The law of extremes

A lemon on a table

In 1635 a painter in Haarlem, Willem Claesz. Heda, set a banquet table on a canvas about 107 by 111 centimeters (42 by 43¾ inches), his largest known still life. It is now in the National Gallery of Art in Washington, where it is called Banquet Piece with Mince Pie. Pewter plates and a pitcher, glass goblets, a gold chalice, a brass candlestick, and the remains of a pie are heaped on a white cloth over a dark green table. At the left edge lies a lemon, cut so that its rind curls down in a long spiral over the edge of the table. The museum notes that the rind, the plates, and a knife are set over the edge to make them seem to reach into our space.

Heda’s skill is likeness: you can tell pewter from glass from pastry. His arrangement is calm, and a quiet message sits inside it. The museum reads the snuffed-out candle as a sign of how suddenly death can come, and a cut lemon is often read as pretty to look at and sour to taste, though scholars argue about how much any one lemon was meant to say. In this course’s reading, likeness, design, craft, feeling, and meaning share one frame, and none is allowed to take over. Even so, one thing here is pushed. Heda painted his tables almost entirely in grays, and the Rijksmuseum in Amsterdam calls the range of gray tones he could paint astounding.

Two things in the popular telling need fixing. Heda is sometimes described as a painter nobody remembers. He was a leading still-life painter of Haarlem, and museums on both sides of the Atlantic still hang him. And “classical” here means an established tradition, not Greek or Roman classicism: a Dutch table is not a Greek temple. The art historian Svetlana Alpers argued in The Art of Describing (1983) that seventeenth-century Dutch pictures are above all an art of describing the world, rather than telling stories from scripture or myth. That is why Heda makes a good starting point. He shows a whole in which nothing has been pulled out.

One element, pushed to its limit

This course proposes a way to read what happened next. In the tradition Heda belongs to, line, color, likeness, feeling, structure, and skill are held together in one harmonious whole. In modern and contemporary art, it argues, an artist again and again lifts one of these out of the whole and pushes it as far as it will go, until it cannot go further. Then the road has reached its end, and the next artist has to turn. The course calls this the law of extremes (极端法则).

Treat it as a hypothesis, because a hypothesis can be tested. If the law is useful, you should be able to take a painter, name the one element he lifted out, and watch him push it step by step. Mondrian is the clearest case this course has, which is why this lesson follows him.

Critics have long noticed a pattern like this. The closest is Clement Greenberg’s. In “Modernist Painting,” an essay written for a Voice of America lecture series and usually dated 1960 (it was printed in 1961), he argued that each art became modern by removing whatever it borrowed from the others, so that painting was left with what it alone has, a flat surface. The resemblance is real, and so are two differences. Greenberg’s end point is one thing, the medium itself, not any element pushed in any direction. And he insisted that modernism is continuity with the old masters, not a break with a harmonious whole. He is a famous cousin of this thesis, not a witness for it.

The first thread

In this reading, the painter who pulled the first thread was Vincent van Gogh, and the element was feeling. In a letter to his brother Theo from Arles in August 1888, he wrote that instead of copying exactly what was before his eyes, he used color more arbitrarily, to express himself forcefully (letter 663). In June 1889, at Saint-Rémy, he painted the Cypresses now in the Metropolitan Museum of Art: two dark trees that twist and flame in thick strokes, his hand as visible as the tree. Yet that month he told Theo that the cypress was beautiful in its lines and proportions, like an Egyptian obelisk (letter 783). Even the painter of feeling looked for structure. What matters here is the shape of the move: feeling had always shared the picture with likeness, and now it begins to lead. As Lesson 1 argued, once photography could copy the world, a picture could carry something a camera could not, the painter. Older painters had hands too: Heda’s grays were his own.

From a tree to a grid

Piet Mondrian (1872–1944) was born in Amersfoort, in the Netherlands. His Evening: The Red Tree (1908–10, 70 by 99 centimeters, Kunstmuseum Den Haag) sets one tree alone, a habit the museum traces to Van Gogh shows in Amsterdam, and it calls the painting an explosion of fiery red and cobalt blue. A popular telling says this tree came before Picasso’s Cubism, so that Mondrian found his road alone. It did not. While he painted it, Picasso and Braque were inventing Cubism in Paris, and in 1908 a critic wrote of Braque’s “cubes.” Mondrian first saw their work in the autumn of 1911 in Amsterdam, at the first Moderne Kunstkring exhibition in the Stedelijk Museum, which he helped organize: twenty-eight works by Cézanne and others by Picasso and Braque.

The activity below lets you slide through the steps that followed. Gray Tree (1911) was painted in Holland before he left; whether before or after the show is not known. In grays alone its branches echo in arcs, and its museum calls the influence of Cubism enormous. At the turn of 1912 he moved to Paris and dropped an “a” from “Mondriaan.” In Flowering Apple Tree (1912) the trunk is hard to find, and the gaps count as much as the branches. From 1914 he sat out the war in Holland, mostly in Laren, and turned from trees to the sea. Coast drawings led to Composition 10 in Black and White (1915, Kröller-Müller Museum), sometimes called Pier and Ocean: short black horizontals and verticals gathered into an oval, his first painting in black and white alone. The museum says the breakwater is still recognizable in the vertical lines at the bottom. In 1917, after meeting Bart van der Leck, a painter of flat primary colors, Mondrian brought color back as floating planes of dark rose red, deep blue, and dark ochre (Composition in Color A). By 1918 he was painting regular grids, and by 1921, back in Paris, the grid had opened into the form most people know: black lines, flat planes of red, yellow, and blue, and what he called non-color, white, gray, and black.

In this course’s reading, each step lifts something out of Heda’s whole. The subject goes, then the curves, then depth. Color leaves twice, in 1911 and 1915, and comes back flat and pure. What is pushed furthest is structure: the bare lines and rectangles that hold a picture up. Mondrian’s own words complicate this. In October 1917 Theo van Doesburg launched a magazine, De Stijl (“The Style”), whose first issue opens with Mondrian’s essay: every relationship in nature, he wrote, is governed by one, “that of the extreme one and the extreme other” (our translation, like the Dutch quotations below). The thesis pushes one element to its limit; Mondrian’s extremes are a pair, held in balance. Even on this road there was a boundary. In the mid-1920s (sources say 1924 or 1925), Mondrian left De Stijl after Van Doesburg, who had started the magazine, proposed diagonal lines. Mondrian kept to horizontals and verticals.

A program, and a hand

The road was more than a method. Mondrian joined the Dutch Theosophical Society in May 1909, and the books of the former priest Mathieu Schoenmaekers (1915 and 1916) greatly influenced him. In January 1914 he wrote to the Dutch critic and collector H. P. Bremmer that he wanted to “abstract everything” until he reached “the foundation of things”: something universal, which no single tree could show. The law of extremes describes only the second half of that story, the method of reduction. The aim is Mondrian’s own, and you cannot read it off the pictures.

Nor was the method cold. In the same letter he called his lines “constructed consciously but not calculated” and “led by high intuition,” and in 1918 he wrote in De Stijl that the artist “cannot place himself entirely above the subjective.” The paintings bear him out. In 2001 two Harvard curators, Harry Cooper and Ron Spronk, examined eleven Mondrians with imaging and found that he composed by eye and revised in an “intuitive and exploratory” way, a process they called “quite physical, almost violent.” He took canvases off their stretchers and scraped old paint away. Behind the pure line there is a hand. (Later retellings add that the effort made him faint or wrecked his health. We found no source for either.)

In one canvas of 1921, Composition with Red, Black, Yellow, Blue and Gray (Kunstmuseum Den Haag), the museum finds colors that are not truly primary and a white that is not truly white. He moved lines, took some out, and nudged others, and the bottom edge is almost 1.5 centimeters shorter than the top: attentive and precise, the museum says, not perfect. And people like to say that he built his grids on the golden ratio. No one has shown that he did. The astrophysicist Mario Livio, in 2002, listed Mondrian among the artists about whom the literature is full of “false claims and misconceptions.” Whether the golden ratio belongs in classical painting is a question for Lesson 4.

Which way is up?

The picture that stands for the road’s end in this course is Composition with Red, Blue and Yellow (1930, Kunsthaus Zürich), which Mondrian painted at the request of a friend, the Zurich architect Alfred Roth. It is only 45 centimeters square, with a large red field at the upper right. He painted his initials and the year, “PM 30,” at the lower left, and on the back, on 30 January 1930, he wrote a dedication to Roth in French: the fine work of today, it says roughly, is to reckon only with relationships, creating them and seeking their equilibrium, in art and in life. The museum records that when he repeated the layout on larger canvases, five centimeters bigger each time, he kept the width of the black strokes. On one of them, Composition No. II (51 centimeters square, privately owned), the stretcher bears one word, according to its 2022 auction catalog: Haut, “top.” So the way up is on record; the question is only whether feeling can find it. If he placed every line by feeling, this course argues, a quarter turn should leave a corner short of weight. Try it below.

What does the evidence say? In 2000 the researchers Latto, Brain, and Kelly showed thirty Liverpool undergraduates eight Mondrians, half of them diamond-shaped, each turned in eight ways, for five seconds at a time. People preferred horizontal and vertical lines to tilted ones, and the original beat every tilted turn. But among the upright turns, only the half turn scored clearly lower. A quarter turn, the very test above, made no reliable difference. In 2012 the psychologist George Mather reported that viewers picked the intended way up of abstract paintings about half the time, against one in four by chance. Feeling finds something, then, but the effect is small, and it is different from knowing.

Museums have missed it, too. A story circulates of a museum that could not tell which way up to hang a Mondrian. We could not trace it. The documented cases are two. In 1941, in New York, Mondrian began New York City I in oil and colored paper tape, and left it unfinished and unsigned. The Kunstsammlung Nordrhein-Westfalen in Düsseldorf bought it in 1980. In autumn 2021 the Italian artist Francesco Visalli wrote to the museum about a photograph of Mondrian’s studio, taken days after his death in 1944, in which the picture stands the other way up. In October 2022 the curator Susanne Meyer-Büser announced that it had probably hung upside down since it was first shown, in 1945: the denser lines belong at the top, “like a dark sky.” The museum left it as it is, because the tapes are “hanging by a thread,” and it allowed that Mondrian may have turned the picture as he worked, so that there may be no right or wrong way up at all. The second case is Matisse’s cut-paper The Boat (1953), a boat and its reflection. It hung upside down at the Museum of Modern Art in New York for 47 days in 1961, while some 116,000 visitors passed it, until a stockbroker, Geneviève Habert, noticed on her third visit. The New York Times reported it on 5 December.

The law, tested

What does Mondrian tell us about the law? It fits well in one way: the staircase from Red Tree to the grid is this course’s best case of a road in which each step keeps less of the whole. It fits badly in others. The road was not straight: he turned to the sea, color left and came back, and he kept painting flowers to sell. The result is not pure idea, because there is a hand behind it. It is not only reduction, because the aim was spiritual, and his own extremes came in pairs. And it was not one road. In this reading, Van Gogh gave Mondrian feeling, Cubism gave him structure, Theosophy gave him an aim, and Van der Leck gave him flat color, which makes four roads, where the popular telling names two.

Mondrian crossed to New York in the autumn of 1940 and died there of pneumonia on 1 February 1944. In New York the black lines went: Broadway Boogie Woogie (1942–43, oil on canvas, 127 by 127 centimeters, Museum of Modern Art) has none, only yellow lines broken by small blocks of red, blue, and gray. It is often read as the grid of Manhattan, laid out in the Commissioners’ Plan of 1811 with 12 avenues and 155 cross streets. That is a common reading, not something we know he said. In this reading even he turned, and the painter who pushed structure furthest had written of equilibrium on the back of a small canvas in 1930. Where the road of extremes really ended, and what came after, is the question of Lesson 4.