Where the law ends

A statue with no head

At the top of the Daru staircase in the Louvre, a marble goddess stands on a ship’s prow, wings spread, her robe pressed to her body by an unseen wind. She has no head and no arms, and her right wing is a plaster restoration. This is Nike, the Greek goddess of victory. Charles Champoiseau, a French diplomat, found her in April 1863 on the island of Samothrace, then Ottoman and now Greek, in about 110 fragments, says the Louvre. She reached Paris in May 1864 and has stood at the head of this staircase since the 1880s. Her head and arms have never been found. Parts of her right hand have: fingers in 1875 and the palm in 1950. The Louvre dates her to 200–175 BC, “probably” about 190.

This course draws a lesson from her, and it belongs to the law of extremes (Lessons 3 and 4): an artist takes one element out of a harmonious whole and pushes it as far as it will go. That is this course’s own interpretive thesis, a way of reading modern art, not a settled fact of art history. In this reading, classical art does not simply copy a body. It uses the body to carry a hidden design of balance and proportion, and when the surface breaks, as with the Nike or the armless Venus de Milo (found on Milos on 8 April 1820), we glimpse the design. Modern art does the opposite: in Mondrian’s grids and Malevich’s square it strips the figure away and puts the structure on the wall, bare.

Two points of precision first. English often calls all ancient Greek sculpture “classical,” but strictly neither statue belongs to the Classical age: the Nike was carved early in the second century BC and the Venus around 150–125 BC, both in the Hellenistic age. Nor is the Nike’s pose the textbook contrapposto, the relaxed stance of a standing figure with one leg easy, as in Polykleitos’s Doryphoros, a bronze of about 440 BC that we know only from Roman marble copies. She is not at ease. She is landing.

“Great because broken” is also only a reading. In 1909 the Italian poet Filippo Tommaso Marinetti declared in the first Futurist manifesto that a roaring racing car “is more beautiful than the Victory of Samothrace.” Neither reaction shows that a hidden design is the reason. Even the pale silhouette is partly modern: Greek statues were painted, and the Louvre’s restoration of 2013–14 found traces of blue on her wings.

What the Greeks measured

There is real evidence that Greek sculptors thought in numbers. Polykleitos of Argos, working in the fifth century BC, wrote a treatise, now lost, that later writers called the Canon. One saying from it survives, quoted by the engineer Philo of Byzantium: perfection comes about “little by little” (para mikron) through many numbers. The physician Galen reports that it set each part of the body against the others, finger against finger and the fingers against the palm and wrist. Roman marble copies of the Doryphoros survive in Naples and Minneapolis, but the numbers are unknown. The archaeologist Rhys Carpenter judged that nobody had recovered the recipe, and that still stands. A popular account says Greek sculptors measured countless people and averaged them; we found no source for that. What the sources support is smaller: a famous sculptor wrote that beauty came from many small number relations.

The idea outlived the statues: in Book III of De architectura, the Roman writer Vitruvius set out the proportions of the human body, and around 1490 Leonardo drew a man in a circle and a square to match. For the Greek habit of finding number in beauty and harmony in the heavens, see Course 1, Why science began in Greece.

In painting, one hidden geometry is documented. Between about 1415 and 1420 the Florentine architect Filippo Brunelleschi experimented with linear perspective, and around 1435 Leon Battista Alberti described the method in De pictura. Its core is a rule: parallel lines running away from the viewer meet at one point. In Leonardo’s Last Supper (about 1495–98, Milan) the lines of the room meet at Christ’s head (sources differ on the exact spot). The structure is hidden under the figures, as this course’s picture says, and anyone with a ruler can find it.

The golden line that was not there

The series this course draws on goes a step further: every classical painting hides a line at the “golden section,” about 0.618 of the picture’s width, which Mondrian then shows. This is folklore. The ratio is real. Euclid, about 300 BC, defined it as cutting a line in “extreme and mean ratio,” and Luca Pacioli’s Divina proportione (1509), illustrated by Leonardo, treated it in the geometry of solid figures. But the earliest known printed use of the term golden section dates from 1789, nearly three centuries after Leonardo, and phi became its symbol only from about 1910. Nobody has shown that painters worked this way.

The astrophysicist Mario Livio said in 2002 that the literature is “bursting with false claims and misconceptions” about the ratio in the arts, naming Giotto, Seurat, and Mondrian. On the Mona Lisa, he wrote, no document shows that Leonardo used it on purpose. The mathematician George Markowsky challenged the Parthenon claims in 1992. Hunts for golden lines succeed for a simple reason, which the next activity shows: count a picture’s features, decide how close counts as “on” a line, and the odds of at least one hit climb fast.

The same folklore reaches the seventeenth century. This course’s example is Nicolas Poussin’s Et in Arcadia ego (the Louvre’s version, 1637–38), where shepherds find a tomb inscribed “Even in Arcadia, there am I.” Two corrections. The woman beside them is not a goddess; she is said to be modeled on an ancient Roman statue, the Cesi Juno. And Poussin did not create the French Academy. The Académie royale de peinture et de sculpture was founded in 1648 by twelve artists around Charles Le Brun, while Poussin, in Rome since 1624, spent only December 1640 to autumn 1642 in Paris and died in Rome in 1665. His ideas, drawing before color, shaped its doctrine.

A black square in the corner

On 19 December 1915 by the Russian calendar then in use (1 January 1916 by ours), an exhibition opened in Petrograd (now Saint Petersburg) with a title like a countdown: 0,10 (Zero-Ten): The Last Futurist Exhibition of Paintings. It ran into January with some 150 works by 14 artists, 39 of them by one painter. High in the corner of his room, where a Russian Orthodox home hangs its icon, was Black Square by Kazimir Malevich, a Kyiv-born painter of the Russian avant-garde: oil on linen, on a canvas 79.5 centimeters square, now in the State Tretyakov Gallery in Moscow. A black quadrilateral, its corners not quite right angles, sits on a broad painted white ground, and the catalogue called it simply “Quadrilateral.” In a letter of May 1916 Malevich called it a bare, frameless icon of his time. In his manifesto of the time he wrote, “I have transformed myself in the zero of forms,” and he named the new art Suprematism.

Popular accounts tie the square to the October Revolution of 1917. It was shown nearly two years earlier. Nor was it a bolt from the blue. Malevich worked in a Cubo-Futurist style in 1912–13, and his designs for the Futurist opera Victory over the Sun (1913) included a curtain with a square outline, which he later named as the square’s first appearance. He later dated the square itself “1913,” on later versions and in documents, backdating it to the opera. In 2015 X-rays at the Tretyakov revealed two earlier paintings under the black, and its researchers concluded that the square was not spontaneous.

This course follows Mondrian rather than Malevich because Mondrian shows the road in small steps, while the square looks like a flash of insight, hung where an icon goes. That is half true at best. Malevich’s route also had steps, from Cubo-Futurism to the manifesto, and in 1918 it led on to White on White (Museum of Modern Art, New York).

Nor was he “wiped out.” In autumn 1930 the secret police arrested and interrogated him in Leningrad on suspicion of spying, and released him before the year was out. In his last years, under growing pressure, he painted figures again, a turn he had begun in the late 1920s, and he died of cancer on 15 May 1935. He was laid out beneath a Black Square and given a Suprematist funeral, with a black square carried on a banner. Some colleagues were less lucky: Vera Ermolaeva was shot in 1937, Gustav Klutsis in 1938. For Malevich, “silenced” is the fair word, and the pressure on him was real.

An empty room and a white canvas

Yves Klein pushed on another element. The Void (Le Vide) ran from 28 April to 12 May 1958 at Iris Clert’s gallery in Paris, opening on Klein’s thirtieth birthday. The room was empty and painted white, with a blue window, a blue curtain at the entrance, Republican Guards at the door, and blue cocktails. His own color, International Klein Blue, was pure ultramarine pigment held in a synthetic resin. In 1962, the year he died, he coated a small plaster cast of the Victory of Samothrace in it. Accounts often say he patented the blue. He did not. On 19 May 1960 he deposited a Soleau envelope (no. 63471) with the French industrial property office, which records a date. It is not a patent.

On 9 March 1960, in a Paris gallery, three models covered in blue paint pressed their bodies against paper while musicians played Klein’s Monotone-Silence Symphony: a single D-major chord, held, and then silence (twenty minutes of each, in the score). Klein, in white tie and gloves, never touched the paint. He called the method “the technique of living brushes” (our translation), and the critic Pierre Restany named the pictures Anthropometries. The series this course draws on links them to Leonardo’s Vitruvian man and the Shroud of Turin. Klein left no statement tying them to Leonardo; the shroud is critics’ language, though he did title some imprints Suaire (“shroud”). By this reading’s own test, which is to keep going until nothing is left, an empty room goes further than a white canvas.

Artists said the canvas was spent, and white came early. Malevich reached it first, with White on White in 1918, and in 1919 he urged viewers to swim out into the white, free abyss of infinity. In Moscow in 1921 Alexander Rodchenko showed three canvases, pure red, pure yellow, and pure blue, at 5 × 5 = 25; by his own account years later, he had taken painting to its logical end and declared it finished. In 1951, at Black Mountain College in North Carolina, Robert Rauschenberg painted all-white panels. John Cage wrote in 1961 that they were “airports for the lights, shadows and particles.” They were first shown in summer 1952, in a Cage performance piece, and in New York in September 1953. The three-panel version now at the San Francisco Museum of Modern Art is believed, the museum says, to have been painted by Brice Marden in 1968, as Rauschenberg allowed: the idea mattered, not the hand. In August 1952, at Woodstock, New York, the pianist David Tudor played nothing for the length of Cage’s 4′33″, which Cage said came after the white paintings.

Ad Reinhardt, who painted square, nearly black canvases in the 1960s, is often quoted, in several versions, as calling them the last paintings anyone can make. The exact wording is unconfirmed. “White is the end” was an opinion several artists held, not a fact of art history.

The cut, and what came next

Lucio Fontana (1899–1968), an Argentine-born Italian artist from Rosario, worked mostly in Milan. He pierced canvases with holes from 1949, two years before Rauschenberg’s white panels. This course reads his cut as the turn: when white ends the road, the artist leaves it, and Fontana opens the canvas. The first cuts (tagli) date from 1958, not the 1960s: a blade drawn through a single-color canvas. He titled such works Concetto spaziale, “spatial concept,” with the subtitle Attesa, “waiting,” for one cut or Attese for several. In 1967 he told the critic Carla Lonzi that by piercing the canvas he had created “an infinite dimension.” He was speaking of the holes, not the cuts.

The neat story has two problems. First, white came long before the cut, from Malevich in 1918 on; Klein’s empty room opened in April 1958, months before Fontana’s first cuts; and his holes came before the white panels. So the road did not end in white and then turn. Second, a cut that opens a surface is not clearly a turn away from the extreme. It can be read as one more step along the same road, breaking the flat surface that Clement Greenberg, in Lesson 3, called painting’s own ground.

Art did not stop. In April 1964 Andy Warhol showed his Brillo Boxes, printed to look like supermarket cartons, at the Stable Gallery in New York. That October the philosopher Arthur Danto asked why Warhol’s box was art when the ordinary cartons, which look just like it, were not. His answer was something the eye cannot see: a certain theory of art. In 1967 Sol LeWitt wrote that in conceptual art “the idea becomes a machine that makes the art.” None of these is a last painting.

So how does the law of extremes do? Supported: many artists did choose one element (color, shape, emptiness) and push it, and some said they had reached the end. Not supported: a single road ending in white, since white came early, in 1918, Klein’s void goes further by the course’s own test, and Barr’s own 1936 chart split into two branches; a forced next step; or the idea that this is the only story. Linda Nochlin’s “Why Have There Been No Great Women Artists?” (ARTnews, 1971) and Okwui Enwezor’s “The Postcolonial Constellation” (2003) ask whose road it is. This course’s practical moral, which you can take or leave, is that an idea pushed hard should leave a way to turn. As a lens the law is useful. As a law, it is unproven.