The Fifth Desk · Evaluation
Act I · The Map
Piet Mondrian · oil on canvas, 127 by 127 cm, a square hung square · the single painting scored: a grid of yellow lines broken into small units of red, blue and grey, with larger rectangles of colour across and between them, on an off-white ground, and no black · painted in New York, 1942 to 1943 · The Museum of Modern Art, New York, since 1943 · finished and signed in the painter’s lifetime, whole and unaltered after him
Mode
Abstract painting as rhythm; the painter’s grid with its black line taken out and its colour made the structure
Mythos
The city as a new world, the dance named in the title, and the grid as the order of the universe, the last built as doctrine
Phase
Painted in New York, 1942 to 1943, about two years after the painter arrived from London; finished within a year of his death
Presentation
Oil on a square canvas of 127 by 127 cm, hung square: yellow lines broken into units of red, blue and grey, larger rectangles across and between them, an off-white ground
Register
High joy and a constant brightness; a flicker the eye cannot settle
Scale
One square, the size of a window, seen whole and read in detail from one standing distance
Governing Proposition
A square of off-white canvas, 127 centimetres a side, is crossed by yellow lines, and every line is broken along its length into small units of red, blue and grey, so that it no longer divides the field but pulses across it. There is no black anywhere. The wager of the canvas is that a painter of seventy could take out the element his system rested on and keep the system, and that a fixed grid of right angles, the most static of forms, could be made to carry a city and its music without depicting either.
Act II · The Essay
Movement I
The canvas is square, 127 by 127 centimetres, and it hangs square, not turned on its corner as a lozenge. On an off-white ground run yellow lines, vertical and horizontal, to the edges or near them, and every line is broken along its length into small units of red, blue and a light grey, set at irregular intervals. Across the lines and between them sit larger rectangles of colour, several holding a smaller rectangle of another colour inside them. There is no black anywhere on the canvas. The title is the painter’s.
At first sight it is a square of light about the size of a window, alive at every edge. The small units seem to travel along the yellow lines as the eye moves over them. The large blocks read now as lying on the surface and now as set back behind it, so that the field opens and closes. The eye cannot settle anywhere, and the whole canvas stays bright. It is delight, not grandeur: the square is the size of a person’s torso, and it is made to be seen whole and read in detail at once, from where one stands.
Piet Mondrian painted it in New York in 1942 and 1943, at seventy, about two years after he arrived from London in October 1940. The Museum of Modern Art acquired it in 1943, the year it was finished, and it has been in that one collection for eighty-three years. It is a single painting, finished and signed in his lifetime, and it is scored alone. His other New York canvases, the transatlantic pictures begun in Paris or London and reworked in New York, and his writings stand around it as context.
Movement II
From about 1920 Mondrian painted by one system, which he called Neo-Plasticism and had drawn out of Cubism: black lines on white, a few planes of primary colour, and a balance that is never symmetrical. He held it for two decades and it made him famous. In his doctrine, inflected by theosophy, the meeting of vertical and horizontal was the meeting of spirit and matter, male and female, the cross as the order of the universe. Every painting he made under the system carries that grid.
In the classic compositions the black line is a boundary. It divides the field, and the colours sit in the compartments it makes. Every position was worked for balance, so that nothing tilts. The authority of the painter rested on the rigour of the system, and the black line was its central element.
In New York the line changed. In New York City (1942, Centre Pompidou) the black is already gone and the lines are coloured. The unfinished New York City I, in Düsseldorf, is laid out in coloured tapes. A painter of seventy had overturned the element his system rested on, at the risk of seeming to abandon his own doctrine. Broadway Boogie Woogie takes the turn one step further and completes it.
Movement III
The step is to break the coloured line itself. A line made of units is a beat; an unbroken line is a boundary. Broken into small squares of red, blue and grey, the yellow lines no longer divide the field but pulse across it, and balance becomes rhythm. The large rectangles are the slow accents against that fast pulse. Take one away and the rhythm loses an accent and the balance tilts; take away a yellow line and the field loses a beat. Only at the scale of the small unit could a red square be blue, or sit a little further along, without loss.
The square carries the rest. No direction dominates it, and the vertical and horizontal pulses are equal, as the grid of streets is. The canvas resembles neither Manhattan nor a piano, and both are in it: the city as a structure of intervals, the music as a structure of pulse. And it shows that order and motion are not opposed. A fixed grid of right angles, the most static of forms, is made to vibrate, and equilibrium is shown as something dynamic rather than at rest. Without black the colours are not held in compartments; they are the structure, and the field is all light.
The placing was searched for, with moving tapes and repainting, and visible repainting in places shows a search not always resolved. Four hues and a white are calibrated so that no unit dominates: the yellow light enough to read as line, the red and blue weighted so the small units balance across the field, the grey a rest. The edges are painted, not masked in the final surface, straight without the deadness of a ruled line; the whites are worked and the colour planes built up. Every element is a rectangular plane of pure colour, horizontal or vertical, with no diagonal, no curve, no mixed colour and no second kind of mark.
Movement IV
The title names the music and the dance, and Mondrian was a known dancer. In an interview with James Johnson Sweeney in 1943, as usually reported, he set true boogie-woogie beside his own painting: the music did away with melody as his painting did away with natural appearance, and both built instead from the steady opposition of pure elements. The words are paraphrased here because their wording cannot be fixed.
The city as a new world, the exile’s arrival in the grid of Manhattan with its lights and traffic, comes with the title and with the painter’s late history, and the canvas carries it as atmosphere. Broadway on a night in 1942 is named, and evoked, and stays a name. What the canvas makes plain is a condition of modern life, the city lived as rhythm. Much of what it gives besides is a state, exhilaration and pulse.
The city, the music, the dance and the moving eye are one rhythm seen four ways. A fifth order, the universal equilibrium of the painter’s doctrine, is held in the grid as doctrine and is not made visible. Everything else is absent: no person, no family, no labour, no state, no story. The war the painter had fled is outside the frame.
Movement V
Mondrian died in New York on 1 February 1944. On the easel was Victory Boogie Woogie (1942 to 1944, now in the Kunstmuseum Den Haag), a lozenge, unfinished. Whether Broadway Boogie Woogie completes his system or dissolves it, with the next step left unmade, is still argued, as is whether it is a structure or an optical event, whether its tie to jazz is analogy, translation or only a title, and whether the blocks that advance and recede break his own law of the flat plane.
It hung at the Museum of Modern Art from 1943, before the postwar generation of New York painting, and the American abstract artists around him carried it on. The all-over field of equal intensity, the optical painting of the 1960s and the grid of later painting and Minimal art have claimed it as a source, and Krauss’s essay “Grids” (1979) takes Mondrian as its type. Much of his reach belongs to the compositions of the 1920s and 1930s rather than to this canvas. Outside painting its reach, into design and into the image of the modern city, is very wide.
The canvas has never been cut or altered after the painter, and it has been on view almost continuously since 1943. His built-up whites are known to crack and yellow in his paintings; how far this one shows it is not known here. His manner has become the most copied style in modern design, and a style become a pattern risks being seen through its copies. So far the canvas has outlived them. The small units still travel along the yellow lines, and the eye still cannot hold the pulse at rest.
Act III · The Twelve
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.
Score: 8.7 / 10
Two things can be stated, through image, and they hold. A pure abstract order can be the image of a lived place and its music without depicting either: the canvas resembles neither Manhattan nor a piano, and both are disclosed in it, the street grid as a structure of intervals and the music as a structure of pulse. And order and motion are not opposed: a fixed rectilinear grid can be made to vibrate by breaking its lines into beats, so that equilibrium is shown as dynamic rather than at rest, the painter’s own claim made visible. These are propositions about the city lived as rhythm, plain to anyone before the canvas. Held below the top because much of what it gives is a state, exhilaration and pulse.
Score: 8.1 / 10
Elevation is real and of one kind: delight, a lifting of the spirits, the eye kept moving by a flicker it cannot settle. It comes at the first sight, a square of light alive at every edge; in the small units, which seem to travel along the yellow lines as the eye moves; in the large blocks, which read now as on the surface and now as set back, so that the field opens and closes; and in the absence of black, which leaves the whole canvas bright. What holds it is height of kind: no grandeur, no terror, no transport by scale, for the square is the size of a person’s torso, not of a room. The brightness is sustained across the field rather than rising to recurring summits.
Score: 8.0 / 10
The archetypes are present and mostly evoked. The city as a new world, the exile’s arrival in the grid of Manhattan with its lights and traffic, comes with the title and the painter’s late history, and the canvas carries it as atmosphere. The grid itself, in his theosophically inflected doctrine, is the meeting of vertical and horizontal, spirit and matter, male and female, the cross as the order of the universe; it is built into every painting he made from about 1920, as doctrine, not acquired by a particular. The dance, the body moving to a beat, is set in the title by a painter known as a dancer. Broadway on a night in 1942 is named and evoked, and does not become archetype on the canvas.
Score: 7.6 / 10
The inheritance is the painter’s own: Neo-Plasticism as he fixed it from about 1920, black lines on white, a few planes of primary colour, asymmetric balance, held for two decades and made famous, with the Cubism he drew it from behind it. The departure: black is gone; the line is made of colour; the line is broken into units, so that it no longer divides the field but pulses across it; balance becomes rhythm, and a fixed system a field of movement. A painter of seventy whose authority rested on that system overturned its central element, at the risk of seeming to abandon his doctrine. Held below the top because the coloured line without black was begun in New York City (1942) and the tape works, and the tradition left is one he had made himself.
Score: 8.8 / 10
Would a different form change what the work knows? Almost entirely. The broken line is the knowledge: a line made of beats is a rhythm, an unbroken line is a boundary, and the canvas knows the city and the music only because its lines are made of units. The absence of black is the knowledge: with black the colours would sit in compartments; without it they are the structure and the field is all light. The square is the knowledge: no direction dominates, so the vertical and horizontal pulses are equal, as the grid of streets is. The size lets the field be seen whole and read in detail at once. Held a step below the top because the form completes a system, and part of what it knows the system already knew.
Score: 9.1 / 10
Evidence over promise: eighty-three years of continuous return in one of the most visited collections in the world, and a large literature. The questions stay open: whether the canvas completes Neo-Plasticism or dissolves it, with Victory Boogie Woogie the next step left unmade; whether it is a structure or an optical event, and how far it anticipates the optical painting of the 1960s; whether its relation to jazz is analogy, translation or title; how it was made, with tapes and repainting; whether the blocks that advance and recede break the painter’s own law of the flat plane. The canvas yields at two distances and never settles. Held below the top because many of the questions concern the system and the late turn rather than this canvas alone.
Score: 8.6 / 10
Field: abstract painting in New York and Europe in the 1940s. The intrinsic force: a reorganisation of the grid, from a structure that divides to a field that pulses, and of colour, from an infill to the structure itself; with Victory Boogie Woogie, the last move in the century’s most rigorous programme of abstraction. The discount: much of the painter’s reach belongs to the compositions of the 1920s and 1930s, not to this canvas. Achieved reach is scored with intrinsic force: at the Museum of Modern Art from 1943, before the postwar New York generation; carried by the American abstract artists around him; claimed as a source by the all-over field, the optical painting of the 1960s and the grid of Minimal art, with Krauss’s essay “Grids” (1979) taking Mondrian as its type; and very wide in design and the image of the modern city.
Score: 8.7 / 10
Weighed on form, then presence, then fabric. Form: whole, one canvas, never cut, never altered after the painter, eighty-three years old. Presence: as wide as any modern painting has, on view at the Museum of Modern Art almost continuously since 1943, reproduced without end, its standing never eclipsed; fame is presence, not proof, and lifts the figure only a little. Fabric: oil on canvas. The painter’s built-up whites are known to crack and yellow in his paintings; how far this canvas shows it is not known here, and no more than the general risk is charged. Against it too, the manner is the most copied style in modern design, and a style become a pattern risks being seen through its copies. So far the canvas has outlived them.
Score: 9.1 / 10
Judged as command of oil on canvas in a medium of interval and colour, to the same anchors as any medium. The making is load-bearing at every point. Colour: four hues and a white calibrated so that no unit dominates, the yellow light enough to read as line, the red and blue weighted so the small units balance across the field, the grey a rest. Interval: the placing of the units along the lines, irregular and never random, is the rhythm, and was searched for by moving tapes and repainting. Edge: painted, not masked in the final surface, straight and exact without the deadness of a ruled line. Surface: the whites worked, the colour planes built up. The costs: the range of mark is narrow by design, and visible repainting in places shows a search not always resolved.
Score: 9.0 / 10
Take the two most distant elements: a small grey square set in a yellow line near the edge, and a large red rectangle holding a smaller square of another colour within the field. They obey one law: rectangular planes of pure colour, set horizontal and vertical on a white ground, in a balance that is never symmetrical. Every element is that law at some size; there is no diagonal, no curve, no mixed colour and no second kind of mark. The law is total. But narrowness is not coherence, and the territory is small by choice: four colours, two directions, one kind of form. Within it the range from line to block and from fast beat to slow accent is wider than in the classic compositions, and the law holds across it. Held for the territory’s size.
Score: 8.9 / 10
An abstract field holds few orders, and this one holds five: the city, as a structure of streets and movement; music, as pulse and syncopation; the body, in the dance the title names; consciousness, in the viewer’s eye kept moving by the field; and a cosmic order, the universal equilibrium of the painter’s doctrine, held in the grid. The first four are integrated, one rhythm seen four ways; the fifth is present as doctrine and not made visible. What holds the axis lowest of the twelve is what is absent: no person, no family, no labour, no state, no story, and no history, for the war the painter fled is outside the frame. The figure describes the form.
Score: 6.6 / 10
Act IV · The Reckoning
8.4 / 10 · Final Average
Placement: Tier IV · Canonical
Strongest Dimensions
The Living Form and The Imperishable at 9.1, then The Made at 9.0 and The Inner Law at 8.9. A form in which the broken line, the missing black and the square are the knowledge; a single canvas, whole and on view for eighty-three years, that has outlived its own copies so far; a command of interval and colour load-bearing at every point; and one law of rectangular planes of pure colour holding from the smallest unit to the largest block.
Limiting Dimension
The Encompassed at 6.6: the city, the music, the dance and the moving eye are one rhythm, and the order of the painter’s doctrine is present only as doctrine; the person, the family, labour, the state, story and history are absent. Below the rest, The Archetypal Deep at 7.6, The Sublime at 8.0 and The Unconcealment at 8.1: Broadway is named and evoked rather than made archetype, the elevation is delight without grandeur, and much of what the canvas gives is a state of exhilaration. The four are one fact: a square of pure relations that holds a city as rhythm and nothing that lives in it.
The Necessity Cap clears at 8.7 against a threshold of 7.5. The Coherence Floor clears with room: The Living Form at 9.1, The Made at 9.0, The Inner Law at 8.9, each against 7.0. The Epochal Gate is unmet: The Imperishable at 9.1, The Swerve at 8.8 and Pressure on Tradition at 8.7 clear the bar of 8.5, but The Unconcealment at 8.1 falls short by four tenths and The Archetypal Deep at 7.6 by nine. The Universal Minimum is met (no axis but The Encompassed falls below 7.6, against 7.5) and The Encompassed, which is exempted, clears its own floor of 6.0 at 6.6. The twelve sum to 101.2, an average of 8.43 that displays 8.4.
Basis · a reading from knowledge of the canvas as it hangs at The Museum of Modern Art in 2026, well known from reproduction and from an extensive literature; its composition, format, colour, date and history are known securely, and its present condition is not known in detail. The work scored is the single painting, oil on canvas, finished and signed in the painter’s lifetime: nothing in it is lost or replaced, and it has not been altered since him. New York City (1942), New York City I, Victory Boogie Woogie, the transatlantic canvases and the writings on Neo-Plasticism are context, evidence of the sequence the painting belongs to, and are not scored. No words of the painter are quoted: his remarks to James Johnson Sweeney in 1943 are paraphrased, since their wording as usually given cannot be fixed. The fragility of the whites and the copying of the manner are weighed only as facts of survival, and neither is charged to the painter. Facts that could not be verified are not given, among them the number of lines and units, the gallery where the canvas was first shown, the terms of its acquisition, and the present state of its whites.