that neither holds the other more than she is held. The plain ground is required too, since any room or landscape would place them in a world, and the claim is that they are one. What yields is the softness of finish everywhere at once: drapery folds and hair band are permitted ornament, and the sweetness of the child’s look could go. The economy is the Holy Family’s, a formula’s, more than one the panel found.
René Magritte · Visual art
7.6 · Tier III
Five things: a man, an apple, a wall, the sea, a sky. Take any away and the picture changes what it says. Without the apple there is a dull portrait of a clerk; without the sea and the low wall the man stands in no place, and the apple floats in a studio rather than in the world; without the bowler and the overcoat he is someone in particular rather than anyone. The parts are required, and the frontal, upright format is what a portrait would be. What holds the axis below the high eights is the backdrop: wall, sea and sky are the painter’s stock setting, used across many canvases, present because they are his rather than because this picture alone compels them.
Robert Zemeckis · Film
7.5 · Tier III
Judged on structure, and structure is the film’s strength. Nearly every object set in the first movement is paid in the second or third. The clock-tower flyer, pressed on Marty for a quarter and kept for his girlfriend’s phone number, gives Doc the one fact the return requires: the minute of the lightning. The Twin Pines Mall becomes the Lone Pine Mall because Marty runs down one of farmer Peabody’s pines. Doc’s fall from the toilet, mentioned as a date, is how Marty proves himself in 1955. What gives is real: the audition and the Darth Vader visit to George’s bedroom run long as comedy, Strickland’s two appearances partly repeat each other, and the plants carry plot far more than meaning. Permitted, not compelled.
Søren Kierkegaard · Literature
8.7 · Tier IV
The spine is tight and every main part is required. The Exordium gives Abraham four ways of failing, so that the true Abraham is defined negatively before he is praised; the Eulogy praises him as the poet praises the hero; the Expectoration shows that praise cannot reach him; the three Problemata test him against the ethical in three forms, the universal, duty and disclosure. Remove the Exordium and the book loses its proof that Abraham cannot be retold; remove Problema III and silence is asserted, not shown. What holds the axis is the last third. Problema III sprawls: Agnes and the merman, Sarah of Tobit, Faust, Gloucester and the bride at Delphi are worked at a length the argument does not compel. Necessary in its frame, loose at its end.
George Eliot · Literature
8.6 · Tier IV
The subtractive test is passed in most of the book and failed in its proportions. Remove the aunts and the book loses the Dodson law that Tom inherits and that judges Maggie in the end; remove Stelling’s Latin and the novel loses its argument that education misfits both children; remove Bob Jakin and Maggie has no witness from below. The suit against Pivart, the ruin, the curse in the Bible and the horsewhipping of Wakem are each required by the vengeance Tom carries. What holds the axis lowest of the twelve is the reverse of padding: the childhood is given room and the adult crisis is not, and the flood settles in one short book what the novel argued could not be settled. A part is missing more than a part is idle, and the end is decreed rather than compelled.
Erwin von Steinbach and others; spire by Johannes Hültz · Architecture
8.6 · Tier IV
Run the subtractive test part by part, and much resists. The nave cannot go: its wide bays, glazed triforium and great clerestory are the argument that wall can be glass. The Angel Pillar cannot go: a single pier carrying the Judgment is the south transept’s reason. The rods of the west front cannot go: they are what the front is. But the whole is a sum of campaigns, each answering the last, more than one argument compelling its parts. The belfry stage could be taken away with the loss of a mass, not a meaning; the single spire is an accident of money and time, never compelled; the nineteenth-century crossing tower is not needed. Parts are required; the whole is assembled with great intelligence.
Wallace Stevens · Literature
8.6 · Tier IV
At the level of the single poem the necessity is often absolute. “The Snow Man” is one sentence whose every clause is needed to arrive at its last line, “Nothing that is not there and the nothing that is”: take away a tercet and the listener never becomes nothing himself. “Anecdote of the Jar” and “The Emperor of Ice-Cream” could not lose a line. But the unit is the body, and at the level of the body the subtractive test bites. A first book gathered over eight years carries bagatelles that could go without loss, “Floral Decorations for Bananas” and “Exposition of the Contents of a Cab” among them, and its longest poem, “The Comedian as the Letter C”, is its least necessary: Crispin’s voyage is spun out in a diction so ornamental that whole verse paragraphs could be cut. The great poems would stand higher; the book stands here.
Sergei Prokofiev · Music
8.6 · Tier IV
The subtractive test meets resistance in the drama’s spine and finds give in the dances. The Prince’s dissonant chords must stand, because they are the law the feud breaks. The ball is required, since Romeo, Juliet and Tybalt’s recognition meet there; the fights are required, since Mercutio’s death turns comedy to tragedy; the epilogue is the whole of the ending. The give is in about a fifth of the score, dance for its own sake: the Dance of the Five Couples, the Dance with Mandolins, the street festival, the Morning Serenade, the Dance of the Girls with Lilies. Each could go with a loss of colour, not of argument. The town at play is the world the lovers stand outside, which keeps the axis from falling lower.
Bertolt Brecht · Literature
8.5 · Tier IV
The epic form chooses scenes rather than a chain of causes, and the subtractive test bites at the edges. The spine resists it. The appetite of the first scene, milk, a bath, a boy taught with a washstand and an apple, is required by the recantation of the thirteenth; the telescope sold to Venice in the second as his own invention is required, since this Galileo trades truth for comfort from the start; the plague scene, where he will not leave his observations, is the courage the recantation betrays. The middle, the sixth, seventh and ninth scenes, is economical. What holds the axis lowest of the twelve: the fifteenth scene, a coda the play can lose and often does, and the carnival of the tenth, which shows a reach the eighth has already argued.
J. D. Salinger · Literature
8.5 · Tier IV
The spine is required: expulsion, the flight to New York, the nights in the hotel and the bars, the secret visit home to Phoebe, the night at Antolini’s, the plan to go West, and the carrousel. The argument, that the boy is falling and can no more stop himself than he can stop others, needs that descent and that end, and Allie’s mitt, Jane Gallagher and James Castle are the hidden cause and could not go. But the subtractive test bites in the middle. The first New York night (the three women from Seattle in the Lavender Room, Ernie’s, the taxis) and the second (Sally Hayes, the skating, Carl Luce at the Wicker Bar) repeat one encounter, a stranger found phony and a boy lonelier afterwards, more often than the knowledge needs. Perhaps a sixth of the novel is permitted by the voice’s charm rather than compelled; that the repetition is also the drift of a breakdown keeps the charge from being heavier.
Terrence Malick · Film
8.5 · Tier IV
The plot is a few hinges, and every one is planted: the doctor’s examination of the farmer, overheard by Bill, which makes the marriage a wager on a death; the lie that Abby is Bill’s sister, which makes every embrace in the open fields a danger; the foreman’s watching; the locusts, which force the household into one fire. Remove any and the film falls. What gives is the texture between the hinges, most of the running time: the flying circus, the inserts of animals, birds, wheat and water, the passages of harvest work. The season and the labour require some of it. Some is plainly the residue of a film found in the cutting room, bound by narration into a shape it was not shot for, and that holds the axis among the lowest.
Paul Thomas Anderson · Film
8.5 · Tier IV
Judged on structure and cut. The film is built as a drift, and most of what looks loose is required. The portrait studio and the cabbage field show, twice and in rising danger, that Freddie cannot hold a job or a place, and the second ends with a man poisoned by his liquor, which is why a stowaway needs a ship. The first Processing is the hinge, and nothing else binds the two men. The two cells answer it; the motorcycle answers the yacht; Lynn is the past the Cause promised to recover, found closed. What holds the axis here: the exercises repeat one point at length, the New York and Philadelphia episodes do similar work, and the passage from the cinema to England is a joint where a cut could fall without the whole changing.
Buscheto and Rainaldo · Architecture
8.4 · Tier IV
The governing parts are compelled. A long colonnaded nave carries procession to the altar; double aisles hold a city’s congregation; galleries enlarge it; a crossing marks the meeting of the arms. The banded marble is the fabric’s own coursing made visible, tying arcade to wall. But the subtractive test finds more here than in a building of the first rank. Each transept is a whole basilica with its own apse, joined at the crossing rather than grown from the nave, so the cross reads as three churches meeting. The dome answers a plan that did not ask for one. The façade’s four galleries are set by height and open on the roof’s slope. Rainaldo’s lengthening shows the nave could take more bays without loss.
Pérotin · Music
8.4 · Tier IV
The large plan is compelled from outside the composer, by the chant. Which words take polyphony, in what order, and on which pitch each tenor span sits are fixed by the gradual, and the alternation with the choir’s plainchant is required by the liturgy; nothing there can be removed. Inside each tenor span the necessity weakens. Sustained-tone organum is additive by nature: the upper voices fill the held note with patterned phrases, sequences and voice exchanges, and the subtractive test finds phrase units over the long opening F, and over later held notes, that could go without loss to the argument, only to the span. Length is not charged; the span is part of what the work does. The phrase units are what could go.
Hayao Miyazaki · Film
8.4 · Tier IV
The first half is close to proof against subtraction. The parents’ meal, the bridge crossed on a held breath, the stair down the outside of the building to the boiler room, the contract and the stolen name: each step is required, and each is the condition of the next. The river spirit’s bath could not go; it proves that work done well is a cleansing. The cost is the long middle. No-Face’s feast is needed and runs long, and it is crossed by a second plot, Haku, the seal, the paper birds, Boh and the bird turned to animals, explained in a hurry and partly by Kamaji. A part could be lifted from the middle and the story still close.
Claire Denis · Film
8.4 · Tier IV
Judged on structure and the cut. The film is Galoup’s memory, set down in Marseille after his discharge, and memory licenses its fragments. Its spine resists subtraction: the drills are the order Sentain disturbs, and without their weight the envy has nothing to defend; Forestier is required, since Galoup’s love of the commandant is what Sentain threatens; the salt flat is the act, the bed and the pistol its cost, the dance its release. Around that spine the give is wide for ninety minutes. The nightclub returns more often than it advances anything; Galoup’s Djiboutian girlfriend is present more than she is used; several town scenes could be reordered without loss, and where order is free a part is not compelled.
Henryk Górecki · Music
8.4 · Tier IV
Three movements, three mothers, three centuries, and the subtractive test meets resistance at the large scale. Remove any one and the triptych becomes a pair, and the second movement’s reversal, a child consoling the mother, loses the two laments it reverses. The first movement’s slow accretion is the argument, not padding: the canon must climb voice by voice for the soprano’s entry to arrive at the top of a pile of grief, and must unwind for the Lament to sink back. Length is not charged. The give is in the detail: the descending half of the arch repeats what the ascending half built and carries less, and the last movement’s strophes and ostinato run past what the verse needs. The slowness is compelled; some of the duration is permitted.
The Flaming Lips · Music
8.4 · Tier IV
Twelve tracks of sequence and two remixes, about fifty-nine minutes, on a spine the record requires. Race for the Prize must open: it states the subject, mortal people working against death, as a fanfare. Waitin’ for a Superman is the hinge and could sit nowhere else; Feeling Yourself Disintegrate is the compelled late summit, and Sleeping on the Roof the exhalation that must follow it. The Spiderbite Song and What Is the Light? carry turns the course needs. The test bites in three places, and they hold the figure: Buggin’ is a light summer song whose idea the record states better elsewhere, The Observer adds texture and no turn, and the two remixes restate the two strongest songs after the record has already ended on the roof.
Dionysus Flambouras · Literature
8.4 · Tier IV
The subtractive test finds less than the length suggests and more than the method can afford. Most of what is here is required: the bins of the third movement are the ostinato the book needs before a wall takes a child, and the sale’s circulating objects make the Patels’ absence legible before the fifth movement explains it. What could go is of two kinds. Some is said twice: the morning after the sale settles new objects into drawers as if they had always been there, twice in two sentences; Marlene’s tact with a younger mother’s body comes once at the sale and again at the lake; the confidently wrong rumour, a bylaw, a stroller, a spring under the lake, a woman in Burlington, has made its point by the second. Some is the encounters: the furnace room at Christmas repeats what the guest bedroom at Halloween showed, and the shoveller’s virtue, shown once in silence, is named outright when it recurs. Held at 8.1, clear of the cap and the lowest mark the work earns on its own terms.
Joseph Haydn · Music
8.4 · Tier IV
Inside each quartet the subtractive test meets resistance. No. 2 is built on its falling fifths, which return in the canon and the finale; the Emperor variations cannot lose a variation without losing an instrument’s turn at the tune; the Alternativo of No. 6 is nothing but the scale it is built on. The give is at the level of the set. Six was a publishing convention, and it shows: the home keys run G, D minor, C, B flat, D, E flat, with no plan, no return and no cross-reference. Remove No. 1 or No. 4 and the set is smaller, not broken. Some movements are lighter: the minuets of Nos. 4 and 5, and No. 4’s quickening close.
Philip Roth · Literature
8.3 · Tier IV
The test is subtractive, and the form half licenses the cuts it invites. A complaint to an analyst circles by nature, and the returns to the mother, the father’s bowels, the bread knife and the shiksa are the symptom the book diagnoses; most of the repetition is required. The order is required too: the mother first, then the body’s secret life in “Whacking Off”, then the family as an Oedipal theatre in “The Jewish Blues”, then the women, then the exile to Israel, where the whole apparatus fails. Remove Israel and the book loses its proof that the bind is not a matter of place. What is permitted lies in the middle. The catalogue of three Gentile women, the Pumpkin, the Pilgrim and the Monkey, runs longer than its argument; the Monkey’s chapters repeat their quarrels and their Rome episode past the turn; several tirades restate a grievance already won. Perhaps a sixth of the book is permitted rather than compelled.
Quentin Tarantino · Film
8.3 · Tier IV
The subtractive test is hardest here, because the film’s manner is digression, and much of what looks removable is paid. The watch Koons carried through a prison camp is why Butch goes back to the apartment, which is why he meets Vincent coming out of the bathroom; Vincent’s visits to the bathroom, a joke repeated, kill him at the third. The gun on the kitchen counter, the adrenaline needle and the bullets that miss are each required by what follows. The talk is the content: the way these men pass the time between deaths. What gives is the length of that talk, the foot-massage argument, the pilot Mia describes, and stretches of the cleanup before the Wolf arrives, which could be shortened without the loss of a fact the film needs.
François Truffaut · Film
8.3 · Tier IV
The spine is necessary and simple: a boy pushed, a little at a time, from a family and a school that have no room for him into the hands of the state. Most scenes carry a step. The calendar and the lines he never finishes; the lie that his mother has died, which her arrival exposes and which licenses the stepfather’s slap; the candle that sets the Balzac shrine alight and turns reverence into an offence; the typewriter, stolen to sell and then returned, which is the step from mischief to the police. The subtractive test bites in the middle third. The rotor, the puppet show and the gym master’s run are fine and bear on the theme, but each could go without the argument failing. The episodic form permits them rather than requires them.
Alan Moore and David Lloyd · Literature
8.3 · Tier IV
The spine resists subtraction. V’s killing of the Larkhill officials, Prothero, Lilliman and Surridge, is the vendetta, and the vendetta is what the book must pass through before it can become something else, the making of a successor. Evey’s arc, from a sixteen-year-old trying to sell herself on the street to the second V, is required at every stage, the imprisonment above all. The test bites in the panorama. Rosemary Almond’s fall into the cabaret, Helen Heyer’s manoeuvres and Alistair Harper’s gangland each pay something, but the Heyer plot runs past its need, some early chapters are permitted rather than compelled, and the Fate computer is leaned on and then dropped in one reveal. Perhaps an eighth of the book is serial habit.
Bill Evans Trio · Music
8.3 · Tier IV
The subtractive test bites harder here than on a record composed as a sequence. The album was chosen from five sets of one day, and its companion, Waltz for Debby, drawn from the same day, shows that the choice might have gone otherwise: another performance could stand in for “All of You” and the record would still be what it is. Inside the performances little is idle. “My Man’s Gone Now” holds a single slow descent for six minutes and nothing could go from it; “Jade Visions” is under four minutes and complete. The slack is on side two, where “All of You” runs past eight minutes and its middle is the trio at work rather than arriving. The choice has a principle, the bassist’s record, and the six pieces answer to it.
Björk · Music
8.3 · Tier IV
Ten tracks in about forty-three minutes, and the subtractive test finds little slack in the first half. Hunter must open: it sets the march, the strings and the self that goes out alone. Jóga is the landscape argument made sound, Bachelorette the drama, and Pluto the eruption that All Is Full of Love requires, since the calm of the close means nothing without it. The test bites in the second half. Immature is slight, a self-reproach that restates in a thinner palette what 5 Years and Unravel carry, and could go with small loss. Alarm Call is a change of light before Pluto, but it is the weakest song and runs long for what it does. All Neon Like holds its trance a little past need. Two soft places and one long one hold the figure.
Euripides · Literature
8.2 · Tier IV
Subtract a scene and ask what goes. The prologue of Apollo and Death sets the bargain and the threat to come, Apollo foretelling that a man will take her from Death by force; without it the ending is a trick. The quarrel of Pheres and Admetus looks detachable and is not: it is the only place the bargain is judged in the open, and it turns the husband’s grief into the shame he must learn. The servant’s complaint lets Heracles learn the truth from below stairs. What could go is softer: the ode on Apollo’s herding serves by praise rather than event, and the consolations after the death repeat. The chain is Apollo’s contrivance, and contrivance is the play’s subject, which holds the axis short of the top.
Ingmar Bergman · Film
8.2 · Tier IV
The road is built so that every station returns Isak’s image to him: the Almans are his marriage replayed by the living, Åkerman the good he did and forgot, his mother the source of the cold, the hitchhikers the youth he gave up, with Sara doubled, and Evald the cold handed on. The subtractive test bites at three points. Remove the Almans and the second dream loses its examiner; remove Åkerman and the verdict has no counterweight; remove the mother and the line to Evald and the unborn child is cut. It gives in more places than a film so short can afford. The students’ quarrel about God is a debate in outline that the lunch illustrates rather than needs; the Almans’ cruelty is pitched as a lesson; the evening at Lund carries less than its length. The design is compelled; several of its stations only illustrate it.
Andrei Tarkovsky · Film
8.2 · Tier IV
Judged on structure; the spine is required. The swamp crossing introduces Ivan as what the war has made him, a scout who gives orders to a lieutenant. The attempt to send him to the Suvorov school is the hinge, since his refusal is a refusal of childhood itself. The dugout, with the Dürer album and the game of war with a knife and a bell, shows play turned to revenge; Katasonov’s death, kept from him, prepares the crossing past the hanged scouts. Each dream falls where the waking story has just taken something away. What gives is the birch wood, a romance that carries the theme but is detachable in plot and long for its share; the old man in the burnt village could be shorter.
Geoffrey Chaucer · Literature
8.2 · Tier IV
The test is whether the poem’s three unlike parts, the book, the garden and the parliament, are each required. The book and the parliament plainly are. Cicero’s dream sets the “commune profit”, the common good, against private desire before any bird appears, and the parliament stages exactly that quarrel: the eagles’ courtly suits against the lower birds’ demand that business be done and the season served. The temple of Venus is required as well, as the sterile, sighing love that Nature’s fertile hill answers. What holds the axis here is the length of the inherited material: some sixteen stanzas adapted from Boccaccio’s Teseida, and a catalogue of trees and another of birds that run on the momentum of the tradition. The first line earns its place; some of the garden’s inventory does not.
Metallica · Music
8.2 · Tier IV
Eight tracks, and the record’s plan compels most of them. Fight Fire with Fire must open: a few bars of nylon-string calm broken by the fastest riff on the album states the subject, peace undone in an instant. The title track, For Whom the Bell Tolls and Fade to Black each give death a different agent, the state, war and the self, and Creeping Death gives it a god; The Call of Ktulu is the compelled close, the dread with the words removed. The plan of mirrored sides, each opening fast, gives Trapped Under Ice its place, though its premise repeats the title track’s. Escape is the one track the record could lose with gain.
Aleijadinho · Architecture
8.2 · Tier IV
The church does one thing: it gives a lay brotherhood a house of prayer and burial that declares its saint and its standing in the town, and little in it is idle. The front is interlocked: the towers drawn back so that the central bay can advance, the portal climbing into the medallion and the medallion into the frontispiece, so that taking away any one breaks the composition rather than thinning it. Inside, the plain nave is required, the white ground on which pulpits, retable and ceiling read. What yields to the subtractive test is below the summit of the making: side altars and fittings that are ordered rather than compelled, and a volume that is the region’s type rather than a form drawn from this purpose.
Michael Jackson · Music
8.2 · Tier IV
Nine tracks in about forty-two minutes, and the record has no argument the parts are required by: it has a run of songs, each built to stand alone, and the test is whether each earns its place. Billie Jean, Beat It, Wanna Be Startin’ Somethin’ and Human Nature do, each the strongest of its kind on the record and each hard to imagine it without. Thriller earns its place as the set piece, and The Lady in My Life closes in warmth. The test bites three times: The Girl Is Mine is a light duet whose tone breaks from everything around it, Baby Be Mine is competent with nothing of its own, and P.Y.T. restates the lighter mode. Held where it is because three of nine could go and the order could change without loss.
David Lynch · Film
8.2 · Tier IV
Judged on the film as released, about 89 minutes, and its main parts answer the subtractive test. The planet frames the whole and returns at the end; the walk with the grocery bag lays down the world’s law before a word is said; the dinner delivers the child; the room is the child; the radiator and the woman across the hall are the two escapes; the head and the scissors are the catastrophe. The long durations are not slack, since duration is how the film makes entrapment felt. But the test finds real give. The pencil factory is a joke the film could lose at small cost, the worm crawling in the cabinet repeats work the bed scene does, and in a dream form many single images could have been others without the whole failing.
Thomas Cole · Visual art
8.2 · Tier IV
Subtraction, part by part. The diagonal cannot go: it is the picture’s argument, wild above and to the left, settled below and to the right, and everything in the field is sorted by it. The storm cannot go: it is the time the title names, and without it the left half is only woods. The river’s loop cannot go: it is the hinge on which the halves turn, the one form in the valley neither wild nor made. The painter cannot go: without him the canvas is a view; with him it is a choice made from a place, and his look back puts us on the summit. The broken tree is the storm’s mark in the near ground. What yields is extent: the plain could lose a band, and some foreground foliage and rock is permitted rather than compelled.
Krzysztof Kieślowski · Film
8.2 · Tier IV
Judged on structure. The Polish half resists the subtractive test almost completely: the singing in the rain, the heart that tightens at the audition, the crossing of the Kraków square where Weronika sees a French girl boarding a tour bus, the concert and the fall. Each is required, because the second half will be read by the first. The death is the hinge, and the burial seen from within the grave is its seal. In France the structure loosens. Véronique’s giving up of her singing is required, the one act by which the dead girl’s warning passes to the living one, and the puppet show is required. What gives is the clue-trail: the shoelace in the post, the cassette of station sounds, the café at Saint-Lazare, the hotel. It is the author’s method made visible, which keeps the charge small, but it makes its point at length, by a mechanism of pursuit the argument permits rather than compels, and a shorter, harder second half is imaginable.
Martin Scorsese · Film
8.2 · Tier IV
Judged on structure and on the length, which is argued, and argued well where it matters. The last forty minutes after the killing, in which nothing happens but age, are compelled by the whole: Russell in prison unable to chew his bread, Frank choosing a coffin and a burial vault, a daughter who will not see him. Without them the film is another rise and fall. The car journey is required too, since its slowness is the dread. The subtractive test bites in the middle hour, on about a tenth of the film. The Bay of Pigs truck run and the Kennedy business are glancing and could go without loss; Hoffa’s rivalry with Tony Pro makes its one point, that his pride will not bend, several times over; some convention and testimonial-dinner scenes are assembled rather than required. In a film whose knowledge is time, an hour that spends time on chronicle is a real cost, and the figure carries it.
Bob Rafelson · Film
8.2 · Tier IV
Judged on structure, and the structure is episodic by design, so the subtractive test bites harder than in a plotted film. Much of it resists. The piano on the truck shows in one comic image that Bobby’s gift is intact and that he will use it only where it costs nothing. Elton’s arrest removes the one man in the oil-field life who looked up to him. Partita in the studio shows the family’s art first as work. The field with the father is what the whole journey exists to reach, and the gas station completes the pattern of leaving. What gives: the double date and the bowling alley make one point twice, and the Samia evening restates what the house has shown.
Woody Allen · Film
8.2 · Tier IV
Judged on structure. The film was found in the cutting room, and what was kept resists the subtractive test better than its looseness suggests. The opening joke about a club and the closing joke about eggs make one argument: why a man stays in what he knows is absurd. The lobsters of the first summer return in the second, with another woman, who does not laugh. The awkward talk on the balcony is answered by Annie singing in a club, and her songs return at the close. The trips to Los Angeles are required, because the break is Annie choosing a city Alvy cannot live in. The form permits more than it compels: the cocaine sneeze, the Los Angeles party and several street interviews are single jokes the film could lose without losing a fact it needs.
Louis Sullivan and Dankmar Adler · Architecture
8.1 · Tier IV
Judged on purpose, structure and site. The scheme is compelled by the purpose as Sullivan read it: shops and an entrance at the street, needing breadth and openness; a stack of identical offices above, needing identical cells and light; a top storey for tanks, machinery and services, needing no office windows. Base, shaft and attic are the three functions in three forms, and the light court is required by light. Take away the attic and the shaft has no end; take away the recessed spandrels and the stack is no longer one thing. What resists the subtractive test is the building’s most famous move: the intermediate piers, by the histories’ account, carry nothing. Their defence holds at the level of the image, not of the frame. Well above the cap, held below the buildings whose every part is structural.
Sumerian, under Ur-Nammu and Shulgi · Architecture
8.1 · Tier IV
Judged on purpose, structure and site, as it stands. The subtractive test finds almost nothing to take: no ornament, no interior, no surface that does not carry. The mass is the purpose, to lift the god’s house above the flood plain and the city, and its scale is compelled by that purpose and by what mud brick will bear, a solid body battered so that it does not slump. The baked skin keeps water out of the core, the weep holes let it out, the reed mats bind the courses, and procession compels the three stairs. What holds it is the part that compelled the rest and is gone: the stairs and the mass serve a lost summit, so the necessity is read from what it served rather than seen whole.
Nick Ut · Visual art
8.1 · Tier IV
The subtractive test, run on the frame. Take away the girl and it is a road after an air strike, one of thousands. Take away the screaming boy at the left and her open mouth stands alone, one cry rather than a condition; he doubles the scream. Take away the soldiers and the image loses its second subject, armed men walking calmly behind running children, which is where its accusation lives. Take away the smoke and the cause leaves the picture, and the fire becomes a caption. Each is required. What yields is at the edges: the frame was cropped without loss, the children at the right are less needed than those at the left, and the foreground is empty tarmac. The core is inevitable; the frame around it is a news editor’s.
Mastodon · Music
8.1 · Tier IV
The subtractive test bites less here than on most rock albums of this length. The two suites are the spine and cannot go: The Czar carries the Russian centre of the journey in four named parts, and The Last Baron gathers the record’s riffs and brings the soul back. Oblivion must open, setting the sung register before any of the weight. The title track, the grief song, stands second to last so that the elegy comes just before the return. The test finds slack in the middle. Divinations, a short single led in by a banjo figure, is not needed for the journey, and Quintessence and Ghost of Karelia share a gallop so closely that one could go with little loss. Two soft places in seven, neither in the spine.
Spike Jonze · Film
8.1 · Tier IV
The film’s elements are required by one idea, that a self can be occupied, and nearly all of them pay. The half-height floor, first a sight gag of stooping clerks, is the first sign that the building has a hidden storey for hidden men. Craig’s puppetry is the whole plot in small: the man who works marionettes ends by working a man. Lotte’s menagerie returns as the cage, and the chimpanzee Elijah’s memory of his capture is the cage’s meaning. The Turnpike drop gives the fantasy a cost and a running joke at once. The give is late: the lore of vessels arrives as exposition when the plot needs it, and the celebrity montage runs past its point.
Mughal, under Shah Jahan · Architecture
8.1 · Tier IV
Judged on purpose, structure and site. The court is compelled by the Friday congregation of an imperial capital: it is the building’s reason, and it is sized to a city, not a quarter. The platform is compelled by site and meaning together, a natural rise built higher so that coming to prayer is an ascent out of the bazaar. The three stairways follow from a platform entered from three sides of a city. The prayer hall is required in kind, for the qibla wall and the covered rows, but it is shallow, more facade and screen than hall, and its depth is not argued by its use. The corner pavilions and some gate ornament would go without loss.
Roman, under Caracalla · Architecture
8.1 · Tier IV
Judged on structure, purpose and site. The bather’s sequence compels the spine: undress, exercise, sweat, cool, swim, so tepidarium, caldarium, frigidarium and natatio stand on one axis in the order of the body’s passage, with nothing between them the passage does not use. The caldarium projects to the south-west because the sun is a heater. The platform is raised because furnaces, fuel and slaves had to move beneath the bathers unseen. The mirrored halves double the flow and keep it moving in a ring. What yields to the subtractive test is the precinct: libraries, exedrae and gardens are generous rather than required, and the scale, beyond any need of the bath, is permitted by largesse, not compelled.
Built for Ashikaga Yoshimasa · Architecture
8.0 · Tier IV
The subtractive test bites hard on small buildings, and these pass it. In the Kannon-den nothing is spare: two storeys, two manners, one image, one roof, one finial. Take away the upper storey and the building is a villa room; take away the lower and it is a chapel raised on posts. The work is a dwelling put under a sanctuary, and both are required. The Dōjinsai is the extreme case: four and a half mats, a desk, a window, shelves, and nothing goes without the room ceasing to be a place to read, write and set out a few things. What holds the axis is that much is given rather than compelled: the stacked pavilion is inherited, and its proportions follow a type.
Wassily Kandinsky · Visual art
8.0 · Tier IV
The subtractive test, disc by disc. The black circle in its corona cannot go: it is the picture’s weight, its darkness made into a body, and without it the field would be confetti on a ground. The large discs that cross or touch it cannot go, because the transparencies where they overlap are where the picture’s principle is shown. The dark, clouded ground cannot go: it is the space the discs float in, and it gives them their glow. What yields is the swarm of small discs. Their number and places look searched for balance rather than compelled by it: two or three could move or vanish and the picture would remain itself. One form in many sizes has fewer required parts than it seems.
Meret Oppenheim · Visual art
7.9 · Tier III
The test is short because the parts are few, and each is required. Take away the spoon and the work loses the one thing made to go into the mouth: the cup is met at the lip, but the spoon crosses it, and furred it makes tasting unthinkable. Take away the saucer and the set ceases to be a service laid out for a guest and becomes one odd cup. Take away the fur and nothing is left but crockery; change it for something long or dark and the effect turns comic or bestial rather than intimate. What yields: any cup of the pattern would serve, as with Fountain, and the longer title, reported to be another hand’s, is not compelled by the object. The requirement is the economy of a single idea.
I. M. Pei · Architecture
7.9 · Tier III
Judged on purpose, structure and site. The problem was real: the Louvre was entered at the ends of a U of wings over half a kilometre long and had no room for service. Put the entrance under the middle of the court and the hall needs light, and the entrance needs a mark in a court whose every front is a palace front. A pyramid gives the most light and the clearest sign for the least bulk: it rises to a point, so it hides the least of the pavilions behind it, and it stays well below the cornice. The small pyramids light the passages below. Subtract the pyramid and the hall is a basement. What yields: the pools are as much barrier and mirror as requirement, and the single entry the problem compelled has since become a funnel.
Wes Anderson · Film
7.9 · Tier III
The subtractive test finds little slack in a short film. The opening trap and Fox’s promise are what the whole film breaks. The tree, bought against Badger’s advice, is the property the farmers will dig out from under him. The three farms are three raids rising in danger and three trades in one economy. Bean’s cider cellar gives Rat his station and the flood its water; Kristofferson’s arrival gives Ash a rival, and his capture gives the rescue its object. The tail Fox loses is worn as a tie for the rest of the film, the price paid in his body. What gives: the whack-bat game is partly gag, and the last act’s rescue gathers by contrivance.
Henri de Toulouse-Lautrec · Visual art
7.9 · Tier III
Judged figure by figure. The rail cannot go: it is the viewer’s barrier and the composition’s one strong line, putting us outside the party and close to it at once. The green face cannot go: without it the picture is a group portrait of friends at a table; with it the table becomes something seen past, and the room a place one is entering. The painter and his cousin crossing the floor are the observer inside the scene, and La Goulue at the mirror, a performer making her face, is required for the same reason. What yields is the table itself: its sitters are likenesses whose number and placing the occasion permits rather than the picture compels. The added strip is the most necessary part of it.
Jeff Nichols · Film
7.9 · Tier III
The subtractive test finds little to take, because each dream produces a waking act. The dog’s bite produces the pen and the giving away of Red; a dream of Dewart produces the request to move him off the crew, which costs Curtis his one friend and then his job; the dreams of Hannah taken from the car produce the shelter. The insurance is load-bearing, since Hannah’s implant surgery hangs on the job he loses by taking the excavator, and his mother’s illness, come on at about his age, is the hinge of the middle. The beach, the least necessary-looking element, is the most required: without it the film is a case history. What gives: the first hour repeats itself, two dreams make one point, and the counsellor restates the mother.
Alexandros of Antioch (attributed) · Visual art
7.9 · Tier III
Judged on what stands. The figure is one turning movement, and its parts serve it: the right hip pushed out over the weight leg, the left knee lifted and thrust forward under the drapery, the torso turning against the legs, the head turning back again to its left. The drapery is not ornament. It carries the mass of the lower body and the action of the knee, and its slipping knot below the navel is the figure’s one event, the moment between clothed and bare. What yields under the subtractive test is the drapery’s bulk, more than the movement requires. The arms are gone, so the test cannot be put to the whole design; what remains is close to necessary.
Beach House · Music
7.9 · Tier III
Ten tracks, and the subtractive test finds more of them required than the record’s polish would suggest. Myth must open: its keyboard figure and the slow lift of its chorus set the mode and give the record its word for itself. Irene must close, the long piece that turns ten songs toward an ending by repetition and then by silence. Wild and Lazuli are required as the two plainest ascents; Wishes and On the Sea earn their places as the record’s warmest and its most inward. That is six of ten, each holding a distinct office. Held from the top by the middle: Other People, Troublemaker and New Year restate the sway, the organ bed and the rising refrain without turning them, and the record would survive losing one.
Howard Hawks · Film
7.8 · Tier III
The subtractive test finds very little to cut. Every scheme Walter runs serves one end, getting Hildy back to the paper: the lunch, the insurance policy, the counterfeit money that lands Bruce in jail, the stolen wallet, Bruce’s mother carried off by Louie. The repeated arrests of Bruce look like padding and are the engine; each return of the dull fiancé measures how far Hildy has gone back into the story. The escape, the desk, the reprieve and Pettibone’s arrival are the play’s mechanism, which Lederer’s script tightens rather than extends, and the film runs without a slack scene. What gives: Bruce’s gags are one gag at three speeds, the press room’s card game is partly texture, and the farce’s later turns are required in kind rather than in particular.
Lucian Freud · Visual art
7.8 · Tier III
The picture has almost nothing to subtract. Take away the sofa and the body loses what bears it: the sag of the cushions, the arm the head rests on, the worn pattern against which skin is read as skin. Take away the floor and the sofa floats; that strip places the scene in a room where work is done. Take away the title and the picture loses its one sentence about the world outside the studio. Every part of the body is load: the weight falling to one side, the folds where flesh meets flesh, the hand, the sleeping face. What is permitted rather than compelled is extent: the upholstery at the edges carries less than it is given, and a margin at either end could go. The life size is compelled. Held below the top because the parts are few, and their necessity is a single motif’s, not a structure’s.
Anish Kapoor · Visual art
7.7 · Tier III
The subtractive test finds almost nothing to take, because there is almost nothing but one surface. Remove the arch and the work is a mirrored mound: it loses the gate of its title, the walk under and the chamber. Remove the omphalos and the inside stops answering the outside; the work becomes all exterior. Leave the seams showing, as they were in 2004, and the cloud breaks into panels and the illusion of a liquid body fails. Every element is required by what the work does. What holds it below the mid eights is the looser question: is this outline required? The lobed plan could swell or shorten by a metre and the work would know nearly the same things. The necessity is in the kind of form, seamless, convex outside, concave within, open beneath, more than in this form.
Frans Hals · Visual art
7.6 · Tier III
The test is subtractive, and the canvas has little to subtract. There is one man and nothing else: none of the props of the formal portrait. The elbow cannot go: it is the picture’s thrust into our space and its claim. The hat cannot go: its black brim is the largest dark in the picture, frames the face and gives the eyes their shade and the smile its secrecy. The lace collar is the light the head is set against, and its scale is the man’s display. The plain ground lets the silhouette carry everything. What yields is the extent of the embroidery: required in kind, but its sheer amount is permitted by the commission’s appetite for finery more than compelled.
Indus Valley (Mohenjo-daro) · Visual art
7.6 · Tier III
Judged part by part, the figure has few parts and almost none can go. The hand on the hip is the attitude: without it she is a standing figure, with it she is someone. The arm laden with bangles is the counterweight, the asymmetry the pose depends on, and the bangles are the one place where ornament becomes structure, since they make that arm heavy and the stance read as weight. The raised chin is the address: she looks past the viewer, not at him. The bent knee shifts the weight and makes the stillness a pause rather than a pose. What holds the axis near 8 is the summary handling of the hands and the face, unfinished more than compelled; at this size some things are as the casting left them.
J. R. R. Tolkien · Literature
8.9 · Tier IV
The subtractive test bites in the first book and almost nowhere after. From the Council of Elrond the parts are required: Moria loses Gandalf, so the company must break; the breaking sends two hobbits to Fangorn and the Ents to Isengard; Faramir is the test Boromir failed; Shelob is the gate; the Scouring brings the war home. Even the Barrow-downs pays its debt, in the blade with which Merry wounds the Witch-king. What holds the axis lowest of the twelve is what could go: the slow prelude from the party to Crickhollow, the house of Tom Bombadil, explained at the Council and set aside, and verse that ornaments rather than carries; perhaps a twentieth to a fifteenth of the whole.
Fernando Pessoa · Literature
8.9 · Tier IV
The body passes the subtractive test at the level of its persons and fails it at the level of its poems. Remove Caeiro and the other two lose their master and their measure: the odes of Reis are a classical discipline built on Caeiro’s paganism, and “Tabacaria” is the poem of a man who cannot do what Caeiro claims to do, see without thinking. Remove Reis and the system loses its stoic pole; remove Campos and it loses the modern city and the self that suffers itself. The poems are another matter, and that is what holds the axis lowest of the twelve. Many Reis odes restate one counsel, enjoy the hour, expect nothing, the gods are indifferent, in near-identical terms, and could go by the dozen. The Poemas Inconjuntos repeat the Guardador less well. The late Campos includes drafts Pessoa never finished, and the body as edited keeps them: assembled from the papers he left, it carries what its maker would have cut.
Federico Fellini · Film
8.8 · Tier IV
Judged on structure: the film has no verbal part separable from its making. The subtractive test is its own subject, since the writer engaged on Guido’s script tells him early that it is a string of episodes with no problem to hold them. The film is built to survive the charge. The tunnel sets the suffocation and the fall; the cemetery, the farmhouse and the beach supply the parents, the anima and the Church that the harem and the ring gather up. What holds it lowest is the hotel society, permitted rather than compelled: the French actress and her agent, and much of the production talk, could be thinned without loss. That the crowd is partly the argument earns back only part of the height.
David Foster Wallace · Literature
8.8 · Tier IV
The test is subtractive, and no book on this desk is more exposed to it. The case for the length is real: a novel about a culture that will tolerate nothing but pleasure must make its reader work, and its thousand pages and hundred pages of notes are the opposite of the film at its centre. The core is required. The Eschaton must stay, the map mistaken for the territory on four tennis courts; the Marathe and Steeply dialogue must stay, since it states the book’s question about what a person chooses to serve; Gately’s hospital chapters must stay. But much could go without the knowledge changing: several of the residents’ case histories, the long run of Orin’s seductions, the Wardine section, a good part of the tennis drills and the set pieces of the satirical future. A tenth or more of the main text is permitted rather than compelled, and that holds the axis lowest of the twelve.
William Gaddis · Literature
8.8 · Tier IV
The test is subtractive, and the book is built to resist it and partly fails. The design is required: the class trip that buys one share; JR’s empire grown from the mail and the school’s pay phone; Edward Bast drawn in as its agent while his music shrinks; the teachers, Gibbs and Eigen, failing at their books in the apartment on 96th Street; the corporate world of Typhon and Governor Cates that JR’s paper touches and disturbs. The repetition is functional: a world of unceasing transaction must be heard unceasing, and the reader’s fatigue is part of the knowledge. But the test still bites. The drunken scenes in the apartment run long past their turn, the school administration’s calls recur with diminishing return, and some of the corporate talk restates what is already plain. Perhaps a tenth of the book is permitted rather than compelled.
Arthur Rimbaud · Literature
8.8 · Tier IV
The test is subtractive, and it has to be put twice: to the pieces and to the book. Within the pieces it finds almost nothing to remove. “Départ” is four short lines and every one is required, from its opening “Assez vu.”, seen enough. “Aube” runs from its first sentence, the summer dawn embraced, through the chase of the goddess to the fall at waking, and no clause is idle. Put to the book, the test returns another answer. Rimbaud set no order; the sequence every reader meets is an editor’s, and the book could lose “Ouvriers”, “Fête d’hiver”, “Bottom” or “H” with its argument intact. The pieces are compelled; their gathering is permitted. The cap is met with room, and the axis is held where it is because it judges the unit, and the unit was assembled by other hands.
Roberto Bolaño · Literature
8.8 · Tier IV
The test is subtractive, and it is hard on a book of more than a thousand pages left unrevised. The core holds. The crimes part must keep its length: its argument is that the killings are numberless and that the city, the police and the reader grow used to them, and three cases chosen would make a thriller of what the book shows as routine. The Archimboldi part carries the European half of the horror, the Eastern Front and the killing of Jews in a Polish village, and the critics’ convergence on Santa Teresa is required. What holds the axis at the foot of the twelve is what is permitted rather than compelled: the critics’ love triangle and their London episodes run long; the Fate part spends pages in Detroit and on a boxing match that could go with little loss; several dreams and digressions repeat rather than turn. Perhaps a tenth to an eighth of the whole is slack the author did not live to cut.
Mary Shelley · Literature
8.7 · Tier IV
The spine is compelled. The argument needs every layer of the frame: Walton’s ambition at the outside, Victor’s confession within it, the creature’s voice at the centre, and inside him the cottagers, through whom he learns what a family is by watching one through a chink in a hovel wall. Remove a frame and the argument loses a term. What holds the axis lowest of the twelve, with The Made, is the material between the necessary scenes. Victor’s lamentation repeats itself in a vocabulary of despair that barely varies from the second volume to the third; the journey through England with Clerval, at Oxford and in Cumberland, runs long for what it carries; and Safie’s history is a novella’s worth of plot told in summary. The parts are required; their proportions are not always.
Mikhail Bulgakov · Literature
8.7 · Tier IV
The three strands require one another. Remove Yershalaim and the Moscow satire has no measure of what its cowardice costs; remove Moscow and Pilate’s sin has no present; remove the lovers and nothing joins them, since it is the Master’s novel that is the Jerusalem strand and his release of Pilate that closes it. What holds the axis lowest of the twelve is the episodic middle of the Moscow satire: Styopa flung to Yalta, the house manager Nikanor Bosoy’s dream of the currency theatre, Berlioz’s uncle from Kiev, the buffet manager Sokov, the fire at Griboedov’s. Each is good, and each exposes one more instance of the cowardice and greed the Jerusalem strand judges, so that the cumulation is part of the argument; but several could go without the work losing a fact it needs, and the unrevised state of the text shows in loose joins between them. A spine that is necessary, with limbs in part assembled.
Robert Browning · Literature
8.7 · Tier IV
Inside the great monologues almost nothing is idle. In “Fra Lippo Lippi” the night arrest, the friar’s account of being taken in by the monks, the Prior’s demand that he paint the soul, and the promised Sant’ Ambrogio picture with Lippo hiding in its corner each turn the argument about flesh and spirit a notch further. “Andrea del Sarto” is tighter still, one evening’s talk in which every concession (“Well, less is more, Lucrezia”) is a self-sentence. But the unit is the book, and the subtractive test bites. Perhaps a dozen of the fifty-one could go without loss to what the book knows: “The Twins”, “Protus”, “Women and Roses”, “Misconceptions”, “Before” and “After”, “In Three Days”, the pair “One Way of Love” and “Another Way of Love”. “Bishop Blougram’s Apology” is longer than its argument, and “In a Balcony”, a dramatic scene set among monologues and lyrics, carries less than its length. Necessity in the parts, assembly in the whole: that holds the axis lowest of the twelve.
Antoni Gaudí · Architecture
8.7 · Tier IV
Judged on purpose, structure and site, and the structure resists the subtractive test hard. Each column leans along the line of its load, found by hanging models, and branches where the vault needs carrying; the stones are chosen for their loads; the hyperboloid openings both lighten the vault and admit its light. Take away a branch and a vault falls. The plan is compelled by the liturgy and the expiatory idea, the cloister wrapped round to set the temple apart from the city’s traffic. What yields is the programme’s scale: eighteen towers, three façades each a total narrative, a Nativity in which a hundred figures could go and the meaning stand. That magnitude is permitted by ambition, not compelled by worship, and the plan’s own axis ends at a construction site.
Anonymous · Literature
8.7 · Tier IV
Subtract a link and ask what goes. In the first two thirds nothing can: Roland names his stepfather Ganelon for the deadly embassy; Ganelon, wounded in his pride, names Roland for the rearguard; Roland refuses the troops Charles offers; Oliver asks three times for the horn and is refused three times. Take one away and the disaster has no cause. The repeated laisses are not redundant: they hold a decision still while it is made. What holds the axis lowest of the twelve is the Baligant episode. Its argument is real, that Roncevaux is one battle in a war of Christendom against all heathendom and that Charles himself must be tested in single combat, but it is made at great length through catalogues of pagan divisions, and the poem would stand without much of it.
Venetian builders · Architecture
8.7 · Tier IV
Run the subtractive test on the core and it resists. Five domed squares, each pier a hollowed cluster that carries its dome and opens the space; the cross that sets the altar over the relics in the eastern arm and the crypt below. The domes are required by the plan and the plan by its model. But the work is accretive by nature, and much of it yields: the façades carry a forest of reused columns stacked in two orders, many doing no structural work; the raised timber shells, the spoils set into walls, the reliefs scattered over the flanks. What holds the axis at 8.0 is that any one of them can go without loss to the whole.
Ivan Goncharov · Literature
8.6 · Tier IV
The long first morning is not padding but the argument: the stillness must be felt in duration before the Dream explains it, and the slow years on the Vyborg side are the book’s answer to the summer with Olga. Remove either and the novel loses its proof. What holds the axis lowest of the twelve: the subtractive test bites in three places. The procession of visitors in Part One, each showing a career Oblomov declines, is a needed device, but four could be three without loss, and its satire of Petersburg occupations is the most dated stratum. The swindle of Tarantyev and Mukhoyarov is mechanical and could be shorter. Stolz’s Part Four chapters with Olga are needed, but told rather than dramatised.
Anonymous · Literature
8.6 · Tier IV
Subtract a joint and ask what goes. Along the spine almost nothing can: Brünhild deceived by Siegfried in the cloak of invisibility, the ring and girdle carried off from her chamber and given to Kriemhild, the quarrel at the cathedral door, the murder at the spring, the theft of the hoard, Rüdiger’s oath to Kriemhild, the betrothal of Giselher to Rüdiger’s daughter, planted so that Rüdiger’s death can cost what it costs, and Hagen’s breaking of the boat. What holds the axis lowest of the twelve is the courtly surface laid over that spine: the long robing for the Iceland voyage, festivals and tournaments told at length, Kriemhild’s progress with its welcomes at Passau and Pöchlarn. Perhaps a tenth of the poem could go without loss.
Federico Fellini · Film
8.6 · Tier IV
Judged on structure, with the small verbal part of Steiner’s speeches and the party talk. Some movements are required beyond argument. The prologue sets the law, the sacred carried as cargo and the question lost in the noise. Sylvia is the life at its most radiant; the miracle is the sacred as broadcast; Steiner’s three appearances are one argument, and the last cannot stand without the first two; the father’s night, Fregene and the beach close the circuit. What gives is in the middle: the castle’s ghost hunt adds little the Maddalena night had not set, and the miracle’s crowds, the dance at Caracalla and Steiner’s salon run past what they argue. That holds the axis lowest: in a form where no episode causes the next, the parts are required in kind more than in length.
Pablo Neruda · Literature
8.6 · Tier IV
The book’s method is accumulation, and accumulation invites the subtractive test. In “Galope muerto” and “Sistema sombrío” the chains of simile could lose a third of their links and keep their sense; in parts of the first volume the prose poems and the minor lyrics, “Lamento lento” and some of the sonatas, restate the mood of the strong poems without advancing it, and a dozen poems could leave the book at little cost. Against that, the strongest poems are necessary in the strict sense. “Walking Around” builds its revulsion item by item until the list itself is the weariness, and “Sólo la muerte” needs each of its sinking images to arrive at death as a sound without sound. The cap is met; the axis is held here because the subtractive question has real answers inside the book.
Le Corbusier · Architecture
8.6 · Tier IV
Judged on structure, purpose and site. Building by building the subtractive test is resisted well. The High Court’s parasol is required by sun and monsoon: it shades and ventilates the courts beneath and is the building’s figure. The Secretariat’s brise-soleil is required by the Punjab sun, and its ramps carry the people the slab holds. The Assembly’s hyperboloid is the chamber itself, its height the air and light the room needs. What holds the axis lowest is the plain. Its scale is permitted, not compelled: the distances that keep the powers apart are so great that the buildings lose hold of one another, and the walk between them in the sun is a cost never repaid. The Secretariat’s length is repetition, required only by quantity; and the plain’s head, made to close on a fourth building that does not stand, is a gap.
William Faulkner · Literature
8.6 · Tier IV
The subtractive test bites harder here than on Faulkner’s tightest novels, because the book was built in part from stories and the joins show. What holds the axis lowest of the twelve: the Labove chapters are a novella of their own; the goat deal between Ratliff and Flem and some of the trading tales of “Flem” could go with little loss; and “The Long Summer” sets Ike’s pastoral and Mink’s killing side by side under a theme, loves bought and unbought, more than under a plot. The spine holds, and the large pieces are each required by the argument: without Eula, Flem has nothing to buy; without the horses, the treasure scheme has no community to fleece.
Dziga Vertov · Film
8.6 · Tier IV
Judged on structure, the frame is required. The cinema at the start and the close, with an audience watching what the camera has gathered, is what turns a city symphony into a film about how a city becomes a film. The cameraman is required as the figure who makes the seeing visible in every reel; Svilova at the bench is required, since her freeze frames are the one place the film halts to show its own material. The day is required for the rhythm it carries. The give is in the catalogue: beach, slow-motion sport, the magician, the shooting gallery and the beer hall accumulate, and any one could go. The method is additive by programme, and the subtractive test finds slack exactly where the method invites it.
Ernest Hemingway · Literature
8.6 · Tier IV
The spine is as tight as any in the American novel: one bridge, one order, one attack, three days. Pablo’s treachery, Sordo’s horses, the snow in May that betrays the tracks, the planes over the pass and Andrés’s message all tighten on the same hour. The told episodes earn their place. Pilar’s tale is the moral ground the bridge stands on; Sordo’s hill is the death Jordan will die, shown first to others. What holds the axis at the foot of the twelve is the middle. The love scenes repeat their own vocabulary, Jordan’s monologues on the Party, his father and what he will write afterwards circle back, and the banter at the cave runs past its point. Perhaps a tenth to an eighth could go without the knowledge changing.
Jacques Tati · Film
8.6 · Tier IV
Judged on structure. The design is a curve, not a plot: a day in a city of straight lines and grey glass that warms, through the night’s collapse, into a dawn of circles and colour. The large parts are required: the office and the exhibition set the grid the Royal Garden breaks, the flats at dusk show the private life the restaurant throws together in public, and the dawn carousel answers the airport. But the method is accretive, and the subtractive test finds much that could go singly without loss: the exhibition’s slamming door and silent broom, the lamp salesmen, a run of business in the restaurant’s middle hour. Abundance is the point, which lightens the charge; still, the Royal Garden runs long even for its function.
Henry of Reyns and successors; Henry VII Chapel by Robert and William Vertue (attributed); west towers by Nicholas Hawksmoor · Architecture
8.6 · Tier IV
Run the subtractive test across the whole church. The east arm resists it: apse and ambulatory gather the chapels round the shrine, and without the shrine the plan loses its centre. The raised crossing is required by coronation, a stage seen from four arms. The buttresses carry the vault, and the Purbeck shafts are the order of the wall. Much of the rest yields. The nave is a continuation, compelled by fidelity to a design more than by a purpose of its own. The Lady Chapel was built for a cult of Henry VI that never came and for a tomb, and could be taken away with the church still whole. Hawksmoor’s towers finish a front rather than complete an argument. The monuments are accretion: hundreds could go, and many crowd the arches and screen the wall.
Cormac McCarthy · Literature
8.6 · Tier IV
The test is subtractive, and the book gives it two answers. The spine passes it: the wolf, the murdered parents, the brother, the bones, each crossing compelled by the one before and each loss the condition of the next. The tales pass it in principle. The priest at Huisiachepic, the blind man and the gypsies are not ornament but the book’s argument, three accounts of how a life becomes a story and what the story owes the world. What holds the axis, level with the lowest of the twelve, is degree. The priest’s tale runs for many pages, and the later tales return to its themes in its own idiom, so that the third restates more than it adds. The second crossing’s round of cantinas and ranch hands, of hospitality, warning and departure, repeats a pattern the first had made, and the third part is slight. Perhaps a tenth of the book could go without the knowledge changing.
Anonymous · Visual art
8.6 · Tier IV
Judged on structure. The Hall of the Bulls resists the subtractive test: two groups of aurochs face each other across the rotunda, horses and stags run between them, the Unicorn opens the frieze, and removing any of the four aurochs breaks the ring. The Axial Gallery is a sequence with an end, narrowing to a horse painted round a pillar. The Shaft holds the one human, and the species are sorted by chamber: distribution, not accumulation. What fails is the Passage and above all the Apse, where no engraving among the hundreds laid over one another can be shown to be required. What is compelled is compelled strongly; what is not is a third of the cave.
Ursula K. Le Guin · Literature
8.5 · Tier IV
The subtractive test mostly fails to find slack. Remove the hearth tales and the book loses its proof: “Estraven the Traitor”, the old tale of two sons of feuding Domains who love across the feud, is the prophecy of Estraven and Ai, and Estraven’s own descent is in it. Remove “The Question of Sex” and the reader has only Ai’s prejudiced eye on the Gethenians. Remove the ice and there is no novel. What holds the axis lowest of the twelve is the Orgoreyn middle: the Mishnory chapters set out Obsle, Yegey and Shusgis and the factional plot at a length the argument does not compel, and the reader waits for the ice. Pulefen is required; some of what leads to it is not. The parts are required; a few are longer than required.
Anonymous · Architecture
8.5 · Tier IV
The lowest axis, with The Encompassed, and the reason is the whole. Run the subtractive test on the parts and much resists: in St Hugh’s Choir the shafts, ribs and arcading are each necessities of a bay reasoned through; the double transept answers a liturgy of many altars and a long processional east end; the Angel Choir is compelled by its purpose, a larger, lighter eastern arm for a saint and his pilgrims, its square end giving the window the whole wall. What yields is the accumulation of two and a half centuries. The west front is the clearest case: a Norman front wrapped in a screen wider and taller than the church behind it, a stage not compelled by the body. The Galilee porch and the chapter house vestibule are ordered rather than required.
Jonathan Swift · Literature
8.5 · Tier IV
The subtractive test meets a book whose subject is excess, and the case for its bulk is real. A parody of the swollen modern book must swell, and the prefaces stacked four deep before the first section are required: the reader must wade through apparatus to feel what the hack has done to the book as an object. The alternation is required too. Remove the digressions and the tale is a pamphlet allegory; remove the tale and the digressions lose the history of scripture abused that they mirror. What the test finds is inside the parts. Section X, on authors and readers, adds little the Introduction and Section VII have not shown; Section XI runs Jack’s grotesqueries well past the point its argument is made; and several mock-learned passages repeat a joke at the length of the thing they mock. Imitative excess has a diminishing return, and the book pays it.
Anonymous · Visual art
8.5 · Tier IV
Judged panel by panel, since the cave is not one composition but a sequence of panels laid down by several hands across a span the dates cannot close to less than centuries. In much of it the subtractive test gives: lone animals, single rhinoceros heads, partial outlines, a bear here, a mammoth there; remove many and the cave stands. The panels do not give. On the Panel of the Horses each of the four heads is placed against the last, and to take one is to lose the recession. On the Lion Panel the overlapping heads move one way, and the line is the hunt. The pendant is a woman and a bison on one rock, and either alone is another thing. Necessary in the panels, permitted in the field around them.
Robert Johnson · Music
8.5 · Tier IV
Inside each side almost nothing is idle. A 78 held about three minutes, and Johnson writes to that length: “Hellhound on My Trail” has three stanzas and no instrumental verse it could lose, and “Me and the Devil Blues” moves from the knock at the door to the burial by the highway in two minutes and a half. The subtractive test bites on the album, not the songs. “Kindhearted Woman Blues”, “Rambling on My Mind”, “Terraplane Blues” and “When You Got a Good Friend” share figures, turnarounds and a frame, and two or three could go with no loss of what the record knows. “32-20 Blues” and “Milkcow’s Calf Blues”, answers to other men’s records, are the most separable. A compilation chosen from a corpus was not compelled as a whole.
Terry Gilliam · Film
8.5 · Tier IV
The plot itself is tight, and its first cause is a beetle. The insect in the teleprinter turns Tuttle into Buttle, and from that misprint come Buttle’s death, the refund that sends Sam to Jill’s building, Jill’s complaint that makes her a suspect, and the arrest. Tuttle’s duct work brings Spoor and Dowser down on Sam’s flat; Ida’s surgery is paid at Mrs Terrain’s funeral, where she appears with Jill’s face; the flight dreams prepare the escape that the ending reveals. What holds the axis lowest of the twelve: much of the long cut is permitted rather than compelled. Several dreams make one point in different costumes, and the restaurant, the department store and the Shangri-La Towers run long in the middle hour, as the shorter American cut shows.
Johann Bernhard Fischer von Erlach · Architecture
8.5 · Tier IV
Run the subtractive test. The portico, the two columns and the inscription cannot go: they are what the vow and the claim require, and without the columns the church no longer says whose vow it pays and in whose name. The interior is tighter still: the oval drives one axis from the door to the glory, the chapels are subordinate, and nothing in the main room is idle. What holds the axis at 8.0 is the facade’s width. It is a screen more than twice as wide as the body it fronts, its pavilions and their carriage arches serve nothing the oval needs, and from either flank the columns stand free of the church. That width was permitted by the programme, not demanded by the building.
Pirro Ligorio · Architecture
8.5 · Tier IV
Run the subtractive test. The garden’s bones are compelled. The slope forces terraces; the river above the town forces a garden that is a descent of water; the descent forces the stairs and ramps, and the cross-walks that carry water sideways along the contour, as the three channels of the Hundred Fountains do. Take away the central axis or the Hundred Fountains walk and the garden loses its argument. The set pieces resist: the Owl, the Dragons, the Rometta, even the fishponds are discrete episodes, and the Rometta has largely been lost without the garden ceasing to say most of what it says. The palace, a convent made over, is the eye from which the garden is read, not built with the same compulsion.
Ernest Hemingway · Literature
8.5 · Tier IV
Within the best stories the subtractive test finds almost nothing. “Hills Like White Elephants” is a few pages, and every exchange turns the screw: the beer, the anise, the bead curtain, the bags carried to the far side of the station. “The Killers” spends nothing between the door opening and Nick’s decision to leave town; “In Another Country” is built of the machines, the hawks and the major’s grief, each load-bearing. Across the book the test bites, and harder than in a book bound by interchapters. “Banal Story”, a page of mockery ending on Maera’s death, could go without loss; “To-day Is Friday” is a sketch whose single turn does not justify its form; “A Pursuit Race” and “A Simple Enquiry” are slighter than their neighbours. Four of fourteen removable: that sets the axis.
Alain Resnais · Film
8.5 · Tier IV
The subtractive test is strange here, because the film is built so that its blocks can be repeated, reframed and recombined, and a work of interchangeable parts invites the question of what could go. Some things resist it absolutely: the opening passage through corridors under the narration, which sets the law; the statue argued over in the garden, the film’s emblem of a fixed past read two ways; M’s game, whose rules one man alone knows; the ending, told with a death and then refused. What gives is the middle stretch, where returns to the salon, the bar and the shooting gallery repeat a point already made, and some iterations of A’s room add variation without pressure. The interchangeability is the content; the surplus of returns is the cost.
Octavio Paz · Literature
8.5 · Tier IV
The scale is a law and not an outcome. Paz’s note gives the poem 584 lines, the synodic period of Venus in days, and the count is part of what the poem means: no passage can be cut without breaking it. That answers the subtractive test for the whole. It does not answer it for the line. Within the number, the chains of image in the opening and in the woman made a world run past need: “voy por tu cuerpo como por el mundo”
“I go through your body as through the world” is required, and several of the images after it restate it rather than move it. The roll of the dead risks the catalogue, some names doing work others have done. Madrid, 1937, the going out of the self and the six closing lines are beyond cutting. A necessity real in the design and looser in the texture holds the axis at the foot of the twelve.
Van Morrison · Music
8.5 · Tier IV
Eight tracks in about forty-seven minutes, and the subtractive test meets the record at an angle, because its method is repetition. Morrison circles a phrase until it turns, and the circling is the subject: memory returning to one place. Cut the repeated close of “Cyprus Avenue” or the long farewell of “Madame George” and those songs lose their arrival; they resist. The test finds give elsewhere. “The Way Young Lovers Do” is a brassy jazz waltz in another register from everything around it and could leave with little loss. “Ballerina” runs past what its material asks, “Beside You” is loose in the middle, and “Slim Slow Slider” stops rather than concludes. Four strong necessities against three or four places of give hold the figure, the record’s second lowest.
Sergio Leone · Film
8.5 · Tier IV
The length is mostly compelled. The subject is the weight of thirty-five lost years on one man’s memory, so the childhood has to be long enough for the boys’ pact, Dominic’s death and Deborah dancing in the storeroom to bear the whole later life, and the 1968 scenes have to be slow, because Noodles is now a man with nothing to do but look. The two rapes cannot be removed: the film’s account of Noodles stands on them. What holds the axis lowest is the 1932 to 1933 material that is assembled rather than required: the union plot, the baby swap in the maternity ward, parts of the Detroit jewel robbery. Each could be shortened without loss of knowledge.
Balthasar Neumann · Architecture
8.5 · Tier IV
Judged on purpose, structure and site. The ceremonial core resists the subtractive test. Take away the low vestibule and the stair has nothing to rise from: the compression is the condition of the release. Take away the white hall and the imperial hall arrives without a threshold, colour crowding colour. The single vault is compelled by the ceiling it carries and the ceiling by the ascent beneath it, so structure, route and image are one fact. What holds the axis at 8.0 is the bulk: the wings answer a court’s need for apartments, offices and courts, ordered rather than compelled; the long city front repeats its bays beyond what the programme asks; and the Hofkirche sits behind windows set by the façade, not by the church. The palace is necessary at its centre and assembled at its edges.
Godspeed You! Black Emperor · Music
8.5 · Tier IV
Length is not the charge. A record whose argument is the long approach must spend time, and the quiet ground before each climax is what the climax answers. The subtractive test bites inside the sides. Storm and Sleep resist it: in each the recorded voice or the quiet ground is required by what rises after it, and the old man’s memory is what Monheim’s long build is for. Static is the soft side: Atomic Clock and Chart #3 are passages of texture that could be shortened, and its climax comes late. The last side is the most assembled, and two of its seven movements, Edgyswingsetacid and the glockenspiel duet, would cost colour, not sense.
Andy Warhol · Visual art
8.4 · Tier IV
The subtractive test meets a work whose argument is that its units are interchangeable. Remove a column of heads and the grid is four by five; the repetition still says what it says, and nothing in the image tells why twenty-five rather than twenty or thirty. That permission is real and is charged. But the large parts are compelled. Take away the black panel and what remains is a gaudy sheet of publicity, the death gone; take away the colour panel and what remains is decay with nothing to decay from. Take away the fading at the right and the passage from presence to absence stops before it ends; take away the misregistration and the colour becomes a picture of a face rather than a mask laid on one. Compelled at the level of the halves and the gradient, permitted at the level of the count.
Robert Wiene · Film
8.4 · Tier IV
Judged on structure, since the words are few. The frame is required: without it the painted world is a style, and with it the style becomes a mind. The fair is required, since it shows the doctor’s power as entertainment before it shows it as murder. Cesare’s prophecy makes Alan’s death fated and gives the town its terror. The flight over the rooftops and the death on the hillside are required: the instrument fails when it meets a desire of its own. The diary gives the doctor his motive. What gives is the middle: the second suspect runs on procedure, the police and the officials take more scenes than their point needs, and Jane’s visit to the cabinet repeats a purpose already served.
Sly and the Family Stone · Music
8.4 · Tier IV
The subtractive test finds a real core and real give. Family Affair, Luv n’ Haight, Runnin’ Away, the title’s empty track and the two Africa closers cannot go without the record losing its argument, because the argument is a turn from the band’s own past, and the remade Thank You is where the turn is completed. The give is in the middle of side two and in the length of side one’s closer. Brave & Strong and Time are sketches of the same sedated groove and could change places with little loss. Spaced Cowboy belongs to the record’s law, but no moment depends on it. Africa Talks to You runs nearly nine minutes on a vamp whose middle could lose a third. Low and Remain in Light carry less slack.
Parmigianino · Visual art
8.4 · Tier IV
Test by subtraction. The Virgin’s elongation cannot go: it is the picture’s claim, beauty pushed past nature into an artifice of grace, and the title the painting has carried is its verdict on itself. The Child’s slack, deathlike sprawl cannot go, since the devotional meaning rests on the hanging arm. The vessel held toward the Virgin stays; so do the drop to the tiny prophet and the column, the leap of scale that makes the space unreal and the Marian emblem against which the neck is set. What yields: the angels at the left are packed past need, two or three heads at the back are filler, and the unfinished colonnade is required in intention and only partly realised.
Renzo Piano and Richard Rogers with Gianfranco Franchini · Architecture
8.4 · Tier IV
Judged on structure, purpose and site. The governing idea passes the subtractive test: to give a library, a museum and a centre of industrial design floors without a single column, the structure goes to the edges and the ducts go outside, and the floors are clear. The gerberettes follow from that span: they shorten the girders and turn the outer zone into a carrying zone for services and escalator. The square follows from the purpose, the public ground made the entrance. Much yields. The flexibility that compels the inside-out section was never used as promised: the floors were partitioned within a decade, and the moving floors and great screens on the façade were dropped. And the saturation of the colour code is rhetoric as much as necessity.
Lars von Trier · Film
8.4 · Tier IV
The spine is strict, and the subtractive test finds each step of the descent caused by the step before. Bess prays for Jan’s return and is answered by his accident, which she believes she caused; his request that she take lovers and tell him becomes, in her logic, the price of his life; each encounter is worse than the last, and the community closes its doors in proportion; the last trip to the ship is the sacrifice her logic has required from the start. Remove the hospital, the confession in the church or the first encounter on the bus and the chain breaks. What gives is length: the wedding and the first married days run long on texture already established, Terry and the rig crew are present more than they are needed, and the inquest is reached by a slack passage.
Roman, under Diocletian · Architecture
8.4 · Tier IV
Judged on purpose, structure and site. The Roman enclosure is compelled: a residence for a retired emperor in a frontier century, on an open shore, needed walls, gates, a guard and a protected way from the sea, and the camp plan gives them all in one figure. The peristyle is required by the ceremony of appearance; tomb and temple face each other across it because cult and burial belonged to the emperor’s person. What holds the axis lowest is the fill: the northern quarters are a generic grid of service blocks, and the town is accretive by nature, houses filling bays and arcades walled up as rooms. Much of it could be otherwise, though the walls and streets decided where it could stand.
Antoni Gaudí · Architecture
8.4 · Tier IV
Judged on structure, purpose and site, and much resists the subtractive test. The pillar frame is compelled by the free plan; the courtyards by light and air for flats deep in an Eixample block; the catenary arches by the roof they carry, each as tall as its span requires, so that the attic rises and falls and the roof terrace with it. The stair towers and chimneys are exits and flues before they are figures, and the chamfered corner is turned in one curve, not two faces. What yields is the front’s motion: carved stone hung on a frame, chosen rather than required, the most visible thing in the building. The rooms bend round the courtyards into shapes that use did not ask for.
Charles Barry and Augustus Pugin · Architecture
8.4 · Tier IV
Judged on plan, structure and purpose, and this is the lowest axis. The plan resists the subtractive test at its spine. Take away the Central Lobby and Lords and Commons have no common ground, nor the public a place to meet its members; take away the royal axis and the Crown cannot reach the Lords without passing the Commons; take away the division lobbies and the vote has no form, for a division is a walk through one door or the other. Westminster Hall is compelled by the site, the one great room the fire spared, and Barry made it the door. What holds the figure here is how much yields: a uniform panelling along the river front that says nothing of the rooms behind it, courts and passages that read as a warren grown rather than required, and ornament that could be halved without loss to use.
Kyivan Rus builders, under Yaroslav the Wise · Architecture
8.4 · Tier IV
Run the subtractive test on the core and it holds. The five aisles, the stepped vaults and the domes are not ornament: each dome lights the bay beneath it, the steps carry the thrust down to the outer walls, and the pyramid brings every line of the church to the central dome and the Pantokrator in it. The galleries enlarge a church built for the whole Christian body of a capital converted within living memory, and the choir gallery gives the prince the place above the nave his court’s liturgy required. What yields is number and later work: thirteen domes exceed what lighting needed, an argument rather than a structural need, and the Baroque gables, pilasters and raised galleries could go without loss to what the building does.
Anonymous · Architecture
8.4 · Tier IV
In the hemicycle almost nothing yields to the subtractive test: the piers are as thin as the vault allows, the triforium is glazed because wall there would be idle, and the chapels open from the ambulatory in the order the liturgy and the light require. The height is not compelled by purpose. No liturgy needs forty-eight metres; the margin over Amiens is chosen, a claim of the bishop, who was a count, and of his chapter. The argument of the building is height itself, and on those terms the height is necessary. What holds the axis lowest of the eleven is the work as it stands: piers inserted because the vault failed, crowding the straight bays; a closing wall to the west that is a stop, not a part; and a choir and transept of this size without the nave they were built to serve.
Robert Penn Warren · Literature
8.4 · Tier IV
The lowest of the twelve, level with one other. Subtract and see. The bones are required: the schoolhouse whose fire escape collapses, the picnic at which Willie learns he was a dummy, the hospital he means to build clean, the Byram B. White affair, Tom’s football injury, and the double catastrophe of the Judge’s suicide and Willie’s shooting. Each act of Jack’s turns a screw that the next needs, and the Cass Mastern chapter, which a hostile reader would call a detachable novella, is the book’s key. What holds the axis here is the flesh: Jack’s recurring set pieces of reflection, the Great Sleep, reprises of the same mordant wisecrack, scenery that repeats a mood already won. A book of four fifths the length would know the same things.
Philip Roth · Literature
8.4 · Tier IV
The spine is required at every joint. The word “spooks” must come first, because the book turns on a man destroyed for a racism he could not have meant, by a college that does not know what he is. The secret must be withheld until the second part, so that the reader convicts him wrongly too. The boxing, Steena Paulsson and the visit to his mother must all stand, since they are one decision seen three times, and the close on the ice must stand, since it puts the narrator face to face with what killed him. What could go is the surplus around that spine: the long arias on the impeachment and the persecuting spirit of 1998, the department satire around Delphine Roux, and stretches of Les Farley’s interior that restate his war after it has been shown. Perhaps a tenth of the book is permitted rather than compelled, and that holds the axis lowest of the twelve.
English embroiderers (probably Canterbury) · Visual art
8.4 · Tier IV
Judged episode by episode. The argument is an oath, its breaking and its sanction, and most of the length is required by it. Harold’s journey, capture and rescue put him in William’s debt; the Breton campaign shows him valiant and armed by the duke, which binds him further; the oath on the relics is the hinge; Edward’s death and Harold’s crowning are the breach; the comet is the sign; fleet, crossing and battle are the consequence; Harold’s death is the sentence carried out. What yields to the subtractive test: the Breton campaign runs long for what it adds, the preparations at Hastings are generous beyond need, and long stretches of the borders are ornament that could be other ornament. Necessity is high and not complete.
Eastern Ganga builders, under Narasimhadeva I · Architecture
8.4 · Tier IV
Judged on structure, purpose and site. The plan is the Kalinga programme, and each part is compelled by use: the sanctuary for the image, the audience hall for the approach and the gathered worshippers, the dance hall for the offering of music and dance, all on one axis to the east. The chariot is not a fancy laid on that programme but its frame: the platform must be high to carry the building, and making it the sun’s car turns the base course into the reason for the whole, so the wheels and horses are required. What holds the axis at its figure is the quantity of carving: whole bands of figures, scrolls and miniature shrines could be thinned without loss, and on parts of the walls ornament is accumulated rather than compelled.
Chen Kaige · Film
8.4 · Tier IV
Judged on the full version. The long opening at the school is required, though it runs to nearly a third of the film: the mother cutting away the boy’s sixth finger so the school will take him, the beatings, the line Douzi cannot speak as a girl until Shitou forces a pipe into his mouth, Xiao Laizi’s sugar haws and his hanging. Every later turn draws on it. The sword is planted early and paid in the last shot, and Juxian is required, the rival whose marriage breaks the stage pair. What holds the axis lowest is the middle of the chronicle: the trial after 1945 and the opium withdrawal run as episodes, and the historical markers, soldiers in the hall and a change of flags, are permitted rather than compelled.
Nine Inch Nails · Music
8.4 · Tier IV
Fourteen tracks in about sixty-five minutes, and the descent requires its stages. Mr. Self Destruct must open, a self announcing its own destruction in noise; Heresy is the loss of God, The Becoming the turn from man into machine, Closer the body used to erase the self, the title track the act, and Hurt the aftermath, without which the record could not end. A Warm Place is required as the one respite, the warmth that is gone. The test bites in the middle, and that holds the figure. Ruiner, I Do Not Want This and Eraser restate one self-loathing at one pitch, and any one of them could go; Reptile is long for what it adds; Big Man with a Gun is a crude provocation the argument permits rather than compels.
Don DeLillo · Literature
8.4 · Tier IV
The test is subtractive, and the double structure resists it at its core. Oswald’s life and the plot each need the other, since the book’s claim is that they converge without either causing the other. Branch must stay: he is the reader of the archive, the present from which the whole is seen, and the proof that the event cannot be closed. Marguerite’s monologues stay, since Oswald is made out of her. Where the test bites is the conspiracy’s middle. The plot passes from Win Everett to Laurence Parmenter to T. J. Mackey and down through a widening set of operatives, exiles and hired men, and several of these figures, and the meetings among them, add personnel rather than turns; the mob strand and some of Ruby’s preliminaries say again what has been said. The widening chain is itself the argument, that a plot escapes its makers as it passes down, and it cannot be cut to two men; but perhaps a tenth of the whole could go without the knowledge changing, and that holds the axis lowest of the twelve.
Hoysala builders · Architecture
8.4 · Tier IV
The subtractive test bites less than so much carving leads one to expect. The stepped plan is not decoration added to a box: each projection lengthens the wall and turns it to the light, and the friezes need that length to run unbroken round the building. The platform is required by the circuit, since the temple is read by walking it. The twin plan is compelled by the dedication, a pair of lingas for king and queen, and the paired Nandi pavilions answer it. What could go is real but small: many repeated band figures, since repetition is the method and the count is open. And the part that would have closed the composition upward was never supplied, which leaves the necessity of the low mass less sure.
Alvar Aalto · Architecture
8.3 · Tier IV
Judged on plan, section and structure, under purpose and site. Much resists the subtractive test. The courtyard is compelled: a northern house turns its rooms to a sheltered, sunny enclosure, the sauna wing and the wall close it, and the forest is left open. The open living space is compelled by the brief, a family that entertained and lived among paintings, so walls give way to shelving and changes of level. The studio is lifted where its light is. What yields is what made the house famous: the canopy’s bundled poles, the rattan on the columns, the changes of cladding from render to boarding to stone. Each could be removed and the house would work. They carry the meaning; the test asks what is required, and here much is chosen.
Aghlabid builders · Architecture
8.3 · Tier IV
Judged on purpose, structure and site. Prayer is additive, rows of worshippers side by side facing one wall, and the hypostyle is the form that purpose least resists; it is also the form that yields most readily to the subtractive test, since an aisle or a bay could go and the hall would pray the same. What is required is the order laid over the forest: the wider central aisle and the qibla aisle that make a T, the dome before the mihrab and the dome at the court, so that direction is built and not only implied. The court is required for ablution and overflow, and its slope to the cisterns ties rain to use. What yields: the irregular outline, the tower off the axis, the mismatched spolia, the fortress walls.
Rembrandt van Rijn · Visual art
8.3 · Tier IV
Judged figure by figure. Tulp cannot go: he is the lesson, the one figure apart, the voice. The corpse cannot go: it is the light and the occasion. The forearm cannot go: it is the hinge between the dead hand that no longer closes and the living hand that shows how it closed. The three heads leaning over the arm, at three distances, carry the act of attention; the book at the feet carries the authority the body is checked against. What yields is at the rim. The figure at the far left and the one at the top, who looks out, are the most separable, and the surgeon holding the paper is half required, half a sitter. The core is compelled; the rim is the commission.
Antoine Watteau · Visual art
8.3 · Tier IV
Judged figure by figure along the procession. The herm cannot go: it is the goal or the memory of the pilgrimage and the point where the reading starts. The three couples at the right cannot go: one seated and still persuaded, one rising, one already walking with the woman turning back. They are the picture’s argument, and any one removed breaks the sequence. The boat cannot go; it is the end of the line. What yields is the populated middle and left: the couples crowding down to the shore are a company rather than a sequence, and a pair could be lost without loss. The putti over the boat are convention. The proportion is compelled, since the oblong is the length of a walk. A strong spine and a permitted crowd.
William Thornton, Benjamin Latrobe, Charles Bulfinch and Thomas U. Walter · Architecture
8.3 · Tier IV
Judged on purpose, structure and site. The plan answers the constitution: two houses of equal standing, two wings, joined at a centre that belongs to neither. Take away the rotunda and the chambers are two buildings; take away a wing and the bicameral settlement is gone from the plan. Walter’s extension was compelled by purpose, the old chambers outgrown as states were admitted, and the dome by the extension, since Bulfinch’s low dome sat too small over the lengthened front. What resists the subtractive test: the dome’s height and its peristyle are required by symbol and by the view down the Mall, not by any use beneath them, and the long marble fronts repeat a bay that could be shorter or longer with little loss.
Jacob Lawrence · Visual art
8.3 · Tier IV
Judged panel by panel and as a count. The frame panels cannot go: the first, a station crowd pressed toward three gates marked Chicago, New York and St. Louis, states the event; the last, the platform crowded again under the caption “And the migrants kept coming”, leaves it open, and together they make a cycle that does not close. The lynching panel cannot go, nor the handcuffed men seen from behind, nor the riots, nor the crowded housing of the North: each is a cause or a cost the argument needs. What yields is the middle of the catalogue of causes, where floods, the boll weevil, failed crops, low wages and dear food state one cause, poverty, in parallel. The count is partly compelled and partly permitted.
Arnolfo di Cambio (attributed) · Architecture
8.3 · Tier IV
Run the subtractive test on the first block. The priors lived shut in the palace for their two months of office, and a commune torn by faction needed a house that could hold against its own city. Hence the blind rusticated walls below, the one door, the gallery from which defenders could drop on assailants, and the tower as watch, bell and sign, its height meant to stand above every private tower. Nothing in the block of 1299 is idle. What yields is the interior the centuries left: rooms enlarged, joined and refitted for a republic, a duke and a municipality, each compelled by its own purpose, and a Salone whose raised roof served display, not assembly.
Luis Buñuel · Film
8.3 · Tier IV
The premise is one subtraction, a door no one crosses, and the frame built on it resists the subtractive test at every joint. The servants’ flight is required, since the masters must be left alone with their forms. The doubled arrival is required, since it plants the law of repetition that later opens the room. The coda is required, since it shows the spell belongs not to one household but to the Church and the state. The test bites in the middle. The confinement is built of vignettes, the Kabbalistic rite with chicken feet, the crawling hand, the bear on the stairs, Francisco Ávila’s pill box, and several could be lost singly without the whole changing. Together they give the decay its duration; singly, not each is needed. Tight at the frame, porous inside it.
Led Zeppelin · Music
8.3 · Tier IV
Nine tracks in about forty-one minutes, and the record stands on four required places. Whole Lotta Love must open: the riff states the record’s law in its first bars. Heartbreaker must open side two. Ramble On is the one place the record widens its world, and Thank You is required for another reason: it is the one song of devotion without strut, and without it side one would be all appetite. The test bites elsewhere: Living Loving Maid is slight, Moby Dick is a frame for a drum solo, a document of a concert practice, The Lemon Song holds its jam past the song’s need, and Bring It On Home quotes its source at length. The required places carry the record; the rest is permitted.
Orson Welles · Film
8.3 · Tier IV
The spine is required. The bomb sets the quarrel over jurisdiction that sets Vargas against Quinlan; the shoebox, empty when Vargas uses the bathroom and full of dynamite when Quinlan’s men search it, is the hinge of the case; Quinlan’s dead wife and her unpunished strangler explain why he plants evidence; the bullet Quinlan once took for Menzies is what makes the last betrayal cost. Grandi’s murder in the hotel, with Susan unconscious on the bed, is where both lines become one crime. The subtractive test bites on the Susan line. The Mirador sequence, the night man’s twitching, the leather-jacketed gang and the drug party make one point at great length; the reconstruction’s intercutting improves the proportion without removing the excess, and several of the connective scenes by another director could go.
Zapotec builders · Architecture
8.3 · Tier IV
Run the subtractive test on the governing decision and it holds. The plaza is the shape of the ridge: its long axis, its width and its closure by the two great platforms are what the hill allows and what the assembly of a capital asks. Outcrops of bedrock were kept as the cores of the central buildings, so the spine stands where the rock stood. The platforms with their broad stairs are the stage the plaza requires, and the temple, patio and altar groups give each side a repeated unit of rite. What holds the score at the foot of the twelve is accretion: some twelve centuries of building over building, groups of uncertain use on the east side, and a fill that is the sum of many campaigns. Several structures could go without loss to the whole.
Michael Mann · Film
8.3 · Tier IV
The spine resists subtraction: two crews, a thief’s and a cop’s, each shown at work and at home, set on a course that one meeting declares and one runway closes. The parallel exposition is required, since the film’s argument is the symmetry, and the length is the argument’s. Most strands pay. Breedan’s job at a diner, under a boss who skims his wages, delivers him to the bank as driver and to his death; Van Zant’s double cross keeps McCauley in the city; Charlene’s signal on the balcony is the one mercy that breaks the code. What gives: Waingro’s killings of prostitutes are convenient rather than compelled, Lauren’s attempt at suicide works as a device, and the set quarrels in the Hanna household run long.
Milan Kundera · Literature
8.3 · Tier IV
The subtractive test is hardest to put to a novel that is half essay, and it mostly fails to find a cut. The structure is a set of variations: Tereza’s arrival at Tomas’s flat, with a book under her arm, is told from his side and then from hers, and each telling adds what the other could not know. The dictionary of misunderstood words is required, since it is the whole account of why Franz and Sabina cannot love each other. The sixth part, which tells us that Tomas and Tereza are dead before the seventh shows them alive, is required by the book’s argument about weight. Where the test bites: Sabina’s later life in America, Franz’s Grand March and several essay passages restate a point the action has already made, so that perhaps a tenth of the book is permitted rather than compelled.
Christopher Wren, with Hawksmoor and Vanbrugh · Architecture
8.3 · Tier IV
Judged on purpose, structure and site. The governing decision is compelled twice over: Webb’s block already stood on the river, and the Queen’s House had to be kept in view, so the hospital could not close its axis and had to split into two halves, each answered by its twin. Given that, the domes are required where they stand, marking the hall and the chapel, the two communal acts of the house, at the head of the colonnades that carry the eye to the Queen’s House. What resists the subtractive test is the scale of magnificence over the purpose: a hospital for old sailors needed wards, a refectory and a chapel, not a palace front, long colonnades and a second dome given to symmetry. The defence is that display was the foundation’s purpose.
Ancient Egyptian, under Amenhotep III and Ramesses II · Architecture
8.3 · Tier IV
Judged on purpose, structure and site. The purpose is the Opet festival: the barque of Amun travels from Karnak to this southern house, and the king, entering with him, renews his royal ka. Almost every part of Amenhotep III’s temple answers it. The colonnade is a corridor for a carried boat; the sun court is the place of public appearance; the hypostyle and vestibules narrow, darken and lower toward the sanctuary where the barque rests; the birth room says why the king belongs there. The subtractive test bites less at the front. The Ramesside court is a second forecourt added to a temple that already had one, and its bend is accommodation, not compulsion. Purposeful in its core, adjusted at its front.
Built for King Kashyapa I · Architecture
8.3 · Tier IV
Judged on purpose, structure and site. The site compels the design: a sheer rock on a flat plain dictates an ascent, a summit that is refuge and seat, and a plan that must manage water. The parts answer it. The moats are defence and reservoir at once; the water garden lies on axis with the rock so that the approach is framed; the boulder gardens take the natural rocks as their pavilions instead of clearing them; the gallery clings where the face allows; the cistern makes the refuge habitable. What holds the axis here is the ruin: the summit superstructure, the lion’s body and much of the terraces are known only in footings, and the subtractive test cannot be put to parts that are gone.
Robert Smythson (attributed), for Bess of Hardwick · Architecture
8.3 · Tier IV
Judged on plan, section and structure under purpose and site. Much is compelled. The three storeys are the three ranks of the household, and the ceilings rise as rank rises. The towers are rooms, closets and stair heads, not turrets, and they let a block without a courtyard hold more apartments. The glass in the outer walls requires the flues in the inner ones. The hill gives the house its visibility, and visibility was its purpose. What resists the subtractive test: the symmetry is held at a cost, with windows on the fronts that answer no room behind them or meet a floor halfway; the banqueting rooms on the leads are pleasure, not need; and the glass exceeds the light it is needed for. Display was the purpose, and that defence carries part of the way.
Mark Rothko · Visual art
8.3 · Tier IV
Judged on the cycle and, where it can be judged, on the room. The motif is necessary on every canvas: the dark field, the open rectangle within it, the edge that dissolves rather than closes. Take away the rectangle and a canvas is a ground; take away the ground and the rectangle has nothing to open in. The nine at Tate pass the subtractive test at the scale of a room: the canvases face one another, the eye moves from one portal to the next, and the enclosure needs its walls. What yields is the number. The cycle is a run of variations for a room that was never hung, and no final choice of its canvases was ever shown. Any one canvas could leave the Tate room and the cycle would still say what it says. The scale is compelled; the count is permitted. Below The Rothko Chapel (9.0), where every canvas has its wall.
John Updike · Literature
8.3 · Tier IV
The test is subtractive, and the spine passes it: the rhythm of the action is the book’s argument, flight, return, flight, return, flight. The night drive south must stay, since it shows that the running has no destination; Ruth must stay, as the life he runs to; Eccles and Kruppenbach must both stay, since the moral question is posed between them; the drowning must stay, and must be told from Janice’s side. What the test finds is a surplus of rendering. The golf lessons with Eccles run long, the weeks at Ruth’s apartment repeat their texture, Mrs Smith’s garden is visited more than once to say one thing, and the sensory description, Updike’s gift, at moments goes on past the point where it adds knowledge. Perhaps a tenth to an eighth of the book is permitted rather than compelled, and that holds the axis near the foot of the twelve.
Mon and Burmese builders · Architecture
8.3 · Tier IV
The stupa resists the subtractive test almost wholly. Its purpose is to enshrine a relic and to be circled, so it is solid, and every stage of its profile is a stage of one ascent from a square base to a point. Remove the plinth and terraces and the bell has nothing to rise from; remove the octagon and the square cannot become round; remove the bud and the hti and the figure has no end. The hill and the four stairways are required too. What yields is the platform: shrines, pavilions, bells and image houses accumulated by donation, many interchangeable, much of it removable without loss. The stupa compels; the terrace permits.
Filippo Brunelleschi · Architecture
8.2 · Tier IV
The loggia passes the subtractive test better than most fronts. Each bay is a measured unit, and the columns, arches and small domes are what the unit is made of; take one bay away and the measure is not shortened but broken, because the nine bays read as a count of equal things. The steps are required: they lift the loggia off the square and make it a threshold. The domes are required by the square bays, and the ties by the slender columns. What yields: the loggia is a screen in front of the hospital more than its consequence, and the front does not tell what lies behind it. The pedimented windows are a decorum the upper storey could do without, and the tondi, later and loved, are additive.
Michelozzo · Architecture
8.2 · Tier IV
Much is compelled. The rustication graded from rough to smooth is required by what the front must say: weight and defence at the street, refinement where the family lives, ease above. The cornice is proportioned to the whole front because it crowns a single block, not a stack of floors, The courtyard is required by the type: light and air to a deep block on a crowded street, and a centre the closed front could not give. What yields: the corner loggia, a required part, is walled; the Riccardi bays add nothing the elevation needed; and at the courtyard corners parts are placed by the module rather than compelled by it.
Wifredo Lam · Visual art
8.2 · Tier IV
Judged figure by figure and stalk by stalk. The four figures cannot go: they are the frieze, and the picture’s claim is that the field is peopled, so that each body taken out would leave the cane merely cane. The scissors cannot go: they are the one made thing, the one sign of cutting and of labour in a field of growth. The verticals cannot go: they make the figures stalks and the stalks figures. What yields is the density. The leaves and lesser stalks in the margins and the lower band could be moved or lost with small effect, and the four bodies share a vocabulary so closely that one of the middle pair could go and the frieze would close up.
Anselm Kiefer · Visual art
8.2 · Tier IV
The subtractive test on a single image. The path cannot go: it is the work’s one line of force, and it places the viewer. The trunks cannot go: they are the forest and the frame of the path. The snow cannot go, for without it the blood has nothing to stain. The red cannot go: it is the only thing in the picture that happened, and it lies on the ground, below the names. The names cannot go: without them the canvas is a winter wood in the manner of Friedrich; with them it is a history. What yields is the roster itself. A list is the one form in painting assembled by nature, and a network of names invites the question which could be dropped or added without loss; the joining lines read more as diagram than as necessity.
H. H. Richardson · Architecture
8.2 · Tier IV
Run the subtractive test, and it bears hardest at the centre. The tower cannot go: it is the room as well as the sign, the crossing opening upward into it, so that the congregation sits under the one volume the square sees from outside. The short arms follow from that decision, since a long nave would lose the preacher, and preaching was the parish’s reason for the plan. The weight of the granite is compelled by the image of a rock and paid for in the piles below. What could go lies at the edges: the porch of the 1890s, which ornaments an entrance Richardson left plain; some of the windows; the chancel of 1938; and some scale, permitted rather than compelled, in a church of a cathedral’s presence built for one parish.
Shona builders · Architecture
8.2 · Tier IV
Judged on structure, purpose and site. On the hill the subtractive test is passed well: the walls run between boulders and close the gaps the rock leaves, so the line of every wall is compelled by the hill, and nothing is laid out against the ground. The batter is compelled by dry stone, since a wall without mortar raised that high must lean in and thin as it rises. In the valley the purpose is separation, not defence: there are no parapets, walkways or defended gates. What resists the test is the second wall that makes the passage, the chevron band and the tower, required by meaning rather than use; and a wall of half the height would screen as well.
Jane Campion · Film
8.2 · Tier IV
Judged on structure, and the spine resists the subtractive test. The piano left on the beach is the cause of everything, since Stewart will not carry it and Baines will. The trade of the piano for eighty acres makes Ada’s voice a piece of property; the bargain of one black key per visit turns the lessons into a ledger that counts down; the key inscribed for Baines and carried by Flora to Stewart is the hinge; the axe answers the key, a finger for a key. The Bluebeard pageant is required. Counted in full, the give is real: Aunt Morag and Nessie repeat the settlement’s gossip more than they advance anything, Stewart’s hearing Ada’s voice and releasing her is a convenience the plot needs, and the Nelson coda, after the sea has settled the drama, is permitted rather than compelled.
Richard Linklater · Film
8.2 · Tier IV
Run the subtractive test and the frame holds. The coach’s pledge, held over Pink from the first scenes to the field at dawn, gives the night its question; the paddling gives Mitch’s night its threshold, and his return home at dawn its close. These two arcs, a senior who will not be bound and a freshman admitted, are the spine, and they cross at the Emporium, so that each needs the other. The looseness around them is the film’s argument, that nothing in such a night is required, and it is kept with discipline. What holds the axis: the mailbox baseball, Pickford’s cancelled party, the paint on O’Bannion and Mike’s fight with Clint could each be swapped for another episode of the same kind.
Norwegian builders · Architecture
8.2 · Tier IV
Judged on purpose, structure and site, the frame is compelled almost member by member. Sills keep the posts off the ground; staves carry the roof; planks stand in the grooves of sills and plates; the raised central room lifts the roof on posts so that a small nave stands tall; the steep roofs shed the western rain. Little in the carcass could go without loss. The subtractive test bites twice. The north portal was not required by the building of about 1130: its builders could have made a plain door, and the work is richer for their choice but was not compelled to it. And the later changes, the lengthened chancel, the cut windows and the box pews, answer to a later liturgy rather than to the frame. A small building whose parts are mostly required, its most famous part kept by decision.
Bruce Springsteen · Music
8.2 · Tier IV
Twelve tracks of under five minutes, and the subtractive test finds most of them carrying an office. The title track must open: its riff and verses are the record’s whole argument. My Hometown must close, the one quiet song, where the argument is spoken plainly. Downbound Train, I’m on Fire and Glory Days are each required: a man losing job, girl and house in order; desire as illness; the past as the only wealth left. Bobby Jean and No Surrender carry the friendship. Working on the Highway and Darlington County, two jaunty songs ending in a chain gang and a handcuffed friend, partly repeat each other, and Cover Me and I’m Goin’ Down restate the bright mode without turning it.
Almohad builders, under Abd al-Mu'min and Yaqub al-Mansur · Architecture
8.2 · Tier IV
Judged on purpose, structure and site, and the minaret passes the subtractive test closely. The ramp is the access that the call to prayer and the building of a tower of some 69 m both required; the stacked rooms at the core are what the ramp winds round and what stiffens the shaft; the openings grow larger and the ornament richer as the tower rises, where weight can be spared and the eye needs scale. The hall passes less well, and the reason is its type: a hypostyle is additive, and an aisle more or less changes its size, not what it is. What resists subtraction there is the hierarchy, the wide central aisle and the transept that gather the rows to the mihrab, and the court that opens the whole to the sky. Beside it lies a whole mosque begun and given up, the record of a building not compelled at its first try.
Johann Wolfgang von Goethe · Literature
8.2 · Tier IV
The cycle has a spine, and the frame passes the subtractive test. The first elegy finds Rome mute until love opens it; the elegy of study by day and love by night joins the two halves of the argument; the elegy of the north sets the grey day against Roman light; the private bond deepens into something like a marriage under the gods; and the last poem admits that the secret will out. Remove the first elegy or the elegy of study and love and the book loses its argument. But a cycle of elegies is additive by nature, and the test bites in the middle: the allegorical pieces, Fama and Amor as rivals, Amor as the quarrelsome house guest, could go with little loss, and several middle elegies could change places without the book knowing anything different. Goethe’s own withholding of four poems shows that the set could shed members. Necessity sits in the frame and in perhaps half the poems, not in all twenty.
Basil Spence · Architecture
8.2 · Tier IV
Judged on purpose, structure and site. The governing decision resists the subtractive test absolutely. Remove the ruin and the new church is a competent modern nave; remove the new church and the ruin is a memorial without a congregation. The right angle, the porch and the glass screen are each required to make the pair one place, and the screen above all cannot be taken out without the building losing its argument. The sawtooth walls are compelled by the decision that the windows face the altar. What yields: the nave is a received longitudinal volume, its scale permitted by the brief more than compelled; the chapels are added pods, the Chapel of Unity an annex to a programme; the flèche is ornament; and much of the interior is an armature for art the unit sets aside.
John Ford · Film
8.2 · Tier IV
Judged on structure, and a road is the hardest form to make necessary: stations can be added or taken away. Ford keeps most of them earning their place. Muley’s flashback is required, because it shows dispossession as weather with a contract behind it; Grampa’s death is required, because the old man cannot be separated from the land; Granma’s death across the desert, kept back by Ma until they arrive, is required. What could go without loss: some of the filling-station business, the comic grace of the camp’s committee men, part of the dance, and the closing speech in the truck, which says in words what Ma’s face and Tom’s walk up the rise have shown. The order that sets the camp last, after the killing, makes the end feel arranged rather than compelled.
Rainer Werner Fassbinder · Film
8.2 · Tier IV
The subtractive test holds on the main line. The wedding in the bombing gives the marriage its paper and its single night; the placard at the station makes the waiting public; the bar and Bill give Maria her first exchange of body for survival; the killing of Bill puts Hermann in prison, so the marriage is deferred by law; the contract between the two men makes the deferral a transaction; the will discloses it; the gas ends it. Each step requires the next. What gives is in the margins. The mother’s courtship by Wetzel and the marriage of Betti and Willi are mirrors the film could lose at some cost; the office scenes repeat one point; the drunk on the train is a set piece rather than a joint.
Mimar Sinan · Architecture
8.2 · Tier IV
Run the subtractive test on the architecture first, and it holds. The platform over shops is compelled by the site: on a narrow, valuable plot in the city’s busiest market a mosque at street level would have been swallowed, and a mosque without rents would have lacked endowment. The stair, the terrace standing in for the court there was no room for, and the double portico answer the same constraint. The octagon gives a centred room with no superfluous member. The tiles are the question. They are in the unit and they are the building’s character, but a hostile eye can remove a good share of them, the repetition of panel types and the portico façade, and lose emphasis rather than meaning.
Pierre Peysson and Jean de Louvres, under Benedict XII and Clement VI · Architecture
8.2 · Tier IV
The purpose is of unusual complexity: a sovereign court, a curia, a treasury, a liturgy, a household and a garrison on one rock. The subtractive test bites in places. The Palais Vieux is a cloister turned inward and armed, every wing assigned, consistory, Tinel, chapel, guests and treasury tower, and little could go without loss. The Palais Neuf answers what the old palace lacked: an audience hall for the courts of the Rota, a chapel for the papal liturgy in state, a stair and a window for blessing crowds. What holds the score: two palaces placed side by side and fitted at the seam, towers added as needs arose, a plan that is a sum of campaigns.
Renzo Piano · Architecture
8.2 · Tier IV
Judged on purpose, structure and site. Much is compelled. The shells’ curved backs and their slatted double skin are the ventilating device: take them away and the rooms need machines in a hot, humid, windy climate. The scatter of cases along a ridge, in villages, follows from the site and from the programme’s model of the Kanak settlement, the great house and its lesser huts along an allée. The low range is set into the slope so that the shells read from the lagoon as standing on the land. What yields: the upper part of each tall shell holds no room, its height image and draught together; the low range could be another building without loss of idea; and the number of cases and their three heights are a programme’s choice.
Paolo Uccello · Visual art
8.2 · Tier IV
Subtract piece by piece. The fallen soldier in the London panel, laid with his head toward the vanishing point along a line of recession, cannot go: he is the battle and the system at once, a death drawn as a demonstration. The broken lances strewn on the ground are the floor grid made of war; remove them and the space loses its measure. The rearing and falling horses, the raised lances that close the upper field like a fence, the commander’s red and gold headdress at the centre: each holds a station. What yields is the edge. The hills behind, with their hares, hounds and small running figures, are permitted more than compelled; the hedges are as much a tapestry convention as a necessity; and the Louvre panel restates the London panel’s means. Necessary at the core, assembled at the margins.
Gustav Klimt · Visual art
8.2 · Tier IV
Judged wall by wall. The three fields cannot go: the frieze is a passage from longing through trial to fulfilment, and each wall is one term. The knight cannot go, since the suppliants’ appeal needs someone to receive it; the end wall cannot go, since it is the whole resistance; the embrace cannot go, since it is the answer. The bare spans hold too, as the intervals of the walk, without which the frieze would be a row of tableaux. The test gives in the repeated parts: the genii run on longer than the argument needs, the second wall’s poetry, arts and choir say nearly one thing in three steps, and the allegories above the Gorgons are a list more than a structure.
Teutonic Order builders · Architecture
8.2 · Tier IV
The castle serves three purposes at once, convent, seat of a state and fortress, and the subtractive test runs differently in each part. The High Castle resists it best: the closed square is the cloister of a religious house and a keep in one, each wing a necessity of the rule (church, chapter, dormitory, refectory), its walls the convent’s enclosure and its defence together, the dansker thrown out because latrine and last tower had to stand over water. The three baileys follow from a growing state. What could be otherwise lies in the Lower Castle, service buildings required in kind but not in this order, and in the Grand Masters’ Palace, where display outruns the fortress.
William Hogarth · Visual art
8.2 · Tier IV
Judged on the eight as a chain. Each fall is required. Remove the arrest and the rescue that ties Sarah Young to him goes, and with it the meaning of the marriage, where she stands at the back of the church with his child while he marries money. Remove the gaming house and the second fortune is never lost; remove the Fleet and Bedlam arrives without its cause. The first scene is required by the whole: the hoard that makes him. What yields is the middle of the first half. The levee and the tavern are both scenes of spending and display, and the series would lose colour more than logic without one of them. Within scenes much is permitted rather than compelled: the chain is compelled, its density partly accumulation.
Gerrit Rietveld · Architecture
8.2 · Tier IV
Judged on plan, section and structure, under purpose and site. The upper floor passes the subtractive test as well as any house of its decade. Take away the partitions and a family of four sleeps in one room, or the day loses its open floor; take away the central stair and its rooflight and the floor has no centre to divide round; take away the corner window and the room loses the act by which it opens to the air. The fittings are compelled by small rooms and a household without servants. What resists the test is much of what gives the house its look: planes run past where any use needs them, slabs and painted members sit where the composition asks for them, and brick walls are dressed as freestanding planes they are not.
Victor Horta · Architecture
8.2 · Tier IV
The plan is compelled by the plot. A Brussels row house was conventionally three rooms in an enfilade from street to garden, the middle one dark. Horta cut the house in two and set the stair and a top-lit well between the halves: the dark room is removed and replaced by the source of light. The half levels follow from the cut, since front and rear blocks need not share floor heights, and the stair becomes the spine every room hangs from. The vestibule column is there because the open vestibule needs a support that does not wall it. What resists the test is the ornament: the painted tendrils and the density of curling line in mosaic and glass could be thinner without loss to plan or use.
Peter Behrens · Architecture
8.1 · Tier IV
The subtractive test splits the building in two. The long side passes it almost entirely: the span is set by the turbines and the crane, the bay by the frame, the leaning glass by the need for daylight on the shop floor, the pin bearings by the hinged arch. Nothing there is idle. The gable fails it on engineering terms and passes it on another. The battered concrete corners bear nothing the steel does not already carry, and could go with no loss to the hall’s working; what they carry is the claim that a turbine hall is a monument. Since that claim was part of the purpose, they are compelled by it, but the necessity is rhetorical, not structural, and that holds the axis at 8.0.
Shreve, Lamb and Harmon · Architecture
8.1 · Tier IV
Judged on purpose, structure and site. The building is unusually compelled. Its purpose was rent at the greatest height a fixed lot, a fixed budget and a fixed date would bear, and the massing follows: the zoning resolution of 1916 sets the base and the first setback, and the tower rises over the quarter of the lot that the law freed from limit. Ornament is almost nil; the flush cladding with its metal strips exists to let stone be set fast without fine fitting. Subtract the lobby relief and the few chevrons at the setbacks and nothing of use is lost, but little was there to subtract. What fails the test is the top: the mooring mast was a pretext for height, a dock no airship could use, its 200 feet bought for the record.
Sawai Jai Singh II · Architecture
8.1 · Tier IV
Judged on each instrument and on the ground. Within the instrument almost nothing yields. The Samrat’s gnomon must lie at the latitude, parallel to the earth’s axis; its quadrants must be arcs of the circle the shadow traces; its size is the size its precision requires. The Jai Prakash bowls must be two, because each leaves out the strips in which the observer walks and the other supplies them; the Ram Yantra’s cylinders are paired for the same reason. Form is set by the sky and the latitude, not chosen. What holds the axis is the ground. It is a collection, instruments side by side as a laboratory’s furniture stands: the twelve zodiac dials measure in another frame what one Samrat already measures, there are large and small versions of one type, and several could go without loss to the whole.
Maya, under Jasaw Chan K'awiil I · Architecture
8.1 · Tier IV
Judged on purpose, structure and site. The purpose is to raise a dead king’s shrine over his body to a height seen from the whole plaza and above the forest, and nearly everything obeys it. The tomb at the base is the reason for the mass; the solid terraces are the mountain the shrine needs to stand on; the steepness makes height out of a modest footprint; the one stair is the one way up. The temple is as small as the corbel vault allows, since the rite was for few and seen by many. What resists the subtractive test: the bulk is fill, its terraces ordered more by meaning than by load, and the roof comb is height and image added to a temple that would stand without it, though height and image were the purpose.
Geoffrey Bawa · Architecture
8.1 · Tier IV
Judged on plan, section and roof, under purpose and site. Much is compelled. The roof is the climate’s answer: steep pitches and long eaves for monsoon rain, shade for the verandahs, the two tiers letting hot air out. The cluster is compelled by the programme’s hierarchy: one chamber, then committee rooms, offices, dining and the members’ spaces, each a pavilion scaled to its standing. What resists the test: the water is compelled by a decision, not by the land, for the marsh was flooded to make the island, so the setting that most necessitates the form was itself designed. The chamber is sealed and cooled, so the verandah logic stops at the house’s own centre. A pavilion or two could go without loss of the idea.
John Everett Millais · Visual art
8.1 · Tier IV
Judged on the configuration. The figure laid along the long axis cannot go: she is the line of the stream and of the picture. The willow cannot go: it is the first thing Gertrude names, it is the only thing that leans toward her, and it carries the robin. The open hands and the face above the water cannot go; without them this is a body, not a woman singing. The bank cannot go as a mass, because its equal finish is the argument. Below that the subtractive test bites. The flowers are an inventory more than a structure: take the pansies or the poppy from the water and the picture loses a sign, not a support. The architecture is necessary; the population of the bank is permitted.
Thai builders, under Rama II and Rama III · Architecture
8.1 · Tier IV
Judged on structure, purpose and site. The prang is a solid monument, not a room, so its necessity is that of a figure of the cosmos made solid, and most of its parts are compelled by that figure. The tiers are the heavens of Meru stacked toward the pinnacle; the steep stairs are the ascent; the demons and monkeys carry the levels as bearers carry a world; the four corner prangs are the quarters, each with its god, and the centre cannot make its claim without them. The site compels too: the tower answers the palace across the river and is placed to be seen from the water. What yields under the subtractive test is the density of the surface: the count of porcelain flowers is permitted, not required.
Burial · Music
8.1 · Tier IV
Thirteen tracks in about fifty minutes, and the subtractive test splits. The short pieces where the beat falls away look removable and mostly are not: they are the spaces between the rhythms, the street between two clubs, and the record’s argument needs the beat to fall away as often as it does. Archangel must come early, as the clearest statement; Untrue must stand at the centre; Raver must close, the rave remembered at last at its own tempo. The test bites in the beat tracks. Near Dark, Ghost Hardware, Shell of Light and Homeless share one tempo, one swung pattern and one palette, and one of them could go with little lost; which one is hard to say, and that is the finding.
Eero Saarinen · Architecture
8.1 · Tier IV
The section is compelled. The roof hangs; a hanging roof pulls its supports inward; so the piers lean outward, thick at the base and swelling toward the cable anchorage, and the landside row stands higher than the airside so that the hall lifts toward the arriving road and drops toward the field. Nothing in the cross section is idle. The plan is compelled by an operating idea: if vehicles carry passengers to the aircraft, the terminal need not reach them, and one compact hall can serve the field. The subtractive test bites on the length. A modular hall can lose or gain bays without loss of sense, and the extension of the 1990s proves it: the length is permitted by the module, not required by an argument.
Anselm Kiefer · Visual art
8.1 · Tier IV
The subtractive test, part by part. Take away the pyramid and the fragments have no centre and the wires no apex to climb to; the tomb in which the god is restored is gone. Take away the wires and the shards are debris: the scattering remains, but the gathering, the act the myth turns on, disappears. Take away the circuit board and the wires converge on nothing, and the modern term of the analogy is lost. Take away the shards and there is no dismembered body. Four parts, each required, and the work is built of little else. What yields is the field around them: the burnt crust is a manner shared with many canvases of these years, and a few shards more or fewer would change nothing.
Peder Vilhelm Jensen-Klint; completed by Kaare Klint · Architecture
8.1 · Tier IV
Run the subtractive test and there is almost nothing to take away: no plaster, no painted programme, no carved capitals, no cycle of glass. What stands is wall, pier, vault and light, all of one brick, each element answering to the one material and the one section. The scale is compelled by the idea: a memorial to the poet of the Danish congregation had to be a hall that holds the singing congregation, and its front had to be seen over a suburb not yet built. The charge falls on the west front. Necessary as a sign, it is wider and taller than the nave behind it needs, and at moments reads as a screen set before the building rather than its end.
Richard Serra · Visual art
8.1 · Tier IV
Judged twice, on each sculpture and on the room. Each sculpture passes the subtractive test almost absolutely: a torqued ellipse is one or two plates, and nothing can be taken from it; the lean, the gap of the entry and the curvature are all there is. The room is weaker. The sequence has a stated logic, simple to complex, closed to open, from the single ellipse through the double and the spirals to the sections of torus and sphere, with Snake giving the walk its long run. But three torqued spirals stand in one room, and removing one would cost a variation, not a necessity; and Snake, made eight years earlier for another occasion, was absorbed rather than required. The scale is compelled by the body and permitted by the hall.
Antonio da Sangallo the Younger; Michelangelo; Giacomo della Porta · Architecture
8.1 · Tier IV
Judged on plan, structure, purpose and site. The courtyard resists the subtractive test: five bays a side, the orders stacked as the ancient theatres stacked them, every arcade carrying a gallery the rooms need for passage. The axis from portal to river is compelled by the site and by the ceremonial of arrival. The cornice is compelled by the front it crowns: without it thirteen equal bays of brick have no end, and Michelangelo sized it to the height, not to the storey. What yields is the scale. A cardinal’s house became a pope’s family seat, and the block grew because the family rose, not because use required it; the size is permitted by fortune more than compelled by purpose.
Massive Attack · Music
8.1 · Tier IV
Nine tracks in about forty-five minutes, and the subtractive test finds a core it cannot touch and a margin it can. Safe from Harm must open: it sets the law at once, a slow breakbeat under a borrowed jazz bassline, a woman’s voice of warning and a man’s half-spoken verse sharing one track. Unfinished Sympathy must stand at the centre as the height, and Hymn of the Big Wheel must close, turning the city’s watchfulness out onto the world. Blue Lines is required as the crew’s plain statement. The test bites in three places: Be Thankful for What You’ve Got restates the soul inheritance without turning it, Lately adds little to Daydreaming in the same mode, and Five Man Army runs long for what it does.
DJ Shadow · Music
8.1 · Tier IV
Sixty-three minutes and sixteen tracks, and the subtractive test finds a strong core and a soft margin. The four long pieces are required: Changeling and Stem/Long Stem are where the method becomes composition, and Blue Sky Revisit is the needed descent before the end. Midnight in a Perfect World is the record’s statement and could not go. The Transmissions are required as frame: without them the album is a run of tracks, with them a broadcast received in sleep. The test bites at the margin. Untitled and Organ Donor are sketches; Why Hip Hop Sucks in ’96 makes its point in a breath; The Number Song displays the craft more than it argues.
Sidney Lumet · Film
8.0 · Tier IV
Judged on structure and the screenplay’s economy, the spine is required at every joint. Beale’s announcement that he will kill himself on the air brings the ratings that hand the news division to Diana; the broadcast to the windows makes him a property; his exposure of the CCA deal brings him before Jensen; Jensen’s conversion makes him unwatchable; unwatchable and impossible to fire, he must be killed. The Mao Tse-tung Hour, set up as comedy, is the instrument already in place. What gives is the Schumacher thread. Louise’s one scene is compelled; the affair, at its length, is not: the weekend at the shore, the lovemaking narrated as programming and Max’s farewell speech make one point three times.
Built for Frederick II · Architecture
8.0 · Tier IV
Run the subtractive test on the geometry and almost nothing can go. Remove a tower and the octagon breaks; alter one room and the ring of eight breaks; court, body and towers are one figure taken three times. Nothing is assembled: the whole is deduced. But a building is judged on purpose as well as structure, and the purpose here is undocumented and the plan does not compel one. The ring of rooms without a corridor makes every passage a passage through rooms, and there is no service quarter. The parts are required by the figure more than by a life lived in them, and that holds the axis below buildings where geometry and use compel the same parts.
Steven Spielberg · Film
8.0 · Tier IV
The subtractive test meets resistance almost everywhere. The trail of Reese’s Pieces is how a frightened boy draws the creature into the house. The sympathetic link, set out at school and at home, is what later makes the creature’s dying Elliott’s dying. Halloween is required: a sheet is the only disguise under which E.T. can leave the house, and it carries the first flight. The scene in the garage, the brothers smelling their father’s shirt, is the one that names the wound the creature fills. What gives: the frog liberation intercut with the drunk creature at home makes one point with a set piece’s extravagance, and the Peter Pan reading to Gertie restates a figure the film already holds.
Richard Rogers · Architecture
8.0 · Tier IV
Judged on purpose, structure and site. The parts answer a stated argument: a market needs one great room that can grow; services wear out and change faster than structure; so the room is left whole and the services are put outside, where they can be reached and replaced. The towers answer the site, taking up the odd angles of a medieval plot so that the block within can be regular. Take away the atrium and the market has no room; take away the towers and the floors lose their freedom. What resists the test is the degree of expression: ducts, cranes, brackets and steel are shown at a size the argument permits rather than compels. Compelled in its plan, chosen in its rhetoric.
Pierre Bonnard · Visual art
8.0 · Tier IV
The subtractive test bites hardest on the three large things, and they hold. Take away the tub and there is no enclosure, nothing for the body to lie in or be held by; its long rim is the drawing that keeps the colour from dissolving entirely. Take away the tiled surround and the picture loses the field against which the body goes pale and quiet: the walls and floor carry the heat, and that inversion is the picture’s point. Take away the steep viewpoint and the body would be seen, not looked down upon. Below that the test gives. The tiles are a lattice of touches, any patch of which could be otherwise without loss, and the width of the surround at the edges is permitted rather than compelled.
Fernando Meirelles and Kátia Lund · Film
8.0 · Tier IV
The subtractive test bites at the edges and not at the centre. The chain of deaths is tight, and each is paid for by an earlier one: Marreco killed by the boy Dadinho; the motel robbery told first without its killer and later with him; Zé’s rape of Mané’s girlfriend, which turns a bus conductor into a soldier; the boy Otto, whose father Mané killed in a bank robbery, killing Mané; the Runts killing Zé. What gives is the novel’s sprawl, kept in. The history of one apartment passing through many hands is a set piece the argument does not require; Rocket’s sexual comedy and his job at the newspaper run longer than the frame they carry; several middle killings repeat a point already made.
The Walkmen · Music
8.0 · Tier IV
The required parts are many, and they carry the record’s turn. Dónde Está la Playa has to open: a late night out in a drunk’s swing, the party known to be ending. In the New Year is required as the one burst of hope, the turn of the calendar sung as a vow. Red Moon is required as the hush at the centre, and On the Water carries the image the record keeps returning to. The long run of slow songs that follows is the settling the record is about, and its length is part of what it says. What holds the figure is plain: several of those songs share one mode, and one or two could go with little loss.
Robert Rauschenberg · Visual art
8.0 · Tier IV
The subtractive test is unusually well documented, because the work was found by subtraction over four years. In the first state the goat stood on a shelf against a hung painting; in the second, before a tall canvas; both left goat and painting as two things side by side. The third state took the wall away, laid the painting down as the ground, and added the tyre. The core now resists removal: without the tyre the goat is a trophy on a plinth; without the goat the tyre is refuse on a painting; without the platform the pair is a sculpture with no claim on painting. What gives is the platform’s collage, whose scraps could be other scraps, and the daubed face reads as an added gesture.
Wassily Kandinsky · Visual art
8.0 · Tier IV
The subtractive test, form by form. Take away the haloed black circle and the canvas loses its centre of gravity: the scattered sharp forms at the lower right have nothing to be set against, and the field drifts right with no pole. Take away the fan of crossing lines at the lower right and the opposite pole goes, the place where the field is most acute and most dense. The two masses, the open ground between them and the diagonal tension across it are required. What yields is the middle order: several small circles in the upper cluster, a number of thin lines and some small triangles could be moved or removed and the balance would hold. The density is chosen, not compelled one by one, and the method is accumulation balanced rather than Mondrian’s stricter reduction.
Byzantine, under Archbishop Ursicinus · Architecture
8.0 · Tier IV
Judged on purpose, structure and site, the basilica is spare to the bone. The nave is as long as procession to the altar needs; the aisles are a passage and a place to stand; the arcade carries the clerestory and nothing more; the timber roof is the lightest cover for the span; the windows are as large as the walls allow, because a church of mosaic needs light. The plan thickens in one place, the apse, and it thickens for the altar, the bishop’s throne and the saint’s grave beneath. Nothing is idle. What holds the axis: the necessity is the type’s more than this building’s, and the apse is required as picture as much as structure. The campanile is a later need, met beside the church rather than within it.
Tokugawa builders · Architecture
8.0 · Tier IV
Judged on plan, purpose and site, and the purpose was the staging of rank. Run the subtractive test. Take away the Tōzamurai and no visitor is held under painted tigers before he is admitted; take away the Shikidai and the exchange of gifts and messages has no place; the Ōhiroma, with its raised floor, is where the hierarchy becomes visible and cannot go; the Kuroshoin and Shiroshoin, smaller, darker, more private, are the inner steps of the same graded access. The echelon plan follows from the sequence. What resists: ramparts and moats in a pacified capital, display as much as defence, and room after room of gold where fewer would carry the argument.
Decimus Burton and Richard Turner · Architecture
8.0 · Tier IV
Judged on purpose, structure and site, almost every part is compelled. The purpose is to let light and warmth reach tall tropical palms through an English winter. The curve of the roof meets the low sun more squarely and sheds water and condensation; the central block is tall because the palms are, and the wings are lower because the plants they house are; the iron is thin because every member casts a shadow. The gallery puts the visitor among the crowns. The chimney sent away to the campanile keeps the profile clean and the smoke off the glass. What resists the subtractive test is small: the cast-iron ornament of stairs and gallery brackets, and a symmetry the plants did not require. The programme is single, and that holds the axis where it is.
Talk Talk · Music
8.0 · Tier IV
Eight tracks in about forty-five minutes, and most pass the subtractive test. Happiness Is Easy must open: its children’s choir and slow, patient groove set the record’s question, innocence handed down and found wanting. April 5th is the stillest piece on side one and its hinge, a spring morning held in near-silence; without it the side would be three songs. Living in Another World is the record’s centre of force, and Time It’s Time its compelled end. Chameleon Day looks removable and is not: almost nothing, a voice and sparse keyboard, it clears the air so that the close can begin from silence. The test bites at I Don’t Believe in You and Give It Up, well made and nearer the band’s earlier song form.
David Cronenberg · Film
7.9 · Tier III
A lean chamber film, and for most of its length it resists the subtractive test. The stocking through the pod, the baboon turned inside out, the steak that tastes synthetic are steps in one argument: the machine cannot carry flesh until Brundle learns the flesh, and the learning dooms him. The fly is planted in one shot and paid off by the computer’s report; the sugar, the shed parts, the corrosive vomit are the disease’s grammar, each used again. Three passages give. The bar, the arm wrestle and Tawny restate a strength the gymnastics already showed; the maggot dream repeats a fear the clinic carries; Stathis is thin until the plot needs him. For a film of ninety-six minutes, that is a real share.
Paula Rego · Visual art
7.9 · Tier III
Judged group by group, the canvas resists subtraction. Remove the woman standing alone at the left and the dance becomes a festivity, not a ritual seen from outside by someone it has passed by. Remove the ring of three at the right and the picture loses its argument through time, girl to woman to old woman on one strand. Remove the couples and nothing is left for the lone woman and the ring to stand against. Remove the building on the rise and the moonlit sea and the night loses the hard ground that makes it an institution rather than a party. What yields lies within the groups: the second couple is the least legible passage, and the sand between groups is in places spacing more than pressure.
Louis Sullivan · Architecture
7.9 · Tier III
Judged on purpose, structure and site. The upper elevation is compelled almost wholly: a department store needed floor after floor of open sales space lit from the street before electric light could do it, and the steel frame let the wall become frame and glass and nothing else. The Chicago window, wide and shallow, is the most light the bay could take; the thin terra cotta reveal is the fireproofing of the frame made visible. The base is compelled less strictly: a store sells through its windows, and the ornament frames them. The corner cylinder answers the busiest crossing in the Loop and gives it its door. What resists the subtractive test: the cast iron could be half as dense and the store would sell as before, and the rounded corner is a choice, not a necessity.
Gordon Bunshaft (Skidmore, Owings and Merrill) · Architecture
7.9 · Tier III
Judged on purpose, structure and site. The parts are compelled, and the reduction is the argument. The slab is as thin as daylight across an office floor asks; it stands where the zoning let it rise straight; the lower block takes the services and the larger rooms the slab cannot hold and keeps the street wall at one storey; the open ground and the court are what lifting the block makes possible. Take away the lower block and the slab is a stick on a lot; fill the ground and the building’s gift is gone; give it setbacks and it is a tower of the 1930s. What resists the test: the roof terrace and the court are amenities a purpose permits rather than compels, and the floor area given up is a choice of image over rent, not a necessity of use.
Roman, under Augustus · Architecture
7.9 · Tier III
Judged on purpose, structure and site, and the type is among the most compelled of ancient building. The podium raises the god’s house above the forum and makes the stair the only approach. The porch is the place of the threshold, deep enough to be a room of its own. The cella is closed because the image lived in the dark. Little can be subtracted: take away the podium and the building loses its authority over the square; take away the depth of the porch and the frontal approach collapses into a façade. What yields is the wrap of half-columns on the cella, ordered rather than required, an argument of appearance. The necessity is the type’s, finely kept, not discovered here.
Norman Foster (Foster and Partners) · Architecture
7.9 · Tier III
Judged on purpose, structure and site, more of this tower passes the subtractive test than most towers do. There is no ornament to remove: the diagrid is the structure and the pattern, the dark spirals are the lightwells, the taper is the profile. The circular plan and the swelling-and-tapering section were argued from the site: a smaller footprint for the floor area, a plaza returned to the street, wind led round the tower instead of down it, less bulk seen from the lanes of the City. The argument is weaker than the form. The lightwells and the rotation were drawn for a ventilation scheme whose use is disputed; the curve was chosen first and justified by wind second; and curved floor plates fight the office fit-out.
Built for Tokugawa Iemitsu · Architecture
7.9 · Tier III
Run the subtractive test against site and purpose. The substructure cannot go: the hall stands on a slope that falls away to the Otowa ravine, and the grid of posts and tie-beams is what brings the worship hall level with the sanctuary. It is structure shown as structure, every member doing work, and the depth of the grid is set by the depth of the fall. The stage cannot go: it is where offerings of dance and music were made toward the Kannon, and where the pilgrim comes out into the view. The wings frame it. What yields is the hall itself, broad, deep and dark, of a type shared with many Kannon halls, some of its bays given to storage and votive display.
Floating Points, Pharoah Sanders and the London Symphony Orchestra · Music
7.9 · Tier III
The subtractive test meets an unusual design: one keyboard figure repeated almost the whole length, with everything else moving over it. The figure cannot be cut; it is the work’s ground and its promise kept. The string ascent of the sixth movement is compelled by the patience of the five before it, and the near-silent last minutes are compelled by that climax. The test bites in two places. Where a movement is a passage rather than a part, it could be folded into its neighbour without loss. And in the first half the saxophone’s phrases sometimes circle without adding. Stasis is the method and is not charged in itself; only where it ceases to build.
Andy Warhol · Visual art
7.8 · Tier III
Judged on the parts, which are thirty-two near-identical canvases. Inside each the subtractive test barely bites: a frontal can on a bare ground, nothing that could go without the can ceasing to be this can. Across the set it bites differently. Remove one canvas and no single meaning breaks; what breaks is completeness, since the work’s claim is to the full range, and the set was kept together in practice rather than sold singly. The names are the one thing that changes, and they are required: without them the set is one image repeated. What is charged is that the count is borrowed, set by a product line rather than compelled by an argument the painter built, and the painter’s single cans and many-can canvases show the idea surviving at other numbers.
Amrita Sher-Gil · Visual art
7.8 · Tier III
The subtractive test, figure by figure. The group is the subject: take away any one of the three and the picture becomes a pair, a conversation, which is what it refuses to be. Three bodies held close without exchange is the point; a pair would read as intimacy, a crowd as genre. The dark ground cannot be lightened without letting the figures out into a room, a place and a story, and its shallowness is the confinement. The tight crop is required for the same reason, and the modest scale is compelled by the intimacy the picture wants. What yields is in the lower half: the hands and the folds carry less than the faces and the masses of colour, and parts of the drapery are permitted rather than compelled.
Jeff Koons · Visual art
7.8 · Tier III
The test is subtractive, and the parts are few. Remove the seams and pinches and the steel forgets the toy: it becomes a stylised rabbit, a modernist animal, and the argument that air has been made permanent goes. Remove the mirror and it is a cast of a toy in grey metal, a souvenir of Oldenburg. Remove the blank face and the reflection has nowhere to put the viewer. Remove the carrot and the figure loses its one gesture, the thing that makes a toy a performer. Each part is required. What gives is the choice of toy, one source among several, as Koons’s own Inflatables show. Held at 8.0: the necessity is of a single idea, which the object fixes rather than compels.
James Cameron · Film
7.8 · Tier III
The subtractive test finds little idle, because nearly everything shown in the first hour is spent in the last. The power loader Ripley works on the Sulaco to prove herself to the marines is the weapon she fights the Queen with. The motion tracker, introduced as equipment, becomes the film’s clock of terror. Bishop’s knife trick sets up the distrust he must overcome; Newt’s doll’s head in the colony foretells her taking; Hicks showing Ripley the pulse rifle and its grenade launcher is paid in the hive. The long wait before any creature is seen is required. What gives holds the axis where it stands: the dropship’s crash is a device to strand them, Burke’s betrayal is signalled early and paid in one expected turn, and much of the marines’ banter repeats a single note.
Pierre Koenig · Architecture
7.8 · Tier III
Judged on structure, purpose and site. The subtractive test finds little idle. The L is set by the pad: one arm along the street edge, holding the bedrooms and closed for privacy, the other turned out to the drop for the view, and the pool placed in the angle, where the pad is widest and where its water doubles the city. The steel frame is compelled by what the house exists to give, glass from floor to roof with almost no column in the way, and by the site, where a light frame on few points could reach out over ground no masonry house could sit on. The closed street walls are as required as the open glass ones: they make the turn into the view the house’s one event. What holds the axis at 8.0 is that the purpose is narrow and the compulsion is chiefly of site and view, where Villa Savoye (8.6) argues every element as doctrine.
I. M. Pei · Architecture
7.8 · Tier III
Judged on site, purpose and structure, almost every line in the building is the site’s. The trapezoid is what L’Enfant’s diagonal left; the line that splits it into two triangles separates display from study without a corridor; the gallery triangle’s axis takes up the West Building’s axis, so the two buildings are one composition across Fourth Street, and the marble is the older building’s marble. Remove the triangle and the building loses its site; remove the court and the galleries lose their plan. What yields: the court is larger than circulation requires, much of its height monument rather than use; the tower rooms are compelled by the geometry more than by the art they show; and the bridges duplicate routes.
Minoan · Visual art
7.7 · Tier III
Judged figure by figure, nearly everything in the field resists subtraction. The bull is the event and the frame: its stretched body is the long axis of the panel and the ground on which the act happens. The vaulter cannot go, being the act and the picture’s height. The figure at the horns cannot go: the leap begins there, at the point of danger, and without it the vault has no origin. The figure behind, arms out, receives the landing and closes the arc. Three figures read as three moments of one act or as a team, and either way the number is compelled. What yields is the border, the palace’s ordinary frame, permitted rather than required; its ornament is generic, and the panel was one of a set.
P. G. Wodehouse · Literature
7.7 · Tier III
The subtractive test finds very little idle. The book is a farce of four interlocked troubles, and each is wired to the others: Gussie Fink-Nottle cannot propose to Madeline Bassett; Angela has broken with Tuppy Glossop over whether the thing that menaced her at Cannes was a shark or, in Tuppy’s view, a flatfish; Aunt Dahlia has lost money at baccarat and must wheedle a cheque for her paper out of Tom Travers; and Anatole, whose cooking keeps Tom sweet, gives notice when Bertie’s advice sends every plate back full. Remove any thread and the machine stops. The gin in Gussie’s orange juice is planted, doubled and paid off. Held below the top because the necessity is that of clockwork: the parts are required by the mechanism rather than by anything the work must say, and Bertie’s digressions, though they are the voice, are permitted rather than compelled.
Berthe Morisot · Visual art
7.6 · Tier III
The subtractive test finds very little to remove. The mother is the watcher and the picture’s one dark weight; without her the whites have nothing to stand against. The child is the object of the watch. The veil is the event: it both joins and separates them, and its diagonal is the composition. Her hand on the veil is the hinge, the one point where she touches what she watches, and it touches the curtain, not the child. The window curtain behind is the softest element: it echoes the gauze and admits the light, but it is permitted rather than compelled. The economy is real, and some of the necessity is owed to the narrowness of a picture of two figures and a hanging.
Ferdowsi · Literature
9.1 · Tier V
Length is not a cost; the question is whether the parts are required. The argument is the life of a kingship through time, glory given, abused and withdrawn, and it compels a chronicle that runs to the end: Yazdegerd’s death in the mill has its weight because the line has been carried from the first king. Slight reigns bear load: Fereydun’s division founds the feud the heroic age exhausts. What holds the axis at 7.9 is the matter a chronicle admits and its argument does not need: Daqiqi’s thousand couplets, which the poet himself judged weak; battles of the Turanian war that repeat their pattern; Alexander’s marvels; the testaments, sermons and letters of the Sasanian reigns. A sixth or more could go.
Giovanni Boccaccio · Literature
8.9 · Tier IV
The architecture is compelled: ten tellers, ten days, a hundred tales, answering the hundred cantos of the Commedia. The themes move from Fortune through industry, love lost and love won, the saving word and the trick to magnificence; the plague is required, since without it the garden means nothing; and without Dioneo’s licence the book loses its disorder inside order. What holds the axis lowest is the subtractive test applied tale by tale. The retorts of the sixth day are slight by design; the seventh and eighth days repeat the mechanism of cuckold and gull more often than the knowledge needs; several adventures of the second turn on the same wheel. Perhaps a sixth of the hundred is permitted rather than compelled: removed, such a tale costs the symmetry, not what the book knows.
Emily Dickinson · Literature
8.9 · Tier IV
Inside the great poem the subtractive test fails almost entirely. In “After great pain, a formal feeling comes” (J341) no line can go: three stanzas move from the nerves to the feet to “This is the Hour of Lead”, and the close, “the letting go”, holds the poem’s whole argument in its last words. “I heard a Fly buzz” (J465) is built so that its last line, “I could not see to see”, cancels all that came before it. But the unit is the body, and the body is a life’s output, never selected by its maker for a reader. Many of the 1,775 poems are slight: riddles of the bee and the clover, valentines, verses sent with flowers, a long run of late quatrains in the aphoristic manner. Many say again in a weaker stanza what a stronger one said, and many stand in variants she never chose between. The fascicles are a private gathering, not a sequence with an argument. That is what holds the axis lowest of the twelve: the necessity is in the poems, not in the body.
Anonymous · Literature
8.9 · Tier IV
Subtract and see. The spine is required: Kiyomori’s pride through Books 1 to 6, the flight of the Taira from the capital in Book 7, the battles of Books 9 and 11, the extinction of the line in Book 12, and the Initiates’ Book, which turns extinction into salvation. Take out Giō in Book 1 and the close at Ōhara loses its first statement; take out Shunkan on the shore of Kikai-ga-shima and Book 3 loses its measure of what Kiyomori’s anger costs. What holds the axis lowest of the twelve is accretion. The temple wars of Mount Hiei and Nara, Mongaku’s long penance at the waterfall in Book 5, the Chinese exempla set into the exile episodes, the court appointments and processions, and several captivities of Book 10 could go without the knowledge changing. Each was a recitation that stood on its own, and the composite shows it.
William Gaddis · Literature
8.8 · Tier IV
The test is subtractive, and it bites hardest in the second part. The spine is required: Camilla’s death at sea and the son raised by a Calvinist aunt; Wyatt’s turn from the ministry to painting; the forgeries made for Recktall Brown and authenticated by Basil Valentine; the flight to Spain and the search for the mother’s grave. Otto, who lifts Wyatt’s talk for a play, is required, since plagiarism is the forgery of the word; so is Mr. Pivner, the father Otto has never met, who carries the counterfeit into money and into the self-help of the age. What holds the axis lowest of the twelve is the bulk of the Greenwich Village parties. Their sameness is part of their argument, a society of copies talking past one another, but the argument is made long before they end. A tenth or more of the book is permitted rather than compelled.
Terrence Malick · Film
8.8 · Tier IV
The large parts pass the subtractive test. The creation is required: the epigraph is God’s answer to Job, and the creation is that answer staged, so without it the questions whispered to God have nothing to meet them. The death is required before the childhood, so that every scene of R.L. is watched as a scene of the dead. Inside the childhood the stations of the fall are required in order: the slip, the BB gun, the prayer under the car, the confession, the move. The give lies between them, and the version issued in 2018 shows it, adding matter of the same kind without changing the film’s shape. A fragment of the boys at play could be exchanged for another without loss, and adult Jack’s scenes are the clearest permitted matter. That holds the axis lowest; length is not charged.
D. H. Lawrence · Literature
8.7 · Tier IV
The spine is required. The two couples are an argument made by contrast, and neither can be cut: Gerald and Gudrun are the will carried into love and so to death, Birkin and Ursula the attempt at another way. The set pieces bear weight: the mare at the crossing is Gerald’s whole relation to life, shown before it is turned on Gudrun, and “The Industrial Magnate” shows the same will remaking the mines. What holds the axis lowest of the twelve is what the subtractive test removes: Birkin’s doctrine restated to Hermione, to Gerald and to Ursula with diminishing return; the satire of Breadalby and the London bohemia, which runs on after its point is made; and the same adjectives, “dark”, “mindless”, “potent”, pressed past use.
Percy Bysshe Shelley · Literature
8.7 · Tier IV
Act I is required in every part. The curse is recalled, not spoken anew, so that Prometheus hears his own hatred in the mouth of the Phantasm of Jupiter and can withdraw it. Remove the Furies and the revocation is untested; remove Mercury and tyranny has no servant. Act II is required as Asia’s descent to the source of power. What holds the axis at 7.9, the lowest of the twelve, is the later half. In Act III Ocean and Apollo talk over the fall and the Spirit of the Hour and the Earth describe a world remade: the poem tells rather than moves. Act IV, the crown of the work, is also its widest expanse; whole runs of the duet of the Earth and the Moon could be shortened without loss. The six consoling Spirits of Act I are more than the argument needs.
Friedrich Nietzsche · Literature
8.7 · Tier IV
The subtractive test splits the book. The essay parts pass it: the first takes apart the philosopher’s will to truth, and the free spirit, the religious nature and the natural history of morals are its consequences, each required by the one before; the ninth part’s question of rank is what the whole has been asking, and the poem answers it in another voice. What fails the test lies in the interlude and the eighth part. A good share of the hundred and twenty-three sayings could go without loss, the sallies on women and marriage above all, which repeat each other and the seventh part; and the sketches of the English, the French and the Germans carry much that is notice of the 1880s rather than argument. That removable tenth, in a mid-length book, is what holds the axis below eight.
Joseph Heller · Literature
8.6 · Tier IV
The lowest of the twelve. The book’s engine is a single logical figure, the self-sealing rule, and it is run again and again: in the catch itself, in the loyalty oath crusade, in Major Major, who may be seen in his office only when he is not in it, in Clevinger’s trial, in the dead man in Yossarian’s tent who cannot be removed because he never officially arrived, in Doc Daneeka declared dead because he was on a manifest. The repetition is partly the argument, for the rule is everywhere because it is the order of things, and the mechanism must be in the reader’s hands before it is turned on the reader in Rome. What holds the axis there is the subtractive test. Scheisskopf’s parades, much of the Major de Coverley and Chief White Halfoat material and stretches of the hospital could go with little loss: they restate rather than advance.
Salman Rushdie · Literature
8.6 · Tier IV
The book is built to digress, and most of its digressions are its argument: Saleem cannot tell one life without swallowing his grandfather’s nose, the perforated sheet, the silver spittoon and Methwold’s hairpiece, because his claim is that the life is made of them. Much passes the subtractive test. The perforated sheet, a woman known only in pieces, returns as the narrator’s whole method; the babies switched at Narlikar’s home carry the book’s question of who inherits. What holds the figure here, the lowest of the twelve, is that a hostile cut finds slack. Book Two’s long Bombay middle repeats its comic routines; the Pakistan years and the Brass Monkey’s turn into Jamila Singer run longer than they earn; the Sundarbans, though strong, is a stretch the argument permits rather than compels; and the teller’s anticipations are repeated past need. The cap is cleared with little to spare.
Catullus · Literature
8.6 · Tier IV
Inside a single poem the subtractive test fails on almost every line. Poem 85 cannot lose a word, and 101 and 5 are as tight. The body is another matter. A dozen invective squibs could go, the Gellius poems, the run on Aurelius and Furius, the jokes on stolen napkins and bad breath, and the Lesbia poems, the brother poems and 64 would need none of them; several are slight occasions that survive because the book does. Whether the arrangement is the poet’s is unsettled, so the sequence cannot be argued as compelled. What holds the axis lowest of the twelve is not the shortness of the forms, which is not charged, but that a share of the hundred and thirteen is occasional verse whose removal costs the body little. It clears the cap by four tenths.
Charles Baudelaire · Literature
8.6 · Tier IV
The book invites the subtractive test and answers it itself. The dedication calls the whole “à la fois tête et queue”, “head and tail at once”, and says that a vertebra may be taken out and the two pieces of the twisting fantasy will join again without trouble. That is a poetics of non-necessity at the level of the whole, and an honest one: the order is not an argument. The best pieces are pressed hard. “Le Mauvais Vitrier”, “Le Gâteau”, “La Fausse Monnaie”, “Perte d’auréole” and “Assommons les pauvres!” each turn on one act and one sentence, with nothing idle. But the prose doublets are lesser versions of poems the reader already has, and “Les Dons des fées”, “Portraits de maîtresses” and “Le Galant Tireur” could go with little lost. The strongest third is irreducible; the whole, by its own avowal, is removable.
John Milton · Literature
8.5 · Tier IV
The subtractive test, applied to an oration, asks whether each head is required by the case. The four heads are an argument in true order: licensing is shown to be an invention of the Council of Trent and the Inquisition, so its pedigree is charged before its merits are weighed; reading is defended in principle; the order is shown to fail on its own terms; its cost to learning and truth closes the case. That spine is necessary. What could go is real: the survey of the first head runs long through Greek and Roman practice and the early Councils, and the catalogue of what else a licenser would have to license is extended past its point. Necessary at its heart, amplified at its edges.
Virginia Woolf · Literature
8.5 · Tier IV
The spine passes the subtractive test. Sasha is lost on the ice; the poem “The Oak Tree” is carried in Orlando’s breast through three centuries and published at last; Nick Greene meets him as a hungry Elizabethan and her as a knighted Victorian critic; the change of sex stands at the hinge. Take any of these away and the argument fails. The test bites inside the chapters. The satire of embassy ceremony at Constantinople runs long for what it gives; the evening among Pope, Addison and Swift is a run of literary anecdotes that could be cut or doubled without loss; the Archduke’s courtship is one joke told twice. What holds the axis lowest of the twelve is play that the book’s high spirits want and its argument does not. The short, compelled scale keeps it clear of the cap.
Naguib Mahfouz · Literature
8.5 · Tier IV
The subtractive test is hard on a work of this length, and the three volumes answer it differently. The first largely passes: the morning rituals, the coffee hour, the father’s nights with singers, Amina’s confinement and the wedding preparations build the order that 1919 and Fahmy’s death will break, and little could go without thinning the law of the house. The second carries Kamal’s love for Aida Shaddad at a length that is itself the subject, but its chapters on Yasin repeat a pattern the first had fixed. What holds the axis lowest of the twelve is the third: some of it reads as chronicle filled in, the deaths of Aisha’s husband and sons are summarised more than required, and Kamal’s self-examination returns in speeches that repeat their positions. The scale is compelled by the subject, time passing through one house; the margin of repetition is measurable.
Philip Glass and Robert Wilson · Music
8.5 · Tier IV
The subtractive test meets a work whose material is repetition, and asks whether its durations are required. In large part they are. The Act I diagonal is the scene: shortened, it would become a dance number rather than a span of time spent watching one body cross and return. The knee plays cannot go, since without them the acts would be separate pieces, and each family of images needs its third appearance, because the third is the first two transformed. Length is not charged. What holds the axis is give the test finds: the Trials, Act III above all, run long in text play that adds little after its first turns; much of the staging keeps a slow tempo for its own sake; and the convention that lets the audience leave and return admits that not every minute is compelled.
Robert Altman · Film
8.5 · Tier IV
Judged by the subtractive test, which makes no exception for a form chosen to admit the inessential. Much is required. Barbara Jean’s collapse at the airport, her breakdown on the Opry stage and her death are one line; Kenny’s violin case is planted early and carried to the end; Sueleen’s evening at the smoker, arranged by Triplette and Delbert Reese, ties the campaign to the music; the Walker truck passes through every day and makes the rally inevitable. The multiplicity is itself required, since the subject is a crowd. What holds this axis lowest is what could go without loss: Opal’s monologues among the school buses and the car lot repeat one joke, the cameos are ornaments, the Tricycle Man is a signature, several songs outrun the drama, and L.A. Joan’s thread circles.
Henri Matisse · Visual art
8.4 · Tier IV
Judged on the composition, since the canvas has no words. The subtractive test gives more here than on most large canvases of its rank. The arch of trees cannot go: it makes the glade a stage and gives the field its two curtains. The reclining woman with raised arms at the centre cannot go; she is the picture’s axis and its pose of ease. The small ring of dancers cannot go, the one figure of community and motion. But the rest is an anthology. The embracing couple, the garlanders at the left, the piper and the herdsman are drawn at different scales from different sources, and two or three could be removed without loss to what the picture says. Necessity is in the structure and the scale, not in the population.
The Beatles · Music
8.4 · Tier IV
Fourteen songs in about thirty-five minutes, and none sprawls: inside each track there is no slack, and each ends as soon as it has said its piece. Norwegian Wood, Nowhere Man, Girl and In My Life are what the record is; remove them and it is a lesser album. The songs a subtractive test would question next, Wait, sturdy and generic, and You Won’t See Me, long for what it says, give a variety the quieter songs need. What holds the figure is two songs the record could lose: What Goes On, an older country song handed to Ringo Starr, which could go with no loss but variety, and Run for Your Life, the closer and the least considered song here. The cap is met.
Barma and Postnik Yakovlev (attributed) · Architecture
8.4 · Tier IV
Run the subtractive test on the building as it stands. The core resists it. Nine churches answer nine dedications, each a feast of the campaign; take away one of the eight round the centre and the star of the plan, which is the commemoration, fails. The central tent is required as the vertical that gathers them, and the small, divided interiors follow from nine altars wanted on one basement. The rest is permitted rather than compelled: the profusion of kokoshnik tiers, a different pattern on every dome, the church of 1588 set off the symmetry at a corner, the belfry, the porches, paint on every surface. Each could be other, or absent, without the building knowing less. Necessity is strong at the centre and weak at the edges.
Frank Herbert · Literature
8.4 · Tier IV
One of the two lowest of the twelve. Book One is close to necessary throughout. The gom jabbar test on Caladan, the move to Arrakis, the banquet, the hunter-seeker, Yueh’s betrayal and Leto’s poisoned tooth each turn the trap a notch, and the reader is shown it from every side, because the plot is a contest of plans. Subtraction is easier further on. Several Harkonnen chapters restate what is known, the Baron’s grossness elaborated rather than advanced; the Fenring thread is set up at length and paid off in a few lines; Thufir Hawat’s long service to the Harkonnens ends in a gesture. Book Three leaps two years and more between chapters and summarizes what the first two books dramatized, so that the jihad, the book’s real subject, arrives as vision rather than event, and Paul’s prescient reflections recur in near repetition. A compelled first half and a loose last third hold the axis here.
W. H. Auden · Literature
8.4 · Tier IV
The test is subtractive, and the book answers it in two voices. The great poems resist it: nothing can come out of “Musée des Beaux Arts” without loss, and the Yeats elegy requires every stage of its turn, from the report of a death through the argument of its second part to the incantation of its third. But the book is a gathering, not a composed sequence, and several of the place poems and lighter pieces are occasions taken because they were there. It also carries what its maker later cut or disowned: the stanzas on Kipling and Claudel, “the necessary murder” of “Spain 1937”. Being questioned is not proof of idleness, but the slack is there. High necessity in the best third, a miscellany’s looseness around it.
Matthias of Arras and Peter Parler; completed by later hands · Architecture
8.4 · Tier IV
Run the subtractive test. The medieval choir is compelled: the radiating chapels are the burial and altar places a royal and archiepiscopal church needed, and the double flyers are what the high glazed choir requires. The Wenceslas Chapel stands where it does because the saint’s grave was there, in the place of his rotunda, and that one fact bends the whole south side, pushing the transept front and the main door toward the palace. What yields is five centuries of accretion: chapels crowded with tombs, a Baroque helmet on a Gothic tower, an organ loft moved. And the nave and west front answer a cathedral’s type, not a necessity the choir dictated.
Anonymous; Octagon by William Hurley and Alan of Walsingham · Architecture
8.4 · Tier IV
Run the subtractive test. The long Norman nave is compelled by monastic use, by the lay nave and the processional way of an abbey that held a saint, and by the module that rules its bays. The Octagon is the one place where necessity and invention coincide: a collapse demanded a crossing, and the answer widened the hole to the full span of nave and aisles, so that no part of the new centre is idle. The Lady Chapel answers Marian devotion, placed where the plan allowed. What resists is accretion: the Galilee, the chantries, the tower’s added stage, the asymmetry of a lost transept. The building permits these; the whole does not compel them.
Frank Gehry · Architecture
8.4 · Tier IV
Judged on structure, purpose and site, and the plan passes the subtractive test. The site drops from the city grid to the river, and the building answers with a descent from the plaza into an atrium below the street. The Puente de la Salve crosses the plot, and the building passes beneath its deck to a tower that closes the composition. The long gallery runs along the river under the bridge because only there is the length to be had, and the three kinds of gallery answer three kinds of art. Each of these is compelled by site or programme. What holds the axis is the skin: nothing in the programme or the site requires the curvature of the titanium volumes, and many of the roof forms could be otherwise without loss.
Andrei Tarkovsky · Film
8.4 · Tier IV
Judged on structure and duration; length itself is not charged. Much that looks dispensable proves required: the forty minutes on Earth are the measure the coda returns to, and without the weed in the stream, the horse, the rain on the veranda table and the father’s house the last shot would have nothing to answer. The burning of Kelvin’s papers is needed for the leaving, and Hari’s arrivals and deaths are required to the frame. What holds the axis lowest is three stretches that carry more length than the argument compels: Berton’s testimony, which tells in exposition what the station will show; the drive, which could lose half its length without the film losing a thing it knows; and the scientists’ quarrels in the second part, which restate positions already taken.
Peter Jackson · Film
8.4 · Tier IV
The subtractive test is hard on nine hours, and the theatrical cuts pass it better than their length suggests. Each film is driven by one physical errand: get the Ring out of the Shire; hold the company’s halves together while the war opens; reach the mountain while the city stands. Most scenes advance it, and the scale is compelled by the war. What could go is visible, and it holds the axis lowest of the twelve. In The Two Towers Aragorn’s fall from the cliff and the Arwen dream after it serve a love story the trilogy does not need, and Faramir’s detour to Osgiliath is plotting. In The Return of the King the Army of the Dead is a mechanism, and the codas are paced as if each were the last.
Jorge Luis Borges · Literature
8.4 · Tier IV
The best pieces could lose nothing. “Del rigor en la ciencia” is a single paragraph in which no clause could be cut, and “Borges y yo” turns on its last sentence, “No sé cuál de los dos escribe esta página” (I do not know which of the two of us is writing this page). But the unit is the book, and the book declares its own assembly: the epilogue calls it “colecticia y desordenada”. Several pieces could leave without loss: “Las uñas”, “Un problema”, “Diálogo sobre un diálogo”, and among the poems some of the occasional elegies and the ode for 1960, which read as a public poet doing his duty. Perhaps two thirds of the contents pass the subtractive test. The axis stays well above the floor because the book’s centre, the maker unknown to himself, is in nearly every piece.
Japanese, under Emperor Shōmu · Architecture
8.4 · Tier IV
Run the subtractive test from the image outward. A seated bronze figure many times the height of a man must be roofed, and the hall’s height and depth are compelled by it. In the hall of 1709 the compulsion tightens: narrowed to seven bays, its walls stand close round the figure, and the great columns, the tie-beams and the unceiled roof exist to hold a cover over the body. The axis from gate through court to hall is required by approach and rite. What yields to the test is the dress of the front, the cusped gable and the doubled roofline, display set on a structure that does not need it; and a precinct that lost its pagodas is larger than its program. The gate stands near the top of the axis; the hall’s envelope holds it down.
Wim Wenders · Film
8.4 · Tier IV
Judged on the film as cut. The first movement resists subtraction better than it seems to. The drift from apartment to apartment, the library’s murmur and the thoughts on the underground are the angels’ condition, and their accumulation is how eternity is made to weigh: cut them and the fall has nothing to fall from. Homer is required, or the city’s memory is only footage; Falk is required as the hinge; the suicide is required as the failure of pure witness. What holds the axis lowest of the twelve lies after the fall and in display: the circus’s closing told and retold, Marion’s monologues saying what the images carried, two concerts held for their music, Falk’s shoot partly play. A film about drift is not wholly exempt from drift.
Aretha Franklin · Music
8.4 · Tier IV
Inside the tracks almost nothing is idle. “Respect” is two and a half minutes in which each added element, the title spelled out, the answering “sock it to me”, the stop before the saxophone break, is required by the argument of the song. The title track is a vamp and a vow and needs nothing more. The subtractive test bites on the album as a whole: “Good Times” is a light party song that could go without loss, “Soul Serenade” puts words to an instrumental and carries the least weight, and “Save Me” is a strong groove over a thin song. Three of eleven tracks, about seven minutes, are separable. The record was assembled from sessions as an album of songs, not composed as one argument.
John Crowley · Literature
8.4 · Tier IV
The test is subtractive, and the domestic spine survives it. Smoky’s walk to Edgewood, the marriage into a family that knows itself to be in a story, Sophie’s sleep and the stolen Lilac, Auberon’s going to the City and his loss, the departure at the Parliament: each is the Tale moving one step, and little there can be cut. The test bites on the second plot. Russell Eigenblick, Barbarossa woken into a failing America, and Ariel Hawksquill, the memory artist who hunts him, are joined to the family late and loosely; their chapters could be much reduced without loss to what the book knows, and the political allegory is the part least compelled by its argument. Auberon’s long decline in the City also runs past its need. The length is not the charge; the charge is that perhaps a sixth of the book is permitted rather than required.
Terrence Malick · Film
8.4 · Tier IV
The large parts are required. The arrival is the premise, the captivity and reprieve the bond, the winter among the Powhatan the paradise that the famine ends, the false word of Smith’s death the breach, and Rolfe and England the second life the first could not become. But inside the phases the subtractive test finds real give, and it holds the axis lowest. Shots of grass, water, sky and hands are often interchangeable, and some recur past what they carry; the voices return to the same questions; the hostage-taking and the girl’s passage into English life are elliptical to the point that cause is lost. Heaviest of all, two versions released within a month, each defensible, show that whole passages can be moved or removed and the film remain itself: much is placed rather than required.
Ottoman builders, under Mehmed II and successors · Architecture
8.4 · Tier IV
The armature passes the subtractive test. Remove a gate and the gradation of access that is the palace’s purpose collapses: the First Court open to any subject on business, the Second to those summoned to the Council, the Third to the sultan’s household alone. The site is compelled: the acropolis of the conquered city, the ground that commands both seas and both shores. What yields is the flesh. The Harem’s several hundred rooms grew by accretion and fire into a warren whose parts could go without loss of its idea, and many kiosks of the Fourth Court are occasions, not necessities. Necessary in its order, assembled in its members.
Ming builders (and earlier dynasties) · Architecture
8.4 · Tier IV
Judged on purpose, structure and site, and the answer depends on the scale of the test. Put it to a section and little yields: the wall takes the crest because the crest commands both valleys and the slope does half the work; the towers stand at intervals set by sight and bowshot, each answering its neighbours; the passes sit where the valleys force traffic; the material is what the site gives. Put it to the system and much yields. The line was argued at court for two centuries, built in campaigns, doubled near the capital and extended where policy rather than threat drove it. Long stretches could go and the frontier hold; trade, tribute and the field army were alternatives.
Philip Roth · Literature
8.4 · Tier IV
The test is subtractive, and the book half invites it. The excess is the argument: Sabbath answers death with appetite, and a lean book about him would contradict him. The spine is required: Drenka’s death; the funeral of his friend Linc, which takes him back to the city of his theatre; his stay with Norman and Michelle Cowan and his abuse of their hospitality; the visit to his ancient cousin at the Jersey shore and the box of his dead brother’s things; the return to Drenka’s grave. Inside that spine the riffs repeat. The sexual transcripts and recollections run past the point where they add knowledge; the provocations at the Cowans’ restate one another; some tirades are performance for its own sake, which the book knows, since its hero is a performer. Perhaps a seventh of the whole is permitted rather than compelled, and that holds the axis lowest of the twelve.
Roberto Rossellini · Film
8.3 · Tier IV
The spine is strong at both ends. Pina’s death must fall where it does: the first half builds a wedding, a family and a building full of life so that one burst of gunfire ends all of it and turns chronicle into Passion. The second half is required by the first; the betrayal, the torture and the execution are the price of what the tenement held. What holds the axis lowest of the twelve is the middle register. The parish comedy of the frying pan and the turned statuette makes one point well and repeats it. The Marina and Ingrid strand is melodrama the story uses more than it needs, and the drunk officer’s speech at the club states what the torture has already shown.
Danny Boyle · Film
8.3 · Tier IV
The first hour holds to the subtractive test. Jim’s walk across an empty Westminster Bridge and into Piccadilly, the wall of notices for the missing, the church full of bodies, the killing of Mark within seconds of his infection: each piece teaches a law the rest of the film obeys, and none can go. The road north is looser but earns its idyll, since the supermarket and the horses are what the survivors lose at Manchester. What holds the figure is the last third, where parts are permitted rather than compelled: the chained soldier Mailer exists to be released on cue, and Jim’s return through the house relies on arrangements set down for the purpose. Two further endings were shot or boarded, so the close was chosen among options.
Edward FitzGerald, after Omar Khayyam · Literature
8.3 · Tier IV
The subtractive test finds little to cut inside a quatrain and a good deal across the sequence. Each stanza is a closed epigram: two rhymed lines set the case, the third withholds the rhyme and turns, the fourth shuts the door. “Came out by the same Door where in I went” (27) is required by the three lines before it, and nothing in them is idle. The frame is required too: dawn, the cry to open the tavern, the noon of argument, the potter’s house, the rising moon and the empty glass. What holds the axis is the sequence. The fifth edition is twenty-six quatrains longer than the first, and some additions restate what is said, as the run on the vanity of learning and the seventy-two jarring sects says one thing several times. On this axis the first edition is the tighter poem.
Francisco Goya · Visual art
8.3 · Tier IV
Judged on the configuration: the frieze resists subtraction at its centre and gives at its edges. The queen cannot go; she is the axis, set where a dynastic portrait puts the king, and the picture’s argument begins with that displacement. The king cannot go, forward and a little aside, glittering and blank. The painter in the dark cannot go: he is the one point of view inside the picture and its quotation of Velázquez. The bride without a face cannot go; she is the succession not yet decided. But the commission required every member, and much of the row is the list, not the design: the half-hidden profile and the couple with the infant could be thinned, and the dark canvases carry nothing legible. Required at the core, permitted at the flanks.
Apichatpong Weerasethakul · Film
8.3 · Tier IV
The subtractive test is harder than the film’s calm suggests, because it is built as a sequence of panels rather than a chain. Much is required. The dinner is the hinge: the dead arrive at the table without fuss, and the film’s law is set. The cave is required, since Boonmee’s death must return him to the place he believes he was born. The Lao worker who dialyses a man haunted by the communists he killed is required for the film’s history. What gives is the princess and the catfish, never fixed to Boonmee and standing as a detachable episode; the opening buffalo and the hotel room are looser in their claim than the centre.
Claude Monet · Visual art
8.3 · Tier IV
The subtractive test bites harder on a series than on one canvas. The series needs number: one cathedral in one light is a picture of a church, and thirty are an argument about time. But the argument does not compel thirty. Several canvases are near repetitions of one hour in one weather, a showing of fewer carries the whole argument, and ten well chosen would carry most of it. Within each canvas necessity is high: there is nothing in the field but façade, light and the strip of sky, and nothing could go. What holds the figure below 8 is what the set could lose without loss: the overworked canvases, where the crust has grown uniform and the hour is no longer legible.
Itō Jakuchū · Visual art
8.3 · Tier IV
The test is subtractive, and the set is judged as a set. Some of it resists. The phoenix and the peacock are its two summits, white against colour, the imagined bird against the real one; Insects at a Pond, Shells and the two fish scrolls carry the realm out of the air into water, mud and shore, and without them the gift would be a book of birds, not of living beings; the snow scrolls carry winter, the plum and moon carry night. Remove one of these and a domain of the world goes with it. But the set is additive in kind, thirty offerings each complete on its own silk, and the several chicken scrolls are a strand of variations, one or two of which could go. Within each scroll the crowding is chosen and largely compelled.
Sergio Leone · Film
8.3 · Tier IV
The design is picaresque, a road with stations, and the subtractive test finds give at several of them. The rope scam is shown twice where once would establish the bond and its betrayal; the desert torture of Blondie runs long; the Union camp, after the beating, is the slackest passage; the ruined town’s episode, Tuco in the bath and the gunfight in the street, answers the genre’s appetite more than the story’s. That the extended restoration could put back scenes that sit easily in the film says the same: the form tolerates addition. Against that, the spine is hard. The divided secret forces the partnership, Angel Eyes’ route through the camp forces the meeting, and the bridge must fall before the cemetery can be reached.
Hans Puchsbaum and others · Architecture
8.3 · Tier IV
Run the subtractive test on the body and it holds. A hall whose three aisles stand nearly level cannot be covered by three roofs; the one steep roof over all of them is what the section compels, its pitch required against snow and for the long fall of water. The piers carry vault and roof directly, and their saints stand where the hall gives no wall to hold an image. The side towers are compelled by the campaign: the Romanesque front was kept, so height had to rise elsewhere. What yields is the rest. The south tower’s height is a sign, not a use; the north tower stops where money and will stopped; many of the aisle altars could go without loss of purpose.
Kanye West · Music
8.3 · Tier IV
Thirteen tracks in about sixty-nine minutes, and the subtractive test finds a frame that is compelled and a middle that is permitted. Dark Fantasy must open, the storybook prologue naming the fantasy of the title. Power must come early, the claim to sovereignty the rest of the record will pay for. Runaway is the centre of gravity, placed late and long; Lost in the World and the Gil Scott-Heron coda are the compelled end. The test bites in the middle. So Appalled is six voices on one loop, its argument made already; Hell of a Life restates Monster’s appetite in a thinner mode; Blame Game’s Chris Rock skit runs past its use. About a fifth of the record is permitted rather than required, and that holds the figure.
Philip K. Dick · Literature
8.2 · Tier IV
The middle of the book resists the subtractive test. Once the bomb has gone off on the Moon, each stage of the regression is required: the stale cigarettes and the soured cream, the coins bearing Runciter’s profile, Wendy Wright found dried to a husk, the elevator that turns into an old cage, the drive in a LaSalle into Des Moines in 1939, the funeral, the stairs. Each turn of entropy tightens one question, who is dead, and each epigraph marks the cost of the remedy. The test bites in the first third. The tour of Runciter Associates, the testing of Pat Conley and the long gathering of the inertials run longer than the plot uses; Pat Conley’s power to alter the past, built with care, is dropped once Jory is named; and several inertials are names, not persons. Perhaps a fifth of the book is permitted rather than compelled.
Marc Chagall · Visual art
8.2 · Tier IV
Judged on the configuration. The core resists subtraction. Remove the animal and the man has no one to look at, the line between the eyes has no end, and the title’s I faces nothing; remove the man and the picture is a farmyard. The milkmaid inside the animal’s head is required, because she makes the head a memory and not a beast. The great circle is required as the structure that cuts the field and holds the two heads in one wheel. What gives is the upper band: the inverted woman, the scythe bearer and the houses upside down are a count rather than a structure, and could be more, fewer or rearranged while the picture knew nearly the same thing. Their density is the accumulation of a remembering mind, permitted more than compelled, and that band holds the axis under 8.
James Stirling, Michael Wilford and Associates · Architecture
8.2 · Tier IV
Judged on purpose, structure and site. Much of the building is compelled, and compelled from outside. The public right of way the city required becomes the path; the slope from the road to Urbanstrasse becomes the ramps and the podium; the parking the brief asked for becomes the base the whole stands on; the old gallery’s U becomes the new gallery’s U, so that the two read as one institution. The rotunda gathers all three: it is where the path, the galleries and the axis of the old building meet, required by the plan rather than placed on it. The subtractive test bites at the edges. Take away the pink and blue rails, the coloured canopies, the fallen stones and much of the glass wall’s undulation, and the museum loses wit, not use.
Antoni Gaudí · Architecture
8.2 · Tier IV
Taken element by element, the necessity is strong. The viaducts exist because roads had to climb a steep hill without cutting it; their columns lean because the thrust of earth and roadbed leans, and the walks beneath them are shade bought from that structure. The hall exists to hold up the terrace and to gather its water. The bench is the terrace’s parapet and its seating at once, and its curves give the alcoves that make a crowd into groups. Little is idle. What holds the axis down: the whole is the fragment of a programme that failed, a sequence of public episodes whose order the missing houses would have justified, and some pieces, the lodges and the calvary, could be taken away without the rest collapsing.
The Who · Music
8.2 · Tier IV
The record is a salvage: the larger work it was drawn from had a frame that would have required its songs, and the record keeps nine and drops the frame, so necessity has to be found song by song. Baba O’Riley must open, the pulse on which everything after is laid. Won’t Get Fooled Again must close, the long argument the record has withheld. The Song Is Over, Getting in Tune and Behind Blue Eyes each carry what no other track carries. The subtractive test bites three times: Love Ain’t for Keeping would cost a breath, My Wife is a fine comic song from another author and another world, and Going Mobile is a light pleasure of the road. About a fifth of the record is permitted rather than compelled.
Frank Sinatra · Music
8.2 · Tier IV
The subtractive test finds the sequence more required than any one song. Each track is a slow song of loss in a related key of feeling, and several could go with little loss to the whole: “Deep in a Dream” and “I See Your Face Before Me” make nearly the same move, and “I’ll Never Be the Same” restates what its side has already said. But the test bites where it should. The title song opens the night and sets the hour; “Mood Indigo” turns Ellington’s blues into the singer’s colour; “Dancing on the Ceiling” has no substitute; and “This Love of Mine” closes the record in Sinatra’s own words. The length is permitted by the mood rather than compelled, and is not charged; the interchangeability is.
George Gilbert Scott and William Henry Barlow · Architecture
8.2 · Tier IV
Run the subtractive test on the shed and almost nothing goes. The Regent’s Canal, crossed north of the station, fixed the height of the deck; the deck’s girders are the ties of the arch, so platform, warehouse floor and roof are one structural fact; one span leaves the tracks above and the columns below free of each other; the undercroft is the space the raised deck leaves, put to work. Nothing in the iron is idle. The hotel yields more. Its purpose was real, but Scott built beyond the brief, and the towers, the gables and the profusion of carved and polished stone are ordered by display. The extension of 2007 is compelled by the length of the trains, and plain. A compelled core stands inside an elective front.
Built for Rao Jodha and successors · Architecture
8.2 · Tier IV
Judged on purpose, structure and site. The defensive shell passes the subtractive test almost whole. The walls are where the rock ends; their batter and bastions are what the cliff requires to be unclimbable and what cannon later required to be survived. The approach turns at each gate because a straight ramp can be rushed and an elephant cannot charge round a corner. What yields is the palace crown. Courts, pavilions and halls were added reign by reign, each a ruler’s statement, and several could be taken away without the fort losing its purpose or its figure. The rule of the whole, wall below and screen above, is necessary; the number and sequence of its rooms are accretion.
The Rolling Stones · Music
8.2 · Tier IV
Nine tracks in about forty-two minutes, and the subtractive test finds more than one cut. The frame is required: Gimme Shelter must open, the storm announced, and You Can’t Always Get What You Want must close, the storm’s aftermath settled into a hard bargain. Love in Vain is required as the inherited blues the record measures itself against, and Midnight Rambler as the violence of the opening made a figure; You Got the Silver is slight and earns its place as the one tenderness. The test bites at Country Honk, a remake of a single already released, whose function is relief; at Live with Me and Monkey Man, two tracks in one mode of leering swagger that restate each other; and lightly at the title song, which says at five and a half minutes what it says in two.
Godspeed You! Black Emperor · Music
8.2 · Tier IV
Length is not the charge, and most of this length is compelled. A crescendo is an argument made of time: the rise of The Sad Mafioso cannot be shortened without becoming a gesture. The monologue is required, since without it the lament has no city to mourn, and the trains, the preacher and the voice that opens Providence are each the document a movement answers. But the subtractive test bites in three places, and together they hold the figure: Black Helicopter restates the dread the preacher has set, the string loop of Providence runs past its purpose, and the long silence before the last passage is convention. The LP of the year before shows the form was revisable, one selection of at least two.
Josef Hoffmann · Architecture
8.2 · Tier IV
Judged on purpose, structure and site. The purpose was a house for a rich, collecting family that wished to live inside art, and a stage for receiving. Hall, dining room and music room are the rooms that purpose demands, and the plan gives them their order, the hall as the spine from which the others open. The edging is the most compelled part: it is how this wall says what it is, and without it the house would be a white villa of no particular kind. The massing resists the test. The grouped blocks, the bays and the stair tower are composed for the eye from the street, and the tower’s figures and dome could go without loss to the house or its use. Much of the luxury is permitted by the budget, not compelled.
Luigi Vanvitelli · Architecture
8.2 · Tier IV
The test is subtractive, and the work answers it in two halves. The spine is compelled. Take away the octagon at the crossing and the four courts lose their single point of command; take away the park axis and the long gallery points at nothing; take away the cascade and the axis has neither source nor end. The descent of the water from the hill toward the house is the argument of the whole, and every basin on the way is required by it. The bulk is permitted rather than compelled: the rooms are repeated bays of one module, the long fronts could lose a third of their length and say the same, and the English Garden is a second argument set to one side.
Claude Lorrain · Visual art
8.2 · Tier IV
The subtractive test finds the canvas necessary in its spine and assembled at its edges. The seaport was a formula the painter had used for more than a decade: architecture at the sides, a ship at one wing, a low sun at the centre, a quay of small figures in front. A palace front could be exchanged, a boat or two dropped from the quay, and the subject renamed, Ulysses, Cleopatra or Saint Ursula, with little loss; the painter made such exchanges across the series. What resists removal is the axis of light. The sun, the shimmering path on the water and the queen’s descent toward it are bound together, so that the departure is the light. Remove any one and the picture loses its centre.
Henry Bacon · Architecture
8.2 · Tier IV
Run the subtractive test on purpose, structure and site. The purpose is to hold a figure and two texts and to close an axis two miles long, and much is compelled by it. The open east front is required: the figure must look down the Mall, and a door would break the line. The three chambers are required, one figure between two speeches. The podium is required by the flat ground and the distance. What resists: a peristyle on four sides of a building entered from one, an attic of names that could go, Ionic screens as much decorum as structure. Symbolism binds the parts more than need, and here symbolism is a purpose.
Jackson Pollock · Visual art
8.1 · Tier IV
The subtractive test, on a frieze. Take away one of the black uprights and the beat falters there, but the procession closes over the gap: the rhythm is serial, and a series bears a missing term more easily than a composed structure does. Take away the colour that swings across the uprights and the canvas becomes a row of signs; colour binds them into one motion, and it cannot go. Take away a metre at either end and the painting reads the same, which is the frieze’s cost: its length was fixed by the wall it was made for, not compelled by the argument. What resists removal is the lateral drive, with the uprights as the counter-pressure that makes it visible. The parts are necessary as a class more than one by one.
Master James of St George, under Edward I · Architecture
8.1 · Tier IV
The site compels much. The peninsula between the Seiont and the strait gives water on two sides and supply by sea, and the castle draws its long shape from it, the waist of the plan following the old motte and the ground. Defence compels the King’s Gate’s sequence of barriers, the towers’ command along the curtain and the shooting galleries of the south front. The castle had a second purpose, to be the seat of royal government in the new principality and to look it, and the bands, the polygonal towers and the eagles serve that. Subtract them and the castle still holds, but half its purpose is gone. What resists the axis is the unfinished interior: the inner reason was never built.
Mike Nichols · Film
8.1 · Tier IV
The first half resists the subtractive test almost entirely. The moving walkway at the airport, the aquarium in Benjamin’s room, the diving suit at the birthday party, the raft on the pool: each sets a young man under glass or under water, and the film needs every one to make his paralysis visible before it is spoken. The Taft Hotel sequence, fumbled keys and a clerk’s question, is required, because the affair must begin as farce for its later deadness to register. The second half gives. The Berkeley section circles and restates one impasse; Carl Smith is a device; the stages of the chase are serviceable rather than required. The bus is required.
Norman Foster (Foster and Partners) · Architecture
8.1 · Tier IV
Judged on purpose, structure and site, the dome passes the subtractive test better than its origin would suggest. It was demanded for symbol, but it was made to carry work: take it away and the chamber loses its daylight and its exhaust, the public loses its route above the representatives, and the building loses the sign by which it says that the parliament sits. The two ramps are compelled by the route, up and down without crossing; the cone is compelled by light and air; the stripped walls are compelled by the decision to show the record. What yields: the dome’s existence was imposed by a vote over the architect’s first scheme; the inserted floors are efficient office building and could be otherwise without loss; the chamber is stretched to the shell, not the shell to it.
Wassily Kandinsky · Visual art
8.1 · Tier IV
The subtractive test, at two levels. At the structure it holds. The two centres cannot go: the soft, rose-tinged, blurred mass at the left and the hard knot at the right, with its sharp dark lines and harsher reds and blues, are the picture’s argument, one event heard twice, as dissolution and as violence. Take either away and the canvas is a single storm with no counterweight. The diagonal currents cannot go, since they make two centres one field, and the horizontal format is compelled: a deluge is a spread, and the eye must travel. What gives is the population. Many secondary patches and hatchings could be moved, thinned or doubled without loss, more of the surface than in Broadway Boogie Woogie (8.7), and the long course of studies shows a field searched rather than found.
Frank Ocean · Music
8.1 · Tier IV
Seventeen tracks in about fifty-five minutes, and the subtractive test bites more than once. Thinkin Bout You must open the songs, the plain statement of a longing the record will circle. Super Rich Kids, Crack Rock and Lost are three views of getting high from three classes; Pyramids is the centre of gravity; Bad Religion is the confession the record turns on, and Forrest Gump the answer, a love song to a man in the open. The test bites at the edges. Fertilizer is a jingle-length fragment, Not Just Money a spoken aside that states what Sweet Life and Super Rich Kids show, White a pleasant guitar interlude, and Monks the slackest of the full songs. Start and End are a frame more than a necessity. Five of seventeen tracks could go with little lost, and that holds the figure.
Emily Kame Kngwarreye · Visual art
8.1 · Tier IV
Judged on the configuration, and the subtractive test works against an all over field. Take away a panel and three panels of the same field remain; the painter worked her canvases flat on the ground from every side and composed to no centre and no edge. What resists removal is the layering. Take away the under layer of tracks and lines and the dots lose the sense of something beneath them, ground under growth; take away the late cool and white dots and the field closes into warmth with no air. The extent is required in one sense, since a single panel would be a sample and not a land. But the length is permitted more than compelled, and the dots of any passage could be otherwise without loss.
Patricia Highsmith · Literature
8.1 · Tier IV
The subtractive test bites less here than in most crime novels, because the spine is one consciousness under pressure and almost every scene either feeds Tom Ripley’s want or tests his cover. The New York chapters cannot go: the mail fraud, the borrowed apartments and Aunt Dottie’s mean cheques establish a man with no self of his own before he is offered someone else’s. Mongibello is required for the same reason; the scene in which Dickie finds Tom in his clothes, mimicking him before the mirror, is the hinge of the book and needs the slow weeks before it. The axis gives in the middle third. From Rome to Venice one movement, a visitor, a lie, a narrow escape, relief, repeats more often than the argument needs, and the Palermo stretch and some of the Venice social business could be cut with a loss of duration, not of sense. The duration is partly the point, the strain of being two men, but not all of it is earned.
Brian Eno · Music
8.1 · Tier IV
Inside any moment the subtractive test finds almost nothing to remove. 1/1 is a few piano phrases, each a handful of notes, and taking one away would leave a hole the loops would expose every time they came round: the material is minimal to the point that each element bears load. The test bites at the scale. The pieces are excerpts of processes that could run for any length, and their durations are permitted rather than compelled: 1/1 runs about seventeen minutes, not because an argument needs seventeen, and five of them could go with no loss the ear could name. Among the four pieces, 2/2 is the one a hostile listener would cut, the thinnest material on the record. That holds it below Kind of Blue at 8.6.
Abraham Darby III; designed by Thomas Farnolls Pritchard · Architecture
8.0 · Tier IV
The governing decision is compelled by the site. The river was a working highway for barges, so one span and no piers; the banks were unstable ground, so a superstructure as light as the age could imagine; the ironmasters stood at the water’s edge, so iron. Run the subtractive test on the parts and the five frames, the crown joints and the deck are required. What resists it less well is the excess: far more iron than the span needed, part-arcs and rings that are partly ornament, approaches made and remade as the ground moved, and a purpose of display that is not a purpose of crossing. The whole is necessary; the quantity is not.
Ingmar Bergman · Film
8.0 · Tier IV
Judged on structure, the spine of six episodes resists subtraction. The magazine interview sets up the model couple the series will take apart; the dinner with Peter and Katarina shows, in another pair, the open contempt Johan and Marianne believe they have escaped; Mrs Jacobi brings Marianne her own case across a desk; the night of Paula is the break, the evening of the fourth episode a false reconciliation, the office the reckoning, the last episode what remains. Each is required by the next. Much of what hangs on that spine gives. The second episode is diffuse, and the theatrical cut shortens it hardest without harm to the line; the fourth restates positions the third has set. That the maker could cut the whole by nearly half and keep its shape shows how many scenes are chosen rather than required. Length itself is not charged.
Neil Young with Crazy Horse · Music
8.0 · Tier IV
Seven tracks in about forty minutes, and the record’s argument lives in three of them. Cinnamon Girl must open: its riff, its heavy bottom string and the single repeated note of its guitar break state the band’s law in three minutes. Down by the River and Cowgirl in the Sand are the record, each a song opened into a long two-guitar passage that closes its side, and neither could be cut without the album ceasing to be itself. The title song is needed as the one plain statement of place and wish, and Running Dry earns its place as the dirge before the last ascent. The test bites twice: Round & Round holds its idea well past its length, and the sequence would survive losing The Losing End.
Antonio Vivaldi · Music
8.0 · Tier IV
The large plan resists the subtractive test: four seasons make the year, and no concerto can go without breaking the cycle the title promises. Within each concerto the programme gives most episodes a reason to stand where they stand. The storm of Spring’s first movement must interrupt the birds so that they can return; the thunder of Summer’s Adagio must break the slow line, or the fear in its sonnet is not shown; Winter’s ice must come before the winds. The give is in the composer’s habitual means. The episodes run on sequence, a figure repeated a step higher or lower, and many could lose a link without loss; two dances extend themselves by repetition more than by need.
Russian carpenters · Architecture
8.0 · Tier IV
Run the subtractive test against the material. A log building cannot span or rise as masonry does: the length of a pine trunk limits each wall, so the octagon diminishing in stages and the arms bracing it are compelled, and the stepped pyramid is the honest shape of logs carried to some 37 metres. The barrel gables shed rain and snow and are compelled by climate. The low painted ceiling is compelled by use: an unheated room for a summer congregation, closed at a human height. What resists is the dome count. The domes stand on the gables as crowns, not as roofs over spaces. Remove eight and the church loses splendour and nothing of its use.
Jorge Luis Borges · Literature
8.0 · Tier IV
The best stories cannot be cut by a sentence. “El libro de arena” is a lesson in geometry, a sale, an obsession and a disposal, each in a paragraph or two, and its ending in the Biblioteca Nacional is required by the arithmetic of the infinite with which it opens. “El espejo y la máscara” is built in threes, and its third term is necessary to the first two; “Undr” keeps the same law. The book as a whole passes less well. “El soborno” is an academic anecdote the book could lose without losing a thought; “La noche de los dones” says what Borges had said before of memory and initiation; “Utopía de un hombre que está cansado” is in part a catalogue; and “El Congreso”, long by Borges’s measure, runs loose in its middle before the ending gathers it.
Alfred Hitchcock · Film
8.0 · Tier IV
The chain of cause is tight. A hand raised at the Oak Bar to call a bellboy puts Thornhill in Kaplan’s place, and every later episode follows from that gesture and from his own attempts to clear his name. Lehman pays what he plants: the matchbook with the monogram, the gun fired in the cafeteria, the binoculars, the pre-Columbian figure. But the form is a picaresque of set pieces, and the give the subtractive test finds weighs. The auction, the hospital escape and the second half of the Professor’s exposition could be shortened without losing a fact the film needs; the plot’s object, microfilm in a statue, is avowedly arbitrary; and the length is permitted by the chase more than compelled by the argument. What holds the axis up is that each episode tightens the question of identity rather than repeating it.
Jean-Siméon Chardin · Visual art
8.0 · Tier IV
The centre cannot be touched. Remove the ray and there is no picture; remove its opened belly and the ray is merely a fish. The cat is required, though less than it first seems: it is the only living thing and the only motion, the appetite that names what the hung fish is for, and its arching diagonal answers the fish’s vertical. The knife is required: its handle, pushed over the ledge toward us, puts the viewer’s hand at the scene. What yields is the right-hand group. Jug, pot, skimmer, bottle and onions are a second still life, partly a reception piece’s display of range in copper, earthenware, glass, linen and greens, and the bottle or the skimmer could go without loss of meaning. The crowding of the ledge is permitted, not compelled.
Alex Proyas · Film
8.0 · Tier IV
The design is economical where it matters. The stopped clocks, the spiral drawn on the dead woman and scratched by the mad Inspector Walenski, the postcard and billboard of Shell Beach, Uncle Karl’s memory of a boyhood, the syringes of memory: each element set up in the first half returns as a key in the second, and the billboard’s last use, a painted wall that breaks onto void, is the hinge of the film. Bumstead’s accordion and his slow loss of certainty pay into his fall. The subtractive test still finds slack. The prologue states the premise before the film lets it be discovered; Schreber’s explanations restate the experiment; the final duel runs past what the meaning needs.
Don DeLillo · Literature
8.0 · Tier IV
The test is subtractive, and the frame passes it: the crowd of the prologue and the hooded followers of the epilogue are the two terms between which one man’s solitude is set, and neither could go. The poet held in Beirut never appears, and his absence is required, since the book’s argument is that the man in the room has become an image. The middle passes less well. The long scenes in Bill’s house, with Scott and Karen and then with Brita and her camera, set out the hermit’s economy of concealment and then restate it; the exchanges with Haddad argue writer against terrorist several times in nearly the same terms; and Karen’s New York drifts in a way the book does not always make purposeful. Perhaps a sixth of the whole could go without loss.
Woody Allen · Film
8.0 · Tier IV
Judged on structure, and most of the film is required. The overture states the wager, the city as Isaac would write it, and the rest tests it; each of the four couplings answers another; the coda is earned by everything before it, because the list Isaac speaks is the list of a man who has acted on none of it. The subtractive test finds slack in the middle. Jill’s book and her lover come and go as running jokes more than as necessity; the visit to Jill and the scene with Wallace Shawn’s Jeremiah make one point at length; the party in the museum garden and some of the gallery talk are there for texture. None is idle, but each could lose a third without the film knowing less.
Oscar Niemeyer · Architecture
8.0 · Tier IV
Judged on plan, section and structure under purpose and site. The nave vault is necessary in the strongest sense: it is at once roof, wall and the whole of the structure, so that to remove it is to remove the church. The rear vaults follow from the same membrane, stepping the sanctuary and service rooms down into a lower, smaller order, and the brise-soleil answers the western light off the lake. The rest resists the subtractive test less well. The tower stands apart as a sculptural object whose taper is chosen rather than compelled; the canopy is a gesture of joining that could take several shapes; the rear run of arches is in part a wall made to be faced. Nothing is idle, but the necessity is that of one strong idea and its accompanying moves.
John Constable · Visual art
8.0 · Tier IV
Judged on the configuration. The wain is the hinge: stopped in the shallow water of the millstream, it joins the near world of house, dog and stream to the far world of meadow and labour, and without it the picture is two landscapes, a cottage study and a view. The cottage and its smoke are required: they are the home the crossing leaves or returns to. The sky is required, since the light falling on the far meadow is the subject. The meadow and its haymakers are required: they say what the wain is for. What gives is at the margin. The dog is an agreeable accent and could go; the boat and the figure in the rushes at the right are a count, not a structure. The scale is the exhibition’s more than the motif’s, which would hold at a third the size.
Yves Klein · Visual art
7.9 · Tier III
Run the subtractive test on a picture of very few parts. Remove the wall and the figure floats, a trick shot; the wall is the point of departure, and it must be ordinary, a suburban garden wall and not a cliff. Remove the street and the paving and the fall has no floor: the hardness below is the whole risk. Remove the cyclist and the picture loses its indifferent witness, whose back is turned on the event and who makes the leap a private act in a public place. Remove the suit and the jumper is an acrobat. Each part bears load. What yields is the house front, the fence and the exact placing of the cyclist, and the making shows the image could have used another street. Necessary in principle, contingent in its furniture.
Balkrishna Doshi · Architecture
7.9 · Tier III
Judged on purpose, climate and site. The subtractive test bites hard on the corridor. The long shaded galleries are compelled at once by the climate of the Deccan plateau, which asks for shade, cross-ventilation and cover from rain; by an institution that wants its faculty and students to meet by chance; and by a site large enough that the campus must be walked. Remove the pergolas and the corridors become hot passages; remove the corridors and the campus falls into separate buildings. The granite is compelled by place and economy. What resists the test is the extent of the system: the repetition of corridor, court and pergola is in places additive, a grid that could stop sooner or run further, and the residential parts follow the language rather than being required by it.
Snøhetta · Architecture
7.9 · Tier III
Judged on purpose, structure and site, by subtraction. Take away the roof and the work ceases to be itself: the roof is the building’s argument, that the house of a national art lies under ground any citizen may stand on, and the slope that carries it down to the water is compelled by that argument and by a site at the fjord’s edge. The foyer lies where the roof leaves room for it, open to the water; the oak wall lies where the auditorium must be closed; the factory lies behind, where production needs long rooms and loading. What yields: the roof’s field of planes is larger than access requires and is partly drawn for the eye; the fly tower and factory are a plain box the roof does not govern; and the horseshoe hall would serve the opera as well in any house. Above the cap, not by a wide margin.
Fleetwood Mac · Music
7.9 · Tier III
Eleven songs in about thirty-nine minutes, none over five, no instrumental padding and no fade that outstays its song: at the level of the track the record is lean, and the leanness is real necessity. At the level of the album the subtractive test bites. Go Your Own Way, Dreams, The Chain, Songbird and Gold Dust Woman are each required, each a voice or a stance the others lack, and Don’t Stop is the one voice that refuses the past, “Yesterday’s gone”. But Oh Daddy is the slackest song, and I Don’t Want to Know restates what Second Hand News says from the other side. Two soft tracks in eleven: the cap clears with a little room.
Christopher Nolan · Film
7.8 · Tier III
Judged on structure, and most of it resists the subtractive test. Each colour sequence supplies the cause the viewer lacks for the one before: why Leonard has a bruised woman in his car, why a man is tied in a closet, why he is running and cannot tell whether he chases or is chased. The black-and-white strand is required too, since it carries the Sammy Jankis story the ending overturns and is the forward clock the reverse strand must meet. Planted objects pay: tattoos, a licence plate, a burned book and hairbrush, insulin. What gives: the telephone exposition runs longer than its work, the motel clerk’s comedy of two rooms is played twice, the Dodd material is more chase than necessity, and the overlaps, structural as they are, spend minutes.
Wassily Kandinsky · Visual art
7.8 · Tier III
The subtractive test, taken on the large structure first and the small forms second. The large structure resists. Take away the blue disc and the right half has no weight to answer the yellow plane; the opposition the title names collapses into a picture heavy at the left. Take away the yellow plane and the disc floats with nothing to face; take away the red, set between and across them, and the halves no longer meet. The black serpentine line binds the lower field and carries the eye across the division. Those four are required, and the breadth is compelled by the opposition. What yields is the inventory of small forms, distributed for balance: several could move or go without the canvas knowing less.
Antony Gormley · Visual art
7.8 · Tier III
The subtractive test finds very little to remove. The parts are a body, two wings, the ribs, the rust and the hill. Take away the wings and it is a giant standing man, one of the many enlarged figures of its decade; take away the body and it is an aircraft fin or a road sign. Take away the ribs and the steel stands as a smooth casting, and the made, industrial character that ties it to shipyard and pit is gone. Take away the rust and it is a corporate emblem. The scale is compelled: a figure seen at speed from road and rail must be read whole at a distance. What gives: the hill could hold another figure of the same kind with little loss. The necessity is of the type more than of this body.
Jenny Saville · Visual art
7.8 · Tier III
The test is put to four things: the body, the stool, the viewpoint and the text. The body cannot go. Nor can the low viewpoint, which makes the flesh a mass bearing down on the viewer, nor the stool, the small, hard, absurd support the title names: the figure is propped, held up by a thing too small for her, and holding herself up with her own hands. The text is where the test bites. It names, in borrowed theory, what the paint already does; remove it and the canvas loses its second register, the mirror and the act of reading, but keeps its argument. That the text is reversed, made a thing to see and not a caption, partly answers the charge. The cap clears comfortably, short of works where nothing is spare.
John Bradfield and Ralph Freeman (Dorman Long) · Architecture
7.8 · Tier III
Judged on purpose, structure and site. The arch is compelled: a single clear span was needed so that shipping could pass to the upper harbour; the crossing was fixed at the narrowest deep point, between Dawes Point and Milsons Point; and the sandstone of both shores could take the thrust of an arch. The width is compelled by the programme Bradfield wrote, rail, tram, road and foot at once. In the steel nearly every member answers the subtractive test: chords, bracing, hangers, the pins themselves. What does not is what most people would draw first after the arch: the four granite pylons, which carry nothing and could be removed without structural loss. Their defence is visual, and it is the defence of ornament.
Frank Darabont · Film
7.8 · Tier III
Most parts pass the subtractive test, and the strongest are paid together. The rock hammer, the poster and the Bible are set down early and returned in the one reveal. Brooks is required: his parole, his room, his death and the words carved on the beam are the fate Red must refuse, and Red’s later walk through the same room makes the rhyme bear weight. Tommy is required, since his story of the real killer turns Andy’s hope into the warden’s danger and makes the escape necessary. The tax returns, the library letters and the false name build the instrument of Norton’s fall. The give: the narration states what the image has shown, and the beach is a coda the argument permits more than compels.
Nas · Music
7.8 · Tier III
Ten tracks in about forty minutes, and the subtractive test finds little, though not nothing. The Genesis must open: a train, film dialogue and an old verse played back set the record as a beginning and as a recording of a place. N.Y. State of Mind must follow, the night and its danger stated at full density. Life’s a Bitch turns the night to morning, a twentieth birthday, “my born day”, and its cornet coda is the father answering the son. One Love is the one place the record speaks to the absent. The test bites twice, and on a record of ten it bites hard. One Time 4 Your Mind is the slightest song, a relaxed restatement of what Memory Lane does better, and Halftime, made before the record, sits as a showcase more than a step. One soft track and one inherited one, a fifth of the record that could leave with little loss, hold the figure below the eight.
Pierre-Auguste Renoir · Visual art
7.8 · Tier III
The subtractive test, figure by figure. Aline Charigot with the dog cannot go: she opens the picture at the left, and the hands lifting the dog are its nearest point of tenderness. The young Fournaise at the railing holds the left edge against the diagonal. The still life cannot go, because the light on glass and cloth sets the whole key. Caillebotte astride his chair closes the right corner, and the woman leaning toward him turns the group back in. Ellen Andrée drinking at the centre is the pivot. Further back the test gives: Ephrussi and his companion, or one of the heads at the back right, could be taken out and the picture would hold with fewer guests. The crowding is the subject, so most figures are required as a mass, not all as persons. The awning is required: it encloses the company and colours the light.
Andrew Haigh · Film
7.8 · Tier III
Run the subtractive test and the two strands resist it, because each is the other’s proof. The visits home are required: each is a stage in something Adam could not do at twelve, first being seen as a grown man, then coming out to his mother in her kitchen, then hearing his father admit that he heard the boy crying and did not go in, then the leave-taking. Harry is required because the film’s question is whether a man formed by that loss and by the fear of the 1980s can let anyone in now, and the answer is staged in the tower. The fire alarm and the empty building are planted and paid by the ending. What gives: the visits repeat their pattern once more than the argument needs, and the club night restates in delirium what the cutting has shown.
Radiohead · Music
7.8 · Tier III
Eleven songs in fifty-two minutes, and the frame is compelled. Daydreaming is the centre and could not go. True Love Waits must end it, a song with a long earlier life set down last as a plea. Burn the Witch is required as the one outward blow, the menace the private record turns away from. Most songs survive the subtractive test as parts as well as songs: Decks Dark, Glass Eyes and The Numbers each add a height the others lack. The test bites in the middle. Desert Island Disk and Ful Stop could go with a loss of variety, not of meaning, and Tinker Tailor restates the dread more than it advances it.
Alfred Hitchcock · Film
7.7 · Tier III
The subtractive test finds the spine required. The courtroom makes Alicia a traitor’s daughter before she speaks, and the reporters’ word for her is the title. The party and the drunken drive set her self-destruction and Devlin’s watching coldness, the two facts the film tests. The agency scene, the champagne left on the desk, turns love into an assignment; the marriage gives the plot its key and the theme its traded body; the party needs the champagne to run low; the poisoning is the price of discovery, the staircase the payment. What holds the axis is the middle: the agency men in Rio repeat their contempt more than once, and the race track covers ground the dinner had covered.
Ai Weiwei · Visual art
7.7 · Tier III
Judged by subtraction, part by part. Take away the hand and the seeds are industrial casts, and the work’s one claim, that the mass is made of individuals, collapses into a pile of product. Take away the painting and the seed is a blank; the few strokes make each one a seed and each one different. Take away porcelain and the work loses Jingdezhen, the material China sent to the world long before “Made in China” was a phrase. Take away the sunflower seed and it loses its two Chinas, the people as sunflowers turned to the sun and the snack shared in hard years. Take away the multitude and there is a craft object. What gives is the number: a hundred million was set by the hall, not by the argument.
The Walkmen · Music
7.7 · Tier III
Eleven tracks, and the record is lean: no track sprawls, and none repeats another’s arrangement outright. The frame is compelled. “Juveniles” must open, the method stated at once, a ringing guitar figure under a voice pitched near its limit; “Lisbon” must close, slower and resigned, its answer. “Stranded” is the hinge, where brass and a slow sway turn the record from speed to retrospect, and “While I Shovel the Snow” is the hush the close requires. The subtractive test bites in the middle: “Victory” and “Follow the Leader” are brisk sketches in the record’s ordinary manner, and “Woe Is Me” and “Angela Surf City” make the case for pace twice. Both spare songs are brief, and brevity keeps the cost small. The cap is cleared by four tenths.
Takashi Yamazaki · Film
7.7 · Tier III
The film’s spine is a debt, and the subtractive test finds most of its parts required by it. The unfired cannon on Odo Island is the wound; the photographs of the dead garrison that Tachibana thrusts at Shikishima are the debt written down; the minesweeper puts him back on the sea where the creature is; the ejection seat the wartime state never fitted is the ending’s answer to the kamikaze order. Remove the prologue and the ending means nothing; remove Noriko and the infant Akiko and there is no life to return to. What gives: the Takao sequence and the long briefing for the operation carry exposition the film could compress, Noda’s science is stated twice, and Noriko’s survival in the coda is permitted by the plot rather than required by it.
Martin McDonagh · Film
7.7 · Tier III
The subtractive test goes well for most of the film. The breach, the fingers, the donkey’s death and the burning house are a chain, each link caused by the one before, and the hour named for the fire, the hour the men used to walk to the pub, makes the reprisal the mirror of the lost habit. Siobhán’s departure is required: her letter from the mainland states the alternative to the island’s logic. Dominic’s drowning is the price the feud does not count. The test bites on the mechanism: the fingers arrive on a schedule announced and then fulfilled, at moments a device set running rather than a necessity uncovered. A tight film whose design shows.
My Bloody Valentine · Music
7.7 · Tier III
Nine tracks in about forty-seven minutes, and seven of them resist the subtractive test. She Found Now is required as the threshold and Who Sees You as the mode at its most unstable. The hinge and the close are compelled: Is This and Yes is the one place the guitar falls silent, and Nothing Is earns its repetition as the run-up the last track needs. The test bites twice, and that holds the figure. If I Am, the slightest song, could go without loss, since New You makes the case for plain melody better; and the first third holds three versions of one mode, so that Only Tomorrow, the strongest song, is one the sequence would survive losing.
Andreas Gursky · Visual art
7.5 · Tier III
The subtractive test has already been run, and by the maker: the picture is what was left when everything removable was removed. What stands is five bands and a path. Take away the path and the near bank is a flat green field: the image loses its one human mark and its one line of travel, the only sign that this land is kept. Take away the far bank and river and sky collide; that narrow strip of green is the hinge of the whole. Take away the overcast and the river becomes a holiday. Each band bears load. What yields is the exact proportion: a picture this reduced is easily imagined one band a little higher without loss. Reduction is not the same as necessity.
David Fincher · Film
7.5 · Tier III
The line is lean: six chapters, each a place, and after the first each a rung toward the man who paid, with nothing on the way that the climb does not use. The long Paris chapter survives the subtractive test, because the waiting is the matter: the yoga, the heart rate read on his wrist, the fast-food breakfast taken for protein, and the creed, “Stick to your plan”, laid down so that every later chapter can show it fraying. The miss is the hinge the whole film turns on. What gives: the voice-over often states what the image has already shown, a procedure explained while we watch it done; the Florida fight runs past what the argument needs into genre display; and the New Orleans chapter, an assistant pleading for a clean death, could be shorter without loss of a fact.
Geoffrey Chaucer · Literature
9.0 · Tier V
Within a fragment the parts are compelled, because each tale is required by its teller and by the tale before it: the Miller must answer the Knight, the Reeve the Miller, the Friar and the Summoner each other, and the narrator’s “Turne over the leef, and chese another tale” (A 3177) concedes that he may not cut. What holds the axis at its lowest is matter the whole could lose. The Physician’s, Shipman’s and Manciple’s tales could go with little loss; the Monk’s ninety-seven stanzas are long by design, but long; the Cook breaks off after fifty-eight lines. And the plan that would have compelled the scale is abandoned: “every man, save thou, hath told his tale” (I 25), one each, not four.
Jalal al-Din Rumi · Literature
8.9 · Tier IV
The subtractive test is hard on this poem. There is no plot to require anything: tales are opened, left for a gloss, opened inside one another, resumed books later, and some never close. Runs of exegesis could be lifted, one exemplum exchanged for another that teaches the same point, and fifty tales with many homiletic stretches in Books IV and VI could go without the loss of one claim. Rumi calls the tale a measure and the meaning the grain in it, which concedes that the measure can be replaced. What holds the figure is a spine of return: the reed’s complaint is the law every later tale is told under, and some tales bear weight nothing else bears. Moses and the shepherd carries the theology of forms; the merchant’s parrot, which escapes its cage by feigning death, the death before death the whole poem teaches.
William Blake · Literature
8.9 · Tier IV
Plate 3 claims that nothing is placed by chance, and the frame bears it out: the four addresses, the four opening designs, and Los going in at plate 1 and striding out at plate 97 cannot go. What holds the axis lowest is what the subtractive test removes. The catalogues of names, counties and cathedral cities (plate 16 and its kin) state the doctrine that only particulars are real rather than enact it. The laments of Vala and the Daughters return in near-identical formulas, and Albion’s fall is told several times over. And a run of chapter 2 stands in another order in some of Blake’s own copies, so its succession was not compelled.
Friedrich Nietzsche · Literature
8.8 · Tier IV
The test is subtractive, and it bites hardest in the first two parts. The spine is required: the Prologue’s failed descent, with the fall of the tightrope walker and the corpse Zarathustra carries; the turn from the crowd to companions; the thought he cannot yet speak in “Die stillste Stunde”; its confrontation at the gateway; the collapse and recovery of “Der Genesende”; the higher men of the last part. Each part ends on a withdrawal or a seal, and the order cannot be shuffled. What holds the axis lowest of the twelve is the speeches between. In Parts I and II many are freestanding sermons, “Vom Biss der Natter” and “Von Kind und Ehe” among them, and several polemics against priests, scholars and poets repeat one gesture of contempt; the argument would lose no step without them. Part IV earns its length by comedy and the midnight song, though “Von der Wissenschaft” and the Ass Festival are slack. The scale is permitted more than compelled.
Fyodor Dostoevsky · Literature
8.8 · Tier IV
This is the novel’s weakest axis and the case is plain. The spine is required: Myshkin, Nastasya Filippovna and Rogozhin, with Aglaya as the fourth term, and every scene in which they meet. But the novel was written month by month without a settled end, and it shows. The six months between the first part and the second are skipped and then explained by report. The Burdovsky affair, the claim of “Pavlishchev’s son” pressed by the young nihilists, runs long for what it yields. General Ivolgin’s lies and Lebedev’s apocalyptic commentary are rich in themselves and could be halved without the loss of a fact the book needs. Ippolit’s “Necessary Explanation” is necessary in substance and extended past need. What holds the axis lowest of the twelve is that many parts are present because a serial had room for them.
Victor Hugo · Literature
8.8 · Tier IV
The subtractive test bites harder here than on any novel of its rank, and the spine survives it with tighter joints than its reputation allows. The candlesticks (I.2) are the debt every later act repays; Fantine’s descent (I.5) is the price of Cosette; the Thénardier who robs the dead at Waterloo (II.1) is the creditor of Marius’s father, so that the battle is tied to the plot. The convent hides Valjean, and he leaves it in a coffin; the sewer carries Marius. But what is required is the event, not its length. Waterloo needs a chapter for the plot and receives a book; the convent essay (II.7), argot (IV.7) and the histories of 1817 (I.3) and of Louis-Philippe (IV.1) are compelled only in part. Hugo’s defence, that the subject is the whole age, carries their presence, not all of their length, and that length holds the axis lowest of the twelve.
Dionysus Flambouras · Literature
8.8 · Tier IV
Measured as well as impressioned. Verbatim duplication is near a tenth of one per cent of the text, and the repeats that recur are liturgical, Filed under: prior to everything, The form accepted the warmth without converting it. Much is built that could have been asserted: the field at Flax Hill, the interview that takes his cadence, the Bearers’ green books. The cetology now runs to ten short heads written beside a man fallen on the summit, and its middle heads no longer restate the first. The subtractive test still bites in three places. The night-register inventories run past their point; the fourth volume, two-fifths of the whole, ends three offices on one Monday by the same procedure, then states in decree and catalogue what the scene has already done; and the first and third volumes carry a satirical furniture of brands and tickers that accumulates rather than compels. Perhaps a sixth could go. The Necessity Cap clears, not by much.
James Boswell · Literature
8.7 · Tier IV
The subtractive test bites hard, and that is what holds this axis lowest of the twelve. A great deal could go without loss: the annual catalogues of Johnson’s publications and of pieces wrongly ascribed to him; letters printed because Boswell had them rather than because the life needs them; the running quarrels with Hawkins and Mrs Piozzi; Boswell’s own vanities set into the record. The years before 1763 are thin and partly compiled, and the proportion follows what the biographer happened to see. Against that, the core resists removal: the conversations are the life, and in the great scenes nothing is idle. The method is accumulation, and the man appears only through the mass. Still, the book admitted far more than its argument needed.
Louis-Ferdinand Céline · Literature
8.7 · Tier IV
The spine is the descent, and its outward half resists the subtractive test. The war must come first, because everything after it is the war carried into peace by other means; Africa and Detroit are required to show that the same order holds under the palm and on the assembly line. Robinson’s thread binds the halves, appearing at each station before Bardamu, so the episodic form is not merely a string. The return is where the test bites, and it is what holds the axis lowest of the twelve: the Rancy chapters are long, the Henrouilles’ plot to kill the old mother runs through more episodes than its matter requires, and the rants, which are the book’s voice, repeat their single argument more often than any one passage needs. Much of the Toulouse and Vigny material, and of the medical practice, could go with less loss than the book’s scale implies.
George Gordon, Lord Byron · Literature
8.7 · Tier IV
The poem invites the subtractive test and fails much of it. It opens “I want a hero: an uncommon want” (I.1), and has a plan only in jest. Whole runs in the ninth and tenth cantos, the Russian court and the illness, much of the twelfth’s preamble and parts of the English cantos could go without the poem losing an organ; the episodes are serial, and where the poem stops nothing is compelled back into shape. Against that, the digressions are not padding around a story but the poem’s argument, and the great sequences are tight: the shipwreck builds from the leak to the lottery to the sight of land, and the Haidée cantos turn on Lambro’s return with an Odyssean inevitability toward a death that is earned. What holds the axis lowest of the twelve: necessary in its parts and in its voice, assembled in its whole, and stopped where no ending can gather it.
Sigmund Freud · Literature
8.6 · Tier IV
The spine is required. The method is shown on one dream in the second chapter, the thesis stated in the third, the objection from unpleasant dreams answered by distortion in the fourth, the sources gathered in the fifth, the mechanisms set out in the sixth, and the seventh builds the apparatus that must exist if all this is true. Remove any of these and the argument has a hole. The subtractive test fails in three places, and they hold the axis at 7.8: the survey of the earlier literature in the first chapter, a duty performed whose results the later chapters restate; the symbolism section of the later editions with its catalogues, and the colleagues’ dreams in the footnotes, which add instance without argument; and the typical dreams and examples that run on past need. Perhaps a fifth of the book could go without loss of what it knows.
Lu Xun · Literature
8.6 · Tier IV
The subtractive test finds things to take, and that is what holds this axis lowest of the twelve. The major stories resist it: “Kong Yiji” has nothing idle in a few pages, the boy waiter, the counter, the fennel beans and the debt chalked on the board each bearing weight to the last line; “Medicine” is built in four sections, each required, from the dark street of the execution to the grave; “A Madman’s Diary” needs both its classical frame and its vernacular diary. But the book is an assembly of four years’ magazine work, and it could lose “The Rabbits and the Cat”, “The Comedy of the Ducks” and “A Small Incident”, a moral anecdote that states its lesson, with little loss; “The Story of Hair” is a monologue on queues that “Storm in a Teacup” dramatises better. Necessity is high in the parts and lower in the whole.
John Bunyan · Literature
8.6 · Tier IV
The spine is necessary: a man with a burden must reach the Cross to lose it and the River to die, and every station between is a stage of the soul’s experience that Bunyan had lived and set down in Grace Abounding (1666). The order of the trials is not arbitrary: humiliation comes before the dark valley, the fair before the giant, and despair after the companion is gained. What holds the axis lowest of the twelve is the middle. The road form admits addition, and Bunyan proved it, enlarging the Worldly Wiseman episode and other passages in 1679 without strain: the episodes are permitted rather than compelled. The long dialogues, with Talkative, with By-ends and his friends, Hopeful’s account of his conversion and the catechising of Ignorance, could each lose half and the book would know the same things.
Auguste Rodin · Visual art
8.6 · Tier IV
The subtractive test is the work’s weak point, and Rodin ran it on the work himself. He took The Kiss out because its embrace did not belong in a hell; in 1900 he showed the frame almost empty; figures passed in and out for thirty-seven years. At the level of the part much could go. What resists is the field, leaves without panels or ground, and the vertical order it requires: the fall below, The Thinker above it, the Shades over both. That necessity holds from the first plans to the last plaster, and it clears the cap. What holds the axis lowest is that it is a necessity of density, not of these figures in these places: a different selection from the same swarm would still be this work.
Apuleius · Literature
8.6 · Tier IV
The test is subtractive, and this is an accretive book: a short Greek ass story, filled. Much of the filling is required. Aristomenes’ tale and Thelyphron’s warn a man about to meddle with witchcraft, and Lucius hears both and goes on; the Actaeon group in Byrrhena’s atrium is the punishment of curiosity in marble, set before the curiosity begins; Cupid and Psyche, a forbidden look and a fall redeemed by a god, is the frame told small, and the eleventh book cannot be read rightly without it. Remove these and the book loses its argument. What holds the axis lowest of the twelve is the slack of the ninth and tenth books: the stepmother’s tale and some of the baker’s wife’s adulteries run on the Milesian appetite the prologue promised, not on the book’s need, and could go with little loss.
Charles Dickens · Literature
8.6 · Tier IV
The test is subtractive, and a serial of sixty-four chapters does not pass it whole. The spine is required: the child’s loss of mother and home to the Murdstones’ “firmness”, the warehouse and the flight to Dover, the aunt’s house, and the long education of what Annie Strong calls “the first mistaken impulse of an undisciplined heart”. The Emily plot is bound to it through Steerforth, whom David brought to Yarmouth. What holds the axis lowest of the twelve is what could go: most of the Doctor Strong household beyond Annie’s phrase, Jack Maldon, much of Martha, the late chapter in which Heep and Littimer reappear as penitents in a model prison to serve a topical satire, and a share of the comic repetition. Perhaps a tenth of the book is serial padding or occasional satire.
George Eliot · Literature
8.6 · Tier IV
The case against is famous: F. R. Leavis, in The Great Tradition (1948), proposed cutting the book in two and keeping a novel called Gwendolen Harleth. The subtraction fails on its own terms. Gwendolen’s is the story of a self with no larger loyalty than its wants, and the book measures her by a man who finds the loyalty she lacks; take his vocation away and his rebukes to her become a clergyman’s. The Alcharisi is Gwendolen’s double and Deronda’s origin at once, and only the double plot makes her both. What holds the axis lowest of the twelve is bulk: much of the Jewish strand is expository, and Mordecai speaks at a length the scenes do not compel. The architecture is necessary; much of that bulk is not.
Limbourg brothers · Visual art
8.6 · Tier IV
Judged on the programme, part by part. The calendar resists subtraction: twelve months are twelve, each bound to the sky by its lunette, and the alternation of the lords’ months, January’s feast, April’s betrothal, May’s ride, with the labourers’, February’s snow, March’s ploughing, June’s mowing, July’s shearing, October’s sowing, is its argument; take any month away and the year is broken. The Anatomical Man, the hinge between the calendar and the body, cannot go. What holds the axis lowest is that a book of hours is an assembly by nature. Many of its miniatures are required by the liturgy rather than by the book’s argument: a Penitential page or a later Passion scene could go without loss, Colombe’s pages could go with gain, and the scale is permitted by the commission more than compelled.
Lewis Carroll · Literature
8.5 · Tier IV
The subtractive test bites harder than the book’s fame suggests. It is episodic by construction: a child passes through encounters, each a closed scene, and several could go without the line breaking. The Caucus-Race and the Mouse’s tale (chapter III), the Lobster Quadrille (X) and much of the Mock Turtle’s schooling (IX) could be removed, and the book would lose jokes, not knowledge. Its own record says the same: the story told on the river in 1862 and written out as Alice’s Adventures Under Ground was expanded for publication, so the frame admitted parts rather than required them. Two spines bear load and hold the figure near eight: the size changes, which carry the question of who Alice is, and the garden glimpsed through the little door in chapter I and found in chapter VIII to be a tyrant’s croquet ground.
Khmer, under Jayavarman VII · Architecture
8.5 · Tier IV
Judged on structure, purpose and site. The parts that carry the meaning resist the subtractive test. The towers multiply because the faces must look everywhere: one face would be an image, faces on every tower a presence, and the repetition is the purpose. The three levels are required by the ascent from the common world of the outer reliefs, through the myths of the inner gallery, to the faces and the Buddha at the top. What yields, and holds the figure at the foot of the page with The Inner Law, is the plan as built. It records its own revisions: galleries altered as it rose, a terrace so crowded that towers nearly touch and courts shrink to shafts, spaces left over rather than intended. The building was assembled toward its idea, not compelled into it.
Paul Celan · Literature
8.5 · Tier IV
The test is subtractive, and in a collection it falls unevenly. “Todesfuge” cannot lose a line: each refrain returns because the order it records returns, and each variation arrives exactly where the fugue requires the new voice. “Espenbaum” is as close: every couplet pairs a thing in nature with the mother who did not come home, and none could go. “Corona” builds to its close and stops. But the book also holds poems whose images are exchangeable, the genitive chains of the surrealist years in Bucharest and Vienna, where one mill of death could stand for another, and a number of the later love poems could go without the book losing its argument. The centre is necessary; the margin is assembled.
Luis Cernuda · Literature
8.5 · Tier IV
The subtractive test is put to a life’s verse, and it finds necessity in the design and surplus in the parts. The design is required: one title over an order by date, so that the conflict the title names works itself out across forty years, from the young man at the window of the first poems to the old exile who has the reality and has lost the object of the desire. The late poems need the early: “Peregrino” answers the gardens of the first books, and “Díptico español” answers “Elegía española”. What holds the axis at 7.8, the lowest of the twelve: the first two sections are apprenticeship, kept as the start of a story rather than for their own necessity, and the long meditations of Como quien espera el alba and Vivir sin estar viviendo repeat their argument more than they advance it.
Samuel Johnson · Literature
8.5 · Tier IV
One of the two lowest of the twelve, and the subtractive test shows why. The scope was set by booksellers. Take away the lives of Sprat, Halifax, Stepney, Duke, King, Yalden, Pomfret or Walsh and nothing Johnson has to say is lost: several are thin compilations from Cibber’s Lives and like sources, done to fill the set, and the Life of Young is largely Croft’s. Against that, the great lives are compelled from within. In the Milton, the Dryden and the Pope the life is required by the criticism and the criticism by the life, and the Savage is a life that is its own argument. The minor lives serve as ground and as history, but a history could lose a dozen of them. About half the book is required, and that half supremely.
Constantinian, Crusader and later builders · Architecture
8.5 · Tier IV
The core is compelled as few buildings are. The site was fixed by the tomb and the rock, not chosen. The rotunda is required by the tomb, which Constantine’s builders freed from the hill so that a circle could close round it; the Calvary chapels are required by the rock; the Crusader church by the purpose of bringing every station of the Passion under one roof. Beyond that core the subtractive test finds much that could go. The chapels of the communities are placed by possession, not purpose; the walling-in of the crossing, the screens, the piers of 1810 and the altars and lamps could be taken away with no loss to what the building says. The sideways entry is an accident of history.
Euripides · Literature
8.4 · Tier IV
The spine is necessary and economical: a chain of reversals in which every decision is taken back. Agamemnon recalls the summons by night; Menelaus seizes the letter; the women arrive; Menelaus relents, and the relenting no longer matters, because the army knows. Remove a link and the trap does not close. What holds the axis lowest of the twelve is what the transmitted text carries around that spine: two prologues that overlap, a catalogue of ships in the parodos far longer than the women’s spectacle needs, a messenger’s narration of a substitution the play has not prepared, and scenes that repeat what they have done. Something near a sixth could go without loss to the argument, more than in the strongest tragedies.
Giulio Romano · Architecture
8.4 · Tier IV
Run the subtractive test part by part and much of the building resists it, because the joke requires the rule. Take away the dropped triglyph and the court is merely correct; take away the rough block beside the dressed one and nothing is said. The Sala dei Giganti is compelled throughout: one room with its corners rounded away, one image, no exit for the eye. But the whole was not compelled. It grew out of stables, and the fronts, the rhythms of the bays and the order of the rooms bear the marks of existing walls and of campaigns added one to another. The four fronts are not four answers to one problem; the circuit of rooms is a suite of themes ordered by occasion. What holds the axis here is a plan accreted, not required.
Jorge Luis Borges · Literature
8.4 · Tier IV
One at a time the essays pass the subtractive test almost as well as the fictions. “Kafka y sus precursores” is two pages: the precursors, Zeno, Han Yu, Kierkegaard and Browning, with Bloy and Lord Dunsany named after them, and then the turn, and nothing could go. “La esfera de Pascal” runs one metaphor from Xenophanes to Pascal in a few pages without a spare clause. The book does not pass. It keeps what a journalist’s collection keeps: “Dos libros”, the note on Shaw, the polemic against Américo Castro, reviews whose subject has dimmed, a Valéry essay that is mostly a pairing. Remove a quarter of the book and the book is stronger. Held above the cap because the core is required and the weak pieces are short; held well below the fictions because this collection shows that it was assembled.
J. G. Ballard · Literature
8.4 · Tier IV
The design is required: the first chapter states the end, and every encounter after it is a step on the road to the flyover. Helen Remington joins the narrator to the man he killed; Gabrielle carries the wound made erotic; Seagrave’s death rehearses Vaughan’s; Catherine is the marriage the system absorbs. None of them could go. What the subtractive test finds is the litany: the dashboard, the instrument binnacle, the chromium, the wound, the semen, the photograph, laid out again in each encounter in the same clinical order. The repetition of encounter is the meaning, an obsession shown as obsession. But in the middle chapters the inventories return after their law is learned, and several encounters could go with nothing learned lost.
Miles Davis · Music
8.4 · Tier IV
Ninety-four minutes in six pieces, and the subtractive test finds both resistance and give. “Pharaoh’s Dance” must open: it states the method, an ensemble without a centre, and its edited form announces that the studio is the composer. The title track is the centre of gravity. “Sanctuary” must close, the brew ending in a hush. The give is large. “Spanish Key” is the most separable side, a long rock vamp; “John McLaughlin” is an excerpt cut from the sessions and stands as an interlude more than a piece; and inside the two long pieces there are stretches where the vamp holds and nothing turns. Length is not charged; the trance needs time. But a quarter of the record could go without the argument losing a step, which holds it well under Low and Remain in Light at 8.4.
Katsuhiro Otomo · Film
8.4 · Tier IV
The spine resists the subtractive test: two orphans from the same institution, the protector and the protected, and a power that turns the weaker into a god and ends him. Every set piece presses on that one wound: the bar where Tetsuo is slapped, the hospital dream in which toys and milk swarm his bed, his killing of Yamagata, the stadium. What holds the axis lowest of the twelve is what lies around the spine. The film compresses a manga of six volumes into two hours, and the compression leaves surplus that is not required: the council and Nezu’s treachery, the resistance cell and Ryu, Lady Miyako’s cult, each opened and then dropped or closed in a line. Kei’s mediumship, through which the Espers speak, does work the film has not prepared, and the Colonel’s coup is staged and then abandoned at the climax. Necessary on its main line, assembled at its edges.
Almohad builders; cathedral by Gothic masters · Architecture
8.4 · Tier IV
Judged on purpose, structure and site. The Giralda passes the subtractive test almost whole: the core and the ramps are the structure and the way up, the lattice panels lighten the faces where the load allows, and the belfry is required by the new use, bells hung where the call to prayer was given, its stages diminishing as the tower must. The church passes in its spine, the coro and the Capilla Mayor where the chapter’s liturgy is compelled to be. What yields is scale and edge, and that is what holds the axis low: a rectangle fixed by a mosque’s footprint, a breadth of five aisles that is ambition more than use, and an outer ring added room by room.
Sienese builders; facade by Giovanni Pisano · Architecture
8.4 · Tier IV
Judged on plan, structure and use. The core resists the subtractive test: a basilica on a ridge, the crossing at the summit of the hill, the dome over the point where the cathedral stands highest in the city. The choir carried over the slope is compelled by the site and makes the baptistery beneath it, the font below the altar. The striping is not ornament laid on: it is the construction, coursed in the city’s colours. What holds the figure here is how much yields. The crossing’s hexagon is irregular and sits awkwardly against the bays; the cornice of popes, the accumulated chapels, the upper facade’s gables and the profusion of the floor could go, and the church would still say what it says. Necessary at its core, assembled at its surface.
Christina Rossetti · Literature
8.4 · Tier IV
The title poem is close to unsubtractable. Its long catalogues of fruit look like excess and are the temptation itself: the list is the market’s patter, and to cut it would cut the appetite the poem is about. Jeanie, the girl who ate before and died of it, is a few lines, and carries the whole threat of what Laura will become. The sisters’ night, Laura’s wasting, Lizzie’s ordeal and the recovery each bear weight, and the coda, “For there is no friend like a sister”, is the thesis given to the children it names. The cap is set by the book, not the poem: the ballads repeat one plot of the jilted or betrayed woman, the devotional pieces restate one another, and a volume without a third of its poems would know almost all it knows.
Vakataka · Visual art
8.4 · Tier IV
Judged on structure. The threshold resists the subtractive test: the great Bodhisattvas at the shrine door of cave 1 are the turn from the world of the walls to the image in the shrine, and every hall keeps that turn. Below that level the test bites. No jataka is required by another; the cycles are placed by wall space and patron, stories recur between caves, scenes of one story are set out of order, and the ceilings are ornament. Cave 2 could lose its Vidhurapandita and the programme would say what it says. Four halls with separate patrons are an aggregate as much as a structure: necessity holds at the threshold and loosens in the field.
Aldous Huxley · Literature
8.3 · Tier IV
The spine holds. The book shows a world from its making to its uses and then to the one man it cannot absorb, and each block is required by the argument. The hatchery comes first so that every later pleasure is read as manufactured; the Reservation comes before London so that the Savage carries an outside into it; the Controller must speak because the book’s wager is that the system can justify itself. The subtractive test bites in three places. The exposition of the first two chapters runs past what the reader needs. Bernard Marx, set up with care as the misfit who wants to be different, is abandoned once his celebrity is shown to be vanity, and he and Helmholtz Watson are sent to islands in a sentence. Helmholtz, promised as the poet the state cannot use, is given almost nothing to do. Perhaps a fifth of the book is permitted rather than compelled.
James Ensor · Visual art
8.3 · Tier IV
Judged subtractively, the structure is compelled. Remove the mass of the crowd and Christ is no longer lost in his own procession, which is the picture’s argument. Remove the stand at the right and no state watches the crowd go by. Remove the banner and the parade has no politics, only carnival. Remove the front rank of masks against the plane and the viewer is not made part of the throng. The scale, more than four metres, is compelled too: the crush has to exceed the eye. But much is permitted. Mask after mask in the middle ranks could be fewer or other without loss, and whole passages are a count of faces rather than a structure of them. The excess is partly the point, and more than the point needs.
Hermann Hesse · Literature
8.3 · Tier IV
Much is required. The preface sets the bourgeois view of Haller beside his own, and the book’s argument is that he is a product of the order he despises. The Treatise is required in principle, since it supplies the theory of the many selves that the Magic Theatre will stage; the scene at the professor’s, with the Goethe engraving, is exact and necessary. What holds the axis here is that the Treatise explains in advance what the ending enacts, so that the book says its thesis twice, once as essay and once as phantasmagoria, and the second loses force by being foreseen. The middle, the dance lessons and the evenings with Maria and Pablo, earns its place but runs long and repeats its one lesson in several keys. A careful editor could cut perhaps a tenth without loss.
Attributed to Domenico da Cortona, under Francis I · Architecture
8.3 · Tier IV
Run the subtractive test on the keep and it holds. Take away the staircase and the cross of halls has no centre; take away a hall and a lodging loses its anteroom and the plan its symmetry; take away the corner towers and the lodgings lose their closets. The idea of four equal lodgings round a common centre is carried out without remainder. What does not resist is the purpose. A king who came for short stays, an enclosure that took a century and a half to close, a roof of chimneys and lanterns beyond any household’s need: much of the roofscape could go and nothing lived inside would change. The parts are required by the geometry and the display, not by dwelling or the hunt.
Martin Scorsese · Film
8.3 · Tier IV
Judged on structure, and the frame is compelled. The temptation at the end is worth nothing unless the life it offers is wanted, and the first two hours exist to make the viewer feel a man who wants to be let off: the crosses he builds for Rome so that God will hate him, the night at Magdalene’s house, the circle in the desert. The ending needs every station before it, since the old man on his deathbed is judged by the disciples we watched him call. What holds the axis lowest is the middle. The ministry runs as a chain of Gospel episodes ordered by the source more than by the argument; several could go with little loss, and the monastery and some of the preaching restate a doubt already stated. About a fifth of the running time is permitted rather than required.
Charlie Chaplin · Film
8.3 · Tier IV
The film is picaresque, and the subtractive test finds give. The factory is required: it sets the law the rest obeys, the body taken over by the line. The return to the factory and the strike close that law. The girl’s entrance, her father shot in the street, is required: it gives the film its second person and its stake in hunger. Much else is a station of one cycle. The prison could go; the shipyard is a single gag; the department store, the comic summit, could be another night job without loss of meaning. The repeated arrest is the argument, but the stations are chosen for comic yield, not compelled by it, and that is what holds the axis lowest of the twelve.
Diogo de Boitaca and João de Castilho · Architecture
8.3 · Tier IV
The subtractive test divides the monastery. The church passes most of it: six columns carry the whole net of the vault, so none can go, and the transept must be the span it is or the hall breaks into bays. The cloister passes as a cloister, with the chapter house and refectory a house of praying monks requires. What holds the figure lowest is ornament as profusion: a south portal that rises past what any door compels, cloister carving repeated rather than argued, columns carved in a programme that could be thinned without loss, a main chapel rebuilt rather than required, and the nineteenth-century wing, a frontage its uses did not compel. The core is necessary; the envelope is permitted.
Lluís Domènech i Montaner · Architecture
8.3 · Tier IV
The subtractive test bites on a building of this kind, and that must be said first. Much of the ornament could be thinned without the hall failing as a hall: the tiled roses of the ceiling, the floral capitals, the density of mosaic in the foyer. The generation that followed said exactly that. But the parts that carry the work resist removal. The metal frame is required by the site, a cramped plot with no room for outward thrust, and by a programme that wanted a large room high in the building. The glass walls are required by the governing idea, a room of daylight. The proscenium is required by the client’s programme. The extension is servant work, needed and not idle.
Hildegard of Bingen · Music
8.3 · Tier IV
The spine resists the subtractive test. The Souls’ lament gives Anima her reason to leave; her leaving lets the Devil speak; the Virtues’ procession is the company she has left; her return is wounded, so the Virtues must receive what they warned against; and the binding of the Devil is the drama’s one act. Remove the prologue and the drama loses its frame in salvation history; remove the closing chorus and the soul’s wounds lose their answer in Christ’s. The give is in the middle, and it is large. The Virtues present themselves one after another, each with a short declaration and a choral answer, and several stations, Verecundia, Disciplina and Innocentia among them, could go without a step of the argument lost. A litany is additive by nature, and a third of the work is litany.
Wang Xianchen; Wen Zhengming (attributed design) · Architecture
8.3 · Tier IV
In a garden the subtractive test bites differently. The water cannot be removed: every hall faces it, every route bends round it, and the islands exist to break it into near and far. Without the two islands the Hall of Distant Fragrance would look onto an open sheet with nothing to hide and nothing to reveal; without the galleries there would be no means of withholding. But much here is accumulated rather than compelled. The Qing filled the Ming garden with buildings Wen Zhengming’s album does not show, and many pavilions could go without loss; the western part is a second garden joined at a wall, and the eastern lawns answer no necessity of the central idea. The parts are often permitted rather than required.
Nan Goldin · Visual art
8.2 · Tier IV
The subtractive test is hard on a slideshow of some hundreds of frames, and the work’s own history answers it: the sequence changed from showing to showing, slides came in and went out, and the work remained itself. Most single frames are not required. What is required is the architecture: couples, then the men, then the women, then sex, then the bruise, then the long reckoning, so that the pictures of tenderness are read again in the light of the pictures of harm. Some frames bear the load past substitute: without the battered self-portrait of 1984 the photographer never becomes the subject of what she witnesses. The book is tighter than the show, but the method is accumulation, and an accumulation is easily imagined a quarter shorter. Necessity sits in the whole, not the parts.
Ancestral Puebloan builders · Architecture
8.2 · Tier IV
The site compels the governing figure. The house sits on the north side of the canyon, its curved back to the cliff and its open face to the winter sun, and its terraces step down to the plaza so that every upper roof was a working floor in view of the court. The thick lower walls are compelled by the storeys they carry; the plaza wall and the great kivas stand where the plan says the community meets. Below the figure the subtractive test bites. The house is accretive, campaign over campaign, and holds long ranges of near-identical cells, many without hearths, many filled late with refuse or burials, whose purpose is still argued. A wing could be taken away and the house would still be itself; that holds the axis among its lowest.
Aeschylus · Literature
8.2 · Tier IV
The spine is required, and its middle is the most necessary thing in it. Each of the seven pairs advances the one question the play exists to answer: who will stand at the seventh gate. The order of the gates is the order of fate’s approach, and Eteocles’ assignments, made as if freely, leave him the one gate left; remove a pair and the arithmetic of the curse fails. What is not required: the parodos and the rebuke that follows run long on one point, the women’s terror and his contempt; the lament turns on itself more than it advances; and the transmitted close, about a fourteenth of the whole, opens a new action the play has not prepared and does not resolve. That close is the main charge.
George Orwell · Literature
8.2 · Tier IV
The subtractive test bites twice. First, and most plainly, on the political chapters: at the head of the fifth Orwell tells the reader who is not interested in “the horrors of party politics” to skip it, and a book that licenses its reader to skip a chapter has conceded that the narrative does not require it, whatever the record does. Later editions set both analytic chapters as appendices, which confirms that they are separable. Second, the front is long on tedium: firewood, lice, cold, the absence of fighting. Here the test mostly fails to bite, because the tedium is the finding. The spine is required: the revolutionary city, the front, the city turned, the wound, the hunt, the flight, England. Held below 8.0 for the conceded and separable analysis, and for some repetition in the accounts of the front.
Indian builders (Gupta and later) · Architecture
8.2 · Tier IV
Judged on purpose, structure and site, and the governing fact is compelled: a tower set at the place, its image facing east as the Buddha sat, the tree at its back, so that the building stands between the visitor and the seat it marks. Height is required too: on the flat plain of Gaya the tower is the sign that the place is here. The subtractive test bites elsewhere. The faces are a field of niches, tier on tier, ordered rather than required; the four corner towers repeat the centre at small scale and could go without loss of what the temple says; the upper chamber has no purpose the plan makes plain. The core is necessary. Much of the surface is accumulation, and that holds the axis among the temple’s lowest.
Qutb ud-Din Aibak and Iltutmish; upper storeys by Firuz Shah Tughlaq · Architecture
8.2 · Tier IV
The purpose is double: a minaret from which the call could be given to the mosque beside it, and a tower of victory setting a new faith and a new power over the city it had taken. The second compels the scale; the first does not, since no voice carries from seventy metres. Within the shaft much survives the subtractive test. The taper is the answer to height in stone; the balconies mark the storeys and stiffen the ring; the inscription bands are the tower’s statement. What yields: the alternation of flute patterns is not compelled, the balconies were scarcely usable for the call, and the upper storeys read as a completion rather than a necessity.
F. W. Murnau · Film
8.2 · Tier IV
Judged on structure, since the film’s words are titles. The spine is required: the contract that sends Hutter east, the castle that shows Orlok to the man who will bring him, the portrait that sets his desire on Ellen, the ship that carries death by water, the town that dies, and the woman whose giving ends it. The crosscut of the third act, Ellen rising in her sleep as Orlok turns from Hutter’s bed, is the hinge and cannot go. The subtractive test bites elsewhere: Bulwer’s lecture states by analogy what the film shows, the Harding household exists to receive Ellen, and Knock’s escape and the town’s chase are slack and half comic. The core is compelled; the fourth act is permitted.
Bret Easton Ellis · Literature
8.2 · Tier IV
The test is subtractive, and the book’s defence is that the excess is the argument. The restaurant scenes, the morning routine, the inventories of what each guest wears and the reservations sought at Dorsia repeat with small variation; the killings, in the second half, repeat with escalation. Cut the repetition and the argument becomes an anecdote: the claim is that a life composed of interchangeable surfaces has no events, and the reader must be made to undergo that sameness. The three music chapters are required, as the purest form of the voice, which can only praise. What holds the axis is that the repetition outlasts its point. A reader grasps the law of the catalogue well before the book stops applying it, and several killings and several dinners could go without the knowledge changing, perhaps a fifth of the whole.
Sebastião Salgado · Visual art
8.2 · Tier IV
The test runs on two levels. Within the strongest frames little can go: in the wide view of the pit the ladders turn a crowd into an ascent, the terraces give the scale its steps, and the rim is the only exit and the only horizon; take any away and the picture is a crowd in a hole. In the picture of the miner and the policeman the rifle between them is the whole argument. But a series is assembled, and this one admits the question. The carrier on the ladder recurs, the mud-covered body recurs, and several frames make the same point at a slightly different distance; the series has been shown in sets of different size without seeming incomplete. Necessary in its principal images, accreted in its body.
Steven Spielberg · Film
8.2 · Tier IV
Run the subtractive test and the film divides. The landing resists it: without the beach there is no measure of what eight men’s lives are worth against one, and the mission is weighed in its terms to the end. The German prisoner the squad spares at the radar position returns at Ramelle among the attackers and fires the shot that kills Miller; Upham’s plea for him, and Upham frozen on the stair, are paid for in Upham’s last act. The bridge named early as the one to hold is held. What gives is the march: the talk on the road, the sorting of dog tags, the paratrooper’s glider story could be reordered or cut with little loss. The Washington movement is required by the plot but runs to reverent excess, and the frame can be removed outright. Above the cap, well short of a work whose every part is required.
Can · Music
8.2 · Tier IV
Seven tracks in over seventy minutes, and the subtractive test bites harder on a double record than on a single one. Side one cannot go: Paperhouse, Mushroom and Oh Yeah are the songs from which the record descends. Halleluhwah cannot go; it is the record’s centre and its proof that one pattern held long enough becomes a world. Bring Me Coffee or Tea cannot go, since the descent needs its return. The test bites on the second disc. Aumgn and Peking O are what a hostile listener cuts, and within them the cutting is easy: stretches of Aumgn are texture held because the tape ran, and Peking O is as much a collage of incidents as a necessity. Their place is required; their length is permitted, not compelled.
Martin Amis · Literature
8.2 · Tier IV
The subtractive test bites, and the book has a strong defence. Self must be kept drunk, broke, jet-lagged and distracted for the con to work: the binges, the flights, the calls from an anonymous voice on the telephone and the meetings with actors who will not do what the script asks are the means by which a man is kept from seeing that the money he spends is his own. Cut them and the plot becomes an anecdote with a twist. The chapters with Martin Amis and the chess game are required: they are where the trap is shown. What holds the axis is that the repetition outlasts its function: the reader grasps the law of the binge well before the book stops applying it, and several drunken set pieces, and some of the scenes at the Shakespeare, could go. Perhaps a sixth is permitted rather than compelled.
Jim Jarmusch · Film
8.2 · Tier IV
The spine is a dying, and the film’s slowness is required by it: a bullet lodges by Blake’s heart in the first act, and the rest is the time it takes him to die. Most stations are required: the train into the machine, Machine and its owner with the shotgun, the night with Thel that makes him a killer, Nobody the guide, the trading post, the village and the crossing. What holds the axis here is the episodic middle. The trappers’ campfire and parts of the hired killers’ parallel track are comic set pieces that sharpen tone more than they advance the passage, and a share of either could go without loss. The fades make each episode a bead on one string, which keeps looseness from becoming assembly.
Charles Garnier · Architecture
8.2 · Tier IV
Judged on plan, section and structure, under purpose and site. The parti resists the subtractive test. Each function has its own volume, and the volumes rise in the order the use requires: the low entrance front, the dome over the hall, the fly tower highest because scenery must rise its full height above the stage, then the offices and workshops behind. The two pavilions answer two kinds of arrival. The stair and foyers, which take as much of the building as the hall, are compelled once the opera is granted as an evening of society whose intervals are half its use. What yields is the surface: much of the sculpture, the marbles, the gilding and the lesser orders of ornament could go and the house would serve as before. It spends far past what its purpose compels, and stands above the cap, not far above.
Miloš Forman · Film
8.2 · Tier IV
Judged on structure, the spine is required from end to end. The vow, the first hearing, the burned crucifix, the plot against the Requiem, the dictation and the absolution are each a step in Salieri’s war on God, and the frame gives every scene a confessor to answer to. The core resists subtraction: the March of Welcome, which Mozart takes up and mends at the keyboard in front of its composer, is the whole rivalry in one scene. What gives is the middle. The parody of Don Giovanni at Schikaneder’s theatre, the maid planted in the household and much of the court comedy restate what is already plain, and Katerina Cavalieri’s affair is gestured at rather than built. At about 160 minutes the second hour is long by permission, and that holds the axis among the lowest.
William Gaddis · Literature
8.2 · Tier IV
The test is subtractive, and it bites. The main structures are required: the opening scene, the opinion on Cyclone Seven, Oscar’s deposition, the play. Each is a different instrument through which the same failure of justice sounds, and the book loses an argument if any one goes. But the chosen subject is repetition, suits begetting suits and the same grievance rehearsed in new jargon, and the scale is more permitted than compelled. Oscar’s laments to Lily, Christina’s to Oscar and the telephone fragments with lawyers circle a fixed set of complaints well past the point where the circling has shown what it shows. The defence, that the tedium is the knowledge, is the book’s own and partly holds; it holds better over a scene than over five hundred pages. Perhaps a fifth of the domestic exchanges could go without the book knowing less.
Qing builders, under the Qianlong Emperor; rebuilt under Cixi · Architecture
8.2 · Tier IV
Judged on plan, use and site. The core is compelled. The lake was dug as the capital’s reservoir and as the garden’s ground, and the hill was reshaped beside it to face it: take either away and nothing else stands. The front-hill axis is required: it is the one line that turns a hill into a throne and gives the whole lake a point to look at. The Long Corridor is required by the north shore: without it the hill’s foot is a set of separate courts, and the walk in shade and rain is lost. What resists the subtractive test is the garden’s nature. An imperial garden is additive, a collection of scenes, and many pavilions, kiosks and small courts could go without loss; the shopping street and much of the west shore are pleasure, not necessity.
Victor Fleming · Film
8.1 · Tier IV
The Kansas prologue is lean: every element is set up to be paid in Oz, Miss Gulch on her bicycle, the three hands, the crystal ball, and the threat to Toto that sends Dorothy running and so keeps her out of the cellar when the cyclone comes. The road has a rule of addition, one companion and one song at each stop, and nothing on it could be lost. What fails the subtractive test is the middle. The Emerald City sequence, with its song, its horse of a different colour and its grooming, and the Lion’s song of what he would do as king, are vaudeville turns the story waits through; the poppy field is a delay the Witch’s plot barely needs. Necessary at both ends and on the road, assembled in the city.
J. G. Ballard · Literature
8.1 · Tier IV
The spine is required. Each of the three levels needs its witness: Wilder climbs from the second floor, Laing settles on the twenty-fifth, Royal watches from the penthouse, and without one of them the vertical argument loses a register. The frame is compelled as well. The book opens with the dog already being eaten, so every later step is read as a step toward that balcony, and suspense gives way to inevitability. The subtractive test bites in the middle third. The raids, the parties, the blocked chutes, the failed lifts and the broken stairways recur with a sameness that is partly the point, since the regression is incremental; but the repetitions run past the turn each one adds, and several of Wilder’s episodes on the way up restate his descent without deepening it. Perhaps a sixth of the book is permitted rather than compelled, and in a short novel a sixth is a real proportion.
Built for Yajnavaraha · Architecture
8.1 · Tier IV
The subtractive test is passed by the plan and partly failed by its scale. The plan is required by its ritual: the east axis runs from causeway to gopura, across the moat, through the court and the antechamber to the sanctuary, and the concentric enclosures step a worshipper inward toward the image. The three cellas sit on one platform, the libraries face the gods across the court, and little could go without loss. The carving is the hard case, since every surface is worked and some foliate panels repeat; the answer is that density at this scale is the meaning. What holds the axis at 7.8 is that the reduction of the whole Khmer order to near miniature was chosen by a patron, not compelled by the purpose.
Max Ernst · Visual art
8.1 · Tier IV
The subtractive test bites in two places. The terrain cannot lose its corrosion without ceasing to be the picture; the sky cannot go, because its blue makes the rot read as the aftermath of weather on a whole continent rather than a study of texture. The long format is compelled, a continent, a horizon, a panorama of ruin, and nothing in it is idle filler. But the figures read as found and kept rather than required: the method is to look into the accident and elaborate what it offers, and another pass would have offered other figures. The picture is also an anthology of incidents that could be redistributed without its meaning changing. Well above assembled, below the works where every passage carries load.
James Gibbs · Architecture
8.1 · Tier IV
Judged on purpose, structure and site, and the site compels much. A building set free in the middle of a square, seen from every street that enters it and every college that faces it, has no back and no side; a centralised plan answers that, and the round form is the one shape that gives every approach the same face. The memorial purpose, a dead man’s gift made a monument, compels the dome. What resists the subtractive test is the library. A round room is a poor shape for books: the cases sit in wedge-shaped bays between piers, the floor is small for the volume, and the ground storey, an open arcade, held no books and served no reading until the 1860s. The dome is required by the monument and the square, not by readers.
Gustav Klimt · Visual art
8.1 · Tier IV
Judged on the configuration. Three things resist removal: the face, the hands, and the field of gold that has taken everything else. Remove the field and it is a society portrait of a dark-haired woman; remove the face and it is a gold panel. The meaning is in the ratio between them, and the square is required to hold the gold on every side. Below that level the subtractive test bites. The ornament is additive by nature: an eye-motif more or less on the gown, a spiral field moved from the chair to the wall, a band of chequer at the lower edge, and the picture is the same picture. The discs and flecks of the upper field are distributed, not placed. The scale of the gold is compelled; the inventory of motifs within it is permitted.
Iris Murdoch · Literature
8.1 · Tier IV
The test of what could be removed bites here more than on most books at this level. The central line is iron: Charles finds Hartley, decides she must still love him, besieges and finally imprisons her, and loses Titus to the sea. Around it runs a long carousel of arrivals, Lizzie, Gilbert, Rosina at the window, Peregrine, each with a scene of recrimination and reconciliation that often rhymes with the last. The defence is real: every visitor is a former possession of Charles’s, and the parade shows a man who has always treated people as cast; the pages on food and on the theatre are the self-portrait, not ornament. Even so, much of the London visitors’ talk could go with little loss, and the “Postscript” restates in reflection what the “History” showed. Required at the core, assembled at the margins.
Timurid and Ashtarkhanid builders · Architecture
8.1 · Tier IV
Judged on purpose, structure and site. The madrasas are compelled by use: cells round a court for students who lived and studied there, iwans for teaching, corner halls for lectures, a mosque where Tilya-Kori’s quarter needed one. The ensemble is compelled by the square: each portal turns to the centre, and Sher-Dor’s whole form is dictated by the building it answers across the space. What resists the subtractive test is what makes the Registan seen: the pishtaq is a screen raised far above the cells behind it, Sher-Dor’s ribbed domes stand over rooms that do not require them, and Tilya-Kori’s front is an arcade of cells dressed as a wall. The defence holds in part: display was part of the purpose, and the display is not assembled. Three portals, one centre.
Joel Coen and Ethan Coen · Film
8.1 · Tier IV
Judged on structure, under a wager that the plot has no centre: the kidnapping was never one, the briefcase held Walter’s laundry, the millionaire is broke, and the Dude ends where he began. Under that wager the plants are paid with care. The rug is the cause and the last thing missing; the Creedence tapes go with the car; the homework left in the car leads to Larry Sellers; Bunny’s toenail polish undoes the severed toe; Walter’s ringer and his Shabbos rule each pay twice. Donny’s death, the bowling refrains and the Stranger carry the theme and could not go. Held below the top by what is only loose: Jesus Quintana’s two scenes, Knox Harrington’s giggle, the cab driver and the doctor could go without loss to the argument.
Harappan builders · Architecture
8.1 · Tier IV
Judged on purpose, structure and site, and much here is compelled. The platforms that lift both mounds are what a city on the Indus floodplain needs to stand at all. The drains run where water must go: from the bathing floor of a house, through its wall, into a covered channel in the lane, and on to the street. The Bath’s skin of brick on edge, its gypsum joints and the bitumen behind them are each required to make a tank hold water. Doors set on lanes keep the main streets clear. What holds the axis below 8.0: a city of blocks is additive, and a house, a block or a quarter could be taken away without the work ceasing to be itself.
John Cage · Music
8.1 · Tier IV
The subtractive test finds almost nothing to subtract: the score holds no notes. What it holds is a frame (a performer, a beginning, an end, a title that is a duration) and three divisions. The frame resists the test completely. Remove the performer and what remains is ordinary life, with nothing marked off to attend to; remove the end and the frame dissolves; remove the title and the clock that governs the frame is gone. The divisions do not resist. The sources disagree on their lengths, and the published note frees them altogether. A one-movement version would lose the lid closed and opened between movements, and little else. The core is required; the articulation is permitted.
J. R. R. Tolkien · Literature
8.0 · Tier IV
The subtractive test is passed more often than an episodic book should allow. The early adventures look like a string of incidents and are not: the trolls yield the swords that carry the rest; the goblins of the Misty Mountains are the army that comes at the end; the cave yields the ring without which Mirkwood, the Elvenking’s halls and the dragon’s lair could not be passed; the thrush at the door pays off in the dragon’s death. The Arkenstone, planted in the dwarves’ history, carries the last third. What the test finds is a looser middle: Beorn’s house could be cut by half, the dwarves’ arrival is told for its comedy, some songs ornament, and the narrator’s asides could go with no loss. Perhaps a sixth is permitted rather than compelled.
The Velvet Underground · Music
8.0 · Tier IV
Ten songs in about forty minutes, and the record’s pillars are required. Sweet Jane, Rock & Roll, New Age and Oh! Sweet Nuthin’ each hold a person and a condition no other track holds, and the last is the only place the record opens out. Who Loves the Sun must open: the bright, bitter pop song that tells the listener this is a radio record. I Found a Reason earns its place as the one doo-wop devotion, sung low and plain, and Cool It Down belongs to the sound of a working band. Seven of ten stand under the subtractive test. It bites on three: Head Held High has little in it past the riff, Lonesome Cowboy Bill spends its joke in a verse, and Train Round the Bend is a sketch.
Elena Ferrante · Literature
8.0 · Tier IV
The book has a motor, and it is real: two girls measured against each other, each episode a new reading of the scale. A chain of cause runs from the dolls lost in the cellar to the climb to Don Achille’s door, the money he gives the girls, the copy of Little Women bought with it and the dream of writing a book and getting rich, and on to the shoes and the wedding. The subtractive test finds much that could go. The volume proceeds by accretion of neighbourhood incident: the Peluso and Cappuccio households, Melina’s breakdown, the courtships of Pinuccia, Carmela and Ada, the long sequence of teachers and prizes. Much of it is there because a chronicle of the whole street is wanted and because the later volumes will need these people; perhaps a fifth of the incident is permitted rather than compelled.
Ragnar Östberg · Architecture
8.0 · Tier IV
Run the subtractive test, and it bites harder here than on a classical work. The governing parts are compelled: the tower at the corner where land meets lake, marking the city’s seat from every shore; the open court and the roofed court, one for arrival and one for assembly; the stair that makes the banquet hall a forecourt to government; the council chamber above and behind the public halls, where the plan requires it. Much else could be altered without loss. The quotations are many, a Venetian loggia, a Vasa castle tower, a northern hall roof, Byzantine gold, and several rooms feel chosen rather than required. Necessity governs the plan; it does not govern the dress.
Gustav Holst · Music
8.0 · Tier IV
The frame resists the subtractive test. Mars must open, because everything after it moves away from force; Neptune must close, because a fade is the only ending for a sequence that leaves the world; and Saturn, the longest movement, set fifth, is the hinge where the outward planets give way to the inward. Within the frame the test finds give. Mercury could go with little loss to the argument. Jupiter is a chain of dance tunes joined to a broad central tune, its episodes permitted rather than compelled, and the tune was lifted out whole to live as a hymn. Uranus repeats its march past what its idea needs. The movements are routinely played singly, and the suite does not resist it.
Joseph Beuys · Visual art
8.0 · Tier IV
Judged part by part, the core cannot be touched. Take away the coyote and the room is a man in a blanket: the animal is the other party. Take away the felt and the man no longer arrives unseeing, nor is there a shelter for the animal to test and tear. Take away the ambulance and the wrapping and the journey stops being an act of quarantine; the whole of America outside the room is no longer what is refused. Take away the time and nothing is shown, because trust between a man and a wild animal is shown only by duration. What yields is the furniture of rite: the struck triangle and the torch, as the accounts report them, are his standing equipment, and the newspaper delivered daily is an emblem put in place.
Sofia Coppola · Film
8.0 · Tier IV
The drift is the content, and much that looks idle is required: the elevator where Bob stands a head above the businessmen around him, the Suntory shoot where long instructions come back as one line, the sleepless hotel nights. The bar, the night out, the bed scene and the departure are a spine nothing can lose, and the fire alarm is a hinge that returns the two to each other without a word of apology. The lounge singer is required, since the rupture needs her. Held close to the cap rather than well above it because more gives here than a film of this length should: John’s photo shoots and Kelly’s junket restate one point, the talk show is one joke run long, the hospital is half sketch.
Andrew Stanton · Film
8.0 · Tier IV
Judged on the theatrical cut as released, about 98 minutes. The first movement is close to fully compelled. Each object WALL-E saves is paid: the lighter gives light to EVE; the tape of Hello, Dolly! teaches him the held hand he will want and later gives the cue that restores him; the boot he hands her carries the plant; the cockroach proves the planet can still keep a life. The billboards of Buy n Large that look like set dressing are the history of the world told in advertising. The subtractive test bites in the second movement: the rogue robots of the repair ward, the long chases through corridors and the garbage airlock run the plant back and forth more than the story needs, and the awakening of John and Mary is a sketch in two beats repeated. The cap is passed with room; the figure holds where the first half’s necessity meets the second half’s sufficiency.
Robert Venturi · Architecture
8.0 · Tier IV
Judged on purpose, structure and site. Much of the house is compelled, but by an argument more than by a programme. The centre is the clearest case: hearth and stair both claim the middle, and the plan is the record of the claim, the stair squeezed and turned by the chimney, the chimney shifted by the stair. Remove either and the house’s knowledge goes. The split gable is compelled by the same fact: the slot opens over the entrance and lets the chimney show, so that door and hearth read on one axis. What resists the subtractive test: the applied arch over the lintel is a sign that could go without loss to shelter or to the plan, and the stair that rises to a wall is a demonstration as much as a way to a high window. The parts are required by the polemic; some are only permitted by it.
Ray Bradbury · Literature
8.0 · Tier IV
Little is idle at the level of event. Clarisse’s question opens the crack; Mildred’s overdose and the technicians with their machine show the home the fire guards; the woman who burns with her books turns Montag; Beatty’s lecture gives the world its law and Faber the counter-law; the alarm at Montag’s own house closes the trap; the Hound, the river and the book-people resolve it. Remove any one and the arc fails. The charge is in the joints and the talk. Clarisse is removed by report once she has served, which is economy and also convenience. Beatty and Faber explain the world at length in speeches that restate as much as they advance, and Faber’s case is partly Beatty’s in reverse. The war at the end is required by the design but arrives as a stroke, not a consequence. Necessary in plan, assembled in places.
U2 · Music
8.0 · Tier IV
Eleven tracks in about forty-nine minutes, and the frame holds. Beautiful Day must open: it states the record’s argument, joy declared in a ruined landscape, before any song complicates it. Grace must close, a benediction that names the governing idea as a person. Between them Stuck in a Moment, Walk On, Kite and Peace on Earth are required, the four losses the record’s grace must pass through, and In a Little While earns its place as the one song of plain bodily tenderness. Those seven carry about two thirds of the running time. Held from the top: Wild Honey restates the opener’s lightness without its stake, When I Look at the World and New York go with small loss, and Elevation is required by the band’s purpose more than the record’s.
Denis Villeneuve · Film
8.0 · Tier IV
Judged on the theatrical release, the spine resists the subtractive test. The Water of Life is given twice: to Jessica, whose transformation sets the prophecy’s machinery moving, and to Paul, whose waking ends his resistance to it. The worm ride makes him a Fremen and earns him the crowd; the arena on Giedi Prime shows Feyd as Paul’s dark double before they meet; the reveal of Jessica’s descent from the Baron makes the duel a fight between kin. The compression of the novel’s years is a gain in necessity. What gives: Rabban’s failures repeat the Baron’s point, the Emperor’s scenes stand largely as exposition, and the last hour is so compressed that its steps are asserted rather than required.
Taddeo Gaddi or Neri di Fioravanti (attributed) · Architecture
7.9 · Tier III
The structure is compelled. After 1333 the plain lesson was a bridge with fewer and thinner obstructions in the river, and three flat arches on two piers give a wide waterway with a low deck that the banks could meet; the cutwaters stand where the current asks. The shops are compelled by a civic purpose: the commune built the crossing as a street that would pay rent, and the shops financed and held the bridge. The corridor is compelled by its purpose, a duke’s safe passage between seat of government and residence, and takes the only line the bridge offers, along the roof of one row. What yields to the subtractive test is the back-shops: added piecemeal over centuries, irregular, removable without loss to the crossing, though they are much of the picture. Accretion is the work’s nature, so they are not idle; they are not required either.
Chimú builders · Architecture
7.9 · Tier III
Judged on purpose, structure and site. Much resists the subtractive test. The height of the walls is compelled twice: by seclusion, the whole purpose of a palace that shows power as distance, and by the coastal wind and sand, against which the courts are shelters. The single north door, the baffled turns and the audiencias set where the passages narrow are each the control point of a route to the storerooms; remove one and access is no longer governed. The wells are required by a desert city, and the burial platform by a palace that is also its builder’s tomb. What yields is the repetition. The compounds restate one programme, and while succession explains why each ruler built anew, the later compounds add less than the first. The frieze grid could run a metre longer or shorter without loss. The cap is cleared, by three tenths.
Daniel Burnham · Architecture
7.9 · Tier III
The whole figure is the lot. Burnham’s office took the triangle that Broadway’s diagonal leaves across the grid and built it out to the line on all three sides and up to the height the money and the frame allowed. The prow is not a gesture: it is what remains when a speculative tower fills every square foot of a wedge, and nothing can be subtracted from the massing without loss. The three-part division into base, shaft and capital comes from the convention of the tall building in the 1890s more than from this site, but it reads the frame truly. What fails the test is the skin: the Renaissance ornament could be any ornament, and much of it could go without loss. The tip shop blunts the prow at street level.
Gerhard Richter · Visual art
7.9 · Tier III
Judged at two levels, and they part. In the conception the work resists subtraction completely: four photographs, four canvases, one to each. Take a canvas away and one of the four images made at mortal risk is left uncovered or lost from the count, and the cycle no longer answers the four exposures. The covering is compelled as well, since each layer exists to close over what lies below it. At the surface the test meets less resistance. The scraped field admits chance by design, and the particular passage, a drag of grey here, a seam of red there, is not required by what the work says: another pull of the blade would say the same. Necessity sits in the frame of the work and thins in its fabric.
John Wood the Younger · Architecture
7.9 · Tier III
Judged on plan, elevation and site, under purpose. On the front the subtractive test holds: take away a bay and the curve no longer closes into its half-ellipse; take away the giant order and thirty houses no longer read as one body, which is the whole idea. The curve is compelled by the site: a terrace that opens toward the view and the sun instead of turning inward, as the Circus does, and gives every house an equal share of both. What resists: the order is a dress over houses whose floors it does not express; the ground storey could be any terrace’s; thirty is what the land and the market gave; and the backs answer only each owner’s convenience. The front is compelled; the whole is partly assembled.
George Lucas · Film
7.9 · Tier III
Judged on structure. The spine is required and the plot economical: the plans hidden in R2-D2 in the first scene are the object of the whole film and are paid at the briefing; Leia’s message makes Kenobi necessary, Kenobi the cantina, the cantina the Falcon, and the Falcon’s capture brings every party into the Death Star at once. Owen’s bargain over a droid with a bad motivator puts R2 in Luke’s hands, and the burned homestead frees Luke to go. What gives is the middle. The rescue on the Death Star is a run of serial set pieces, the detention block, the trash compactor, the chasm, whose order could be shuffled and whose number cut without loss to the argument, and the cantina is spectacle as much as plot. Much of the middle hour is permitted, not compelled.
Jasper Johns · Visual art
7.9 · Tier III
Judged on the layers the canvas is made of, then on its passages. The given line cannot go: without the borders there is no map and no nation, only a field of primaries, and the wager is that a schoolroom diagram can bear the full weight of painting. The stencilled names cannot go: they are the second given, words as things, and without them the shapes of the states lose the labels by which anyone knows them. The paint cannot go, or the canvas is an enlarged printed outline. What yields is the passage: within a state a red could be a blue, a drip could fall elsewhere, a name could be buried or left clear, and the canvas would know the same thing. The scale is chosen, not compelled. Necessity holds in the design and loosens in the surface.
Harper Lee · Literature
7.9 · Tier III
The test is subtractive, and it is passed more often than the book’s reputation for looseness suggests. The idle summers of Part One return as load in Part Two. The gifts in the knothole of the oak and the blanket put round Scout on the night of Miss Maudie’s fire are how Boo is known before he is seen; the mad dog is Atticus’s courage with a gun, Mrs Dubose his courage without one. The last chapter, Scout on the Radley porch, is required by the first. Against this: Aunt Alexandra’s missionary circle, Dill’s runaway, much of the Finch’s Landing material and some of the school comedy are permitted rather than compelled. The book could lose a fifth of Part One with little loss.
Sigur Rós · Music
7.9 · Tier III
Ten tracks in about seventy-two minutes, and the method is slowness: the long approach is how most of these pieces reach what they reach, so length alone is not charged. The frame is compelled, a brief opening and the slow Avalon at the close, together under a tenth of the running time. Svefn-g-englar must come first, since it sets the scale. The test bites in three places. Hjartað hamast, the one organ-driven rock song, could go with little loss. Olsen Olsen adds height more than a turn. And the long quiet tails of Viðrar vel and Flugufrelsarinn could lose a third without loss.
Ingmar Bergman · Film
7.8 · Tier III
Judged on structure, at about ninety-one minutes. Agnes’s agony is the fixed point, and the memories are required by it. Her own memory of her mother shows why she asks of the living the touch her mother rationed. Maria’s shows the sister who offers caresses and withdraws them when they are needed; Karin’s, the sister who cannot bear to be touched at all. Anna’s prayer before the photograph of a dead child earns the lap she gives later, and the diary is the measure the whole is held against. The give is real, and it holds the axis here. The husbands are drawn in a few strokes and make one point between them; Joakim with the paper knife restates what the mirror has already shown; and a few tableaux hold past their work.
Apollodorus of Damascus (attributed) · Architecture
7.8 · Tier III
Judged on purpose, structure and site. Much is compelled. The hemicycle’s curve is forced by the forum exedra it faces; the terracing is forced by the cut slope, each level a retaining wall that is also a row of rooms; the fire wall between forum and market is required by the city. The Great Hall’s corbels and buttressing arches stand where its vaults need them and nowhere else. Use compels the shop module: a room, a door, a travertine frame, repeated. What yields to the subtractive test is the upper complex: its blocks are agglomerated, set at angles to follow plot and contour, and several could be removed or rearranged without loss to what the building says. The lower half is necessary; the upper half is sufficient.
SANAA (Kazuyo Sejima and Ryue Nishizawa) · Architecture
7.8 · Tier III
Judged on purpose, structure and site. Much is compelled. A museum of contemporary art must hold works of unknown size, so the galleries are boxes of many sizes and heights, each a room sized for a kind of work rather than a step in a sequence. The courts are required, because a deep single-storey plan otherwise has no daylight at its centre; the free zone is required by the city’s brief that the museum be a public place before it is a ticketed one; the several entrances follow from a site open on all sides to the old town. The subtractive test finds the circle itself less compelled: a square or an irregular outline would hold the same boxes and streets. The circle’s refusal of a front is an argument the programme allows rather than demands, and some boxes and corridors could shift without loss. The parts are required; their arrangement is one good answer among a few.
Sumerian · Visual art
7.8 · Tier III
Taken register by register, the plan resists subtraction and its filling does not. The pairing of the two sides cannot go: the object argues that war and peace are the two faces of one order, and a single face would be a different statement. The top registers cannot go, since each gathers its side toward the ruler, the captives brought to him on one side, the cup raised to him on the other. The chariot register cannot go: it is the force on which the rest stands, and the bodies under the hooves are the cost of the order made visible. What yields is the procession. On the Peace side a bearer more or a beast less would change nothing, and the ends could be lost with little loss.
Aphex Twin · Music
7.8 · Tier III
Seventy-four minutes, and the title admits the method: Selected, a choice from seven years of tapes, not a whole composed to need its parts. The subtractive test bites in the second half. Xtal must open, its sung loop and soft kick setting the record’s warmth; Tha must follow, nine minutes that set the scale and the patience the record asks; i is a breath the sequence uses. After We Are the Music Makers the case weakens: Hedphelym, Delphium and Schottkey 7th Path restate the mode without adding to it, and one of them could go with no loss a listener would name. Below Low’s 8.4 and m b v’s 7.9.
Alfonso Cuarón · Film
7.8 · Tier III
Judged on structure and on the economy of the telling, and the spine resists the subtractive test. The debris returns on its orbit, and every station Stone reaches is the only one in range, so the order of places, Hubble, the International Space Station, the Soyuz, the Chinese station and the Earth, is compelled by orbital fact; ninety-one minutes leave no slack scene. What gives lies inside the episodes. The fire on the station and the tangled parachute lines are obstacles placed more than consequences required, and the near misses become serial, each refuge failing in a new way so that the next can be reached. Kowalski’s anecdotes are colour the film could lose, and the dead daughter is given in one block of talk. The vision of Kowalski is the one late device that is also necessary.
David Lynch · Film
7.8 · Tier III
Judged on structure, and much of the film answers itself. The fairground and the lecture theatre are one act in two rooms, a man shown behind a curtain for money and behind a screen for science, and the film needs both before it can ask its question. The Psalm is required: it is the moment the patient becomes a person to the hospital. The society callers are required as the respectable kin of the night porter’s crowd, and the dream frame is required by the close. But the subtractive test finds real give in the second half. The porter’s two parties do one job twice, and the Continental episode, invented against the historical order, spends a long stretch on a second captivity and a second, cruder villainy whose purpose is to bring him to Liverpool Street.
Nick Cave and Warren Ellis · Music
7.8 · Tier III
Eight tracks in about forty minutes, and the subtractive test mostly fails to find slack. Hand of God must open: a slow piano song broken into by a driving loop, it states the record’s whole method in one track. White Elephant is the hinge, menace and grace in one song, and Balcony Man the required close, a morning after the catastrophe. The title song and Albuquerque each carry what no other song carries: love said under rain, and a life arrested in place. The test bites twice. Old Time is a churning loop whose dread restates the opening at a lower definition, and Shattered Ground drifts in the mode Lavender Fields has already set. Two soft tracks in eight hold it from the top.
Agatha Christie · Literature
7.7 · Tier III
The spine is required, and its economy is the book’s first strength. Mrs Ferrars’s death, her letter, the ten minutes in the study, the dictaphone and the telephone call from King’s Abbot station are each indispensable: remove any one and the solution falls. Even the village comedy bears load, since Caroline’s gossip, the mah jong evening and the talk over the hedge supply clues and, above all, cover. The subtractive test bites on the secondary mysteries made to multiply suspects: Ursula Bourne’s secret marriage, Mrs Ackroyd’s debts, Charles Kent’s parentage, Flora’s choice between Ralph Paton and Major Blunt. Each is resolved in turn, and each could be exchanged for another of its kind without loss to what the book finds. They are required by the genre’s need for doors, not by the argument; the spine carries the axis above them.
Chuck Palahniuk · Literature
7.7 · Tier III
The test is subtractive, and a short book of short chapters passes more of it than its manner suggests. The structure is a loop: the roof, the gun and the bomb of the first chapter are the destination every later chapter heads for, and almost every element is planted to be paid off once the narrator learns that he is Tyler. The support groups give him Marla and his first false self; the house on Paper Street, the soap made from fat stolen from a liposuction clinic, the projectionist’s splices and the waiter’s contaminations build Tyler as a set of acts the narrator must later own. What holds the axis is the middle: Project Mayhem escalates through assignments, committees and pranks that add instances rather than turns, and several riffs of deadpan fact, recipes for explosives and for soap, could be thinned without loss.
Paul Klee · Visual art
7.7 · Tier III
Tested part by part, the few organs of the figure hold. Take away the scroll curls and the head becomes a mask, losing its one sign of the learned or the sacred, the hint of rolled paper and of writing. Take away the sideways eyes and the angel becomes a steady, benign icon; its whole unease lives in that displaced gaze. Take away the open mouth with its teeth and the alarm, or the hunger, goes. Take away the raised wings and it is a startled child, not an angel. What yields is the line in detail: the oil transfer leaves smudges and stray marks by its nature, some of them kept rather than required, and the feet and lower body are summary.
Damien Hirst · Visual art
7.7 · Tier III
Judged on the two rooms as one work. The subtractive test is clean at the top level. Remove the living room and the dead paintings are decoration, the butterfly as ornament; remove the dead room and the living one is a butterfly house in a white cube. Each half is required to make the other mean, and the title is the hinge. Inside each room the parts are working parts: pupae on the canvas so that the painting is the birthplace, plants and sugar water so that the room is a habitat, the gloss so that the wing is caught as in amber. What yields is the colour of the monochromes, chosen for chic rather than compelled. Nothing is idle, but more could go than in a work of high necessity.
The White Stripes · Music
7.7 · Tier III
Sixteen tracks in about forty minutes, most under three, and the subtractive test finds a record built against excess: no song is extended past its idea. Dead Leaves and the Dirty Ground must open, the house left behind and the riff that sets the record’s terms. Hotel Yorba, the wish for a small room and a plain marriage, is required, and so are Fell in Love with a Girl, We’re Going to Be Friends and The Same Boy You’ve Always Known, each saying what the others do not. Little Room is needed because it is small, and This Protector is the only quiet ending that fits. The test bites in the middle and late: Expecting, I Think I Smell a Rat and Now Mary restate a manner already shown, and Aluminum is atmosphere more than argument.
Sidney Lumet · Film
7.7 · Tier III
About 125 minutes over one day, and the plot is a trap whose springs are set in its first minutes. Stevie loses his nerve and leaves; the vault holds little, the day’s cash gone; Sonny burns the bank’s register in a wastebasket. From then on much is compelled: the siege requires the crowd, and the crowd Sonny’s performance; the will dictated at night states at last why the robbery was attempted; the calls to Angie and to Leon show whom the money was for. The subtractive test bites in the middle of the day, which repeats its beats, Sonny out to the barricade, the crowd’s cheer, Moretti’s bargaining, more often than the argument needs; the tellers’ jokes and the pizza delivery are texture rather than necessity.
Sahelian builders · Architecture
7.7 · Tier III
The subtractive test is hard on the tower and easy on the hall. In the minaret almost nothing can go: the taper is what mud demands of a shaft of about 27 metres, the walls thickening toward the ground so that an unreinforced material can carry its own load at all; the timbers tie the mass; the openings are what a thick earthen wall allows. The height is compelled by a purpose, a call and a mark seen across flat roofs and open country. The prayer hall is another matter: its extent follows the congregation and the rebuildings rather than an argument, and it could be larger or smaller without loss. The tower’s necessity is near the top of its kind; the hall holds the whole below 8.0.
Marina Abramović · Visual art
7.7 · Tier III
The parts are few and nearly all are required. Take away the second chair and there is a woman sitting in an atrium, a tableau rather than an encounter. Take away the silence and the encounter becomes a conversation, which is another art. Take away the queue and the private exchange loses the public that makes it a spectacle and a pilgrimage at once; take away the duration and the stillness is a pose, not an ordeal. The test bites twice. The table went during the run and the work stood better without it, so the first set-up held a part it did not need. And the length, compelled by the claim that presence is sustained, would hold at somewhat less.
David Fincher · Film
7.7 · Tier III
Judged on structure, the spine holds: the first half builds the case against Nick in the audience as the police and the press build it, the second takes it apart, and neither could be cut. The diary is required to make the audience a jury that can be lied to. The Ozarks interlude looks removable and is not: the robbery at the cabins strips Amy of her money and sends her to Desi, without whom there is no murder to use. The give is weighed in full, and it lies in length as much as at the edges. Andie is a function more than a part, the clue hunt runs a station longer than it needs, and the closing stretch, from the return to the pregnancy, takes several codas to arrive where its first already pointed. At 149 minutes the film is long for its argument: its parts are required in kind more than in length.
Jeff Nichols · Film
7.7 · Tier III
The film is built on rhymes, and the rhymes make most of its parts required. The boat in the tree is the plan and the prize. Mud’s lucky shirt and the cross of nails in his boot heel are the superstitions the snakes then test. The parents’ failing marriage and the houseboat’s coming loss give Ellis’s faith in Mud and Juniper its cause, and May Pearl lets him live in small what Mud claims in large. Take any of these away and another part loses its reason. The subtractive test finds slack at the edges: the middle repeats its errands to the motel and the island, the bounty hunters are gathered at length and spent in one sequence, and the coda is not compelled by what came before.
Olafur Eliasson · Visual art
7.7 · Tier III
The subtractive test is passed by the main parts. Take away the mirror and the screen is a half sun, a stage flat; the disc, the doubling of the hall and the visitors’ sight of themselves all go, and with them most of what the work does. Take away the mono-frequency light and the hall is merely bright; it is the single wavelength that drains colour from faces and clothes and makes the space feel like weather rather than lighting. Take away the mist and the light has nothing to stand in. Where the axis gives: the mist’s daily cycle reads as effect more than argument. Required parts, few, and one of them half ornamental.
Fleet Foxes · Music
7.7 · Tier III
Eleven tracks in about forty minutes, and the subtractive test finds little to take inside the songs. The forms in several sections are lean: the turn in “Ragged Wood” from gallop to slow song is the song’s turn, not padding, and “Quiet Houses” earns its long repeated close because the whole track has been building toward a chant. “White Winter Hymnal” is one stanza and nothing else, and the shortness is the form. The test bites in the second half. “Heard Them Stirring”, wordless, could go with little loss, since the opening and “Quiet Houses” already show the voices as texture; “Meadowlarks” is the slightest song; “He Doesn’t Know Why” says again, less sharply, what “Blue Ridge Mountains” says of the brother. Perhaps a fifth is permitted rather than compelled. The cap is cleared by three tenths.
Alphonse Mucha · Visual art
7.6 · Tier III
Judged by subtraction, nearly every part bears weight. The figure’s length is compelled: the poster’s point is a woman at full human height in the street, and the narrow sheet is the column she makes. The arch is required, since its half-dome is what turns a costumed actress into an icon. The palm is required: it names the scene and the liturgy, and its diagonal is the only line that crosses the figure’s vertical. The lettering is bound into the design rather than set on it. Necessity loosens at the foot, where the mosaic panel and the lower lettering are crowded and the zone could be otherwise without loss; that band of ornament is filling as much as structure.
Alex Proyas · Film
7.6 · Tier III
Judged on the theatrical cut as released, about 102 minutes. The spine is the oldest compelling structure in drama: a wronged man, four debts, four payments, then the master behind them, and nearly all of the film is required by it. Each killing is set by the crow’s guidance and paid in its own key, the needle for Funboy, the burning car for T-Bird, the guns of the boardroom for Skank, and the flashbacks are rationed so that each payment brings back a piece of the loss. Sarah is the living claim on Eric, Albrecht the witness who survived the law’s failure. The test bites at a few joints: Gideon’s pawnshop is a stop more than a step, Myca arrives late as a device, and the boardroom massacre is spectacle the payments do not require.
Robert Motherwell · Visual art
7.6 · Tier III
Judged on the frieze, the format resists subtraction: it is so reduced that each element bears weight. Take away an oval and the alternation of round and upright loses a beat and the frieze lists. Take away a bar and two ovals press together, and the interval that gives the procession its slowness is lost. The light ground is not background but the other half of the rhythm; narrow it and a procession becomes a pattern. What yields is the particular placing. The series shows that these elements could be set otherwise, at another width, with one oval more or fewer, and still be an Elegy, and well over a hundred canvases are the evidence. Necessity holds for the format more than for this arrangement: one compelling solution among many the painter found.
Yayoi Kusama · Visual art
7.6 · Tier III
Judged on the parts, which are few. Take away the mirrors and there is a dark room with strings of lights; the infinite goes. Take away the water and the floor becomes a boundary: the reflection below, which lets the visitor seem to stand on nothing, is what turns a lit box into a field. Take away the darkness and the mirrors show their seams and the cords. Take away the walkway and no one can enter without entering the work’s floor; take away the door, and the closure that makes the infinite private, and the room becomes a corridor. Each part is required. What gives is the content of the field: the number of lights, their heights, their colours and their sequence are one choice among many, and the series fills the same box with lanterns, pumpkins and dots.
Damien Hirst · Visual art
7.5 · Tier III
The parts are few: the cast, the teeth, the pavé, the brow stone and the title. Subtract the teeth and the work loses its one remainder of a body; it becomes a jeweller’s novelty with no one in it. The teeth are the hinge between relic and commodity and cannot go. Subtract the pavé and there is a platinum skull, a vanitas in an expensive metal, without the excess that makes the argument. Set the stones on resin and the claim on value fails, since the cost is part of what the object is. The brow stone yields most: a centre of display that the market needs more than the work does. Held below 8 because the idea fixes only the greatest covering, and the greatest is a budget, not a law.
Jeff Nichols · Film
7.5 · Tier III
The film’s economy is its best claim, and a strong one. It opens in mid flight and refuses exposition, so that every scene earns its information by action: the cardboard on the motel windows, the goggles and the comic book read by flashlight, the headlights switched off on a dark highway tell that the boy cannot bear light and that the men will break the law for him before a word explains either. The Ranch and the state are required, since they are the two readings of the boy the film sets beside the father’s: worship and seizure against love. What gives: Sevier serves partly as a device of exposition in the fourth movement, and the coda adds little the arrival did not hold.
Alex Garland and Ray Mendoza · Film
7.3 · Tier III
The subtractive test is the film’s own method, and it passes it more fully than most films of its length. Nothing is present that the engagement did not contain: no flashback to home, no letter, no backstory, no score telling the audience what to feel. The long opening watch from the window, with its waiting and its jokes, is required, because it is the only measure the film gives of what the blast breaks; the quiet before and the noise after are one structure. What holds the figure below 8.0 is that the necessity is partly a record’s: some of the second half’s repetition, men called, men moved, the radio worked, the vehicles awaited, is required by fidelity to what happened rather than by what the film has to say, and runs at times on its own procedure.
James Montgomery Flagg · Visual art
7.2 · Tier III
The subtractive test finds almost nothing to remove. Take away the finger and the picture is a portrait of a stern old man that addresses no one. Take away the frontal set of the eyes and the finger points at no one in particular. Take away the hat and its stars and the old man is not the nation. Take away “YOU” and the demand has no object; take away the line for the recruiting station and it has no place to be met, and the poster stops being an instrument. Each part is required by what it has to say: you, now, here. What holds the axis below eight is that the necessity is a received formula well executed, over a small thought.
Walt Whitman · Literature
9.1 · Tier V
The subtractive test divides the book. The great poems resist it: in “When Lilacs Last in the Dooryard Bloom’d” each of the three figures, lilac, star and bird, is required, and the poem cannot lose the coffin’s procession without losing the nation that mourns. In “Song of Myself” the catalogues are the argument, not its ornament; equality is enacted by enumeration, and a shorter list would assert a smaller democracy. What holds the axis at the foot of the twelve is the book as a life’s accretion: the late annexes, much of “Autumn Rivulets” and “By the Roadside”, the exposition and redwood poems and “O Captain! My Captain!” could go with the knowledge unchanged, perhaps a third of the poems by count and far less by weight; and some catalogues run past their proof. The core is compelled; the book is permitted.
Samuel Richardson · Literature
8.8 · Tier IV
The test is subtractive, and the book is exposed to it. The design needs its slowness: the first two volumes, in which the Harlowes press Solmes on Clarissa letter after letter, must be long, so that the reader feels the house close on her as she does and her flight seems, when it comes, both forced and chosen. The London sequence is required for the same reason: the trap is made of small deceits, and each must be laid. What holds the axis lowest of the twelve is restatement, not length: the family’s arguments put in near the same terms several times, Anna Howe’s quarrels with her mother and Hickman beyond what they bear, and the long posthumous volume of wills, meditations and the punishments of the minor wicked.
Laurence Sterne · Literature
8.8 · Tier IV
The subtractive test meets a book built to defeat it. Sterne makes digression the structure: “Digressions, incontestably, are the sun-shine”, and the work is “digressive, and it is progressive too”. The returns are required: the clock and the conception, the nose, the name and the sash come back through every volume, and Toby’s hobby-horse is the same in the first volume and the last. But the rubric asks of parts, and parts could go. Slawkenbergius’s tale of noses runs far past its joke; Ernulphus’s curse is given entire; Walter’s theories of names and auxiliary verbs and his Tristrapaedia repeat one comedy; the seventh volume’s flight through France is half a separate book. That excess holds the axis at the foot of the twelve, kept from lower because the book always returns to one parlour.
Terrence Malick · Film
8.7 · Tier IV
Judged on construction, since the dialogue is sparse. The film was cut down from a far longer assembly, and the drift that results is the method: scenes float, voices begin and end without an event to anchor them, and the Bell marriage returns in fragments that are a memory and not a plot. Much of this is required. The hill cannot be shortened without losing the exhaustion it is about, and the return to the village is needed to show that the first world was not whole either. But the subtractive test finds give: the Quintard scene on the ship, the second night in the camp, several voices that belong to no face. Held at the figure by a form that permits its scale rather than compelling it.
Alfred Tennyson · Literature
8.6 · Tier IV
The lowest of the twelve, and the subtractive test shows why. The sequence’s cumulative method admits accretion, and it accretes: the middle run, from the sixties to the eighties, says several times what had been said, in the dream of the career Hallam would have had (LXIV, LXXXIV) and in the speculations on whether the dead remember (LX to LXII). The order of many middle sections could be shuffled without loss, and perhaps a fifth of the poem could go without real loss. Against that, the repetition is in part the knowledge, for grief returns on itself. The door of VII, “Doors, where my heart was used to beat / So quickly”, needs the long interval before the same door in CXIX for the return to mean anything; and the frame of the three Christmases, the turn at XCV and the bells of CVI is required. What holds the axis here is the middle: an order that could take more or less of it without breaking.
Bertolt Brecht · Literature
8.4 · Tier IV
The subtractive test finds a play assembled in part. Its plot is Gay’s, taken over nearly whole: the highwayman marries the fence’s daughter, is betrayed by the whores, escapes through the jailer’s daughter, is retaken and is reprieved at the gallows. Brecht thins Gay’s intrigue rather than thickening it, and the numbers sit beside the scenes rather than growing from them. Several are movable and were moved between versions, the Salomon-Song and the Ballade vom angenehmen Leben among them; Lucy’s aria in the third act is cut in practice without loss; the Jealousy Duet is a turn. What is required is the frame of three finales and the business plot that runs under the love plot: Peachum’s trade in pity, Brown’s partnership with Macheath, Macheath’s plan to go into banking. Those parts could not go. What holds the axis lowest of the twelve is the shuffling itself: a work whose numbers can change places between versions clears the cap by a narrow margin.
Boris Pasternak · Literature
8.4 · Tier IV
The subtractive test finds a required spine and a great deal that could go. Required: the boy at his mother’s grave, his father’s suicide from the train that Misha Gordon witnesses, the candle in the window on Kamergersky Lane on the night Lara fires at Komarovsky, the front at Meliuzeevo, Varykino, the death on the tram, Lara at the coffin, and the poems, which are what the life was for. What holds the axis lowest of the twelve is what could go without the book losing a fact it needs: Liberius’s long harangues in the partisan camp, much of the talk among Gordon, Dudorov and Yuri, the Kubarikha episode, and a fair share of the Epilogue, whose story of Tanya the laundress restates by report what the novel has shown. Perhaps a sixth of the whole. The coincidences are not charged here; they are the book’s law.
Willa Cather · Literature
8.4 · Tier IV
The subtractive test bites, and the book half invites it. Book I is required in nearly every part: the arrival in the dark, the dugout, the snake, the wolves of Peter and Pavel, Mr Shimerda’s death in the snow and his burial at the crossroads, each a stage in the making of the country and of the two children. Book II’s hired girls and the town’s class line are needed for what Jim loses. What can go is less in the episodes than in their measure. Book III, Lincoln and Lena Lingard, is pleasant, slight and largely ornamental to Ántonia’s story, and could lose half its length; in Black Hawk the tramp who throws himself into the threshing machine and the blind pianist d’Arnault are vivid and detachable. The defence is the form: a memoir is made of what memory kept, and the frame says so. It earns some credit, not all. This is the lowest of the twelve.
Stevie Wonder · Music
8.4 · Tier IV
The subtractive test bites hard, because the record is long by choice and says so. Some parts are required. “Love’s in Need of Love Today” must open, its a cappella start stating the law before any band is heard; “Village Ghetto Land” and “Pastime Paradise” carry the social argument and nothing else does; “As” is the summit and the vow. But seven tracks run six minutes or more, nearly half the whole, and the length is not always the argument. “Another Star” holds its vamp for minutes past its turn, “Isn’t She Lovely” extends a harmonica solo over a song complete at three minutes, “If It’s Magic” is slight, and two tracks of the extra disc could go without loss. Permitted rather than compelled in perhaps a fifth of the whole: that is what holds the record’s lowest figure.
Cormac McCarthy · Literature
8.4 · Tier IV
The test is subtractive, and here the book is weakest. There is no plot spine: the novel runs as episodes over some years, and many could go without the book losing a fact it needs. One more drunk, one more brawl at the Indian Rocks or in a bar on the Flats, one more of Harrogate’s schemes: the book has more of each than its argument requires. What resists the test is the accumulation itself, which is the argument, since a descent chosen again each day can be shown only by repetition. The episodes that bear the weight are few and fixed: the drowned man, the workhouse, the son’s funeral, the Reese camp, the mountains, Ab Jones’s death, the fever, the departure. What holds the axis lowest of the twelve is the rest: perhaps a quarter of the book is permitted rather than compelled.
Jack Kerouac · Literature
8.3 · Tier IV
The subtractive test exposes the book more than any other axis, and the outline stands up to it. The argument is that the road never arrives, and the four crossings and the coda are compelled: each is faster and more frantic, leaves Dean more broken and Sal more alone, until in Mexico Dean leaves Sal sick with fever and in New York Sal leaves Dean on a cold corner. The repetition is the argument, and the rise in speed and damage from one crossing to the next is what the book knows. What holds the axis lowest of the twelve is the matter inside each crossing: the Mill City barracks, the night at the opera in Central City, the all-night cinema in Detroit, the travel-bureau cars, many hitchhikers and many parties, permitted rather than required. The narrative’s joint is “and then” far more often than “therefore”, and the Viking text is already a reduction of a longer draft.
Leo Tolstoy · Literature
8.3 · Tier IV
The core is compelled. The trial needs every juror and every lapse: the jury’s answer leaves out the qualifying words that would have cleared Maslova of intent, and that clerical slip is the whole machine of the book in small, a sentence passed by men attending to their dinners. The memory of the aunts’ estate, the Easter night, the child and the brothel are all required. The subtractive test bites in the second and third parts. Nekhlyudov’s rounds in Petersburg, the senator, the officials, the salons, the petitions for prisoners met once, run on a principle of accumulation, and several cases could go with no loss to what the book knows; the visit to his estates, the land given away on Henry George’s terms, is argued at a length the action does not need. The last chapter’s reading of Matthew is a statement placed where a resolution should be enacted. That is what holds the axis lowest of the twelve, though clear of the cap.
Jackson Pollock · Visual art
8.3 · Tier IV
Judged on the field, since the canvas has no configuration in the usual sense, and the subtractive test is harsh to an all-over poured surface, fairly so. Remove one white skein and the field does not open; remove one cigarette or one tack from the impasto and nothing is lost that could be named. The parts are fungible by design: the method was built so that no place on the canvas is privileged. What is required is the density as a whole and the order of layers: take away the pouring and the canvas becomes an encrusted brushed painting of 1946; take away the ground and it becomes a thin web. The upright is permitted rather than compelled. Necessity sits in the layering, not in the units.
Fritz Lang · Film
8.3 · Tier IV
Run the subtractive test. The architecture is required: a city in two storeys, a son who goes down, a woman doubled so that the master can turn the workers on their own city. The Babel parable in the catacombs is required, since the city’s central tower is the New Tower of Babel and the ending answers the parable. The restored footage makes the plot more necessary than the short versions were: Rotwang’s love for Hel, Fredersen’s dead wife and Freder’s mother, gives the inventor a motive and the machine a face it should not have; Georgy’s night in Freder’s clothes and the Thin Man’s pursuit of Josaphat now pay off. What gives is duration: Freder’s delirium, the long Yoshiwara crowd, the chase on the cathedral roof, the long rescue in the flood, each a spectacle the film has already earned once.
Mughal, under Akbar · Architecture
8.3 · Tier IV
Judged on purpose, structure and site, much is compelled. The trabeated system is the ridge’s own stone used as it wants to be used, in short spans, beams and brackets, and the deep eaves and screens answer the sun. The ridge sets the city: the mosque at its highest point, the palace below along the crest, the lake against the fourth side. In the parts the subtractive test bites: the Diwan-i-Khas cannot lose its column or its walkways and still say anything. What holds the axis here, the lowest on the page, is that a palace of pavilions added court by court over a decade and a half is an assembly by nature: several kiosks and houses could go and the complex would read the same, and the Buland Darwaza’s scale is not required by the mosque it fronts and dwarfs.
Mark Z. Danielewski · Literature
8.3 · Tier IV
The test is subtractive, and it bites hard. The core is required: the house, the four explorations, Navidson alone in the dark, Zampanò’s commentary keeping the horror at a scholar’s distance, Johnny’s descent beneath it, Pelafina’s letters at the bottom. Each layer needs the others; take one away and the structure of nested containers, which is what the book is about, collapses. The defence that excess is the subject, a text overfull and larger inside than out, is real and is credited. It does not cover all the excess, and that holds the axis lowest of the twelve: Johnny’s sexual episodes, told at length and repeated, add little after the first two; the long lists of names and buildings are partly the point and partly permitted; several appendix pieces are additive; the invented critical apparatus overruns its parody. Well over a tenth of the book is permitted rather than compelled.
David Cronenberg · Film
8.2 · Tier IV
Run the subtractive test on the first hour and it holds. The station’s hunger for stronger material, Harlan’s pirate dish, the talk show at which O’Blivion is present only on a monitor, Nicki’s appetite for the signal and her going to find it, the Mission’s booths of screens: each carries the claim that the image is entering the body, and none could go without loss. The movement into the hulk and the last shot are required. What holds the axis here is the last third. The Spectacular Optical plot arrives as exposition, and its moving parts, the reprogramming and the murders in turn, could be rearranged without loss; Masha is a device for reaching the next room.
Lana Wachowski and Lilly Wachowski · Film
8.2 · Tier IV
Most of the film is required. The opening pursuit plants every law it will use: the agents can occupy anyone, the telephone is the only exit, the impossible leap fails for an ordinary body. The white rabbit, the cat seen twice and the spoon each return to pay. The pill, the pod and the flush are the hinge on which the whole knowledge turns. The subtractive test finds slack in two places. The instruction movement carries long passages in which Morpheus explains in speech what the images have already shown, and the lobby battle runs past the point at which its meaning is complete. The resurrection is the one turn the film’s own law does not compel. The cap is cleared with little room.
John Vanbrugh with Nicholas Hawksmoor · Architecture
8.2 · Tier IV
Judged on plan, section and structure, under purpose and site. The purpose was double, a monument to a victory and a house for a duke, and the parts are compelled by the first and only permitted by the second. Take away the towers, the trophies and the bust over the south portico and the monument loses its speech; take away the stepped courts and the main block loses the long rise of masses the approach is built to deliver. What holds the axis lowest of the twelve is the dwelling: verses current within a few years asked where in such a house one slept or dined, and the charge is fair. Kitchens lie across a court, the state rooms are an enfilade for ceremony, and the bridge, the Column and the gate arch are compelled by the axis, not by use.
Mudéjar builders, under Peter of Castile, and later hands · Architecture
8.2 · Tier IV
Run the subtractive test on Pedro’s palace and it holds. The bent entrance is required by a court that must not be seen into from the court of arms. The pool and the sunken beds are required by the heat, and the pool sets the axis of the Doncellas. Two cores are required by a king who lived as a public and a private man, and the throne hall is required at the joint between them. Remove the pool or the cupola and the palace loses its sense. What holds the axis low is the complex: nine centuries of accretion, Gothic halls rebuilt after 1755 that could go with little loss, a gallery the court did not ask for, the enfilades of a dynasty. The centre is compelled; the whole is permitted.
Robert Altman · Film
8.2 · Tier IV
The subtractive test has to be run strand by strand, and most strands pay their way beyond themselves. Casey struck by Doreen’s car, the baker’s calls, the hospital and Paul Finnigan’s arrival bind three households. The fishermen beside the drowned girl set the film’s question of what is owed to a stranger, and that question returns in the Wymans’ and the Kaisers’ scenes. The length is compelled because accumulation is the argument: the city is the sum of what each strand does not see, and fewer strands would make a smaller claim. What gives: Stormy Weathers sawing the furniture is a comic set piece whose point is made elsewhere, and the Bushes’ business is thinner than its screen time.
Cindy Sherman · Visual art
8.2 · Tier IV
The subtractive test bites on the single image and fails on the series. Take away any one still and nothing breaks: the method is additive, a repertoire extended until, by the artist’s own account, the types ran out, and some images are thinner than others. A set of sixty or eighty would be the same work. But the multiplicity cannot be taken away. One still is a picture of a woman; sixty-nine stills of one woman who is never the same woman argue that there is no woman behind them. What is required are the constants: one model, no caption, no film, the single figure, black and white. The number is permitted rather than compelled, and the axis is held there, two tenths above the cap.
Johnny Cash · Music
8.1 · Tier IV
Sixteen songs, and the frame is compelled. “Folsom Prison Blues” must open, sung in the place it names, and “Greystone Chapel” must close, a song written by a man in the room and sung back to him. Between them most songs are chosen for this audience: “25 Minutes to Go” counts down a hanging before men some of whom face the same, and “The Wall” and “Send a Picture of Mother” are prison songs sung inside. The test bites in the middle of side two, where three comic songs run together; the show needs release, but one would serve it, and “Jackson” is a hit duet from outside the record’s matter. “Orange Blossom Special” is a showpiece more than a part. About a fifth of the record is permitted rather than compelled.
William Van Alen · Architecture
8.1 · Tier IV
Judged on purpose, structure and site. The massing is compelled: the zoning resolution of 1916 required the setbacks, and the tower rises from a base that fills the lot through narrowing stages to the point where the law let it go straight. What resists the subtractive test is much of what makes the building: the frieze of hubcaps, the radiator caps, the eagles, even the arches of the crown could be removed and the offices would work as before. The spire was compelled by a purpose, to be tallest, but the purpose was rivalry and advertisement, and the floors inside the needle are of little use. The defence is that this building’s purpose was its image, and the image is not assembled: crown, spire and shaft are one rising figure. It carries the axis above the cap, not far above.
The Kinks · Music
8.1 · Tier IV
Fifteen tracks in about thirty-nine minutes, and the subtractive test finds a firm frame and a permeable middle. The title song must open, a manifesto naming the society the record then populates, and People Take Pictures of Each Other must close, turning the record on its own act. Between them the portraits are required as a class but not one by one. Monica and Starstruck could leave with small loss, and Wicked Annabella belongs to the village’s folklore but sits loosely in the order. Within the songs nothing is idle: the miniatures have no slack, and the brevity is the method, not haste. What is required is the frame and the class; which portraits fill it is chosen, and that holds the figure.
Cass Gilbert · Architecture
8.1 · Tier IV
Judged on purpose, structure and site. Much is compelled. The base takes the lot and the light court brings daylight into deep office floors, the rule of rentable space. The tower stands on the Broadway front, where it faces the park and is seen whole, the only place on the lot it could stand. The piers that run unbroken up the shaft are the frame made visible, not applied. What resists the subtractive test is the rest of the Gothic: the tracery, crockets, pinnacles and gargoyles could be shaved off and the offices would work as before. The height above the base answers no office need; Woolworth wanted to pass the Metropolitan Life tower, and the upper floors are small. The defence is that the purpose was an image, and the image is one figure.
Chamberlin, Powell and Bon · Architecture
8.1 · Tier IV
The lowest of the twelve, and what holds it there is the parts the purpose did not choose. Much is compelled. The podium is required by the site: it decks over a railway, service roads and parking, and gives the people a ground of their own above the traffic. Two thousand flats in the City are what the towers and terraces are for; lift the terraces on columns and the courts pass under them as one ground; set the courts round water and the noise falls away; the vaults house the top flats and close each line. What yields: the highwalks were a fragment of a City network never completed, so routes lead nowhere, and the arts centre, added late, is pressed below grade behind entrances no visitor could find without a line painted for them.
Don DeLillo · Literature
8.1 · Tier IV
The test is subtractive, and the spine is required. The cult that kills strangers whose initials match the initials of the place where they die must be there, and so must Owen, whose life among alphabets draws him to it, and James, whose trade in political risk makes him a reader of the same world from the other side. The closing section is required: without Tap’s misspelled prose the book has no answer to the cult. What the test finds is the middle. The expatriate dinners recur, and after the second or third they add tone rather than turn; James’s business trips around the region repeat one discovery, that Americans are moving through places they do not see; and some of the Volterra material, the film-maker’s talk of how he would shoot the cult, says again what Owen has already shown. The talk is the medium of the disclosure, so the dinners cannot go wholesale; but perhaps a sixth of the whole is permitted rather than compelled, and that holds the axis second lowest of the twelve.
Byzantine, under Justinian · Architecture
8.1 · Tier IV
Judged on structure, purpose and site. The founding parts pass the subtractive test. The wall is compelled by the place: a frontier valley open to raids, where monks and pilgrims had to live for months without help. The siting is compelled by the story: the church is set low in the valley against the bush, not on the summit, so that the house of worship and the holy spot are one place. Remove the wall and the community does not survive; remove the chapel and the church loses its reason. What yields is what the centuries packed inside the circuit: cells, storerooms, a mosque, a bell tower and later wings, each needed in its day, none required by the founding form. The core is compelled; the whole is partly assembled.
Ana Mendieta · Visual art
8.0 · Tier IV
Judged on the series as one work, where the subtractive test bites. Within each piece almost nothing could go: a figure, a material, a site, a time for weather to act. Imagen de Yagul is a body, a tomb and flowers; a burning outline is an outline and fire. But the unit is a series of variations, and many of its members repeat a proven figure in a new material without adding to the argument. Remove a dozen Iowa outlines in grass or mud and the work stands with less evidence, not broken. What resists removal is the core run of kinds: the body in the tomb, in earth as absence, in water, as fire, taken by sea. Each is a different relation of self to ground. The cap clears with room.
Bob Marley and the Wailers · Music
8.0 · Tier IV
The subtractive test finds load-bearing parts and slack in about equal measure. Natural Mystic must open: it fades in from silence, the warning arrives before the band does, and the record begins as a thing already in motion. Exodus must close the first side, since its length is the march, and One Love must close the record, since the sermon of side one needs its answer in fellowship. Between these the test bites. So Much Things to Say and The Heathen state what Guiltiness and Exodus state better; either could go with little loss. Turn Your Lights Down Low duplicates Waiting in Vain in a softer register, and Three Little Birds is a charm whose place, rest after the march, is real but thin. The plan is required; several of the songs that fill it are not.
Built for Ashikaga Yoshimitsu; rebuilt 1955 · Architecture
8.0 · Tier IV
The site compels much. The pond’s long axis from the southern shore needs a figure at its end, and the reflection is why the pavilion stands at the water’s edge and not on the slope; the veranda and the landing are the pond’s too. The programme compels the stack: court below, warrior above, Zen at the summit with the relics, and none removed without loss to the claim, the phoenix closing the figure. What holds the axis is the method. The building is assembled from three inherited manners, each brought whole from elsewhere, and its junctions are joins, not growths; and its interiors are slight beside an exterior made to be seen.
Andrei Tarkovsky · Film
8.0 · Tier IV
Judged on structure. The vow requires everything it consumes, and the film is built backward from that demand: the house must be loved, shown and filled with people before it can be given up, so the birthday afternoon is the inventory of the sacrifice. The dead tree and the legend of Pamve are required, since the coda answers them. Otto’s gift of an old map and his talk of inexplicable things are required, since he is the one who sends Alexander to Maria. The boy’s silence after his throat operation is required, since his first words close the film. What gives is in the household: Adelaide’s quarrels, Victor’s plans to leave and Julia’s business repeat one strain, and the first part’s talk restates the opening monologue. A tighter film would lose little there.
Luis Buñuel · Film
8.0 · Tier IV
Judged on structure, the frame is required. Mathieu’s account is given to strangers to justify an act of contempt, so the whole told story is a self-defence, which is what the film knows. The bucket of water is required twice, opening the frame and answered when Conchita, on the train, returns it. The cycle of approach, promise, refusal, flight and return is required in kind: desire is a repetition, and the film must repeat. But the subtractive test finds give in that very repetition. The episodes are near-interchangeable units in a series, and one of the middle returns could go with little loss of meaning, only of duration. The bombings are required as a law of the world and placed with a freedom that looks assembled as often as compelled. That holds the axis two tenths above the cap.
Gu Kaizhi (attributed) · Visual art
8.0 · Tier IV
Judged scene by scene and across the scroll. Within a scene little can be taken away. In the bear scene the beast, the lady stepping forward, the two guards with raised spears and the emperor drawing back while the other consorts flee make one event, each figure a term in a comparison of courage. In the bed scene the curtains, the emperor half turned and the woman’s withheld face are the whole of the doubt. The toilette needs its mirror: the face seen twice is the precept. What yields is the sequence. The scroll is a run of illustrations to a text, and its losses have shown it: the nine stand without the opening scenes, and the order could take one more or one fewer. The family scene is the most permitted, a crowd placed to illustrate a line.
Egyptian (New Kingdom) · Visual art
8.0 · Tier IV
Judged twice, on the two great vignettes and on the roll. In the judgment nothing can go. Without Anubis at the balance no one tests the reading; without Ammit the weighing has no stake; without Thoth the verdict is unrecorded, which in this world means it did not happen; without Horus the justified man has no one to bring him before the king of the dead. Without the heart or the feather there is no scene, and the order from left to right is the order of the event. The Opening of the Mouth is nearly as tight. The roll as a whole is looser: a selection from a corpus of some two hundred spells, some of which could go without loss, as other owners’ rolls show by going without them.
Terrence Malick · Film
8.0 · Tier IV
The spine is required; the passages between its stations are not. A single refusal is put to a sequence of tempters, each with a different argument: the parish priest’s fear for the family, the bishop’s duty to the state, the church painter’s confession that he paints a Christ people admire rather than follow, the lawyer’s offer of service without arms, the officer’s case that the act changes nothing, the judge’s own unease. None could go without a gap in the argument, and Fani’s labour on the farm is the price that makes the refusal a cost rather than a stance. Around that spine the film carries much it does not need. The haymaking, the clouds over the ridge, the prison yard and the letter laid over walking feet return many times, and several could be exchanged or cut without the film knowing less. At about 174 minutes the length enacts endurance in part, and is in larger part permitted rather than compelled. The spine carries the figure; the montage holds it there.
Kallmann McKinnell and Knowles · Architecture
7.9 · Tier III
Judged on purpose, structure and site. The section is the programme drawn out in concrete: the citizen’s business at the base, reached on the level from the plaza; the ceremonial rooms in the middle, each in its own projecting volume; the repeated work of departments in the bays of the crown. Take away the projections and the building no longer says where power sits; take away the overhang and the plaza loses its sheltered edge; take away the brick base and the ground does not run into the hall. What resists the test: the first plaza was larger and barer than any civic use required; the weight of the piers and the depth of the crown are there for expression more than for structure; and the wandering stairs inside are the residue of the section, not its necessity.
Park Chan-wook · Film
7.9 · Tier III
The subtractive test finds the main line hard to cut, because nearly every object planted is paid. The fried dumplings, fed through a slot for fifteen years, are the clue that finds the prison; the five days, the telephone, the purple box, the song of the school, the tooth and the tongue are all given to be used. The fifteen years and the release are one design, and the film’s question, not why he was taken but why he was let go, is answered by its structure. What gives is the machinery. Woo-jin’s reach, a hypnosis that steers two people into love and watchers on every move, is required by the plot more than by what the film has to say, and a different contrivance would serve as well; the gang scenes and the friend Joo-hwan’s errands are slack.
Cy Twombly · Visual art
7.9 · Tier III
Judged on the configuration, as the room presents it. The paired parts resist removal: take away Heroes of the Ilians and the Greek roll call faces nothing, and the premise of two armies with the visitor between them falls. Take away Achaeans in Battle or Ilians in Battle and one side of the war is gone. The Fire that Consumes All before It is the hinge, the one canvas belonging to neither army, and the shades are the end the cycle walks toward. What yields is the middle of each side: Vengeance of Achilles and House of Priam could go with the argument intact. Within canvases the bare ground is a wager the subtractive test cannot always decide.
Godspeed You! Black Emperor · Music
7.9 · Tier III
Inside the two long pieces the subtractive test finds little to cut. Mladic states its modal theme thin and alone, adds the ensemble by degrees and arrives at all eight players in unison on the riff; each stage is needed for the weight of the next. Across the whole the test bites twice. The vinyl edition set the drones apart on a seven-inch record, so the band itself issued its long pieces standing alone; in sequence each drone lets a roar decay into held tone, but the experiment has been run. And the middle of We Drift plateaus, where minutes could go without the argument going with them. Necessity is high in the pieces and moderate across the whole, and that holds the figure.
Rem Koolhaas and Joshua Prince-Ramus (OMA/LMN) · Architecture
7.9 · Tier III
Judged on purpose, structure and site. The building’s argument is that the programme compels the shape: each platform is sized to the fixed function it holds and shifted to reach light, view or street, and the skin is whatever the stack requires, drawn over it. On that test much yields nothing. The Books Spiral is compelled by its claim that a growing collection should never be broken across floors; the two entrances are compelled by the slope; the net is skin, structure and seismic bracing at once. What yields is the residue of the method: in-between floors generous beyond any measured need, the Living Room’s height chosen for effect, the red level’s curving corridors, and overhangs shaped for the view from the street. Above the cap, by two tenths.
Stanley Donen and Gene Kelly · Film
7.9 · Tier III
Judged on structure. The plot is a single problem, a voice that does not match a face, and almost every number is a cause or a consequence of it. The flashback under “Dignity. Always dignity.” sets the gap between what Don says and what is shown. The hidden microphone and the preview, where the voices slip from the faces, are the disaster the second half repairs. “Moses Supposes” is the diction lesson the talkie forces; “Good Morning” finds the remedy; the dubbing session is the remedy; the curtain at the premiere exposes it. What gives is real in a short film: the Broadway Melody ballet, a pitch the plot does not need; “Make ’Em Laugh”, which adds no fact; the montage, which makes its point several times.
Akira Kurosawa · Film
7.8 · Tier III
The subtractive test, run on structure, gives two answers. The house is required: the time spent in one room is the length of the decision, and the board’s offer, made before the call, sets what Gondo will lose, so that the ransom is a price and not a sum. The exchanged costumes are required, since the moral problem is that the child is not his. The train is required and brief. The procedure is required in kind: the whole city goes looking, and the boy’s drawing, the tram on the tape and the smoke each turn the search. What gives is length, and it gives in many places. The briefings repeat each other; the detectives’ reports are given in full where a summary would serve; the nightclub outruns its one task, buying heroin; and Gondo is absent from long stretches of the second half, so that the part which built him is set aside while the procedure runs. Required parts, held at a length the argument does not compel.
Walter Gropius and Adolf Meyer · Architecture
7.8 · Tier III
The test is subtractive, and in the main building it finds almost nothing to remove: pier, glass, spandrel and corner are one statement. The fronts are compelled by use, daylight across deep finishing floors, and by site, a long face set to the railway, where the firm was announced to every train. That much is necessary, but the necessity is local. The plan was not compelled by the fronts; it was Werner’s, drawn first, and the Gropius and Meyer walls were put onto it. Several of the yard buildings could be other without loss to what the work says. The glass corner itself is a wager more than a requirement: the floors could have stopped at a pier with no loss of light. Required in its most famous part and assembled elsewhere, it clears the cap of 7.5 by two tenths.
Rem Koolhaas (OMA) · Architecture
7.8 · Tier III
Judged on purpose, structure and site. The large hall passes the subtractive test better than most halls of its decade. It is a shoebox, the type acoustics recommend, and it is not hung inside a decorative envelope but run as a tunnel through the solid, its long walls carrying the building: remove the hall and the solid falls; remove the solid and the hall has no walls. The glazed ends are its one bold addition, and they answer a stated purpose. What yields is the outline. The faceted shape is a house design scaled up, compelled neither by the hall nor by the site, and much of the circulation is residue made into event. Above the cap, by two tenths.
Christo and Jeanne-Claude · Visual art
7.4 · Tier III
The work is a rule more than a set of parts: a gate across the path, at the path’s width, at intervals, wherever the walkways run. The count of 7,503 is not chosen but yielded by the rule on Olmsted and Vaux’s paths, and the scale is compelled, twenty-three miles because the walks are twenty-three miles. The subtractive test bites in the opposite direction from a painting’s. Take away one gate, or a hundred, and nothing is lost that the eye can find; take away the rule and the work stops tracing the park and becomes a decoration in it. The free-hanging panel is required, since its motion is most of what the gate does, and the single colour is required. What gives is the frame, which carries the cloth and adds little else.
Banksy · Visual art
7.0 · Tier III
The image has so few parts that nearly all of them are required. Remove the balloon and there is a child with a raised arm. Close the gap between her hand and the string and there is a child holding a balloon, a picture of possession, not of loss. Take away the red and the heart is a grey shape with no pull on the eye. The tilt of the body and the lifted hand make the gap ambiguous, release or reach, and the ambiguity is the work. What yields is the figure itself: her dress, hair and stance are conventions any girl in silhouette would supply, and the words of the first wall are dropped in the prints without loss. The test bites at the edges; the core it leaves is a single relation, a narrow compulsion. The cap clears.
James Joyce · Literature
9.1 · Tier V
Length is not a cost; the question is whether the parts are required, and the frame passes. The last sentence runs into the first; the four books are Vico’s three ages and the return; the night keeps its order from the father’s fall to morning. None of that can go. What holds the axis lowest of the twelve is the sediment of seventeen years: the first question of I.6 runs 4,978 words; the names the father is called (I.3), the titles of the mamafesta (I.5), the Norwegian Captain retold through tavern noise (II.3), Shaun’s sermon (III.2) and the middle of the inquest (III.3) say at length what is said briefly elsewhere. Perhaps a quarter could go unmissed.
Valmiki · Literature
8.9 · Tier IV
The spine is compelled from end to end. Kaikeyī calls in her two boons and Daśaratha is bound by his word; then the exile, Śūrpaṇakhā’s mutilation, Khara’s war, Mārīca’s golden deer, the abduction, Jaṭāyu, Kabandha, the alliance bought by Vālin’s death, the search, Hanumān’s leap, the war, the ordeal and the return each follow from the one before. Remove any and the poem fails. What holds the axis lowest of the twelve is the share permitted rather than compelled: the long tales of Book 1, Sugrīva’s recital of the four quarters to the search parties, duels of the war that repeat a pattern without turning it, and most of Rāvaṇa’s prehistory in Book 7. A fifth of the whole or more could go.
Thomas Pynchon · Literature
8.9 · Tier IV
The test is subtractive, and it bites hard. Whole episodes could go without visible loss to the argument: the drill of disgusting English sweets at Mrs. Quoad’s, a good share of the limericks, the Rocketman romp through Potsdam, much of the picaresque of the third part after Slothrop leaves Zurich. The defence is real. The subject is a system that takes in everything, and the Preterite it passes over; a pared version would be the Elect’s book, all signal and no waste. The core is required: the evacuation dream, the conditioning of the infant Tyrone, the Herero history, Pökler, the firing of the 00000. What holds the axis at the foot of the twelve is that plenitude as argument makes excess permitted, not each part compelled, and the cap is cleared by one tenth.
Michel de Montaigne · Literature
8.9 · Tier IV
The subtractive test bites, and the book says where. It was built by accretion, not by design: “I add, but I do not correct” (III.9). The late essays resist removal; III.2, III.9 and III.13 move by digression, and the digression is the matter, since the subject is a mind in motion. But much of Book I could go without loss to what the work knows: its first chapters are exempla gathered under a heading, the commonplace book from which the essay later broke, and the Latin quotations heaped in the later strata often say again what the French has said. The record of a changing self needs its earlier selves, which justifies the strata, not every page. That is what holds the axis lowest of the twelve, a tenth above the cap.
Mark Twain · Literature
8.8 · Tier IV
The subtractive test fails against most of the book and bites hard at its end. Through thirty-one chapters the spine is required: the faked death (chapter 7) frees Huck into the river and a run of false names; the fog and Jim’s rebuke (chapter 15) turn Huck’s conscience for the first time; the Grangerfords and Bricksville show the shore the raft is fleeing; the Wilks fraud ends with the king selling Jim, which forces chapter 31. Smaller cuts are possible: the Walter Scott wreck is half required, and some of the king’s burlesque could go. What holds the axis lowest of the twelve is the Phelps farm: twelve of the forty-three chapters given to Tom’s romance of a prison break, a gag repeated until its knowledge is a fraction of its length. Read as satire on how a free man is treated after his freedom, it is required in part; it does not carry twelve chapters.
Jalal al-Din Rumi · Literature
8.8 · Tier IV
The subtractive test is brutal for this body, and it is what holds the figure here. Some three thousand ghazals come round in the end to one subject; by early report many were composed aloud and taken down as they came; the same images, sun, moon, wine, the reed, the tavern, Joseph, the sea and the drop, return in hundreds of poems, and whole ghazals could be removed without the body losing anything it does not say better elsewhere. Rumi did not select the Divan or order it: the order is the rhyme letter’s. Against that, the best ghazals are as necessary as any lyric in Persian, every line of the resurrection ghazal driving its one turn, and the repetition is the mode of a poetry of return, remembrance made verse. But the axis asks of the whole, and the whole is permitted, not compelled, in its scale.
William Wordsworth · Literature
8.8 · Tier IV
The test is subtractive, and the poem fails it in places, not briefly. The spine is required: the argument is that a mind is made by a few charged encounters and remade by returning to them, and the spots of time, the crossing of the Alps and Snowdon each bear weight. Take out the political books and the impairment of Books XI and XII has no cause. Length is not the charge. What holds the axis lowest of the twelve is what could go without loss: much of Cambridge in Book III, which is half anecdote; the long satire of the infant prodigy in Book V; London in Book VII beyond the blind beggar and Bartholomew Fair; the shepherd tales and the Chinese garden of Book VIII; the chronicle in verse of Books IX and X; and Vaudracour and Julia, a borrowed tale and the clearest removable part, which Wordsworth himself removed. Perhaps a sixth of the whole is permitted rather than compelled.
Luo Guanzhong (attributed) · Literature
8.6 · Tier IV
The test is subtraction, and in a chronicle of a century it bites. The frame is required: the opening sentence’s law of division and union is answered by the unification under Jin, so the sixteen chapters after Zhuge Liang’s death cannot simply go; the heroes’ cause fails and history goes on without them. What holds the axis lowest of the twelve is that much is permitted rather than compelled. Battles repeat their forms: the feigned retreat, the fire attack, the forged letter, the single combat for so many bouts. The six campaigns north run one pattern with diminishing return, Jiang Wei’s nine are told at a pace that admits their redundancy, and the seven captures of Meng Huo tell one fable of clemency seven times. Perhaps a fifth of the book could go without the knowledge changing.
Christopher Marlowe · Literature
8.5 · Tier IV
The frame is iron. The bond fixes twenty-four years (2.1); the opening soliloquy closes the disciplines one by one and leaves only magic; the conjuring, the bond, the dispute on the spheres with the Sins, Helen and the last hour each turn the screw, and none can be cut. The clock is the spine, and the last hour cashes the years. What holds the axis lowest of the twelve is the middle, which fails the subtractive test. Rome, the Emperor’s court, the horse-courser’s leg and the Duchess’s grapes in January could each go with little loss. The dwindling from “A sound magician is a mighty god” (1.1) to tricks at court is the argument, but one or two episodes make it and the middle makes it several times. Robin’s conjuring earns more, repeating the sin at a clown’s scale.
Johann Wolfgang von Goethe · Literature
8.5 · Tier IV
The spine passes the subtractive test. Wilhelm’s error about the theatre must be lived through, the Hamlet production is the summit and the end of that error, and the Tower must be there to name it as error. A great deal else could go without the whole knowing less. The troupe’s wanderings, from the second book into the fourth, repeat the same lessons about actors’ vanity and Philine’s charm; the talk of the theatre with Serlo and Aurelie runs past what the argument needs; and the last two books, with their revelations of kinship and their secret society, are assembled more than compelled. That is what holds the axis at 7.6, the lowest of the twelve: the cap is cleared, not by much.
Thomas Pynchon · Literature
8.5 · Tier IV
The spine is required. Take away Profane and Stencil’s quest has no present to be the delusion of; take away Stencil and Profane’s drift is a comic novel of bohemian New York. The historical chapters pass the subtractive test almost without loss: the chapter of Mondaugen and Foppl’s farm, and Fausto’s confession, could not go. What holds the axis at the foot of the twelve is the Whole Sick Crew: the parties, the songs, the running gags and whole conversations that are noise by design but still noise. The alligator hunt is the exception, since it carries the theme. Perhaps a fifth of the New York line is permitted rather than compelled, and the cap is cleared by one tenth.
Johann Wolfgang von Goethe · Literature
8.5 · Tier IV
The subtractive test is where a lyric collection of this size is weakest, and the Divan fails it in particular places. The Buch der Sprüche is a run of rhymed maxims that could lose a third of its pieces without the book noticing. The Buch des Unmuts mixes the sharp with grumbling at critics and the public that is of its decade. The Buch des Timur, two poems, is a gesture toward Napoleon and the winter of 1812 rather than a book. Against this the Buch Suleika is close to necessary throughout: the exchanges answer one another, and the order carries a love from first meeting through separation to reunion. The Notes are long and in places antiquarian. The slack around the core is what holds the axis at 7.6, the lowest of the twelve.
Thomas Malory · Literature
8.5 · Tier IV
The subtractive test bites harder here than on any other axis. The spine is required: the begetting and the sword, the dolorous stroke that wounds the land, the fellowship founded, its height in Lancelot and Gareth, its judgment in the Grail and its fall, where every earlier loyalty returns as a cause of ruin. The fellowship must be built at length if its breaking is to cost what it costs. What holds the axis lowest of the twelve is the middle. The Tristram books run as a book within the book, a third of the whole, with jousts of one pattern, and they feed the end only through Mark’s treachery and Tristram’s death told in retrospect. The abridged Roman war stands as an episode the later books scarcely remember.
The Beatles · Music
8.5 · Tier IV
Thirty tracks in about ninety-three minutes, and the subtractive test bites here more often than on most records. The case against the test carries weight. The record’s subject is plenitude and dispersal, a band become four writers taking up the whole of popular music, and the fragment, the joke and the pastiche are part of the field it surveys. “Revolution 9”, which looks most removable, is required: the one place the record’s noise is set without a song. What holds the figure lowest is idleness, not length: “Wild Honey Pie”, a fragment; “Why Don’t We Do It in the Road?”, one line repeated; “Don’t Pass Me By”; “Honey Pie” and “Savoy Truffle”, two exercises on one side. The scale is permitted more than compelled.
William Makepeace Thackeray · Literature
8.5 · Tier IV
The double spine passes the subtractive test. Becky without Amelia is a picaresque; Amelia without Becky is a sentimental novel; the book needs both, and needs Waterloo exactly where it falls, killing George while his betrayal is still unread and binding Amelia for fifteen years to a fiction. The note George slips Becky at the Duchess of Richmond’s ball, produced by her in the last number to free Amelia for Dobbin, shows the plot keeping its accounts across the whole length. What holds the axis lowest of the twelve is that a great deal is permitted rather than compelled: Miss Crawley’s illnesses and the scramble for her will, Lady Southdown’s tracts, the younger Pitt’s courtship, the Bute Crawleys’ schemes and much household business could lose a third without loss of a fact the book needs, and the narrator’s sermons repeat their point. Part of the length is the instalment’s.
Nayaka builders (and earlier) · Architecture
8.5 · Tier IV
Run the subtractive test from the centre outward. The two sanctums are the reason for everything, and the walled enclosures, each entered by a gate, are what the ritual of approach requires, a sequence from the street toward the lamp in the dark. That core is compelled. Much else is not. The complex grew by donation over four centuries, and many of its halls are gifts a patron could give and the temple receive: take away the Thousand Pillar Mandapam, now a museum, or a lesser gopuram, and worship goes on unchanged. The stucco hosts multiply figures past what a gateway’s meaning needs. And the tallest towers stand at the outer wall, away from what they mark, their scale set by donors’ rivalry and the city’s sightlines. Required at the centre, permitted at the edges: that holds the axis lowest of the twelve.
Thomas Pynchon · Literature
8.5 · Tier IV
The test is subtractive, and the book invites it. Its argument is that the Line is an act of reason imposed on a world of unruly possibility, and the digressions are that world: the Learned English Dog, Vaucanson’s mechanical duck grown conscious and in love, a Chinese geomancer, tales within tales, songs. The argument needs abundance, so abundance is required in principle, and the frame, the transit at the Cape, the cutting of the Visto, the massacre at Lancaster, Mason’s grief and the last part are each required. What holds the axis at the foot of the twelve is that a good share of the rest is not: many single episodes, and many of the songs and comic routines, could go without the book knowing less, and the frame lapses for long stretches. The method justifies digression as a kind, not every instance of it.
Daniel Defoe · Literature
8.4 · Tier IV
The island resists subtraction. Each stage is required, and each changes what the next can be: the stripping of the wreck, trip by trip, before the sea takes it; the fortification; the fever, the dream and the conversion, placed where the illness compels it; the years of making, the pots, the bread, the canoe too heavy to launch; the footprint; the long fear; Friday; the mutineers. The frame is assembled rather than required. The Sallee captivity and Xury exist chiefly to bring Crusoe to Brazil, and Xury is sold without a backward look. The wolves of the Pyrenees are an adventure appended after the rescue, and the closing pages hurry a marriage and a death into a sentence to point at a sequel. Necessary at the centre, loose at both ends.
Ovid · Literature
8.4 · Tier IV
The subtractive test bites, and the book half admits it. Fifty-one poems turn on a short set of moves: the voyage, the cold, the barbarians, the wife’s loyalty, the friend’s silence or kindness, the plea that Caesar’s anger soften, the claim that the verse has decayed. Many of the shorter poems of Books 3 to 5 could go singly with no loss of argument, perhaps a fifth of the lines. Against this the large pieces are required: Book 2 is compelled by the situation, 1.3 is the book’s origin, 4.10 closes the self the book has built. The monotony is in part the subject, exile as the same day repeated; what holds the axis lowest of the twelve is that the book uses repetition more often than it needs it.
Richard Wright · Literature
8.4 · Tier IV
Book One passes the subtractive test almost whole. The rat in the kitchenette, beaten to death with a skillet while the women scream, gives the cornered thing and its violence before a word of theory; the quarrel with Gus shows the fear of robbing a white man that will kill Mary; the job, the café, the drive each readies the bedroom. Book Two is nearly as tight, and Bessie’s murder, the second killing done coldly, is the book’s harshest necessity. What holds the axis lowest of the twelve is Book Three: Bigger’s thoughts restated, sometimes in the same words, across his visitors; the inquest, trial and cell repeating a closed argument; two long speeches saying what the first two books had shown. Perhaps a sixth could go.
Ralph Waldo Emerson · Literature
8.4 · Tier IV
The lowest of the twelve. The test is subtractive, and the book is made to fail it in part: Emerson built these essays by drawing sentences from his journals into lectures and then into print, and many paragraphs could be shortened, reordered or moved from one essay to another with little lost. “Compensation” and “Spiritual Laws” state the same law of self-acting justice twice; “History” and “The Over-Soul” state the one mind twice; “Prudence” and “Love” add little the others lack. What holds the axis above the cap is the spine. The order is an argument, from the universal mind to the self that must trust it and back through the soul to art. Remove “Self-Reliance” or “The Over-Soul” and the book loses its two poles; remove a third of its sentences and it loses little.
Nikos Kazantzakis · Literature
8.4 · Tier IV
The spine is required. The carpenter who makes crosses for the Romans, the call he resists, the ministry, Judas’s commission, the cross, the vision and the waking: take any one away and the argument breaks. Without the vision there is no last temptation; without the commission the vision has no accuser when the old disciples come. What fails the subtractive test is repetition, and it holds the axis lowest of the twelve. The torment of a God who will not let him go is restated through the first third; the wanderings rehearse a conflict the prologue has already named; the disciples’ quarrels return in scenes whose work was done once; the narration states what a scene has just shown. Something near a fifth, mostly in the first half, could go without losing a turn. It stands just above the cap because the long approach is the weight the vision must lift: weariness with the torment is what makes the offered peace plausible.
August Sander · Visual art
8.4 · Tier IV
The subtractive test, run on a body of some six hundred portraits, finds almost every single picture removable. Take away the Pastry Cook and the tradesmen still stand; take away one farm family and the farm families remain. A typology is additive by nature: the plan could have taken another portfolio, and the maker’s own practice shows its edges moving for forty years. What resists subtraction is the scheme. Remove the last people and the cycle from the soil to the city loses its fall; remove the farmers and it loses its ground; remove the city and nothing is left for the rest to answer. The groups are compelled by the argument, the number of pictures in each only permitted by it.
Gustave Flaubert · Literature
8.4 · Tier IV
The large order is compelled; inside it the subtractive test goes against the book, and that holds the axis lowest of the twelve. The ladder runs from the body’s appetites, food, gold and the Queen of Sheba, to the mind’s, doctrine and heresy, then to all gods, to the cosmos without gods and to life without form. Each rung is a deeper temptation than the last, and the book could not be reordered. But the heresiarchs of the fourth part and the gods of the fifth come as processions in which one figure could be removed, or three added, without loss; the monsters of the seventh are the same kind of list. The scale is permitted by Flaubert’s reading rather than compelled by Anthony’s need. The cap is met, narrowly.
Utagawa Hiroshige · Visual art
8.4 · Tier IV
Judged on the series, sheet by sheet, and here the subtractive test bites. A run of commercial sheets issued over three years as a publisher’s success was extended is a structure that permitted its scale rather than compelled it: one hundred was a round number of the genre, and the series ran past it. Take away a dozen of the quieter summer and autumn views, river prospects and shrine precincts drawn in the older horizontal manner set on end, and the work loses little; take away the shower, the eagle, the cat, the carp or the fox fires and it loses its character. The season frame is required, and within the best sheets necessity is high. Strong within the sheet, loose across the run.
Elvis Presley · Music
8.3 · Tier IV
The subtractive test bites, because the record was assembled rather than made: seven tracks from RCA’s first sessions in Nashville and New York in January 1956, five from Sun masters bought with the contract, and “Heartbreak Hotel”, recorded at the same Nashville sessions, held back. Remove “I’m Counting on You” or “One-Sided Love Affair” and little the record says is lost; “Just Because” and “I’ll Never Let You Go” each double the other. But the test bites at the margins and not at the centre. What the record has to say lives in the alternation of shout and croon, and that alternation requires both kinds of track: take out the ballads and it is a rock and roll record, take out the shouters and it is a crooner’s. Inside the tracks the necessity is plain, in “Blue Moon”, where every element is required, “Trying to Get to You”, which climbs as if compelled, and “Blue Suede Shoes”, which opens the record with a reason. The figure rests at 7.6, a tenth above the cap and no more: the whole is compelled in its argument and permitted in its particulars.
Aristophanes · Literature
8.3 · Tier IV
The spine is required. The god of the theatre goes down to bring back a poet because the city has no good one left, and comes back with a different poet from the one he went for. That reversal is the play’s argument, and the contest that produces it cannot be removed. Much of the first half is detachable routine of the Old Comic kind: the slave’s complaints about his load, the corpse who will not carry the bags for less than his price, the lion skin passed back and forth between master and slave, the innkeepers’ abuse, the whipping test to tell god from mortal. They are funny, and some carry the theme of masters and slaves that the parabasis turns political, but they could be cut or exchanged without loss to what the play knows. What holds the axis at the foot of the twelve is that loose first half: the core is strong, and the cap is cleared by a tenth.
Herman Melville · Literature
8.3 · Tier IV
The test is subtractive, and the book’s design invites it, since a series can lose a member. Much of the series is required. Black Guinea’s list of the gentlemen who will vouch for him names, one by one, the figures who then appear, so the avatars are a promise the book keeps; and each dupe is a different faculty tested: charity, pity, greed, the hope of health, the misanthrope’s distrust. The second half is slack where the first is taut. The evening with Charlie Noble, the toasts, the praise of the press and of wine, and the exchanges with Mark Winsome and Egbert say again at length what the first half showed, and the tale of China Aster could go with little loss. The repetition is partly the argument, since trust is asked for again and again in the same words; but a quarter of the book is longer than its argument compels, and that holds the axis a tenth above the cap.
Pre-Pottery Neolithic builders · Architecture
8.2 · Tier IV
Judged on structure, purpose and site, and the purpose is unknown: that is the first limit. Some parts are compelled. The central pair is the reason for the ring: take away one of the two great figures and the enclosure loses its centre and its symmetry. The pillars set into the ring wall face inward, and with the bench they make the wall a ring of presences round a gathering; that figure requires them. But the subtractive test finds much that yields. The ring walls are rough accretions of rubble, thickened and doubled over generations; pillars were reset, buried in later walls, propped or reused; in enclosure C concentric walls seem added rather than planned. A building whose use cannot be stated cannot show its parts compelled by use. That holds the axis low: the figure is necessary, the fabric round it is assembled.
Miguel de Cervantes · Literature
8.2 · Tier IV
The subtractive test divides the book. Within its best pieces nothing is idle: in Rinconete y Cortadillo every scene of an afternoon in Monipodio’s house serves one disclosure, and the Coloquio is digressive by design, the quarrel over digression being its argument about how to tell a life. The cost is at the level of the book. Remove Las dos doncellas or La señora Cornelia and the collection loses variety, not knowledge; their scenes of disguise, pursuit and reconciliation could be exchanged between them, and the romances’ set speeches could lose a third. The cap is met, narrowly, because the plan of twelve pieces answering one another is itself a reason for most of them to be there. What holds the axis among the lowest of the twelve is the romances’ slack.
Gustave Flaubert · Literature
8.2 · Tier IV
The spine is required. The unpaid army, the stolen zaïmph, the veil recovered in Mâtho’s tent, the turn of the war, the sacrifice to Moloch that brings the rain, the trap in the Défilé de la Hache and Mâtho’s death at Salammbô’s wedding feast: each hinge moves the next, and the veil binds the love plot to the war so that neither can be cut out. The subtractive test fails in the middle. The campaign chapters (VII to IX) run battle after battle and march after march, and much of their matter could be shortened without the loss of a fact the book needs; the inventory of Hamilcar’s treasure and the catalogues of the army’s peoples are there because the documentation was there. That holds the axis at the foot of the twelve, level with The Unconcealment: necessity real in the plan and weak in the volume of the execution. The cap is met at its edge.
Walter Pater · Literature
8.1 · Tier IV
Ask what could be removed from a book gathered out of periodical essays, and it gives two answers. “Luca della Robbia” could go with small loss: it restates the Michelangelo study’s argument about sculpture and relief in a thinner key. “Joachim du Bellay” carries the thesis into France but adds little that the French stories and the Preface have not set out. Against that the frame is strongly required. The Preface sets the method, the Conclusion says what the method is for, and the span from the tales of twelfth-century France to an eighteenth-century German is itself the argument that the Renaissance is a temper and not a period. That span needs both its ends, and has them; inside the best studies the sentences resist cutting. What holds the axis low is that Pater himself treated a part as removable, withdrawing the Conclusion in 1877 and restoring it in 1888.
Juan O'Gorman, Gustavo Saavedra and Juan Martínez de Velasco · Architecture
8.1 · Tier IV
The subtractive test runs two ways. Part of the building is compelled: a closed stack wants no windows, and the blind tower is required both by the books and by the mural it carries. The glazed base is required by reading, which wants light, and the split of light below and dark above is a true partition of use. But much is not compelled. Base and tower are a common modern scheme, podium and block, that could be drawn without the mosaic; and the mosaic distributes its figures by an iconographic logic, not a structural one, so that many passages could be swapped or thinned without loss. The parts required by the books and the parts required by the idea do not fully coincide, and that holds the axis lowest.
Raymond Chandler · Literature
8.1 · Tier IV
The spine is required: a friendship given freely, a debt paid by silence and jail, a second case that turns out to be the first, and a last meeting in which the debt is refused. The joining of the two plots through Eileen Wade’s past is the book’s architecture, and it makes the long Wade middle bear on Terry in the end. What holds the axis lowest of the twelve, level with The Sublime and above the line, is what the subtractive test finds permitted rather than compelled: the trawl through the three doctors whose names begin with V, which delays more than it reveals; the asides on the city and the trades; the set speeches of Harlan Potter and Ohls; and a loose clue chain, joined by a coincidence carried by mood. Perhaps a fifth could go.
William Gibson · Literature
8.1 · Tier IV
The subtractive test bites. The spine is a heist, and a heist assembles a crew: each member is required by the plan, the cowboy for the ice, the samurai for the house, the Flatline for the skill Case lacks, Riviera for 3Jane, and that requirement is the genre’s rather than the book’s. Some parts are compelled by the argument: Case’s lost matrix opens the book on the body as prison, the toxin sacs make the flesh the leash, and Linda Lee is the temptation the end turns on. What holds the axis lowest of the twelve, level with The Encompassed: Istanbul, much of the Freeside tourism, the Panther Moderns and the clone Hideo could go with little loss, and Armitage’s breakdown into Corto is under-used. The density is in the texture, and the texture is the part most easily trimmed.
Oscar Niemeyer · Architecture
8.1 · Tier IV
Judged on purpose, structure and site. The site compels the main moves: the head of a straight axis kilometres long, on a flat plateau under an enormous sky, needs a figure legible from the far end and from the air, and the low platform with two vertical towers is that figure. The bicameral constitution compels two chambers, and the two forms give each house its sign. But the subtractive test bites. The bowl and the dome are signs more than sections: the plenaries under them do not require an inverted dome rather than a dome. The programme was outgrown so fast that the Annexes followed, and the terrace made as public ground has largely been closed. That is what holds the axis here.
Claudio de Arciniega and successors; facade by Manuel Tolsá · Architecture
8.1 · Tier IV
Judged on purpose, structure and site. The plan is compelled by a liturgy and an institution: the Spanish cathedral needs its coro in the nave for the chapter’s hours, processional aisles round it, an apse for the principal retablo and chapels between the buttresses for confraternities, guilds and families, and here each is present and placed where the use asks. The breadth of five aisles and the low, heavy piers are compelled by a lake bed that would not carry a tall, thin Gothic section. What holds the axis this low is accretion: each chapel a separate commission, several retablos removable with no loss to the building’s argument, a front of three periods, and a finish by Tolsá that argues necessity after the fact, not from the start.
Lauryn Hill · Music
8.1 · Tier IV
A long record before its coda, and the subtractive test bites harder here than on most records of this standing. Required: Lost Ones must open, the break from a former partnership stated as rap; To Zion is the centre the rest turns around; Doo Wop (That Thing) is the public sermon; Final Hour is the one place the rapper is answered by the believer; Everything Is Everything and the title song are the compelled close. The test bites in the middle and at the edges. When It Hurts So Bad and I Used to Love Him say twice what Ex-Factor said first, love as injury; Nothing Even Matters is lovely and slack, a duet that idles; Forgive Them Father and Every Ghetto, Every City are needed but long. The classroom passages frame the songs, but no song requires them, and they could be cut back without loss. The coda is permitted, not compelled. The core is necessary and the whole is not: the cap is cleared narrowly, and this is the record’s lowest figure.
John Milton · Literature
8.1 · Tier IV
The spine is required: the descent, the loss in the wood, the deception, the ordeal in the chair, a rescue the virtue itself cannot effect, the return to the father’s house. Remove Sabrina and the masque loses its theology, since the Brothers’ failure is what proves that chastity does not free itself. Remove the Brothers and the Lady’s confidence has no measure. But the subtractive test finds much. The Elder’s doctrine, “Virtue may be assailed but never hurt, / Surprised by unjust force but not enthralled”, is argued, illustrated and argued again; the Spirit as Thyrsis tells what the audience has seen; the passages added for the 1637 print carry the second debate past what the drama needs. What holds the axis near its cap is a work of set speeches as often as of necessity.
John Ruskin · Literature
8.1 · Tier IV
The lowest of the twelve. The book is loose by method. It wanders into family genealogy, the sherry trade of Ruskin, Telford and Domecq, travel itineraries, notes on Ruskin’s later books, asides on politics and religion, and portraits of servants and tutors whose place in the whole is affection rather than need. Many chapters could lose a third without loss, and the second volume has stretches of record whose selection reads as what came to mind. The main line is required: Herne Hill, the carriage tours, Schaffhausen, the aspen at Fontainebleau and Turin are each a step in the making of one eye. What holds the axis there is that the omissions are necessary and the inclusions often are not; the axis weighs what is in.
Nina Simone · Music
8.1 · Tier IV
Nine tracks in about thirty-six minutes, and the subtractive test meets resistance at the ends and gives in the middle. “Be My Husband”, voice, handclaps and drum alone, states the record’s terms at the threshold. “Nobody Knows You When You’re Down and Out” is the first full blues and the first long piano. “Strange Fruit” and “Sinnerman” carry the argument, and the ten minutes of the last are compelled by a build that needs time to become a trance. The test bites in tracks 3 to 7: “Tell Me More and More and Then Some” is the lightest thing here, and two of the slow blues restate the mode without turning it. Two could go with small loss.
Sufjan Stevens · Music
8.1 · Tier IV
Twenty-two tracks in about seventy-four minutes, and the subtractive test bites often. The load-bearing pieces resist it: the UFO prelude must open, in hushed piano and wonder; John Wayne Gacy, Jr. is the moral centre; Chicago and Casimir Pulaski Day are the hinge of the first half; The Seer’s Tower is the descent the close needs, and Out of Egypt the compelled exit. The test finds give in three places. Most short interludes are jokes of titling, a cheer of seconds or a reprise named as a stage cue, and only the Mary Todd reprise and the Lincoln temple do work the sequence needs. The middle fancies could lose one or two without the argument losing a fact. And the length is permitted by the state-album conceit, which invites inventory. That holds the axis lowest; the cap is met, narrowly.
Ovid · Literature
8.1 · Tier IV
The spine is tight: a teacher, a syllabus in three stages for men, and a mirror syllabus for women. The subtractive test bites inside the panels. The catalogues of where to find women in Rome, the porticoes, the theatre, the circus, the triumph, the banquet, are required, because the city is the poem’s subject. Many of the inset myths are not. Daedalus and Icarus is pinned to its lesson by one conceit, that Minos could not hold a winged man, so how will you hold winged Love, and half of it could go without loss to the argument. Book 3 repeats much of Books 1 and 2 turned about, and its cosmetics and coiffure are the thinnest stretch. The parts are mostly required by the joke; the joke does not require all of the parts.
Many masters, from 1386; facade completed in the nineteenth century · Architecture
8.1 · Tier IV
Run the subtractive test on purpose, structure and site. The five aisles are compelled: a cathedral for the largest city of Lombardy, built to hold the city at once. The stepped section is compelled by the debates that fixed it: the Milanese masters cut the height a northern geometry would have given, and the building stands on that decision. The piers and their ties are the structure. What resists is the surplus the building is famous for: its spires and statues could be halved and the church would stand and serve as before, and the statues ringing the piers add without carrying. The front, argued for centuries, is assembled rather than required.
Charlie Chaplin · Film
8.0 · Tier IV
The subtractive test splits the film. What is required is the double: the barber and the dictator must share a face, since the argument is that the tyrant is a little man made monstrous by a crowd, and the little man can be taken for him. Every sequence that sets the two lives side by side bears weight: the oration answered by the ghetto, the globe dance answered by the shave, the arrest of the one answered by the elevation of the other. Much else could go. The 1918 prologue is a long comedy whose only necessary yield is Schultz’s debt and the barber’s lost memory. The pudding scene restates the ghetto’s helplessness, and the Napaloni visit, very funny, runs past what it argues. A required spine, and long stretches made of routines it permits rather than compels.
Wu-Tang Clan · Music
8.0 · Tier IV
Twelve songs and a spoken close in about an hour, and the subtractive test finds a core that cannot go and a margin that can, wider than the core would want. Protect Ya Neck, C.R.E.A.M., Da Mystery of Chessboxin’, Bring da Ruckus and Can It Be All So Simple carry the argument: the clan as one body with nine mouths, the economy of the block, the memory of a simpler poverty. The two solo showcases are required too, since the record is also a prospectus of separate talents. The test bites at the edges, and more than once. Wu-Tang: 7th Chamber, Part II sets verses already heard to a second beat; the torture skit before Method Man is funny once and inert after; the second track is the slightest; and on the posse cuts a weaker verse could often go without loss. The core holds the figure above the cap, and the margin keeps it close.
Tibetan, under Songtsen Gampo · Architecture
8.0 · Tier IV
Judged on purpose, structure and site. The core yields little to the subtractive test: a ring of cells round a hall, the Jowo’s chapel at the east end of the axis, a single entry from the west, and the inner circuit that takes the worshipper round the sacred before reaching it. Each part is compelled by the rite of circumambulation and by the house of one image. The whole as it stands yields more. The outer halls, upper storeys, further chapels and galleries grew as devotion and patronage grew, and many of them could go without the temple’s purpose failing. The thick battered walls and flat clay roofs are compelled by climate and material. That accretion holds the axis down; the compelled core, which still governs the whole, keeps it above the cap.
Wassily Kandinsky · Visual art
8.0 · Tier IV
The subtractive test bites harder here than on a Composition, and the title invites it: the painter named this kind of picture spontaneous. At the scale of the whole the structure resists. A crowded, darker, more violent left gives way to a lighter, more open right, and the canvas needs both: take either away, or the passage between them, and the painting’s argument is gone. The heavy black lines that carry the rhythm and mark the divide could seldom go. At the scale of the single mark the test succeeds too often: many patches and small hooks in the dense left could be moved, recoloured or dropped without loss. Necessary in design, permitted in detail; the cap clears by a tenth.
Rudolf Steiner · Architecture
8.0 · Tier IV
Judged on plan, section and purpose. At the west the forms are compelled by one idea, that a building can grow like an organism and each part be a metamorphosis of its neighbour: the portal, the terrace over it, the pillars under the west window and the fall of the roof are one continuous gesture, and nothing there could be taken away without the front collapsing as a sentence. The test bites unevenly elsewhere. The north and south flanks repeat their window bays rather than transform them; the east, set by the needs of the stage, is a large working body dressed in the same skin; and the great hall is a broad rectangular auditorium that the sculpted exterior does not require. What is required is required absolutely; a good share of the volume is clothed. The figure clears the cap narrowly.
Moshe Safdie · Architecture
8.0 · Tier IV
Judged on structure, purpose and site. At the scale of the dwelling the box resists the subtractive test: take it away and the dwelling above has no garden, the heap no stagger, the rooms no light on three sides. Take away the stagger and the scheme is an apartment slab; take away the upper streets and the clusters are towers. What yields is larger. The three clusters are what the budget left of a settlement many times the size, so the scale is permitted by money, not compelled by the argument. The system carries redundancy at its root: walls and slabs doubled where boxes meet, boxes far heavier than a dwelling needs. The heap is composed, not random, and the axis stands just above the cap.
Vijayanagara builders · Architecture
8.0 · Tier IV
Judged on structure, purpose and site. The axis is compelled: from the east gateway past the stone chariot, up the steps of the open hall and into the dark shrine, each stage is a station of procession and approach, and none can be taken out without breaking the sequence. The open hall’s high plinth and open sides are required by its use as a stage for music, dance and assembly before the god. What holds the axis is the court. The marriage hall, the festival hall, the goddess shrine and the cloister grew with a temple economy over a century; each answers a ritual need, but none is required where it stands. The carving of the piers is profusion as much as necessity. The core is necessary; the court is permitted.
Frederick William Stevens · Architecture
8.0 · Tier IV
The subtractive test bites hard. The core is required: a railway headquarters must house its offices, a booking hall must gather the passenger, and a terminus in a peninsular city must face the town at the head of its lines. The symmetry and the forecourt follow from the role the building claims, the gate of a port city to a subcontinent. Much else could go without loss to what the building does. Gables multiply, turrets crowd, the carving spreads over every surface at one pitch, and the dome stands over a stair, not where trains and people meet. The working station lives in the sheds behind, which the front does not govern. The required parts are well required; the rest is permitted.
Giuseppe Mengoni · Architecture
8.0 · Tier IV
Judged on purpose, structure and site. The long arm is compelled: it joins the city’s two great public rooms, the cathedral and the opera house, by the shortest covered route, and as a street it carries a real flow of people every hour of the day. The glass is compelled by the depth of the block, since a street roofed in anything else would be a tunnel. Where two streets cross under one roof, the octagon is required as a place to pause and turn. Much else could go without loss to the use: the short arm leads to minor streets and is ordered by the cross more than by traffic; the fronts carry far more ornament than a shopping street asks; and the arch is a monument the passage does not need. That a gallery named for the king is a sign as well as a street defends the arch, not the full dress of every bay.
Herzog and de Meuron · Architecture
8.0 · Tier IV
Judged on purpose, structure and site. The governing moves pass the subtractive test. The Turbine Hall is kept empty, and the void is compelled twice: it is the museum’s street and its entry, and it is what lets the building do what no ordinary gallery can. The ramp is required: it brings the street down into the hall and makes arrival a descent. The light beam is required: it lights the upper galleries of a building whose brick walls give little daylight. The galleries sit in the boiler house, where the section asks for them. What yields: many of the galleries could be moved without the building losing what it knows; the vertical circulation of 2000, escalators packed against the hall, was found cramped and confusing; and much of the shell’s grandeur is permitted by the inheritance, not compelled by the museum. The cap is cleared by a tenth.
Federico Fellini · Film
8.0 · Tier IV
Judged on structure, and the subtractive test bites hard. Some parts are required. The bonfire and the manine open the year, and the manine return to close it; the rally, the gramophone and the castor oil are the political spine; the mother’s illness and death are the one irreversible event, placed so that the year cannot simply repeat; the wedding closes the circle with a departure. Much else could go without loss of anything the film knows. The Emir at the Grand Hotel, the Mille Miglia, the motorcyclist, several school sketches and the tobacconist each delight, and each could be exchanged for another anecdote of the same kind; perhaps a fifth of the film is of this order. That holds the axis among the lowest of the twelve: a form of accumulation permits more than it compels.
Donna Tartt · Literature
8.0 · Tier IV
The spine is required and tightly made. The Greek class must be closed and strange, so that a reader can believe five students and a teacher withdrawn from the moral world. The bacchanal must happen, since it kills the farmer and gives Bunny his hold. Bunny’s menace, through the spring trip to Italy he cannot stop talking about and his half-confessions, must be built at length, so that the murder at the ravine arrives as the group’s logic and not as a turn of melodrama. Book II must exist, because the book’s subject is what the murder does to those who did it. The subtractive test finds the licence of that second book: the funeral weekend, the comedy of police and press, Judy Poovey and the parties, the long haze of drink and pills, much of it good and some of it removable without loss. In Book I, Richard’s winter in the unheated warehouse earns less than its length.
Soundgarden · Music
8.0 · Tier IV
Fifteen tracks in about seventy minutes, and the subtractive test finds a required frame and a required centre. Let Me Drown must open: the wish to go back under, stated at once, sets the record’s direction downward. Fell on Black Days is the centre of disclosure, Black Hole Sun the hinge, The Day I Tried to Live the argument, 4th of July the dread placed before the end, Like Suicide the end the record compels. Most of the running time is held by songs the record could not lose. The test bites in the middle of each half: Kickstand is an accent the sequence would not miss, Mailman and Fresh Tendrils restate the heavy mid-tempo mode, and Head Down lengthens the first half rather than deepening it.
Antoni Gaudí · Architecture
8.0 · Tier IV
Judged on purpose, structure and site. The light well passes the subtractive test as well as anything Gaudí built: the blue deepening toward the top and the windows widening toward the bottom exist to send even light down a narrow shaft into every flat, so that colour, opening and use are one fact. The attic’s catenary arches are compelled by span and load, and the main floor’s bay opens the family’s rooms to the avenue. Much else yields. The trencadís, the scaled tiles, the masked balconies and the turret could go and the house be lived in as before, and the piers are carved as bone where a plain pier would bear the same load. The image was part of the purpose, and it is not assembled: that carries the axis just above the cap.
Ustad Ahmad Lahori (attributed), under Shah Jahan · Architecture
8.0 · Tier IV
Judged on purpose, structure and site. The walls are compelled: a citadel for a new capital, high on the city side, where attack and display both faced, and lower toward the river, where the water defended. The public axis is compelled by ceremony: from the Lahori Gate through the vaulted bazaar and the drum house to the hall of audience, each threshold narrows access to the emperor, and no part of it can go without breaking the sequence. The pavilions are compelled by climate and site, open to the breeze off the water. What yields to the subtractive test is the terrace as a series: pavilion follows pavilion, each complete in itself, and several have been lost with the system still legible. As it stands, their necessity is read from their own fabric, not from the plan that held them.
Nok · Visual art
8.0 · Tier IV
Within one head the parts are required. The arched brow runs into the upper lid; the lower lid is drawn straight or bowed so that the eye becomes a triangle or a D; the pupil is pierced, and the piercing makes the eye look; the coiffure, built in buns and crests, closes the cylinder or sphere of the head. Remove the perforation and the head goes blind; remove the brow line and the face loses its frame. The great heads are made from few means, none idle. But the unit is a body, and a body does not resist subtraction: any one figure could go without loss to the rest, and much of the corpus repeats rather than requires. The necessity is a convention’s, economical and exact, above the cap and well short of a composed work’s compulsion.
Hannah Höch · Visual art
8.0 · Tier IV
Judged on the parts, which are many and gathered by accumulation. The subtractive test bites at the level of the piece: remove one crowd, one wheel, one minor head, and the sheet loses a little density, not its argument. Much of the field is a swarm whose members are interchangeable by design, and the method of the montage is additive. What resists removal is the armature: a world of power and a world of its mockers set on one plane; the central whirl, which turns the whole sheet; the machine parts, which make political figures look like components; and the place where the maker enters her own picture. Those carry it. The cap clears with some room; the swarm keeps the axis below the eight.
Ovid · Literature
8.0 · Tier IV
The subtractive test finds much that could go. The book is a sequence of single situations, each pressed to a witty turn, and many are interchangeable: another poem at the door-keeper’s post, a further complaint against a guardian, a ring that wishes to be its owner’s finger (2.15). Within a poem the habit is the run of exempla, and a mythological instance can often be dropped without loss of the point. The architecture carries the necessity. The prefatory epigram says the poet cut five books to three; programmatic poems set and close the terms (1.1, 1.15, 2.1, 3.1, 3.15); and the Cypassis diptych (2.7, 2.8) cannot be parted without losing both the joke and the disclosure. Necessity lives in the frame and the pairs, not in the run of the poems, and clears the cap by a tenth.
Built for Vimal Shah and Vastupala and Tejapala · Architecture
8.0 · Tier IV
Run the subtractive test on the great temples and the core holds. The sanctum holds the image; the closed hall and the vestibule lead to it; the open hall gathers the congregation and its rites of music and dance; the ring of cells makes the court a world of Tirthankaras round the one at the centre, so that the walk round passes every one. The plain closed wall is compelled by a mountain site, a cold climate and a community that guarded its images. What yields is the profusion: almost no ceiling bay could not be simpler without loss to the worship, the carving being the donor’s merit more than the rite’s need. Pittalhar repeats the type; the last temple is a coda. Necessary at the core, accumulated at the edge.
Eero Saarinen · Architecture
8.0 · Tier IV
Judged on structure, purpose and site. Much resists the subtractive test. The shells are roof and structure at once, carried on the four piers, and the skylight seams lie where the shells part, so that light enters exactly where the structure allows it. The section follows the passenger: curb, check-in, rising floor, lounge at the glass, tube, aircraft. Nothing is applied; stair, bridge and counter are moulded from the roof’s own law. What yields is the cause of the form. The shells were drawn as a figure and made to stand afterwards, and a lower, simpler vault would have sheltered the same functions. And the purpose did not compel the building for long: within a decade the wide-bodied jet, baggage and security screening outran the hall.
Joseph Maria Olbrich · Architecture
7.9 · Tier III
Judged on purpose, structure and site. The hall is compelled: a society that hangs and rebuilds its shows wants a large, even room lit from above with no fixed walls, and that is what stands behind the front. The entrance block is compelled by a second purpose, to announce the society and to separate the street from the art: a closed white mass with one door and hardly a window, so that the visitor passes from the city into a sanctuary. What resists the subtractive test is much of what makes the building famous. The dome carries nothing and shelters nothing. The owls, the masks and the garlands could go and the hall would work as before. A manifesto’s image is not mere ornament, and the defence holds in part; the figure stands just above the cap.
Peter Eisenman · Architecture
7.9 · Tier III
Judged on purpose, structure and site. Much of the core passes the subtractive test. Take away the falling ground and the field is a garden of blocks seen from above; take away the aisle of 0.95 metres and the visitor is never alone; take away the rising heights and there is no sinking. Each is required by the experience the memorial is built to give, entry into an order that isolates. What yields is the count and the extent. The joint entry of Eisenman and Serra had some four thousand stelae, reduced by negotiation to 2,711; nothing in the work fixes that number or the boundary, which is the plot’s. The information centre answers a parliament’s demand, not the field’s, and its stair breaks the grid where it lands. The parts are compelled, the size permitted.
Wang Shu (Amateur Architecture Studio) · Architecture
7.9 · Tier III
Judged on purpose, structure and site, the test bites differently on the two halves of the building. The wall is close to compelled: a museum of the city’s history, built where villages were razed, faced with what the razing left. Remove the wapan and the building loses its reason and becomes a large concrete object on a plaza. The bamboo formwork is required too, as the one way of making the new material speak in the voice of the old. The massing is less compelled. The splitting of the upper block, the tilt of its walls and the placing of the deep openings carry the mountain image, but their number and angle could be otherwise without loss. The cap is met by a tenth.
Jean-Michel Basquiat · Visual art
7.9 · Tier III
The subtractive test falls on the marks inside and around the head. The head itself resists removal entirely: it is the work. The frame of its features, the ringed eyes and the teeth are required, since they are where face and skull meet. Inside, the tangle of lines is required as a field, because the painting’s claim is that the head is open, but not mark by mark: many single strokes could go, or be placed otherwise, and the work would say the same. The ground is needed as pressure, a colour for the head to stand against, and is in places more energy than structure. Speed is part of the meaning, and speed leaves surplus.
Jean Nouvel, with Architecture-Studio · Architecture
7.9 · Tier III
Judged on purpose, structure and site, and the subtractive test bites unevenly. The north block’s river face is compelled by the site: it takes the bend of the quai and the line of the Seine. The cleft is compelled by its aim, the view of Notre-Dame driven through the mass. The south screen is compelled by the brief as the building reads it: an institute of the Arab world shading a south face takes up the screen that filters sun in the courtyard house and the mosque. But much behind the faces is generic, rooms housed rather than shaped, and the mechanism the building is famous for proved removable in practice: when it stopped, the building went on working. A part that can idle for decades without loss of use is not wholly required. It clears the floor of 7.5 by a tenth.
Mike Leigh · Film
7.9 · Tier III
Run the subtractive test on the wandering and it mostly resists. Each night encounter is one more face of the same thing, Johnny meeting a person and taking from them what he can use, and the chain thickens as it goes, from a Scottish pair calling for each other in the dark to a watchman’s empty building to a woman in a window. What fails the test is the landlord’s strand: two assaults made to show a cruelty without Johnny’s intelligence, a rich man’s version for contrast, made at length and made again. The film loses little by losing half of it. Sandra’s return, in farce, is permitted more than compelled, and 131 minutes are long for a picaresque whose law is repetition. Above the gate, not by much.
Rem Koolhaas and Ole Scheeren (OMA) · Architecture
7.9 · Tier III
Judged on purpose, structure and site. The case for necessity is the brief: a broadcaster whose departments stood scattered across Beijing gathered into one building, and the sequence of television making, administration, news, production and broadcasting, with the studios in the base, set out as one continuous circuit, so that the loop is the diagram of the process. The structure is compelled by the form, and the diagrid by the forces. What yields to the subtractive test is the overhang: its floors could sit in either tower, and the cantilever exists to close the figure, at a structural cost no programme required. The lean is chosen, not compelled, and the rooms would serve in two straight towers. Above the cap by a tenth.
Pallava, under Narasimhavarman II · Architecture
7.9 · Tier III
The east shrine is compelled by its rock: a sanctum set so near the water that its door, its lingam and the panel on its back wall all receive the sun out of the sea, and so near that nothing could be built before it. That decision fixes the building. The assembly is looser. The plan is an accretion on one line: a second Shiva shrine turned the other way, a cell of the reclining Vishnu lodged between the two, the entry forced round to the west because the sea took the east. Whatever the order of making, which is disputed, the subtractive test answers the same way: remove the west shrine and its tower, and the work loses a second silhouette and an entrance, not its argument. A clear necessity in the governing gesture, a looser one in the whole.
Charles and Ray Eames · Architecture
7.9 · Tier III
Judged on structure, purpose and site. The frame is reduced to what bears: thin steel columns, open-web joists, a deck, nothing applied and nothing cased. The site compels a good deal. The house is set against a retaining wall cut into the hill so that the meadow stays whole, and the row of eucalyptus is kept as its screen, a placing the land required; the life lived there required both house and studio. What resists the subtractive test is the building’s own premise. It is a kit: its panels are interchangeable by design, the colour of any one could be another, and a first scheme and a second, quite different house were drawn from the same catalogue without the system objecting. A building whose parts are announced as substitutable cannot claim that each is compelled. The proportion of court to pavilions and the pattern of panels are well judged rather than necessary. The axis clears the cap by a tenth.
Bernd and Hilla Becher · Visual art
7.9 · Tier III
The subtractive test bites in two directions. The method resists it absolutely: take away the frontal view and the towers become perspectives, incomparable; take away the overcast and the shadows make each picture an occasion; take away the constant scale and the grid compares sizes, not forms; take away a person and nothing is lost, because the absence is required. Each condition bears load. But the parts of the body are substitutable by design. Any tower in a grid of nine could be removed or replaced by a tenth of its type and the grid would know the same thing, and the body could hold a hundred towers more or fewer. A typology needs many and no particular one: necessary as a procedure, assembled as an inventory.
Jasper Johns · Visual art
7.9 · Tier III
Judged on the parts, as the subtractive test asks, and four of them are required. Without the stencilled names the canvas is a late gestural abstraction of the kind Johns had set himself against. Without the disagreement between name, letter colour and ground there is no argument. Without the all-over spread a centre would rank the names, and without the brushed patches the stencils would have no field to be wrong about. What yields is the unit. In an all-over field the place of a given patch, and of most given words, could change without loss, and the names could be a third thinner or thicker with the work knowing the same thing. It is a method more than a structure in which each part has its station: compelled in its four elements, free in their placing.
Billie Holiday · Music
7.9 · Tier III
Twelve ballads of lost love at one tempo, and the subtractive test bites harder here than on most records of this rank. The frame is compelled at its ends. “I’m a Fool to Want You” must open, because it states the record’s condition as a confession: a self that knows its want is ruinous and wants anyway. “The End of a Love Affair” must close, the only arrival the sequence allows. Between them the necessity is cumulative. “You Don’t Know What Love Is”, “You’ve Changed” and “Glad to Be Unhappy” each say what the others do not, but “For All We Know”, “It’s Easy to Remember” and “I’ll Be Around” could trade places, or one go, with little loss. The cap is cleared by a tenth.
Sedefkâr Mehmed Agha · Architecture
7.9 · Tier III
Run the subtractive test. The four semidomes cannot go: each buttresses the central dome and opens the hall on its axis, so that the congregation stands under one continuous vault from wall to wall. The cascade of domes outside is the structure showing itself, and no step in it could go without the next one down losing its reason. Against that the building carries parts permitted rather than compelled. The four piers are thicker than a hall of this span asks; Sinan at the Selimiye had already carried the dome on eight slender supports. Six minarets claim rank, where two would call to prayer. Tile covers galleries where it is barely seen. The core is necessary; the surplus is real and visible.
Maurice Ravel · Music
7.9 · Tier III
The subtractive test is strange here, and it must be put fairly. Remove any one statement of the melody and the work survives, with a steeper gradient and a slightly earlier summit; no single statement is required as the hinges of a quartet are. The case for necessity is that the work’s argument is the gradient itself, and the gradient needs length to be heard as inexorable: eighteen statements is about the number that makes a listener stop expecting change, so that the one change arrives as rupture. The opening rhythm alone and the E major turn with its collapse are required absolutely. But a middle that could lose a pair of statements with small loss is necessary in its plan, not in each part. The cap is cleared by a tenth.
Ancestral Puebloan builders · Architecture
7.9 · Tier III
The site compels the outline. The overhang sets the height of the tallest towers, the depth of the alcove the reach of the rooms, its back ledges the storerooms, and the sloping floor the terracing, so that the village steps up toward the shelter. Nothing is built that the alcove does not hold, and the kivas sink where there is fill to sink them. That much resists the subtractive test. Below the outline the test bites. The village is additive, a growth of household suites and kivas over decades: a block of rooms could be taken away and the whole would read the same. The necessity is the site’s more than the plan’s.
Erich Mendelsohn · Architecture
7.8 · Tier III
Judged on purpose, structure and site. The parti is compelled: a tower telescope needs a vertical shaft clear of vibration and ground heat, a dome for the coelostat, and a laboratory below ground held at an even temperature, and the building is exactly that, a vertical over a horizontal, the light’s path made into the plan. Nothing is applied: sills, hoods and swelling window reveals are the mass itself. What fails the subtractive test is the modelling of that mass. The instrument would work as well in a plain masonry tower or a steel lattice, as other solar towers of the period did; the curves are compelled by an idea of force, not by the optics, the site or the structure, which they disguise. The rear wing is ordinary rooms given the same skin. It clears the cap of 7.5 narrowly, because the figure is one and nothing is added to it.
Nicholas Ray · Film
7.8 · Tier III
Judged on structure, and the spine is required. The compression into thirty hours lets three children meet at the police station before they know each other, so that the family of three made in an empty house at the end is prepared in the first scene. The planetarium is needed twice: its lecture on the end of the earth sets the scale for the chickie run, and the building is where Plato dies. Buzz’s death must fall at the midpoint, so that the second half can be about a guilt no adult will take. What gives: the juvenile officer exists to receive exposition, the three family scenes at the station each state their diagnosis aloud, and the Stark quarrel repeats what the opening has already made plain.
U2 · Music
7.8 · Tier III
Ten tracks, five to a side, and the first side survives the subtractive test almost whole. Sunday Bloody Sunday must open, since it sets the war the title names and the refusal the record makes; Seconds makes that war instant; New Year’s Day carries it into a love song; Drowning Man is the one plea answered by grace, without which the close has nothing to stand on. Like a Song... is required in argument, but its music restates the opener’s attack at greater noise. On the second side cuts come easily: The Refugee is a thin chant, Red Light adds colour and little argument, and Two Hearts Beat as One is permitted, not compelled. Three songs could go and a fourth repeats; the cap is met by a tenth.
Gerhard Richter · Visual art
7.8 · Tier III
The subtractive test bites hard here, and the work invites it. Any one square could take another of the 72 colours and nothing would be lost: by design no part is singly required, because chance placed it. What is required is the rule. The square module, small enough that the window reads from the transept floor as glass and not as a picture of glass; the limited palette; the refusal of any figure. Each is compelled by what the work does, which is to give the opening back its light without giving it an image, and nothing could be added, a figure least of all. Against it, the scale is set by the tracery rather than argued by the work, and the edited chance admits that the procedure was not left wholly to itself. Necessity of the system, contingency of every part.
Joan Miró · Visual art
7.8 · Tier III
The subtractive test is hard on a carnival, and the picture invites it. Some parts are required. The Harlequin is the host, and the hole in his body is the hunger the feast surrounds; take it away and the carnival loses its centre and its cause. The ladder is the one vertical that climbs out of the room, the escape the picture is about. The window holds the outside world at a distance, and the cats with their yarn give the lower right its one sustained action. The wall and floor make a room, without which the swarm would float in nothing. What yields is the swarm: a given insect, fish or note could change or go without loss, for profusion is permitted rather than compelled at the scale of the single sign.
Helen Frankenthaler · Visual art
7.8 · Tier III
The subtractive test, put to a painting made in one session by pouring and soaking. Much of its particular arrangement is the record of a process that could have fallen otherwise: the edge of a pink pool, the run of a blue into the weave, a charcoal contour here or there could differ and the picture would know the same thing. What resists removal is the principle and its few carriers: the bare canvas, which is the light of the picture and not its background; the thinness of the colour, without which nothing is soaked; and the gathering of colour off centre, which leaves the field open. The charcoal is the most removable element. The cap clears; the work is necessary as a decision more than in its parts.
César Pelli · Architecture
7.8 · Tier III
Judged on purpose, structure and site. The purpose is a headquarters for a national oil company and a sign for a nation, and the sign is not assembled: plan, setbacks, crown and pinnacle are one figure, and the figure is the brief. Several parts pass the subtractive test because purpose and structure meet in them: the ring of concrete columns makes the round lobes, the setbacks follow the narrowing core and the load of the columns, and the skybridge is both the gate of the composition and an escape route between the towers. What resists: the second tower is compelled by the image of the gate more than by any programme; the star’s points make awkward corners for offices; and the pinnacles exist chiefly for the record.
Wong Kar-wai · Film
7.8 · Tier III
Judged on structure. The second story resists the subtractive test: the key in the envelope, the goldfish, the tins with their labels swapped, the soap and the towel 663 talks to, the boarding pass drawn on a napkin are each planted and returned, and the story is built of objects carrying feeling between two people who never speak at the right time. The first story gives far more. Its heroin run, its couriers and its blonde wig are a noir sketch whose plot exists to bring two strangers to one night in a hotel room, and much of it could be shortened without loss. The join is necessary in idea and slight in fact: the second story would stand alone, and the first would not. The rhymes are real; the diptych is permitted by the method rather than compelled by it.
Daft Punk · Music
7.8 · Tier III
Fourteen tracks, and the frame is compelled. One More Time must open: it states the record’s subject, a party heard through a machine, and its long beatless middle prepares everything after it. Too Long must close, ten minutes of one loop, the party that will not stop. Between them the core is required: Digital Love, Harder, Better, Faster, Stronger, Something About Us, Veridis Quo and Face to Face each say what the others do not. The test bites in the second half. High Life and Short Circuit are loops with little development, Crescendolls restates the opening at lower power, and Too Long is compelled as an ending but not at its length. About a sixth of the record is permitted rather than required.
Fariborz Sahba · Architecture
7.8 · Tier III
Judged on structure, purpose and site. Much survives the subtractive test. The nine-fold plan is required by the Faith’s own law for its houses of worship, and the three rings of nine carry that arithmetic into the third dimension. The petals are not ornament on a frame: each is a shell, at once structure, roof and enclosure, so that in the inner ring the figure and the building are one fact. The pools are required twice, as the water the flower stands on and, by the architect’s account, as the cooling of a hall without machinery. What yields is the outer two rings. Canopies over doors and roofs over secondary halls, they are compelled by the figure, the bud seen from outside, more than by the hall the building exists for.
Adrian Smith (Skidmore, Owings and Merrill) · Architecture
7.8 · Tier III
Judged on purpose, structure and site, and the purpose was to be the tallest by a wide margin. At the core of the building that purpose compels almost everything. The Y plan is required: three wings stiffen the core and each other, and give every room a short span to the glass. The setbacks are required: each changes the section, so that the wind cannot organise its vortices at one frequency up the whole height, and the spiral is the order in which the wings can give up floors without losing the buttress. Take away a setback and the tower sways; take away a wing and it falls. What fails the test is the top: the spire, much of it above any usable floor, is there for the record and the image. The hotel and the residences are fittings to a height, not required by it.
Frank Gehry · Architecture
7.8 · Tier III
Judged on purpose, structure and site. The auditorium passes the subtractive test: the vineyard terraces, the platform at the centre, the fir ceiling shaped as reflectors, the volume of the room and the organ facing it are each required by the purpose of hearing an orchestra from every side, and the foyers, garden, chorus and rehearsal spaces lie where the section asks. The exterior yields. The steel is a skin on its own armature, standing off the room across a wide residual zone; replace the sails with walls and the orchestra keeps its room, and only the city loses its image. The garage, more than any purpose, set the hall’s height above the street.
George Saunders · Literature
7.8 · Tier III
Two tests, and they part. Within the stories the subtractive test mostly fails to find a cut. The title story moves from the park’s decline to the hiring of a killer, the killings, the haunting and the narrator’s death without a scene to spare, and in “The 400-Pound CEO” each humiliation readies the blow that kills the boss. Across the book the test bites. The stories share a template, a degraded workplace, an abject narrator, a death he causes or suffers, a ghost or an afterlife, and “The Wavemaker Falters” restates the title story’s guilt and haunting in a smaller key, so that one of the two could go with little lost. “Bounty” carries its journey through a run of encounters, several of which could go without the argument changing. Tight in the parts, porous in the whole.
Duke Ellington · Music
7.8 · Tier III
The subtractive test bites on side one. The Newport Jazz Festival Suite was written for the occasion and plays as three blues-based swing pieces that pass soloists in turn: any one of its parts could go and the record would know what it knew, and the suite as a whole could go at the cost only of the band warming. “Jeep’s Blues” is a feature of the kind a set carries by habit, though here it does a job, setting a calm the last track breaks. The last track resists. Its written halves need each other, and the interval is long because the length is the argument. Half the record compelled, half permitted: just above the cap.
Herzog and de Meuron · Architecture
7.8 · Tier III
Judged on purpose, structure and site. The Grand Hall passes the subtractive test: the stage at the centre, the steep terraces close to it, the milled cells of its lining, the reflector, the volume of the room and its separation from the noise of the port are each required by hearing an orchestra in a harbour. The section compels much of the rest. A hall set over a full warehouse block must be reached by a long rise, so the escalator is required; the seam between brick and glass is where the public terrace must fall; the glass body takes its height from the hall inside it. What yields is the programme around the core: the hotel, the apartments and the parking are financing permitted by the section, not compelled by it. Remove the apartments and the work loses rent, not meaning. The roof’s wave follows the volumes beneath only loosely, and the glass is in places an image laid round rooms. The cap is cleared by a tenth.
Arcade Fire · Music
7.8 · Tier III
Eleven tracks, and the frame is compelled. Black Mirror must open, a dread overture in which the band’s sound arrives as a storm before it arrives as song; My Body Is a Cage must close, the one place the record’s fear turns inward into the body and is answered by the organ. Intervention, (Antichrist Television Blues) and No Cars Go are load-bearing, each saying what nothing else on the record says. The subtractive test bites in the middle. The Well and the Lighthouse restates the sea of Ocean of Noise in a busier tune and could go with little loss; the title track is a sketch that names the record rather than advancing it; Black Wave/Bad Vibrations joins two halves that answer each other only loosely. About a quarter of the record is permitted rather than compelled.
Alejandro González Iñárritu · Film
7.8 · Tier III
Run the subtractive test on the first hour and it finds nothing to cut. The attack in the shallows sets the expedition’s flight; the flight puts Glass alone in the brush with the bear; the wound makes him a burden, the burden makes Fitzgerald’s arithmetic, and the killing of Hawk gives the crawl its law. The journey that follows is an ordeal in stages, and each stage changes the body that carries it. Elk Dog’s search for his daughter is required, since it closes the ending. What gives lies in the middle: several episodes could go with a loss of intensity rather than of fact, and the visions of the wife and of the ruined church say one thing more than once.
The National · Music
7.8 · Tier III
Eleven tracks, and the frame is compelled. Terrible Love must open, stating the condition in sound before any song names it, and Vanderlyle Crybaby Geeks must close, a hymn the record reaches only by passing through the rest. Bloodbuzz Ohio, Afraid of Everyone, Conversation 16 and England are each required by what the record says about home, fear, guilt and absence. Lemonworld’s drowsy idleness earns its place as the one glimpse of the ease the dread is set against. The test bites elsewhere in the middle: Anyone’s Ghost restates the opener’s dependency without adding a term, and Little Faith and Runaway share a tempo and a hush, so either could carry that stretch alone.
Bonanno Pisano (attributed) and Giovanni di Simone; Tommaso Pisano · Architecture
7.7 · Tier III
Run the subtractive test. A campanile’s height is compelled by its bells and by the city’s claim on the sky, and the cylinder is a sound answer to a tower seen from every side of an open meadow. The drum, the stair in the wall and the well at the centre are one structure, and nothing is ornament applied to an indifferent shaft. But six gallery storeys repeat one module: one fewer or one more would change the proportion, not the sense. The galleries are the cathedral’s dress carried round a drum, walkways the use does not require, and the bell chamber, which is the use, is the smallest part. The correction alone was compelled by something other than display, and by failure.
Tang, under Emperor Gaozong · Architecture
7.7 · Tier III
Run the subtractive test and little can go: a square tower of diminishing storeys, an opening on each face, a stair within. Every part answers one of two purposes, to keep sacred things high and dry and to raise a person above the city. The taper is compelled in brick, and the stepped eaves shed rain. Two things weigh against it. The tower has been taller than it is and still reads as itself, so its scale is permitted rather than compelled. And the pilasters and corbelled bands are the sign of timber construction carried into a material that does not need them, required by the convention, not by the building. Necessary in mass, assembled in surface; above the cap.
The Beatles · Music
7.7 · Tier III
Thirteen songs in about thirty minutes, and the subtractive test gives two answers. Inside each song almost nothing is idle: two minutes and a few seconds, no solo longer than it needs, a bridge where the song must turn, an end as soon as it has said its piece. If I Fell spends no bar it does not use. But the album is assembled: the first side holds the film’s songs because they were the film’s, the second what else was ready. Any Time at All restates the shape of the title song, When I Get Home and I’ll Cry Instead are workmanlike, and I’m Happy Just to Dance with You, written to give George Harrison a vocal, could go with no loss of meaning. Required songs, in an arrangement that could be otherwise.
Federico Fellini · Film
7.7 · Tier III
Judged on structure. The design is a sequence of hopes, each raised and each taken, and the spine resists subtraction. The Tiber at the opening states the pattern at its crudest and the cliff above the lake repeats it with everything at stake; the pilgrimage is where she asks aloud to be changed and nothing happens, which makes the hypnotist’s stage the place her inner life is first seen, and Oscar the man who has seen it. What gives is a real share of the running time. Lazzari’s night is a self-contained excursion, long, its nightclub and villa making one point twice, and the friends’ quarrels on the Passeggiata repeat themselves. The parts are required in kind more than in length.
Mike Leigh · Film
7.7 · Tier III
Judged on the film as released, and its main line resists the subtractive test. The funeral frees Hortense to search and sets her grief beside Cynthia’s later one; the records office gives the search its cost before it begins; the café take cannot be cut, nor the barbecue, where every earlier strand is paid. What gives is in the middle hour. The sittings run longer than their point needs and repeat their pattern once it is set; Stuart’s drunken visit to the studio opens a strand of Maurice’s past that is only half used; Roxanne’s quarrels with Paul restate her anger more than they advance it. The film is long for what it must carry.
Robert Altman · Film
7.7 · Tier III
Judged on structure and on Michael Tolkin’s script, and the spine resists subtraction. The postcards are required to send Griffin Mill to David Kahane, and their continuing after the killing is the hinge that makes the murder pointless and the guilt unarguable. Habeas Corpus is required twice, as Mill’s weapon against Larry Levy and as the coda’s proof that the industry reverses any ending. Bonnie Sherow is required as the one person who says what the film knows, and is fired for it; the last pitch closes the loop. What gives is texture: many cameos at lunch and at the benefit are interchangeable, the detectives’ scenes run past their point, and the desert resort is extended for atmosphere. The accretion is permitted more often than compelled.
Bong Joon-ho · Film
7.7 · Tier III
Judged on structure. The advance car by car is the plot’s spine, and much of what the tail plants is paid at the front. The red capsules hidden in the protein blocks lead to Namgoong, and his Kronole, an industrial drug the tail takes for a narcotic, is the explosive that ends the train. The children measured in the tail are the parts of the engine. Gilliam’s lost limbs and Curtis’s two arms are repaid in the last scene, when Curtis gives an arm to pull a boy out of the machine. What gives: the front cars are a revue the advance passes through rather than a necessity of it, Franco the Elder returns from death more often than the design needs, and the last truths are spoken rather than found.
Jasper Johns · Visual art
7.7 · Tier III
Judged on the parts, which are many by design. The method of the period, take an object, do something to it, then something else, is additive, and the painting shows it: in places it reads as an inventory of the painter’s devices to 1964, the colour words, the object fixed to the canvas, the cast, the grey ground, the printed page. The subtractive test bites. Take away the newspaper or one band of graded colour and the argument stands with less evidence rather than broken. What resists removal is the core: the painted words against the same words standing out and casting shadows; the chair and cast, where the body enters; the canvas turned to the wall, the one thing withheld. The cap clears, narrowly.
Yorgos Lanthimos · Film
7.7 · Tier III
The spine is strict. A debt, a man dead on Steven’s table after the surgeon had drunk, is called in, and the terms, once stated in the hospital cafeteria, run their four stages in the order given: every symptom announced arrives. The opening heart, Bob’s hair, Kim’s essay, the ranking of the children and the rifle all return as necessities. The subtractive test still finds give. Martin’s mother’s seduction restates what the cafeteria has established; Anna’s bargain with the anaesthetist does work but is staged at length; the headmaster’s ranking could be half as long; and the first movement spends minutes on a flatness of speech grasped by the second exchange. Required in its frame, loose at several joints.
Tame Impala · Music
7.7 · Tier III
Twelve tracks in about fifty-two minutes, and the subtractive test bites more than once. Be Above It is required: its whispered loop and pounding drum set the self-exhortation the record then fails to live by. Apocalypse Dreams is the first summit and cannot go; Feels Like We Only Go Backwards is the hinge; Sun’s Coming Up is a compelled close. But Endors Toi restates the opener’s manner in a busier key, Music to Walk Home By drifts in its middle stretch, and She Just Won’t Believe Me, under a minute, is a fragment the sequence could lose. Elephant is necessary as a jolt and odd as a part. A strong core with soft joins: the figure clears the cap by a tenth.
Michael Mann · Film
7.7 · Tier III
Cooper’s long, digressive novel is stripped to a pursuit, and most of what remains is required. The Cameron cabin is needed twice: first as the frontier household at peace, then burned, so that the militia’s demand to go home has a body under it. The fort’s politics, Webb’s promise and Munro’s refusal to release the colonials, are required, since they make Hawkeye’s arrest and put him inside the fort when it falls. Magua’s grievance, told before Montcalm and again in the village, keeps the last act from being revenge alone. What gives is the exposition the fort carries in speeches, which state what the cabin has shown, and Heyward’s turn from rival to sacrifice, hurried, its middle missing.
Lal Chand Ustad · Architecture
7.6 · Tier III
Judged on purpose, structure and site. The purpose compels the screen: women of a court kept in purdah had to see a street without being seen from it, and the jharokha veiled in jali is exactly that instrument, a seat projected over the street with a stone veil before the face. Each window answers to a seat and a gaze, so the repetition is not ornament counted out; it is the number of places from which to watch. The site compels the thinness: quarters that lay back from the bazaar reached the street with a wall that could be looked through. What resists the subtractive test is the height and the outline. The upper tiers add watchers, but chiefly they add figure, a crest for the street to see, display laid over concealment; the curved roofs and much of the painted detail could go without loss to the use. The cap is cleared, by a tenth.
Norse · Visual art
7.6 · Tier III
Judged on the set, the subtractive test fails as it must for a set: the game requires every rank, and without the bishops the board has no diagonal, without the pawns no front. The stronger question is whether the figuration within each piece is required, and here the carving is economical. The king’s sword across the knees, the queen’s hand at the cheek, the bishop’s crozier and mitre, the warder’s shield: each is a single attribute that names the rank in the hand. What ornament there is sits on the throne-backs. What is permitted rather than compelled is the multiplication of near-identical figures across several sets, and the necessity is the game’s, borrowed, as much as the carver’s.
Dolly Parton · Music
7.6 · Tier III
Ten songs, and nothing within any of them is padded; no song outstays itself, so the subtractive test bites across the sequence instead. The title song is the reason the record exists and could not go. “Traveling Man” is required in a lesser way: its comic turn, a lover lost to the singer’s own mother, gives the record a second register after the opening’s tenderness. “My Blue Tears” and “Here I Am” each carry a part of the voice the record is built on, solitude and the offered self. The two Wagoner songs and one or two of the thinner songs on side two are permitted rather than compelled: the customary complement of the Nashville LP. The cap is cleared by a tenth.
Robert Eggers · Film
7.6 · Tier III
The revenge plot is narrow and drawn tight, and the prologue plants what the film pays: the oath, the Fool and the tree of kings, the berserker’s wolf rite that makes Amleth what he becomes. The Seeress’s prophecy, the maiden-king and the sword drawn only at night or at the Gates of Hel, is fulfilled point by point, and the sword from the barrow is the instrument of the last scene. What gives under the subtractive test is the middle third on Fjölnir’s farm: the knattleikr game, the nightly killings and Olga’s herbal trickery extend a stretch whose turns are known before they come. The axis sits at its cap and not above it.
Damien Hirst · Visual art
7.5 · Tier III
The test is subtractive, part by part. The cabinets are required: without walls of packaging there is no pharmacy, and the room depends on their number, since one cabinet is a sculpture on a wall and four walls are a shop you stand in. The insect-killer and the honey are required: they are the only living process in the room, and without them the work is a display of order with nothing to answer it. The coloured bottles are required as the shop’s old sign and the room’s link to the alchemical past of its trade. Less compelled are the furniture, the counter’s fittings and the footstools as such, and the sheer number of packages: the room is filled to the size of a room, a scale the format permits rather than the idea compels. Much of the work is set-dressing true to a type. Necessity holds, by a little.
Arctic Monkeys · Music
7.5 · Tier III
Thirteen songs, and the songs are lean: almost none has an idle bar, a chorus repeated beyond its need or a solo for display. The frame is compelled at both ends. The View from the Afternoon has to open, the night anticipated with the drums already running, and A Certain Romance has to close, the one song that steps back from the night and judges it. When the Sun Goes Down and Fake Tales of San Francisco say what nothing else says. The test bites in the middle: three songs work the same ground as Dancefloor, and one could go with little loss, and Perhaps Vampires steps out of the night altogether.
Jeff Koons · Visual art
7.5 · Tier III
The test is subtractive, and the form resists it almost entirely. The balloon animal is a closed grammar: one tube, twisted at fixed points into snout, ears, neck, legs, body and tail. Take out a segment and it is not a dog. Take out the knotted nozzle at the snout and the object loses the one sign that it was inflated by a breath and tied off, the hinge of the conceit. Without the mirror finish the steel reads as steel and the membrane fails; at hand size it is a toy. What yields is the plurality: one colour would carry the argument entire, and the five answer the series and the market more than the form.
Alfred Eisenstaedt · Visual art
7.5 · Tier III
The subtractive test, run on a frame its maker did not compose at leisure. The embrace is the work and cannot go, and its halves require each other: the dark uniform and the white, which make the figures read as one shape at any size; the arm locked round her waist and her body bent in a near arc, which give the frame its one strong diagonal; the two faces hidden in the kiss, which make the pair anonymous and so able to stand for everyone. The witnesses behind are required too: they make the act public, a celebration and not a private scene. What yields is the margin: the clutter of the crowd, the shop fronts, the figures cut by the frame’s sides. The centre is necessary; the frame around it is found.
R.E.M. · Music
7.5 · Tier III
Ten tracks in thirty-eight minutes, and most of them are required. Harborcoat has to open: its two voices crossing in different words state the record’s method before any song can be understood. So. Central Rain (I’m Sorry) is the hinge of the first side, the one song where the voice stops evading and repeats an apology. Camera is the needed weight of the second, the only slow piece and the only grief, and Little America has to close, a band on the road naming its own lostness. The test bites in the middle of the second side: Second Guessing and Letter Never Sent say little the others have not said, and Pretty Persuasion could change places with either. About a fifth of the record is permitted rather than compelled, and the cap is cleared narrowly.
Alex Garland · Film
7.5 · Tier III
The spine is tight: a journey to the capital that must end at the President, and an apprenticeship that must end with the apprentice taking the master’s place. The subtractive test holds for the frame. The Brooklyn bombing, where Lee shields Jessie, is answered at the end, where Lee steps into fire for her and Jessie photographs her falling; the petrol station, where Jessie freezes, is answered at the White House, where she does not. Sammy must die so that the cost of the trip is paid before its prize. What gives is the middle of the road: the sniper in the field and the town that keeps out of the war each make a point a single scene states and the next does not deepen, and Joel’s appetite for the scoop is told more than built.
Arcade Fire · Music
7.5 · Tier III
Forty minutes, the band’s tightest record, and most of it resists the subtractive test. Age of Anxiety I must open: a nervous synthesiser pulse and a voice caught in its own head set the condition before any argument is made. Its second part is the escalation into the screen; End of the Empire I-III turns the private toward the civil, a slow piano ballad widening into a lament for a culture; its fourth part is the first half’s exit. The Lightning I, II is the hinge the halves need. The test bites in the second half: Unconditional II (Race and Religion) is slight, its idea spent early, and Unconditional I restates what The Lightning has just said.
The Cure · Music
7.4 · Tier III
Ten songs in under forty minutes, and the record is lean: nothing is padded, and the longest piece is the closer, whose length is its point. In Between Days must open; it states the record’s pace and its subject, love outlived and the self suddenly older. Push needs its long instrumental opening, which is the song’s argument, a surge withheld and then released. Close to Me must sit at the centre of side two, and Sinking must end. The subtractive test bites twice. Screw is a sketch, an abrasive bass figure with little song on it, and could go with small loss; The Baby Screams restates side two’s anxious mode without turning it. Two of ten are permitted rather than compelled.
Steve McCurry · Visual art
7.4 · Tier III
The subtractive test on a close portrait is short, because almost nothing is in it. Take away the shawl and its holes and the image loses its one mark of poverty and its one warm colour, and with them the complementary charge that sets the eyes alight. Take away the green ground and the eyes stop echoing their surroundings; on a grey wall it would be a colder face. Take away the slight forward tilt and the gaze and it becomes an identity photograph. Everything present bears load, and the frame leaves no idle margin. What holds the axis is that the necessity is that of a found moment, not a construction: a frame a fraction wider, or a second later, is easily imagined without loss.
Thomas Gainsborough · Visual art
7.4 · Tier III
Judged on figure and field. What cannot go: the face, pale, steady and young, the one passage of finish; the blue satin, which is the picture’s argument in paint; the hat held low in the right hand, which gives the figure its ease and its one diagonal; the left hand on the hip, which gives it the stance it borrows from Van Dyck. The low horizon is required, because it sets a boy against sky as a cavalier was set. What yields is most of the ground: a serviceable setting of bank, tree and cloud, scumbled in, that could be another landscape without loss. Necessity is high at the centre and thin at the edges, and the cap is cleared by a tenth.
Shepard Fairey · Visual art
7.3 · Tier III
Run the subtractive test on a very small set. Take away the upward gaze and the image is a portrait; with it, the man looks past the viewer toward something not yet in the frame, and that look is what the word names. Take away the word and it is a stylised head, legible as Fairey’s but not as an argument. Take away the red and blue and it loses its claim on the national colours; take away the flatness and it is a photograph again, a candidate rather than an emblem. Each part bears load. What yields is the word itself, carried as PROGRESS and as HOPE without the picture changing, and the detail of the tone boundaries. The necessity is real and shallow: the argument it serves is a slogan.
Paul Thomas Anderson · Film
7.3 · Tier III
Judged on the theatrical cut, about 95 minutes, and the cut is lean. The major elements resist the subtractive test. The harmonium left at the curb in the first minutes becomes Barry’s instrument and the last image. The pudding promotion, which looks like a quirk, is how a man who cannot act on the world finds a loophole in it, and its miles are what he offers Lena at the end. The phone-sex call becomes the extortion, and the extortion turns rage into courage at Provo. What holds the axis near its cap is what gives between them: the four brothers from Utah are a genre engine, run twice to similar effect, and the scene with the dentist brother-in-law restates the party.
Kehinde Wiley · Visual art
7.3 · Tier III
Judged element by element. The figure cannot go, nor the chair: a plain armchair where the state chair or the Oval Office desk would stand is the picture’s one argument about office, a president seated as a citizen. The forward lean and the crossed forearms cannot go, since they turn the official portrait from display to address. The ground cannot go: without it the picture is a competent likeness. The three flowers bear load, making the ground a biography rather than a pattern, and the tendrils crossing in front of the chair and the feet are the one sign that the garden is not a backdrop. What yields is the extent and density of the foliage, permitted rather than compelled, much of it repetition of one decorative unit.
William Blake · Literature
8.7 · Tier IV
The spine is required. The Bard’s Song is the cause of everything after: Milton hears in it the quarrel of Satan and Palamabron over the harrow, sees that his own selfhood is that Satan, and rises, “I go to Eternal Death!” Without the song the descent has no motive. Ololon’s descent answers Milton’s, and the two meet in Blake’s garden; neither half can go. What holds the axis lowest of the twelve is what the subtractive test removes. The catalogues of Los’s sons and daughters, of counties and churches, and the long exposition of the Mundane Shell and the Polypus in Book the First, about a fifth of the poem, could go without loss to its argument. And Blake reordered and added plates between copies: the order was not compelled.
Hart Crane · Literature
8.5 · Tier IV
The test is subtractive, and the book answers it unevenly. The frame is required: the Proem, “How many dawns, chill from his rippling rest”, and Atlantis close one span, and the day from The Harbor Dawn to the midnight of The Tunnel is the road between. Within Powhatan’s Daughter the descent is compelled, each poem one stage further back into the land, from a Manhattan bedroom through childhood to the hoboes’ railroad, the Mississippi and the burning of Maquokeeta. What holds the axis at 7.5, the lowest of the twelve, is the rest: Indiana is sentimental and adds nothing The Dance has not paid for, Virginia and Southern Cross are slight, Quaker Hill states the decline the book elsewhere enacts, and Cape Hatteras is a third longer than its argument. The spine is necessary; a third of the book is assembled.
Ovid · Literature
8.3 · Tier IV
The subtractive test is the book’s oldest charge, and it holds in part. Fifteen women in one situation use a shared repertory: the reproach, the recital of past favours, the catalogue of the man’s ingratitude, the prospect of death, the request that he return. Hermione, Laodamia and Hypermestra could go with little lost to what the book knows, and Phyllis and Oenone repeat Ariadne and Dido move for move. Against this, the strongest letters are each required: Penelope’s opening sets the book’s terms, a letter that asks not to be answered; Medea alone already holds the catastrophe in her hand; Canace writes with a pen in one hand and a sword in the other. Each of the double letters needs its answer. Variation on one situation is the design, and the design is partly what the charge describes. The cap is met, and only just.
Haruki Murakami · Literature
8.3 · Tier IV
The subtractive test finds much that could go, and the axis is the lowest of the twelve. The spine is required: the cat’s disappearance and then Kumiko’s, the well, Mamiya’s testimony, the bat, Room 208. Around it stand figures whose threads are opened and left. Malta Kano drops away; Creta Kano’s story ends with an invitation to Crete, declined and forgotten; and Book Three adds a new apparatus, Nutmeg and Cinnamon’s business of healing, the exchange by computer terminal, Ushikawa, to reach an ending the first two books had nearly reached. Some of this is the book’s dream logic, in which a figure arrives, delivers a story and departs. What holds the axis at 7.5, the threshold the summit asks, is that the close of Book Two showed the work could stand without Book Three’s machinery.
Mughal court painters · Visual art
8.2 · Tier IV
The subtractive test has to be put twice, to the folio and to the cycle, and the answers differ. Within the strongest folios much resists removal: in a siege the wall, the attackers and the defenders are one diagonal of force, and the giant who fills a quarter of the sheet is the episode. But the folios are crowded by principle, and secondary figures, tiles, trees and onlookers are often fill. At the level of the cycle the case is weaker. The romance is episodic, one adventure after another, and its scale was permitted by an emperor’s appetite rather than compelled by an argument. That the surviving cycle still reads as itself after losing most of its parts shows the parts were not required by one another.
John Barth · Literature
8.2 · Tier IV
The test is subtractive, and the book is built to strain it: a picaresque in which abundance is part of the joke. The spine is required: the laureateship granted, the estate of Malden lost by the hero’s innocence, the poem of praise turned into a satire, the marriage that earns the estate back. Burlingame’s search for his parentage, carried by the installments of the Smith and Burlingame journals, is required too, since it is the book’s other half and its argument about history. Between those fixed points the long middle part multiplies captures, escapes, exchanged identities and tales told by strangers, and much of that multiplication is the argument itself: the law that every person is a role, restated until it is believed. What holds the axis is the remainder, episodes that could change places, or go, without the knowledge changing. The design licenses them; it does not compel them.
Wilkie Collins · Literature
8.1 · Tier IV
The plot is a machine of rare closeness, and the machine passes the subtractive test: Sir Percival’s need of his wife’s money, Anne Catherick’s likeness to Laura, Anne’s heart disease, a date of travel and a date of death, the forged entry in the Old Welmingham register. Each is required, and the substitution at the centre stands on all of them. The book is less necessary than its machine, and that holds the axis lowest of the twelve, at the line and not above it. Hartright’s First Epoch lingers; his removal to Central America is an absence engineered rather than lived; Gilmore tells what the reader foresees; the Third Epoch nears Percival’s secret and then Fosco’s slowly. A third of Hartright could go and little be lost. What cannot go is the best of the book.
Alexandre Dumas · Literature
8.1 · Tier IV
The spine is a machine of necessity. One denunciation, written by Danglars with his left hand and posted by Fernand while Caderousse lets it pass, and Villefort’s burning of the letter to Noirtier, generate every later act. Each of the four betrayers is given his own fall in his own currency: Fernand by his past in Janina, Danglars by money, Villefort by the law and his buried child, Caderousse by greed. Little of the frame could be cut. What holds the axis lowest of the twelve is length inside the frame: the serial was paid by the line, and the Roman block, Bertuccio’s vendetta told at Corsican length, the repeated calls of the Paris salons and the Cavalcanti comedy say at length what could be said briefly. Perhaps a fifth of the book.
Leon Battista Alberti · Architecture
8.1 · Tier IV
Judged on what stands. Within the shell the parts are compelled: the three arches of the front answer the Roman arch of the same town and the triple division of a nave; the flank arches are tomb niches, their depth set by the dead they shelter; the high base lifts the order above the street. Take away the flank arcade and the building loses its claim to be a mausoleum of a court. What resists is large. The front is a stump above the cornice, its crowning missing; the shell ignores the Gothic windows behind it, so inside and out are joined by the site, not by the design; and the east end the whole was to lead to was never built. The cap is met, barely.
Ray Charles · Music
8.0 · Tier IV
Twelve songs, six to a side, and the subtractive test bites harder here than on most albums of its standing. The frame is compelled. Bye Bye Love must open: a brisk song of being left, set to big-band swing, states the method in two minutes. Born to Lose must close side one, and I Can’t Stop Loving You must stand near the end of side two, where the record’s ache is gathered. Careless Love is required as the one song that is already blues, the hinge where the two repertories touch. Elsewhere the songs are interchangeable: Half as Much, Just a Little Lovin’ and It Makes No Difference Now could change places with songs on Volume Two, made the same year to the same plan. A collection compelled in its idea, permitted in most of its parts.
Abbasid builders, under al-Mutawakkil · Architecture
8.0 · Tier IV
Judged on structure, purpose and site, and the subtractive test bites. The hypostyle was additive by nature: bays of piers repeated under a flat roof, any row removable without loss of the type, its extent set by the wish for the largest mosque rather than by a congregation’s need that can be shown. The enclosure towers are partly required, buttressing a long thin wall of brick, but their regular march is display as much as support. The Malwiya is the strongest case: its ramp is stair, structure and figure at once, and nothing on it is idle. But a tower of over fifty metres on a flat plain is permitted by power, not compelled by the call to prayer.
Judy Chicago · Visual art
8.0 · Tier IV
The frame is necessary. Three equal sides with thirteen places to a side, the number at the Last Supper and the number of a coven, compel the thirty-nine: they are not a list cut to length. Take away the floor and the guests lose the ground they stand on, which is the argument, that no woman at the table arrived alone. Close the centre and the table gains a head. But the subtractive test bites inside the frame. Which woman sits at a place is an editorial choice, and several places in the second and third wings could be exchanged for names on the floor without loss. The floor is a roll, and a roll of 900 or 1,200 would serve. With The Sublime, the lowest axis: necessary in the figure, assembled in the filling.
Thomas Bohier and Catherine Briçonnet; gallery by Philibert de l'Orme and Jean Bullant · Architecture
8.0 · Tier IV
The river compels a great deal. Bohier’s block stands where it does because the mill piers were there: the foundations are inherited, and the kitchens at water level are the piers put to use. The bridge is compelled as a crossing, and the gallery as a room that is also the crossing; so far the subtractive test removes nothing. What yields is the block’s own fabric and the joints between campaigns. The corner turrets, the dormers and the projecting rooms are ordered by custom and display, and the block could lose a turret without losing what it is. The junction of block and gallery is a seam, not a necessity, and the gallery’s regular bays are repetition, not argument. Required in its essentials, assembled in its parts.
Louise Nevelson · Visual art
8.0 · Tier IV
Judged as the method invites, box by box, and the subtractive test bites hard. The wall is additive by construction, boxes stacked in a frame, each a small composition, and the maker is known to have recombined boxes between walls and between shows. Remove one box near the edge and the wall is a little shorter and no less itself; swap two inside it and the order adjusts. What resists removal is the governing decisions: the one black that makes the fragments one substance, the frontal shallow wall that makes them a facade, the stacking past the viewer’s height that makes a cathedral of a cabinet. Its necessity is a system’s, not each part’s. It stands exactly at the cap.
Denis Johnson · Literature
8.0 · Tier IV
The test is subtractive, and it finds much that could go; the axis is the lowest of the twelve. The spine is required: the Colonel’s operation and his legend, Skip’s apprenticeship to it and his loss of faith in it, the double agent through whom the fiction is to be fed, and the war’s slow corruption of every man who serves it. The Houston brothers, the war from below, are a needed counterweight. What holds the axis at the threshold is a looseness beyond design: the brothers barely touch the main action, Skip’s years over the card files run long, episodes open and do not close, and the coda of 1983 gathers survivors rather than consequences. That a war of fog should be told in fog carries part of the length, not all of it.
Thomas Jefferson · Architecture
8.0 · Tier IV
Judged on plan, section and structure, under purpose and site. Much is compelled. Put the service rooms anywhere but under the terraces and the summit is cluttered and the pastoral front lost: the terraces are required by the idea of a house that stands free of its work. Take away the west portico and the parlor loses its opening to the lawn and the view. But the subtractive test finds a good deal that could go. The dome room, the crown of the house, had no settled purpose and was hard to reach; the mezzanine and third floor exist because a three-storey house was made to look like one; the stairs were squeezed into slots to keep the effect. Forty years of building and taking down leave odd junctions. It clears the cap at the threshold.
Sex Pistols · Music
7.9 · Tier III
Twelve tracks on two sides, and the subtractive test splits the record in two. Holidays in the Sun must open: its refusal of escape sets the frame. God Save the Queen is the centre and could not go. Anarchy in the U.K. and Pretty Vacant state the self and the generation the rest abuses; Bodies is required as the one place the contempt turns on the body, and E.M.I. earns its close. The test bites on the rest. No Feelings, Liar and Problems are three statements of one spite, any one of which could go; New York is a jibe at another scene; Submission is a slower song the record does not need. Half compelled, a third permitted: the figure sits on the line.
David Lynch · Film
7.9 · Tier III
Judged on structure, and the structure divides. Much of the film is paid for by its loop and resists the subtractive test: the message on the intercom, which Fred delivers to himself at the end; the three videotapes, outside the house, then inside, then Fred over Renee’s body; the photograph in which one of two women vanishes; the cabin that burns backwards; the saxophone that reaches Pete through a garage radio. The Mystery Man’s party cannot go. Much of the middle hour can. Pete’s night out with Sheila and his friends, the detectives parked outside the Dayton house, the garage business with Arnie and the porn-film material at Andy’s each do one job, and several do it twice. Length is not the charge; duplication is, and it holds the figure at the line.
Denis Villeneuve · Film
7.9 · Tier III
Judged on Part One alone. Much resists the subtractive test. The gom jabbar is required: it sets the Bene Gesserit’s measure of the human, Paul’s discipline and Jessica’s divided loyalty in one room. The harvester rescue is required: the spice, the worm, Leto’s choice of men over cargo, Paul’s first waking vision. Yueh’s wife, named early, makes the betrayal pay, and the tooth he gives the paralysed Duke pays at the Baron’s table. The close on a real threshold, Paul’s first killing, holds the axis at the cap. What gives keeps it there: the visions of Chani recur in near identical form, Caladan is long in ceremony, and the unit stops at its story’s midpoint.
Joel Coen and Ethan Coen · Film
7.8 · Tier III
Judged on structure and on the screenplay’s economy, and the subtractive test bites on an episodic form. The frame is Homer’s, so the episodes are licensed rather than compelled: nothing the film knows argues the order of the one-eyed giant, the sirens and the Lotus-eaters, and Baby Face Nelson’s robbery could go with little lost but a joke and a herd of cows. What is required is a spine. Everett’s lie, that there is no treasure and that he must stop his wife’s remarriage, is set at the start and paid at the end. The record cut at the radio station saves the three at the rally; the seer’s prophecy, the cow on the roof, the dam and the sheriff’s pursuit are planted and paid. A few strong pegs hold a loose coat, and the figure stands on the line of the cap.
U2 · Music
7.8 · Tier III
Ten tracks, and the frame is compelled. The title track’s drift of broadcast slogans has to come first, and The Wanderer has to come last, the one old voice on the record. Numb, Stay, The First Time and Dirty Day each say something the others do not. The test bites elsewhere. Some Days Are Better Than Others could go with little loss, its idea spent in its first minute. Babyface is slight, though it carries the record’s one study of desire for an image. Lemon holds its groove past what the song needs. A tenth to a seventh of the record is permitted rather than compelled, and it bears the marks of haste.
Radiohead · Music
7.8 · Tier III
Fourteen tracks in fifty-six minutes, and the spine is compelled. 2 + 2 = 5 must open, a plug going into an amplifier and a voice half awake. There There is the centre and the one long ascent. Sail to the Moon is the private counterweight to the public dread, and A Wolf at the Door, a spoken rant over a waltz, is the close the titles have promised, the threat at last on the step. Length is not the charge; duplication is. Backdrifts and The Gloaming are two takes on one electronic unease, and We Suck Young Blood and A Punchup at a Wedding each hold one idea past its use. One of each pair could go, and the argument would stand.
Chinese builders (Northern Wei foundation, Ming and Qing rebuilding) · Architecture
7.7 · Tier III
The site compels much. The halls are as shallow as the ledge and the cantilever allow; the plan is a line because the cliff is a line; the overhang shelters the timber from rain and sun; the height lifts the rooms above the floods of the gorge, the oldest explanation of the siting and a sound one. The beams go where the rock will take a socket. But the subtractive test finds much that yields. The building is a chain of small halls added along the face: one could be taken out, or another added, without loss to the whole. The interiors are ordinary small shrines. Necessity holds in the stance on the cliff, less in the parts.
Imre Steindl · Architecture
7.7 · Tier III
Judged on purpose, structure and site. The plan is compelled by its use: a legislature of two houses wants two chambers of equal dignity, and Steindl set them as mirror images either side of a common hall, so that the plan states the constitution. The long river front answers the water with its length. The dome is required by the plan as its hinge, the place where the two houses meet. What resists the subtractive test is the quantity: some 691 rooms, courts upon courts, pinnacles beyond counting, a scale set by the millennium’s ambition and by a kingdom far larger than the present state. Much of the pinnacling, many bays and much gilding could go with no loss of use or of meaning. The axis meets the Necessity Cap on the plan, with no room.
Soundgarden · Music
7.7 · Tier III
The opening four are required. Rusty Cage states the record’s motion, a body straining against confinement, and its last minute, where the tempo drops and the riff is ground out low and lopsided, is the escape as weight rather than speed. Outshined, Slaves & Bulldozers and Jesus Christ Pose each carry a different part of the pressure: the private low, the slow crush, the public lie. Searching with My Good Eye Closed, the widest space, is required too. The subtractive test then finds give. Drawing Flies and Holy Water could leave with little loss, Mind Riot restates Outshined at a lower heat, and Somewhere is permitted, not compelled: some 13 to 15 minutes of 58.
Beach House · Music
7.7 · Tier III
Eighteen tracks in about eighty-four minutes, and the length is not charged; the test is whether the parts are required. The title track must open, and Superstar, Over and Over and Hurts to Love are the record’s strongest songs, which any version of it needs. Each chapter has its own arc and its own place in the whole, and the record’s heights are spread across them. The test bites in the middle of each. Several tracks restate a mode already set, slow, glowing and in one colour (Through Me, Sunset, Illusion of Forever and Finale among them); each chapter has a song that could stand in another’s place; and the release in four parts, each heard alone, shows that the whole divides without great loss.
Horace Jones and John Wolfe Barry · Architecture
7.6 · Tier III
The parti is compelled. The river below London Bridge was the Pool of London, the busiest reach of the port, which tall-masted ships had to reach, and the East End needed a crossing without a long ramp. A span that lifts at the level of the road is the answer the site required, and the piers in the river, the counterweighted bascules dropping into them and the towers that house the machinery and the stair all follow; the high walkways were required as a route for walkers while the road was raised. What yields to the subtractive test is the costume: the granite and Portland stone, the turrets, the pinnacles and the Gothic detail carry nothing, and the steel could have stood bare. And the walkways failed as a route within sixteen years, because people waited for the bascules instead. Necessary in structure, assembled in dress: at the cap, and no higher.
Alfred Hitchcock · Film
7.6 · Tier III
Judged on structure. The crossed telegrams are required: they fix the two Charlies as one being before either meets the other, so that the girl’s later knowledge is self-knowledge. The emerald ring is required, its engraved initials first the evidence and later a weapon, worn openly at the farewell party. The torn newspaper gives the library its cause, and Joe and Herbie’s game of murder methods carries the dinner scenes. The joints show, and in more than one place: a second suspect killed by an aircraft propeller in the East closes the official case for the plot’s convenience; Graham’s courtship is largely procedure, and his proposal in the garage adds little the stairs had not; the survey men make their point at length. The spine holds at the threshold, with those parts permitted rather than compelled.
Stuart Rosenberg · Film
7.6 · Tier III
Judged on structure. The spine is required: each escape costs more than the last, so the three escapes and their punishments make a ladder rather than a repetition, and the box, the chains and the ditch rise in exact order. The mother’s visit is required by the box, and her death sends Luke over the wall; the poker bluff is required by his name and by the end, where nothing in the hand is again his whole stake. Dragline’s course, from enemy to apostle to betrayer, is a second spine and holds. The joints show elsewhere: the car wash scene lingers past its one point, the eggs repeat theirs, and much of the middle is a run of feats any one of which might go.
The Smiths · Music
7.6 · Tier III
Nine tracks, and the frame is compelled. “The Headmaster Ritual” must open, cruelty taught in school, and the title track must close, cruelty extended past the human; “Barbarism Begins at Home” is the hinge that makes the frame an argument, violence passed from parent to child. “That Joke Isn’t Funny Anymore” is required on other grounds, as the record’s one long held moment of tenderness, its coda its meaning. The subtractive test bites elsewhere. “What She Said” could go with little loss; “Nowhere Fast” restates a manner and a mood; “Barbarism”, at about seven minutes, is a jam whose length its idea does not compel; the title track says its one thing many times. Required and spare parts are close to even, and the figure sits on the line.
Danny Boyle · Film
7.5 · Tier III
The device is the film’s claim to necessity. Each question is answered by a wound or a lesson, so the quiz becomes a biography and the subtractive test seems to hold by construction. The mother killed in the riot gives the question about Rama; the blinding of Arvind in Maman’s begging ring gives the question about the Surdas bhajan; the hundred dollar note Arvind gives him answers Franklin. Those parts are required. But the device that makes every part required is itself the contrivance, the story choosing its episodes to fit the questions. Some episodes serve incident more than need: the Taj Mahal guiding and the stolen shoes, the ride on the train roofs, the comedy of the call centre. The romance repeats one beat in Latika’s three losses.
M83 · Music
7.5 · Tier III
The subtractive test bites more often here than on the strongest albums of the kind. The frame is compelled. Birds is the threshold, a short swell that lets the record begin in mid-air; Unrecorded states the method, a drum machine under a rising synthesiser wall, more plainly than anything later does; Run Into Flowers is the record’s one approach to song; and Lower Your Eyelids to Die with the Sun is the end the whole is built toward, an accumulation that works only after so much drift. In the middle the test bites several times. Cyborg and 0078h read as interludes and sketches that hold a mood without adding a turn, and two or three of the slower atmospheres repeat one another’s swell and release. A shorter sequence would lose little. The cap is met, and only just.
Harold Ramis · Film
7.4 · Tier III
Judged on structure, the subtractive test answers in two voices. The loop requires the first 2 February whole: Ned Ryerson, the puddle at the kerb, the clock radio, the old man begging, the boy in the tree and the man choking in the restaurant are planted on the first day and paid later as tests of what Phil has become. The day of arrival sets the man before the punishment, and the phases must come in order, appetite exhausted before despair, despair before service. What gives is in the middle, and it gives at length: the campaign for Rita repeats the toast, the snow and the slap for comic profit past the point the argument needs, and the costume play is accent rather than step. The axis stands at the cap and no higher.
Luca Guadagnino · Film
7.3 · Tier III
Judged on the theatrical cut, about 131 minutes, and the design is economical where it counts. Every flashback is placed to load the frame match: the junior doubles title shows the boys as one unit before she divides them; the hotel room sets the triangle’s grammar; the knee injury explains why Tashi’s game has passed into Art; the tell at serve, given early as a boyhood signal, is the hinge of the last point. Remove the hotel room or the injury and the ending fails. What gives is the middle: the churros, the sauna, the motel and the car each make one point at more length than it needs, and the score laid over talk reads as insistence. The axis holds at the cap and no higher.
Maurizio Cattelan · Visual art
6.7 · Tier II
Judged on the parts, which are four, with the place of showing as a fifth, and the subtractive test is severe. Take away the banana’s perishability and nothing has to be replaced, so the certificate has nothing to do. Take away the certificate and there is a banana on a wall that anyone can make, which is the work’s joke and its proof at once. Take away the tape and the gesture of attachment goes, cheap and provisional, the way a notice is pinned. Take away the title and the deadpan has no frame. Take away the fair and the price, and the work tests nothing. What gives: the angle and the height, which any version may vary; and much of the necessity is Duchamp’s, inherited rather than compelled here.
Vyasa (attributed) · Literature
9.1 · Tier IV
Two judgments that pull hard apart, and the second weighs more. The spine is as compelled as any plot in the epic tradition: the partition of the kingdom, the dice game and Draupadī dragged into the hall, the forest years, the failed embassy, the war, the night massacre, the women’s lament, the destruction of Kṛṣṇa’s people and the last journey each follow from the one before, and every vow and curse is cashed. Bhīṣma’s vow of celibacy makes the succession crisis; Ambā’s wrong becomes Śikhaṇḍin, behind whom Arjuna brings Bhīṣma down; Gāndhārī’s curse on Kṛṣṇa is fulfilled in the massacre of his own people. Much that looks detachable bears weight: the Gītā stands where the action requires its question, and the teaching on kingship and on the law of distress answers Yudhiṣṭhira’s refusal to rule after the slaughter. But the subtractive test finds more give here than in any other great epic: the Anuśāsana’s long teaching on gifts and their merits, the thousand names of Viṣṇu, the pilgrimage itineraries of the forest books, the long cosmologies, the genealogies that crowd the first book, and duels of one repeated shape. A large share of the whole could be taken away and the poem would lose bulk, not knowledge. The first book’s boast, that what is not here is nowhere, permits everything and so compels nothing. That holds the axis at 7.4, the lowest of the twelve.
François Rabelais · Literature
8.9 · Tier IV
The subtractive test is the axis’s question, and this work fails it more often than any book at its height. Much is required: the giant’s education, turned from the scholastic tutors to Ponocrates, which is the hinge of the first books; the Picrocholine war, which the education is for; Panurge’s question, which binds three books. But copia is the method, and copia adds. The list of Gargantua’s games, the catalogue of the library of Saint-Victor, the litanies on Panurge and Triboulet, and island after island in the Quart Livre could be halved without the loss of a fact the work needs, and some could go whole. The plenitude is part of what the book means, and holds the axis above 7.0; what holds it at the foot of the twelve is that excess, with the slacker grain of the Fifth Book.
Ancient Egyptian · Architecture
8.7 · Tier IV
Judged on the precinct, and much of it could go. The method is addition: each reign owed the god a work, and most paid with a new pylon, court or shrine on the axis or beside it. Purpose compels the axis, since the god’s bark must pass from the river to the sanctuary through ever more guarded thresholds, and the site turns it to the Nile. The hall is compelled too: a sandstone lintel spans only a few metres, and the forest that stone demands is the marsh the cult needed. What holds the axis lowest is the sum: six pylons where the cult needed one sequence of gate, court, hall and sanctuary, and a First Court holding a temple of Ramesses III, Seti II’s shrine and Taharqa’s kiosk, none of them required.
Augustine of Hippo · Literature
8.6 · Tier IV
The plan is compelled: the refutation must clear the ground before the two cities can be built, and the twelve books run origin, course and end, as a history must. What holds the axis lowest of the twelve is the subtractive test, which finds much that could go without loss. Books II and III heap up Rome’s disasters before Christ in a catalogue whose point is made in its first chapters; Varro’s crowd of minor gods is rehearsed at a length the argument does not need; the genealogies and chronologies of Books XVI to XVIII run on, with the Sibyl’s acrostic (XVIII.23); there are the monstrous races and the antipodes (XVI.8 to 9), the wonders of Book XXI (XXI.4) and the miracle list of XXII.8. Each serves; few are required. Written over thirteen years, the work shows its accretion.
Gérard de Nerval · Literature
8.5 · Tier IV
Inside “Sylvie” nothing can be removed: the night at the theatre, the newspaper notice of the provincial festival, the sleepless return to the Valois, the three women folded into one another, and the last leaf where it is all set down as lost. Inside the sonnets the subtractive test fails on every line; “El Desdichado” is fourteen lines with no slack. But the unit is the book, and the book was put together in haste and for money. “Corilla” is a slight theatre scene; “Jemmy” is another man’s story retold; “Émilie” is a war tale whose bond to the other heroines is nominal; “Isis” is half antiquarian essay. Half the volume could go without loss to what the other half knows, and that holds the axis lowest of the twelve.
Wu Cheng'en (attributed) · Literature
8.5 · Tier IV
The subtractive test is the book’s hardest, and much of the middle fails it. The frame is required: the havoc in Heaven makes the monkey who must be bound; the fillet and its spell, given by Guanyin in chapter 14, make the pilgrimage a discipline; Vulture Peak judges the whole road. The number is required too: chapter 99 audits the tally of eighty-one and adds a tribulation to make it whole. What holds the axis lowest of the twelve is which tribulations. The episodes run on a formula: a demon wants the monk’s flesh for immortality, captures him, Monkey fights and fails, seeks help in Heaven or from Guanyin, and the demon proves the escaped mount or pet of a deity and is led home. The great episodes each turn a relation among the pilgrims; perhaps a third of the run is permitted by the form, and could be removed or reordered without loss.
Vladimir Nabokov · Literature
8.4 · Tier IV
The subtractive test is the book’s weakest ground, and the reason this is its lowest axis. The design argues for its proportions: Part One dilates because Ardis is the paradise memory lingers in, and the later parts shrink as remembered time contracts, so the length of the first summer is compelled. Inside that frame much is permitted rather than required. The Villa Venus chapter, the chain of floramors, could go with no loss of knowledge; Van’s career as Mascodagama, the dancer on his hands, is a fine conceit spent at length; the puns, anagrams and literary jabs run far denser than the meaning needs, and the erotic inventories repeat. Lucette’s chapters, the Kim Beauharnais album and “The Texture of Time” are required. Perhaps a fifth of the text is ornament the book enjoys rather than needs.
Thomas Carlyle · Literature
8.3 · Tier IV
The centre is compelled. Book II cannot lose a chapter: the foundling in the Futterals’ basket at Entepfuhl, the starved schooling, the love for Blumine and its loss to Herr Towgood, the wandering, then the three stations, the Everlasting No, the Centre of Indifference and the Everlasting Yea, each required by the next. The frame is required too, since the book’s doctrine is that truth arrives only through a vesture. What holds the axis lowest of the twelve is the subtractive test at both ends. Book I spends chapters (Aprons, Miscellaneous-Historical) on a mock scholarship whose joke is made once and then again; Book III circles one thesis in sermon after sermon, and The Dandiacal Body and Tailors could go with little loss. A third of the book is permitted rather than compelled.
Jean-Luc Godard · Film
8.2 · Tier IV
Run the subtractive test and the film yields a good deal. Its method is accretion: Faure, Céline, Rimbaud, Lorca and Les Pieds Nickelés; a party that speaks in advertising copy; Samuel Fuller defining cinema; a playlet about Vietnam for American tourists; Raymond Devos on a jetty with a tune that will not leave his head; gangster talk of arms and money that the plot never needs to make clear. The playlet and the jetty are the purest cases, delightful and detachable. Against that the spine is required: the flight, the idyll, the betrayal and the death, each paid by the ending. The profusion has a reason, since Ferdinand lives through what he reads; the reason defends the method, not every instance of it, and that holds the axis just below the line of 7.5.
Ralph Ellison · Literature
8.1 · Tier IV
The subtractive test bites harder here than on a composed book, and it is what holds the axis at the foot of the twelve. The core essays are tight: “Richard Wright’s Blues” and “Change the Joke and Slip the Yoke” each build one argument and could lose little. But the book was assembled, not compelled. The two interviews and “Some Questions and Some Answers” go over ground, the Negro writer as American writer, the refusal of protest as a form, the vernacular as resource, that “The World and the Jug” and “Hidden Name and Complex Fate” cover with more force; one of the three could go with nothing lost. In the music part “Remembering Jimmy” and “The Golden Age, Time Past” overlap, and the “Blues People” review is a tributary of the Charlie Christian essay. Assembly is not the charge; redundancy is. The three parts are a sorting, not a sequence the argument requires.
Dante Alighieri · Literature
8.1 · Tier IV
The subtractive test cuts two ways in a body no author ordered. Inside the great poems little can be removed: the six end words of Al poco giorno, ombra, colli, erba, verde, petra, donna, return in every stanza because the poem is about a mind that cannot leave them, and a stanza dropped would break the rotation that is its argument; Tre donne needs each of its exiled ladies, since the lineage of Justice is the case it makes. But much of the corpus is occasional: exchange sonnets, compliments, early pieces in the manner of Guittone and Cavalcanti, whose removal would cost the whole nothing a reader would miss. What holds the axis here, a tenth under the cap: the scale is permitted by survival, not compelled by an argument, and no editor’s order is required by what the poems say.
Built for Tokugawa Iemitsu · Architecture
8.1 · Tier IV
Judged on purpose, plan and site, and here the shrine is weakest. The plan is compelled: the climb up the slope, the gates that meter the approach, the worship hall joined to the sanctuary through a low stone-floored room, and the turn up the cedar stair to a tomb above the shrine all follow from what the place is for, a dead ruler made a god whose body lies higher than his cult. The surface is another matter. Panel after panel on the Yōmeimon, sages, birds, peonies, dragons, children, is additive; a third could go and the gate would say what it says. The ornament is required in kind, a regime meaning to overwhelm, but not in quantity.
Nikos Kazantzakis · Literature
8.0 · Tier IV
The spine is required: two men, a mine, a season, a failure, and the education of the one who watches by the one who acts. Remove Zorba’s tales and the narrator has nothing to learn from; remove the Buddha manuscript and the letters with his friend Stavridakis, and Zorba has nothing to stand against. Both deaths are needed. Hortense’s is comic love ended in squalor, the widow’s is desire punished by the village, and the narrator’s education turns on each. What holds the axis lowest of the twelve is a middle that passes the subtractive test too easily. The tales accumulate rather than build, and several make the same point about women, God and freedom; the narrator’s meditations restate in the abstract what a tale has just shown; and the visit to the monastery could go with little loss.
Arthur Conan Doyle · Literature
7.9 · Tier III
Two tests, and they part. Within a story the subtractive test mostly fails to find waste. “The Red-Headed League” spends its long comic first half on Jabez Wilson, the advertisement and the copying of the Encyclopaedia, and every comic detail is a clue: the notice of dissolution, the assistant’s knees, the pawnbroker’s cellar. “The Speckled Band” plants a whistle, a ventilator, a bell-pull that rings nothing and a bed clamped to the floor, and spends all four. Across the book the test succeeds too easily. The twelve were made as monthly numbers, each complete, and any one could go without loss to the rest; “The Noble Bachelor” and “The Engineer’s Thumb” add nothing the book lacks. The shape repeats. A book whose order could be shuffled is assembled, not compelled.
Peter Gabriel · Music
7.9 · Tier III
Twenty-one tracks drawn from a film’s cues, and the subtractive test bites. The frame is compelled. The Feeling Begins must open, a single reed line out of silence that sets the record’s place and grief before anything is stated, and the run from Passion through It Is Accomplished to Bread and Wine is the necessary close: agony, release, sacrament. Zaar and A Different Drum carry the middle. Elsewhere the record is assembled more than required. Of These, Hope returns within three tracks; With This Love returns for choir; Troubled and Disturbed hold a colour and say nothing another track does not. Perhaps a fifth of the record could go with little loss.
Nine Inch Nails · Music
7.9 · Tier III
Twenty-three tracks in about 103 minutes, and a double album is asked the subtractive question harder than a single. Parts are required. Somewhat Damaged must open, a picked acoustic line built into full assault, the fall the rest lives after; The Day the World Went Away must follow, the aftermath. The Frail and The Wretched are a pair the sequence needs. The Great Below must close Left and The Way Out Is Through open Right, and Ripe (With Decay) is the compelled end. The test bites on Right: Where Is Everybody?, Please and The Big Come Down restate one mid-tempo song without turning it, and Starfuckers, Inc. is not needed; on Left, No, You Don’t is a lesser song. Perhaps a fifth of the time is permitted, not compelled.
Terry Gilliam · Film
7.8 · Tier III
The chain is tight from the first sentence. Jack Lucas, on the air, tells a caller what he wants to hear about the people in an expensive bar, and everything after is the bill for that sentence: the collapse, the bridge, the youths with the petrol, Parry’s rescue, the revelation that Parry was a professor of medieval history whose wife died in that bar. The legend Parry tells in the park is the key to the plot and is paid in the ending, and every major element is paid. What holds the axis below the bar of 7.5 is the middle: the coaching of the courtship repeats its point, the return to Jack’s career takes a quarter hour to show a relapse, and the theft from the castle is extended as caper.
Francesco Bartolomeo Rastrelli · Architecture
7.8 · Tier III
Run the subtractive test. Some of it is compelled. The quadrangle gives a whole court a single closed body with one ceremonial entrance; the four fronts each answer their site, the long front seen from the water, the triple arch on the square, the forecourt toward the Admiralty, the junction with the Hermitage; the state floor rides over a storey of service. Much yields. The river front is a run of near equal bays, and three or four could go without loss of idea or use; the statues, vases, window surrounds and broken pediments order the facade without being required by it. The enfilades are compelled by ceremony, but their rooms have been chosen and rechosen. The scale is permitted by an empress’s purse more than compelled by its argument.
Ptolemaic and Roman builders · Architecture
7.8 · Tier III
Judged on purpose, structure and site. The core of the main temple passes the subtractive test as every Egyptian temple does: pylon, court, pronaos, offering rooms and sanctuary are the stages of the rite’s approach to the goddess, and none could go without loss. Philae’s own necessity is the island’s: the narrowing forecourt and the pylons out of line follow the rock and the shore, an irregularity compelled by ground rather than chosen. But the complex accreted over six centuries, and much of it is additive: colonnades of unequal finish, gates, kiosks and small temples set where room allowed, the Kiosk of Trajan unfinished. Several parts could go without loss to the sanctuary. And the ground that compelled the bends is under water; on Agilkia they follow an island shaped to receive them. A tenth short of the cap.
The Stooges · Music
7.7 · Tier III
Eight tracks in thirty-four minutes, and the subtractive test bites on side two. The frame is compelled. 1969 must open, naming the year as a dead end before anything else is said, and I Wanna Be Your Dog must follow, the record’s thesis in three minutes. No Fun is the second pillar and opens side two as the first song opens side one. We Will Fall, ten minutes of chanted drone, is long beyond its material, but it is the record’s one stillness, the dread beneath the appetite, and without it the record would be a set of garage songs. The slack is elsewhere: Real Cool Time, Not Right and Little Doll restate the first side’s riff and want with less in them. A quarter of the time is permitted rather than required.
Maya (Puuc) · Architecture
7.7 · Tier III
Judged on structure, purpose and site, and the subtractive test bites on a building made by accretion. The core logic is compelled: a mountain of rubble raised to carry a sanctuary toward the sky, a stair as steep as the mass allows, each renewal enclosing the last so that the holy place grows rather than moves; and the oval is an economical envelope for building again and again over one core. But the pyramid as it stands is the residue of several programmes, not one argument. Temple I sits at the foot, partly swallowed; Temples II and III survive as chambers the later form does not need; the west front, with Temple IV two thirds of the way up, and the east front, with its single stair to the summit, answer different purposes. Much could be taken away without loss to what the whole says. A tenth short of the cap.
Johann Bernhard Fischer von Erlach, Nikolaus Pacassi and Johann Ferdinand Hetzendorf von Hohenberg · Architecture
7.7 · Tier III
Run the subtractive test. The axis is compelled. The slope of the Schönbrunner Berg gives the garden its direction; the palace at the foot and the Gloriette on the crest are the two ends of one line, and the parterre, the fountain and the zigzag paths are what that line requires to be walked and seen. Take away the Gloriette and the axis ends in a wooded slope; take away the parterre and the palace has no ground to command. The palace itself resists. It is a reduced design, the hilltop scheme pulled down to the valley and shrunk, then stretched and subdivided for a family and a court; the garden front repeats one bay many times, and the mezzanine is what a new use pressed into an old section. Many parts could go without loss.
Paul Abadie · Architecture
7.7 · Tier III
Run the subtractive test. The hill cannot go: it is the highest point of the city and the mount where Saint Denis was held to have died. The white stone cannot go, for it makes the vow visible from all Paris; nor the dome, the vow’s sign on the skyline; nor the crypt and the deep piers, compelled by quarried ground. The adoration gives the interior one use that the plan serves. But much is permitted. The lesser domes, lanterns, turrets and drum stacked on drum are additive; the campanile stands apart at the rear, a second building in most views. The parts hold by agglomeration more than requirement: a tenth below the cap.
R.E.M. · Music
7.7 · Tier III
Eleven tracks, and four are required: Losing My Religion, Low, Half a World Away and Country Feedback are the record’s argument about love spoken too loudly or not at all, and none could go without loss. Belong and Me in Honey stand close beside them, a parable in the speaking voice and the closing answer. Within the songs little is idle; Losing My Religion is all hook and confession, nothing padded. The subtractive test bites at the edges. Shiny Happy People is a pastiche whose irony the record never spends, Near Wild Heaven and Texarkana give breadth more than necessity, Radio Song opens on a complaint the rest forgets, and Endgame is an interlude. Two of these could go with little loss.
Don DeLillo · Literature
7.7 · Tier III
The route gives the book a spine, and the route is additive. Eric crosses the city along one street for a haircut, and the day is a sequence of stations: advisers who board the car to talk, each with a subject, technology, currency, finance, theory; meetings with his wife, each a failed meeting; encounters with Didi Fancher and with Kendra Hays; a medical examination in the car; a funeral, a riot, a film shoot. Some stations are required: the yen’s refusal to fall, the barber at the origin, Benno waiting at the end. Others are permitted: the advisers’ sessions repeat one form, and the encounters repeat one function. What holds the axis at the foot of the twelve, with one other, is that a quarter of the stations could go without the argument losing a step.
Alejandro González Iñárritu · Film
7.7 · Tier III
Run the subtractive test and the spine holds: the play, the previews, the opening, Riggan’s need to be taken seriously and the voice that tells him he was greater in a costume. Around it much could go. Laura’s pregnancy is announced and dropped. Lesley and Laura’s kiss in the dressing room is an episode, not a turn. Sam and Mike’s rooftop scene repeats what the film says elsewhere about who is real and who performs, and the critic’s scene in the bar states a quarrel already staged. The take cuts both ways: nothing can be cut around, but the camera must walk corridors between scenes, and some of the walking is filler. The ending is required by the conceit of flight. A tight spine carrying detachable parts, just below the line of necessity.
Yorgos Lanthimos · Film
7.6 · Tier III
The first movement resists the subtractive test almost throughout. Each scene in the Hotel states one statute of the world and pays it out later: the dog that is David’s brother, the choice of animal, the toaster that punishes the Lisping Man, the staged skits in which a man alone chokes and a woman alone is assaulted, the Limping Man’s beaten nose, the hunts that buy days. Even the Biscuit Woman’s fall is the Hotel’s law carried to its end. The second movement is looser. The Loners’ rules must mirror the Hotel’s, but the mirror is shown more often than it needs to be, in the raid on the Manager, the trip to the City, the coded gestures; and no clock replaces the forty-five days. Necessity is high in the first hour and moderate after.
Robertson Davies · Literature
7.6 · Tier III
The test is subtractive, and the spine is required. Its first act is the book’s best-made piece: one snowball, one stone, one early birth, one lost mind, and from them every later life. The three miracles are the structure of the narrator’s faith and must stand; the war must stand, since the third miracle happens there; Liesl and the last scene must stand, since the role the title names is given and then enacted. What the test finds is the licence of the memoir. The letter form permits digression, and Davies uses it: the lore of saints and the Bollandists given at length, the travels in Europe and Mexico, the urbane asides on Canadian manners, Boy Staunton’s rise in the sugar business told past its work. These are pleasant, and in part they characterise, since the digressing schoolmaster is the man the letter means to show; but perhaps a sixth of the book is permitted rather than compelled.
Terry Pratchett · Literature
7.6 · Tier III
The spine is tight. A god reduced to one believer, a believer who can forget nothing, and an inquisitor who believes in nothing but the Church: each of the three is needed by the other two, and the end is prepared from the first page’s injunction to “consider the tortoise and the eagle”. Brutha’s memory is not decoration: it makes him useful to Vorbis, carries the Library out of Ephebe, and lets the book end on the transmission of a text. The subtractive test finds a good deal that could go: much of the Ephebian set piece, the philosophers in the bath and their quarrels, several running gags of the Citadel, and the series’ episodic asides, Lu-Tze’s broom and the gods at their board game in Dunmanifestin. Necessary at the spine, loose at the joints.
Tracey Emin · Visual art
7.5 · Tier III
The subtractive test bites hard, and the work’s own history has run it. The core resists removal: the bed itself, at full size, on the floor; the stained sheets, which are the record of the body; and the debris, which carries the days. Take the sheets away, or launder them, and the work is furniture. Take the debris away and the bed is a sickbed without a cause. But below the core almost any single object can go: one bottle or three, these slippers or others. The inventory has differed between installations and the work has not known less for it. Its necessity is of the whole as a deposit, not of its parts as a structure: the parts are required as a class and permitted as items, which holds the axis a tenth below the cap.
André Waterkeyn; André and Jean Polak · Architecture
7.5 · Tier III
Applied to the figure, the subtractive test finds almost nothing idle. A body-centred cubic cell has eight corners and a centre, so there are nine spheres, no more and no fewer, and the tubes run where the bonds run; remove a sphere or a tube and the model is wrong. Applied to use, the test finds a great deal. The spheres are poor rooms, curved floors and low ceilings fitted into a globe chosen for what it depicts, and three of the nine are not open at all. The bipods were compelled not by the idea but by the structure, and the idea had to give way to admit them. The scale is permitted by a world’s fair, not compelled by a programme: necessary as a figure, assembled as a building.
Jim Jarmusch · Film
7.5 · Tier III
The spine is required. A retainer is bound to the man who saved his life; a contract goes wrong because the boss’s daughter is in the room; the boss and his council order the retainer’s death; and the code obliges him to kill upward through all of them except his lord. The last scene follows from everything: he walks into Louie’s gun with his own pistol empty. The subtractive test bites in the middle. The cartoons, the ice cream truck, the hunters and the dead bear, a second car taken, a man building a boat on a roof: several earn their place by rhyme, but the collecting manner admits episodes that could go, and the hunters restate what the slaughter of the birds has said. The drift is a chosen tempo, not slackness; not all of it is required.
Renzo Piano · Architecture
7.5 · Tier III
Judged on purpose, structure and site. The strongest claim to necessity is real: the taper is a sorting of uses as well as a silhouette. The deep office plates sit at the base, the hotel where the plates suit rooms round a core, the apartments where the plan narrows to a few homes on a floor, the gallery where the floor is small enough to walk round and see everything. Form and use are one fact there, and the site over a railway terminus gives the density its reason. What yields to the subtractive test is the height and the tip. Three hundred and ten metres is permitted by ambition and finance, not compelled by the programme, and the unoccupied upper spire is figure, not use.
Robert Eggers · Film
7.5 · Tier III
The spine is tight: the girl’s call in the prologue is the cause of everything after, and the ending, her body given at dawn, answers it. Knock’s commission, the contract signed in the castle and the ship’s rats each pay. What yields to the subtractive test is the long middle in Wisborg. Ellen’s seizures are shown many times, at the Hardings’ table, in bed, before the doctors, and the repetition first establishes possession and then restates it. The collapse of the Harding household is a strong episode but a second plague drama inside the first, and it lengthens the film without changing what it knows. Von Franz half duplicates Sievers before replacing him. The film is not assembled; it is fuller than it needs to be.
The National · Music
7.4 · Tier III
Thirteen tracks in fifty-five minutes, and the subtractive test bites more than once. I Should Live in Salt must open: an address to a brother left behind, it sets the record’s terms of guilt and attachment. Demons states the condition, Don’t Swallow the Cap gives it its fullest form, Pink Rabbits is the record’s centre and Hard to Find a fit, quiet close. But the middle is soft. Heavenfaced and Slipped are slow and beautiful and say again what This Is the Last Time and I Need My Girl say better; one of them could go without loss, and Fireproof, slight and lovely, is near the line. From the sixth track to the tenth the record is permitted rather than compelled.
Talk Talk · Music
7.3 · Tier III
Nine tracks, and the test finds required parts and spare ones. Such a Shame and It’s My Life carry the record’s public argument and could not go. Renée is required for another reason: it is the first long, quiet piece, where the band lets space into the song, and without it side one would be a run of singles. Tomorrow Started does the same office at the head of side two. The test bites in the middle of the second side: The Last Time and Call in the Night Boy restate the brisk mode without turning it, and the record would lose little without one of them; Dum Dum Girl, a fine single, opens in the manner of the band’s first album rather than of this one. The cap is missed by a tenth.
David Lynch and Mark Frost · Film
8.6 · Tier IV
Judged on the whole, and the subtractive test bites hard in places. The pilot and the first season are tight: every strand, the Hornes, the mill, One Eyed Jacks, the Haywards, Cooper’s dream, feeds the question of Laura. The film is close to necessary throughout; its Teresa Banks prologue, the one stretch that might be cut, plants the ring and the logic of the doubles. Most of The Return’s duration is willed: the sweeping, the waiting and Dougie’s slowness are what it is about. What holds the axis lowest of the twelve is the second season after Leland’s death: Ben Horne’s Civil War delusion, James Hurley’s interlude with Evelyn Marsh, Nadine’s return to school, Little Nicky, Dick Tremayne. Several hours could go without loss, and The Return’s Las Vegas brothers and Roadhouse booths add slack of their own.
Roman, under Hadrian · Architecture
8.4 · Tier IV
Judged on structure, purpose and site. Within its parts much is compelled. The Maritime Theatre’s moat, ring and island are one idea, a house withdrawn inside a house, and nothing in it yields. The Cento Camerelle raise the Pecile where the ground falls, so platform and service rooms are one fact. The tunnels are required by a purpose that wanted labour unseen. What holds the axis lowest is the whole, an accretion of campaigns, pavilions and gardens over some fifteen years. Take away the Stadium garden, the Hall of the Philosophers or one of the two bath buildings and the villa loses an episode, not an argument. The site compels the turning axes; it does not compel the number of parts.
Harriet Beecher Stowe · Literature
8.1 · Tier IV
The spine is required. Remove the northern line and the book loses its proof that the slave who resists, George Harris, Eliza on the ice, and the slave who submits, Tom, are condemned by the same law; remove the New Orleans house and it loses its central argument, that a humane, intelligent, unconvinced master changes nothing. What holds the axis lowest of the twelve is how much is attached to that spine: sermon laid over scenes that have already made their point, the Quaker settlement and the Harris line after the escape run long and slack, a run of coincidental recognitions late in the book that the argument does not compel, and the removal to Liberia at the close, a programme attached to a story. Perhaps a sixth could go with gain.
Alan Moore · Literature
8.1 · Tier IV
The subtractive test bites hard. The case for scale is real: a book arguing that every moment of an obscure district persists and matters must give those moments their weight, and the chapters of The Boroughs, each a life in a different century, are its proof by accumulation. Length is not the charge. The charge is that much is permitted rather than compelled. Mansoul, the longest of the three books, runs as a children’s adventure of episodes that add incident more than knowledge once the cosmology is learned; the eternalist argument is stated again in dialogue after the reader holds it; streets and weather are described at a length the argument does not need. A quarter or more of the book could go without the knowledge changing, and that holds the axis lowest of the twelve.
Lev Rudnev · Architecture
7.9 · Tier III
Judged on purpose, structure and site. The site compels much: a single high figure on the city’s highest ground, answering the Kremlin across the bend of the river, and an axis that runs from the river up to the door. The hierarchy compels the rest: a tower that holds the centre and wings that step down to the residences, so that the university reads as one body with one head. But the subtractive test bites. The spire and star, the corner towers and their spires, the sculptured parapets and the clock and instrument faces could go, and the university would teach and lodge as before; the upper storeys of the tower are of limited use. What holds the axis at 7.3, the foot of the twelve with one other, is that so much was compelled by a decree rather than by the institution, though the image is not assembled: tower, wings and spire are one stepped figure.
John Barth · Literature
7.8 · Tier III
The test is subtractive, and the spine is required. Without the goat barn there is no hero who has to learn to be human; without the Assignment there is no quest; without the three descents into WESCAC there is no argument, since the thesis is carried by the failure of the first two teachings and by the third. The frame is required too: the disputed authorship of a scripture is half of what the book says. The encounters of each middle reel, with Stoker in the Power House, the Sears, Eierkopf, Peter Greene and Croaker, each restate the opposition of Passage and Failure in a new costume, which a book about opposites can use. What the test finds is the tour: a college for each nation told past its point, and the campus joke repeated long after it has landed. Perhaps a fifth of the book is permitted rather than compelled.
Herzog and de Meuron, with Ai Weiwei and Li Xinggang · Architecture
7.8 · Tier III
Judged on purpose, structure and site. The concrete bowl passes the subtractive test: a continuous saddle of seats round a track, tightened at the long sides to bring the crowd close to the field, compelled by sightlines. The shell passes in part. Its primary girders carry the roof and descend as columns, so the facade is the structure and holds the stairs. But much of the lattice is secondary steel set to make the weave read as random and continuous; take those members away and the stadium stands, is entered and keeps its roof, losing only its image. The frame was sized round a retractable roof that was then dropped. Much here is permitted by the image rather than compelled by the purpose, and the axis stands at 7.3, below the Necessity Cap.
Martin Scorsese · Film
7.8 · Tier III
Judged on structure, and the test finds both what is required and what is not. The frame holds: the car bomb opens the film and is returned to, so the whole is a fall already known. The first hour’s exposition is required, because the subject is a system and the count room, the suitcase, the front and the chain of watchers must be laid out before the chain can break; the hinge, a grievance in a wired back room, is small and right. But the second half repeats itself: Ginger’s breakdowns come in a run of scenes making one point, Lester Diamond’s scenes repeat his one function, and the television show and Santoro’s successive assaults add incident more than consequence. At 178 minutes the scale is permitted rather than compelled, and a film of two and a half hours would lose little of what this one knows.
Steven Spielberg · Film
7.7 · Tier III
Run the subtractive test and it holds at the ends and bites in the middle. The scattered signs, in the Sonora desert, over Indianapolis, in India and in Indiana, are each required: they make the visitation global and the convergence on Wyoming earned. Roy’s obsession is the spine, and the mountain he shapes in potato and then in earth is the hinge by which private madness becomes public truth. But the household sequences repeat one beat, Roy cannot explain and Ronnie cannot bear it, several times over; the scientists’ strand runs beside Roy’s more than through it, and its decoding and briefings could lose a third; the return of the taken runs past need. The director’s own recuts, which moved material in and out of the middle, confirm from outside that its necessities were not fixed. Required parts, repeated beyond their need: the axis stands at 7.3, below the Necessity Cap.
Danny Boyle · Film
7.7 · Tier III
The central spine resists subtraction. The first crossing is required: it is the initiation the island demands of a boy, and the father’s lie about the kill, told at the feast, sends the son out of the father’s world. The second crossing is its answer: the boy now leads, and the journey ends not in a kill but in a death accepted. Erik, a stranger from a world that has gone on without Britain, shows that the quarantine is kept from outside, and the birth gives the infant the boy carries home. What gives is at both ends. The prologue is paid only by the last scene, and the last scene largely opens another film: remove it and a promise is lost, not a part. The father’s affair, glimpsed and dropped, and the Alpha’s returns as set pieces show joints.
Buena Vista Social Club · Music
7.7 · Tier III
Fourteen tracks, and the subtractive test finds a songbook more than an argument. The frame is placed with care. Chan Chan must open, four chords and a guitar figure that hold the whole record in small; La bayamesa must close, a trova of the east, the oldest kind of song the record holds, ending it where the tradition began. Pueblo nuevo and the title danzón are required as the only places the voices fall silent and the piano speaks. Inside the frame the test bites often. El cuarto de Tula holds its groove past what the song needs; Orgullecida and ¿Y tú qué has hecho? could change places with songs from other records of the same weeks with little loss; three boleros sung by Ibrahim Ferrer say one thing at three tempos. Much is permitted, little compelled.
Federico Fellini · Film
7.6 · Tier III
The test is subtractive, and an episodic film invites it. Some blocks are hinges. The storm over the beauty contest ends the summer and begins Fausto’s marriage in one stroke; the theft of the angel turns his idleness into petty crime and makes Moraldo his accomplice; the carnival dawn strips Alberto of the sister who keeps him; Sandra’s flight brings the belt; the departure needs Guido, the boy who works while the men sleep. Much else is permitted rather than compelled. Riccardo, a voice and a face, could go with little loss; the Natali episode arrives late and does one thing at length; the narration often explains what the image has shown. The looseness is partly the subject, idleness drawn as drift, and partly looseness, and that second part holds the figure below the line at which every part is required.
Guðjón Samúelsson · Architecture
7.5 · Tier III
Judged on purpose, structure and site. The site compels much: a hill at the head of a straight street, seen from the whole low city and the bay, asks for a vertical mark, and the tower set on the street’s axis answers it exactly. The long nave is compelled by a parish church that was also to be the nation’s chief church, a room for great congregations and for music. The front’s elaboration yields to the subtractive test. The stepped wings carry no load the tower needs and house little that requires their height: remove them and the church works as before, losing only its image, which is what they are for. Nave and front answer different necessities, and meet rather than fuse.
Jun Xia (Gensler) · Architecture
7.4 · Tier III
Judged on purpose, structure and site, and much is compelled. The twist and the taper are required by the wind, the dominant load at this height in a region of typhoons; the core and mega-frame are required by the height; the mechanical floors every dozen or so storeys are required by the lifts, the services and the hung skin; the circular inner plan is the efficient section for so slender a tower. Take away the twist and the tower needs more steel. The subtractive test then finds what is not compelled. The height is required by the skyline and the trio, not by a demand for floor space. The atria take a large share of the enclosed volume for an idea of the tower, and the double skin is its largest unforced choice.
Keith Haring · Visual art
7.3 · Tier III
Subtract the slogan and the wall becomes one more Haring frieze, its figures legible as distress but not as a warning; the words carry the load. Subtract the orange and the work loses its claim on the speeding eye: at highway distance it is a beacon before it is a picture. Those two are required. The figures are less so. Haring’s vocabulary is additive by nature, a frieze of interchangeable pictographs that could lose a figure or gain one without the argument shifting. The monster, the money and the pipe are each a clause of the one sentence, that crack devours, and the sentence is said several times. Necessity is real at the level of the whole, a warning at this place legible at this speed, and loose at the level of the parts: a third of the frieze could be redrawn without loss.
Deafheaven · Music
7.3 · Tier III
Nine tracks, and the subtractive test finds a frame that is required and a middle that is not. Shellstar is required as the statement of the new terms: clean voice, chiming guitars, no blast. Mombasa is required absolutely, because the whole record is built to arrive at its last minutes. Great Mass of Color carries the album’s drive, and Neptune Raining Diamonds earns its two minutes as the one breath of a different texture at the hinge. The test bites in the run from In Blur through Villain and The Gnashing: three mid-tempo songs in one bright, reverbed mode, of similar length and arc, and the sequence would lose little without one of them. The scale is permitted rather than compelled.
Chris Sanders · Film
7.3 · Tier III
The subtractive test holds the spine. The crushed nest is the first cause: it leaves one egg, it makes Roz’s task of teaching the gosling to eat, swim and fly a debt rather than a chore, and it plants the guilt that breaks him from her in the middle of the film. Each lesson pays into the migration. What yields is the ensemble and the last half hour. Much of the comic animals’ business could go without loss to what the film knows; the robot farm in the south is a detour spent quickly; the climax against the ship is action stock, not required by the film’s argument about care. A tight first hour and a looser end hold the axis below the Necessity Cap.
Mogwai · Music
7.3 · Tier III
Ten tracks of about four to six minutes, and the frame is compelled. Auto Rock must open, a piano figure repeated until the band gathers under it, the record’s method stated in four minutes. Glasgow Mega-Snake must follow at once, the opposite pole, loud from the first bar. We’re No Here must close, the heaviest and slowest weight left to last; Friend of the Night is required as the one warm melody, I Chose Horses as the one human voice speaking. The test bites in the middle. Acid Food, Team Handed and Emergency Trap are three quiet pieces of one kind, any one of which could go with little loss, and Folk Death 95 repeats a build already made. A third of the record is permitted rather than compelled.
Coldplay · Music
7.2 · Tier III
Eleven tracks, and the subtractive test finds a compelled frame around a middle that is not. Politik must open, hammered chords and the band at full weight, the one place the record faces outward. Amsterdam must close, a ballad that holds still and then lets the band in, the record’s one release from the trap its songs describe. The Scientist and Clocks are each required. The test bites on the second side’s middle: Green Eyes says what In My Place said better, A Whisper restates God Put a Smile upon Your Face with less to say, and Daylight earns less than its length. Two or three tracks are permitted rather than compelled.
David Childs (Skidmore, Owings and Merrill) · Architecture
7.2 · Tier III
Judged on purpose, structure and site. The geometry is spare, and one rule generates the shaft: a square whose edges are cut back as it rises until it ends as the same square turned. Nothing is ornament. The subtractive test still finds much that could go without loss to the use. The 1,776 feet are reached by a mast which, stripped of the radome that was to make it a sculpted spire, reads as equipment set on a prism to reach a number. The podium is compelled, but by threat rather than purpose. The office floors are ordinary deep floors round a core. The parts are required by symbol and by security more than by dwelling, and much was settled by redesign and cost rather than by the work’s own argument.
H. P. Lovecraft · Literature
8.1 · Tier IV
Within the best tales the subtractive test finds little. “The Colour Out of Space” moves from the meteorite to the blighted farm to the well without a scene to spare, and “The Call of Cthulhu” is three documents, each required for the correlation its first sentence fears. Across the body, and inside the long tales, the test bites hard. At the Mountains of Madness gives several of its twelve parts to a reading of the Old Ones’ history from the bas-reliefs; “The Whisperer in Darkness” spends much of its length on letters that tell the reader what the ending will confirm. What holds the axis lowest of the twelve is the template: a scholar, a document, a resistance, and a disclosure the reader has foreseen, delivered as though unforeseen. Many tales could go and the body would know the same things.
Bram Stoker · Literature
8.1 · Tier IV
The test is subtractive, and it bites in the middle. The spine is required: the Transylvanian chapters, the wreck at Whitby, Lucy’s fall, Mina’s contamination and the pursuit east are each a stage of one invasion and its reversal, and the opening four chapters waste nothing. Then the book swells. Lucy’s sickness is told through four transfusions that repeat one movement, the garlic removed by a servant or a mother, the bat at the window, the white face at morning, while the reader knows the cause long before the men do. The councils of war restate what has been learned; the tracking of the fifty boxes runs by inventory; the praise of Mina’s courage is spoken again and again. Length is not charged; repetition is. What holds the axis lowest of the twelve: much of the book is plainly permitted rather than compelled.
Algernon Charles Swinburne · Literature
8.1 · Tier IV
The subtractive test goes badly for the book as a book. It is an assembly of a decade, not a made whole: early Pre-Raphaelite medievalisms such as “The Masque of Queen Bersabe” and “St Dorothy”, and the ballad pastiches, sit beside the mature lyrics in no order that requires them, and many could leave with no loss. Within the great poems the test fails in its own way: “Dolores” says its one thing in its first dozen stanzas and goes on long after, and “Laus Veneris” and “Anactoria” repeat their turns. Against this, “The Garden of Proserpine”, “Itylus” and “A Leave-taking” are compelled from end to end, and in “The Triumph of Time” the length is the tide the poem describes. What holds the axis at 7.2, the lowest of the twelve and below the Necessity Cap, is that excess is the book’s habit, not its occasional lapse.
Sei Shōnagon · Literature
8.1 · Tier IV
Subtract and see: much can go, and the form invites it. A miscellany is open by design. A section on bridges or on islands that is little more than a run of names could be removed with the book’s knowledge almost unchanged, and the four textual lines show copyists rearranging and supplementing it for centuries without anyone feeling a whole broken. What resists removal is real. The opening seasonal section must stand where it does, because it sets the method, a category and a judgment in two words. The first reminiscence of coming to court is required: every later scene of wit is measured from the newcomer’s fear. The late reminiscences and the yamabuki petal carry the undertow. Held by the slack name-lists and by an order no author can be shown to have fixed.
Queen · Music
7.9 · Tier III
The subtractive test bites hard on the first side. Death on Two Legs must open, the curse that clears the stage, and ’39 is required as the record’s first true song. Around them, Lazing on a Sunday Afternoon is a brief turn; I’m in Love with My Car is a slight joke given a heavy arrangement; Sweet Lady is the plainest hard rock on the record and could go without loss; Seaside Rendezvous repeats the music-hall manner at more length. The second side resists far better: each of its five tracks does what no other does. What holds the figure is that the record’s scale is permitted by the variety bill, not compelled by an argument: three of seven first-side tracks could go and the record would know the same things.
George Gershwin · Music
7.8 · Tier III
The subtractive test is answered by the work’s own history. Its first recordings, with the composer at the piano, dropped nearly half its length and remained recognisably the work, and it has been cut ever since. Leonard Bernstein’s charge, that its paragraphs could be removed or swapped without harm, has never been met by a demonstration that they cannot. The chain of episodes in the middle third is the softest: several could go with loss of colour, not of argument. What resists is the frame: the clarinet opening, which the whole answers; the Andantino, which the work spends most of its length postponing; the Agitato that drives back toward it; the Grandioso return. Length is not charged.
Carl Orff · Music
7.8 · Tier III
The subtractive test finds the frame required and much of the interior free. O Fortuna must stand at both ends: its return after Ave formosissima is the work’s one structural argument, and without it the cantata is a suite of springtime, drinking and love. Fortune plango vulnera tells the wheel’s fall in words and is needed beside it. Inside the frame the numbers are tableaux joined by contrast, not consequence. Uf dem Anger could lose Floret silva or Chramer without the whole noticing; Cour d’amours has nine numbers where six would carry the same ascent; Ecce gratum and Tempus est iocundum repeat their stanzas at length. Chosen repetition is credited elsewhere, but it is still material the test can remove. Length is not charged.
Luis Buñuel · Film
7.7 · Tier III
The subtractive test is the hardest this film faces, and on purpose. Its law is that no episode is owed to the one before: the captain’s story is abandoned in a park, the nurse’s father is never reached, the dying man’s cancer is never mentioned again. What is required is the chain itself, each hand-off made by a character crossing a threshold, and the frame, the execution answered by the zoo. The parts are not. Remove the inn or the postcards and the argument would stand; the inn runs long, and the aunt and nephew add little the hatter does not. Necessity belongs to the design, not to its members, and that holds the axis below the cap.
Stephen King · Literature
7.6 · Tier III
The test is subtractive, and the spine is required and well laid. A man who broke his son’s arm drunk and lost his post at Stovington for beating a student takes the caretaker’s job as his last chance, and the hotel works on exactly the faults the first part has shown. The boiler that must be dumped twice a day is planted on closing day and pays out as the end; the wasps’ nest, the scrapbook in the basement and Room 217 each advance the siege. But much else could go. Hallorann’s journey back from Florida is long and repeats its urgency; the hotel’s assaults on the boy come in a series, the hose, the hedges, the bath, the elevator, the party, and several restate rather than raise; Jack’s grievances are rehearsed in his head well past need. The length is permitted by the genre’s pacing, not compelled by the argument, and that holds the axis lowest of the twelve.
Michel Pinseau · Architecture
7.6 · Tier III
Judged on purpose, structure and site. Some of it is compelled. A congregational mosque for a city of millions, and for national prayer on the great feasts, asks for a very large covered hall and a larger open ground, and the hall and esplanade answer that need. The square shaft of the minaret is the regional type, and the qibla governs the plan. The subtractive test then finds much that can be removed without loss to the purpose: the height of the minaret beyond what any call or landmark requires, raised for a record; the laser; the acreage of ornament repeated across surfaces no worshipper reads; a scale set in part by the wish to be largest. The verse defends the sea site as an idea the site illustrates, not as a need the plan answers. The scale is permitted by the patron more than compelled by the prayer.
Zaha Hadid · Architecture
7.5 · Tier III
Judged on purpose, structure and site, and the site argument is real. The bands take their direction from the grain of the plot and the lines of the surrounding streets, and the L-shaped lot is filled by bands that turn its corner rather than by a block set down on it: straighten the bends and the building no longer belongs to its ground. Structure and plan are one, since the walls that bound the galleries are the walls that span. The subtractive test bites on purpose. A museum must show work, and bending walls, sloping floors and continuous voids are not required by showing it; partitions added against the walls are the purpose removing what the form supplied. The stairs across the atrium exceed what circulation needs. Much is compelled by the idea, less by the use.
Haddon Sundblom · Visual art
7.3 · Tier III
Within the single picture the parts are economical and bound to one end: a ruddy face, a fur-trimmed red coat, warm interior light, a bottle placed in the hand at the height of the face, and the gaze or the half-turned smile that makes the reader complicit. Take away the bottle and the picture is a Christmas cover; take away the light and the warmth that sells the drink goes with it. That is the necessity of the brief. Across the body the test is harder: the pictures vary one situation, and a dozen could go without the body losing anything it knows. A body scored as one work is charged for its repetition.
David Mackenzie · Film
7.2 · Tier III
Judged on the 121-minute cut. The spine is clear and its main parts are required: the opening submission is what the rising breaks; the display of Wallace’s remains is the turn; the killing at the altar makes the king an outlaw twice, to England and to the Church; Methven’s broken agreement teaches the outlaw’s war that Loudoun Hill wins. Each hinge holds the next, and none could go. What the subtractive test finds is thin rather than idle. Elizabeth is required by the plot and given too few scenes to be required by the meaning; Douglas’s arc arrives in fragments; the flight through the west is a run of episodes that could be reordered; and the single combat at Loudoun Hill is a convention the battle’s own logic did not need.
Arcade Fire · Music
7.8 · Tier III
Thirteen tracks on two discs, and the frame is compelled. Reflektor must open, setting the thesis and the dance-floor method at once; the Orpheus and Eurydice pair must head the second disc; Afterlife must come near the end, where the descent asks what survives death. Here Comes the Night Time and its slow reprise on the second disc are a real design, the carnival heard again from below. What holds this lowest of the twelve is the subtractive test, which bites hard elsewhere. Flashbulb Eyes is a sketch of the title track’s idea; Normal Person and You Already Know could go and leave the argument whole. Supersymmetry’s long ambient tail is permitted, not required. Some eighteen to twenty-five per cent of the record could be removed with little loss, and several long tracks run past what their material needs.
Paul Thomas Anderson · Film
7.7 · Tier III
Run the subtractive test strand by strand, and the design holds: two dying fathers, Earl Partridge and Jimmy Gator, each with a child he wronged, and a quiz kid of the past and one of the present, so that the ruined child is shown at ten and at forty. The prologue is required, since it states the wager the frogs will cash; Phil’s telephone search is the thread that pulls the son to the deathbed. No strand could go. Much of the length could. Donnie’s declaration at the bar plays one need at twice the length it requires, Kurring’s date with Claudia is drawn out in its confessions, and Linda at the pharmacy and at her lawyer’s strikes one note of guilt twice. The design is required; much of the three hours at full volume is permitted rather than compelled. That holds the axis lowest of the twelve, and below the cap.
William Friedkin · Film
7.4 · Tier III
The subtractive test finds a compelled spine and many permitted limbs, and that is what holds the axis below the cap. The prologue is required: it makes the antagonist older than the house it enters and Merrin’s return a meeting already fixed. The medical sequence is required, since every secular remedy must be exhausted before the priest is called. Karras’s mother is required; his guilt is the door the demon uses. What gives is a great deal. Kinderman’s inquiry is half a detective film the cut never finishes: it supplies one hinge and then idles. The film-set comedy and the party run long for what they carry, and the prologue takes its time.
Quentin Tarantino · Film
7.0 · Tier III
The subtractive test leaves the spine standing. The withheld robbery is what the film is built around, so the warehouse in real time cannot be cut; the “Mr. Orange” section is required, since the commode story, a policeman rehearsing an anecdote until he can tell it as a thief, is how the film says what Freddy is and what talk is in this world; the Blonde section makes Vic’s loyalty and his sadism one fact, and the standoff pays it. But much of a short film gives. The diner sets the code and the talk and runs longer than its work; the Mr. White section with Joe and Alabama is thin; Pink’s escape outside is told by sound alone and left loose. Permitted talk takes a share of 99 minutes, and the necessity is short of the threshold.
Jules Verne · Literature
8.0 · Tier IV
The test is subtractive, and the book is the most subtractable of its order. It is a voyage of stations, and many could go without loss to what it has to say: the hunt in the forest of Crespo Island, the shooting party on Gueboroar, the dugong, the history of the Vigo galleons, much of the Red Sea. The catalogues are the greater charge. The lists of fishes and molluscs by family and genus are in part the argument, the ocean as an inventory too large for its inventoriers and Conseil’s classifying blindness as comedy, and a first share of them is required; but they run far past their work, and an editor could take a tenth of the book in them unnoticed. What is required is real: the captivity, Nemo’s withholding revealed by stages, the ice, and the ending the ramming compels. The spine is necessary; the body is permitted. That is what holds the axis lowest of the twelve.
Alan Moore and J. H. Williams III · Literature
8.0 · Tier IV
The spine is required. Promethea is a story that lives by being told, and the work must show her told, in the hosts and the Immateria; taught, in Faust’s lesson and the Tarot; proved, in the ascent; and released on the world, in the apocalypse. The subtractive test bites on the rest. The science-hero city, the Five Swell Guys and the Weeping Gorilla panels are scenery from Moore’s line, and the crossovers of the last third serve the imprint more than the argument. Inside the ascent whole pages are lecture: Barbara asks, Sophie explains, the sphere is described, and the next issue repeats the shape. That holds the axis at the foot of the twelve: a third of the length could go and what the work knows would remain.
David Foster Wallace · Literature
7.9 · Tier III
The subtractive test bites hard, and in two ways. Within the major sections much is compelled: Fogle’s hundred pages need their drift, the Obetrol, the soap opera, the father caught in the train doors, for the conversion in the wrong classroom to mean anything, and Lane Dean’s afternoon needs every minute of its tedium. But the book as a whole was never ordered by its author. The Editor’s Note says plainly that Wallace left no final sequence, and the arrangement is the editor’s. Many sections could be lifted out with no loss to the argument: several Sylvanshine passages, some interview fragments, sketches of characters who never return; and the comic account of “David Wallace”’s arrival and mistaken identity runs well past its point. Nothing in the assembly can show that its parts are required by what the whole has to say, because the whole was not finished. That holds the axis lowest of the twelve.
Louisa May Alcott · Literature
7.7 · Tier III
The test is subtractive, and it is hard on the book. The spine is required: the father’s absence, the telegram, Jo’s hair, Beth’s fever, the father’s return. But the first part is a sequence of moral episodes, each closed by a counsel, and several could go without loss to what the book knows: “Experiments”, a parable guessed on its first page; “Camp Laurence” and its English visitors; “Castles in the Air”; much of the sisters’ club and its paper. The second part, written to order after the first had sold, is permitted more than compelled: “Calls”, “Artistic Attempts”, the European letters and the long courtship of Amy and Laurie. It earns one necessity: Jo’s refusal of Laurie and Beth’s death, which turn a family idyll toward its real subject. Perhaps a quarter of the whole is assembled rather than required, and that is what holds the axis lowest of the twelve.
The Smashing Pumpkins · Music
7.7 · Tier III
Twenty-eight tracks in about two hours, and the record’s own scale invites the subtractive test. Some of the length is compelled: the day and night frame wants a long arc, the piano piece that opens and the lullaby that closes are required as its two ends, and Porcelina of the Vast Oceans earns its nine minutes as the first disc’s deep centre. Much else could go. Cupid de Locke restates the mood of the title piece; Lily (My One and Only), a music-hall novelty, dents the night side; We Only Come Out at Night and Beautiful are slight; Tales of a Scorched Earth and X.Y.U. repeat the heavy register Bodies and Bullet with Butterfly Wings already carry. A single disc of the strongest fifteen would lose little of what the work knows, and that holds the figure lowest.
Zaha Hadid · Architecture
7.6 · Tier III
Judged on structure, purpose and site, and much yields to the subtractive test. The programme is three ordinary cultural volumes, a hall, a museum and galleries, each a room of conventional shape, and the envelope is laid over them as one surface rather than rising from them. The steel frame exists to hold the surface, not the rooms: the structure is compelled by the image, not the image by the structure. The curl over the entrance and the long sweep to the plaza could be steeper, shallower or placed elsewhere with no loss to any use inside. What resists is the ground folding up into the wall, which makes plaza, approach and building one fact and requires the column-free lobby. The scale is permitted by a state budget, not compelled by the purpose.
Pearl Jam · Music
7.5 · Tier III
Fourteen tracks, and the subtractive test cuts deep. The core is required: Last Exit must open, a song of leaving; Not for You states the public quarrel and Corduroy the private one; Better Man and Nothingman turn the pressure toward a couple; Immortality is the necessary close of the songs. Spin the Black Circle and Whipping earn their places as bursts of impatience, and Pry, To has its reason, a single word spelled out and mangled. What holds the figure lowest of the twelve is a quarter of the running time: Bugs and Aye Davanita could go with little loss, the closing collage holds nearly eight minutes for an idea spent in two, and Satan’s Bed is a competent rocker that adds little.
Vlado Milunić and Frank Gehry · Architecture
7.3 · Tier III
Judged on purpose, structure and site. The site compels more than it seems to. A corner at a bridgehead, on an embankment of nineteenth-century houses each ending its row in a corner turret or dome, asks for a figure that turns the corner, and two towers give one: the glass tower opens the corner to the bridge and the river, the solid tower closes it with a turret as the old corners do. The river block, held to its neighbours’ height, its mouldings and staggered windows answering their cornice lines, is compelled by the row it joins. The subtractive test then finds much removable without loss to the use: the pinched waist, which costs the rooms behind it, the leaning glass, the mesh crown, the window boxes. The defence, that the corner is a sign and the couple the sign, holds for the two towers together, not for each gesture in them.
Moshe Safdie · Architecture
7.3 · Tier III
Judged on purpose, structure and site. Part of the building is compelled. The towers are thin slabs because every room wants the bay or the city; the split into two legs with an atrium between doubles the face with a view while keeping the plan shallow; and the lean of the eastern leg widens the base where the podium needs bearing and gives the eastern rooms a sloping wall of glass over the water. The SkyPark is compelled by nothing but the image and the trade. Remove it and the hotel works as well, and only the emblem goes; remove the lean and the rooms remain rooms. Three towers rather than two or four are set by the room count and the frontage, not by an argument the form makes. Assembled with great skill, not required.
Yousef Abdelky · Architecture
7.3 · Tier III
Judged on purpose, structure and site. Some of it is compelled. A Friday and Eid mosque for a capital needs a hall turned to Mecca and an open court for the overflow, and both stand at the scale the purpose sets: the court is where most of the feast-day crowd would pray. The pools are compelled by climate as well as by image, cooling the arcades on a desert site. Elsewhere the subtractive test yields readily. The domes are multiplied past the spans they roof, many of them caps over bays that would stand without them; the four minarets are the Mughal quartet taken whole; the inlaid columns repeat one module far more often than structure asks. What would be lost is display. The parts are required by an image of splendour more than by what the building has to do.
Oasis · Music
7.2 · Tier III
Twelve tracks, and the subtractive test bites often. Wonderwall, Don’t Look Back in Anger, Cast No Shadow and Champagne Supernova cannot go: they are the record. Morning Glory carries the title and the one surge of aggression after the opener. Beyond them the case weakens. Hello announces a return, “good to be back”, on a partly borrowed chorus; Roll With It is a slogan riff that restates the debut’s manner; Hey Now! circles its figure for over five minutes with no turn; She’s Electric is a pleasant music-hall pastiche with no office in the argument. The long outros are partly the anthem’s insistence and partly length permitted. Perhaps a third could be lost with little loss.
Eduard Riedel and Christian Jank, under Ludwig II · Architecture
7.7 · Tier III
Run the subtractive test against purpose, structure and site. The site compels a great deal: the long, narrow spur sets the sequence of gatehouse, lower court, upper court and Palas along its ridge, and the Palas rises sheer where the rock falls to the gorge. That massing is required. Little else is. The purpose was a set on which one man could live inside legends, and a set is assembled: the Singers’ Hall quotes the Wartburg and was never sung in; the Throne Hall awaits a throne never made; turrets multiply for the silhouette, not the plan; the keep, the composition’s centre, was left out and the castle stands without it. Parts permitted, not compelled: that holds the axis lowest of the twelve, and well below the cap.
John Nash · Architecture
7.6 · Tier III
The subtractive test bites hard. Behind the domes lies Holland’s villa, a neoclassical house of the 1780s, and Nash’s Indian exterior is in large part a skin and a roofscape laid over and beside it: the onion domes and minarets answer no requirement of plan, climate or structure, and the house would work as well without them. Inside, much of the decoration is applied rather than built: painted canvas, carved and gilded serpents, imitation bamboo in iron and wood. The defence is that the purpose was pleasure and display for one man, and that every part serves it; the end rooms are the reason for the extension. But parts compelled only by appetite do not resist the question, and the axis stands well below the cap.
Luca Guadagnino · Film
7.1 · Tier III
The Mexico City section resists subtraction better than the rest. Lee’s rounds of the Ship Ahoy and the other bars, the repeated failed approaches to young men, the white suit going grey with drink, are required: the loneliness is made by repetition, and Allerton enters a pattern already set, so that the pursuit reads as appetite rather than romance. The withdrawal is required too, since the need for heroin and the need for Allerton are one. The joints show after the border. The journey south is episodic, its bus and hotel interludes restating the imbalance between the two men without advancing it; Cotter’s compound dilates on eccentricity; the epilogue is necessary in idea and overextended in execution. A short novel carried to about 137 minutes: the scale is permitted more than compelled.
Wes Anderson · Film
6.9 · Tier II
Judged on the theatrical cut. The spine resists the subtractive test. The escape from a clinic Anthony could leave by the door establishes in one image that the crime is a game Dignan needs; the rehearsal burglary of Anthony’s own family’s house makes the same point inside the family; the notebook plan for the next seventy-five years is paid in the prison yard, where Dignan’s plans have shrunk to an escape he will not make. Mr. Henry’s robbery of Bob’s house is set up by his visits and paid on time. What gives is the middle. The motel stretch, the longest movement, is a pleasant idyll, loosely ordered, that could lose a third without loss; Bob’s departure is under-motivated and his brother’s arrest reported more than dramatised.
Tom Wright (Atkins) · Architecture
7.3 · Tier III
Judged on purpose, structure and site. Some of it is compelled. The island is the brief: a hotel offshore casts its shadow on the sea and not on the beach, and is reached as a destination is reached, across water, which is the luxury sold. The V plan follows from the use, two wings giving every suite the sea, and the atrium follows from the V. The exoskeleton is required by a slender tower on sand in Gulf wind. Then the subtractive test finds much removable without loss to the use: the mast and spire, a large part of the height, holding no rooms; the screen, which closes an atrium nobody needed at that height; the helipad and the restaurant, made to be photographed. The defence that an emblem’s form is its purpose holds for the silhouette, not for height that serves nothing but height.
Michael Graves · Architecture
7.2 · Tier III
Judged on purpose, structure and site. Some of the building is compelled. A full city block, a fixed and very low budget and a programme of open office floors gave a square block of the largest footprint the site allowed, and the stepped base meets the street at the height of its neighbours. The subtractive test finds most of the rest removable without loss to the use: the pilasters, their capitals, the keystone of dark glass, the garlands, all drawn onto a frame that does not ask for them. The small square windows are where the pattern takes from the purpose, in daylight from the people inside. The defence, that a building made to represent a city is a sign and a sign cannot be subtracted from itself, holds on two fronts of four.
Jack Vettriano · Visual art
6.5 · Tier II
Subtract, figure by figure. The servants cannot go: without them a couple dancing on a beach is a mood, and with them it is a scene of people who are served, which is the picture’s one structure; the two umbrellas, held out in a wind, are the act of service made visible. The couple cannot go. The beach and the weather can be argued for: a ballroom dance moved to the open shore under a threatening sky is the conceit, and the wet sand that doubles the figures holds them to the ground. What yields is nearly everything else. Sky, sea and sand are permitted by the conceit rather than compelled by it; the symmetry of maid and butler is a formula; the figures could be moved, turned or exchanged with little loss.
Anonymous · Literature
8.3 · Tier IV
The subtractive test is answered by the transmission itself. The oldest substantial manuscript stops in the 280s of the nights; the printed recensions fill the count with different matter; Galland made up his French volumes with tales no Arabic manuscript of the Nights contains. A work whose contents could be changed this freely is not one whose parts are required. Remove the romance of King Umar al-Nu’man, the encyclopedic display of the slave girl Tawaddud, half the anecdotes of Harun’s court or the run of animal fables, and the frame loses nothing it needs. What holds the axis this high is the frame’s own logic: Shahrazad must keep speaking or die, so multiplicity and deferral are compelled. The necessity is of the many, not of these many.
Thomas Heatherwick · Architecture
6.8 · Tier II
Judged on purpose, structure and site. Inside its own figure the subtractive test finds little idle: the module of two opposed flights meeting at a landing is structure, enclosure and route at once, and remove one flight and the lattice breaks. That is real necessity, the necessity of a closed geometric system. Applied to purpose, the test finds nothing compelled. The work has no programme the stair serves; it is a stair to a view the neighbouring towers already command, at a scale set by the wish for a centrepiece, not by any use. The 154 flights could be a hundred or two hundred without loss to anything but the figure. The barriers of 2024 are compelled, but by its failure, not its purpose. Necessary as a pattern, permitted as a building.
Francis Ford Coppola · Film
6.7 · Tier II
Judged on structure. A spine holds: the fight brings the Motorcycle Boy back; the mugging gives Rusty James his flight above his own body, the one scene in which he sees himself; the pet shop gives the fish, and the fish give the end. The father’s scenes are required, since only he says what the elder son is and what he costs. Around that spine much is mood held at length. The time-lapse skies return more often than the argument needs; Benny’s talk, Cassandra’s two scenes and Smokey’s taking of Patty and the gang are told in a stroke and dropped; school is a gesture. The paring of the novel has left atmosphere where necessity should be.
Francis Ford Coppola · Film
6.4 · Tier II
The subtractive test finds much that could go, and finds it where the film spends its time. Grace Hamilton, the photojournalist, could be removed without loss; Andrew Hagen’s priesthood is a line of dialogue more than a part; Joey Zasa’s feud with Vincent fills the first hour with a rivalry the film disposes of in a street festa; the helicopter massacre at Atlantic City clears the Commission by spectacle, not consequence; the Immobiliare deal is laid out in boardroom exposition. What resists subtraction is a spine: the purchase of absolution, the collapse in which Michael cries for Fredo, the confession, the forbidden love and the opera where the bill comes due. The spine is compelled; most of what surrounds it is assembled, and that holds the figure.