If the idea of monochrome painting occurred to anyone before the twentieth century, it would have been understood as a picture of a monochrome reality, and probably taken as a joke. Hegel likened the Absolute in Schelling to a dark night in which all cows are black, so a clever student in Jena might have had the bright idea of painting an all-black picture titled Absolute With Cows–witty or profound depending upon one’s metaphysics. In 1882 the Exposition des Arts Incohérents in Paris featured a black painting by the poet Paul Bilhaud titled Combat de nègres dans une cave pendant la nuit, which was appropriated in 1887 by the French humorist Alphonse Allais, in an album of monochrome pictures of various colors, with uniformly ornamental frames, each bearing a comical title. Allais called his all-red painting Tomato Harvest by Apoplectic Cardinals on the Shore of the Red Sea.

Only in the most external and superficial respect does Kazimir Malevich’s 1915 black square painted on a white ground belong to this history. For one thing, Black Square is not a picture; it does not, in other words, depict a black square outside the frame. One of its immense contributions to the concept of visual art lies in the fact that it liberated the concept of painting from that of picturing, and thus opened up a new era in the history of art. “All paintings are pictures” would have been a strong candidate for a necessary truth until Malevich proved it false. But it was not a difference that met the eye. Had Bilhaud’s all-black painting of 1882 been square, it might have looked exactly like Malevich’s Black Square.

Black Square‘s radical difference from everything before it does not end there. Malevich’s disciple, El Lissitzky, declared in 1922 that Black Square was “opposed to everything that was understood by ‘pictures’ or ‘paintings’ or ‘art.’ Its creator intended to reduce all forms, all painting, to zero.” I think by its opposition to painting, El Lissitzky is saying that the fact that the square is painted is incidental to the work’s meaning. Malevich himself said later, “It is not painting; it is something else.” And so far as its opposition to art goes, well, you don’t have to study art to be able to paint a black square. Anybody could do it. So though it was almost certainly Malevich’s most important work, and inaugurated a new era in the history of art, it hardly seems appropriate to call it his masterpiece, just because the factors that make for something being a masterpiece don’t really apply to it. It would be curious to think of it exhibited alongside Mona Lisa in a show called “Two Masterpieces.” We marvel at its originality, not its painterly brilliance.

The idea behind what Malevich called Suprematism is that you cannot carry things beyond Black Square. It is as far as you can go: You have reached a point of absolute zero. Which isn’t to say that Black Square is empty–there is, after all, a difference between not being a picture and being a picture of nothing! Calling an empty rectangle a picture of nothing would be a Lewis Carroll-like joke, whereas everything connected with Black Square underscores its seriousness.

Consider, for example, the way Malevich first showed it in the 1915 show “0.10. The Last Futurist Exhibition of Paintings,” to which he contributed thirty-nine Suprematist works. An installation photograph shows Black Square mounted in an upper corner of the gallery, diagonally connecting two walls. This was evidently the position occupied by an icon in Russia: not hung on a wall or propped on a shelf, but in an upper corner. I think the reason would be as follows: Icons were never considered mere pictures of saints, the Madonna or Jesus himself, so they did not aspire to create an illusion, as in Renaissance art. They were not, as Alberti said, a kind of window, through which one would believe one was seeing an external reality. What one believed instead was that holy beings would actually make themselves present in their images. Theoreticians spoke of the mystical presence of the saint in the icon. And its placement near the ceiling was an obvious metaphorical entry point for beings that existed on a higher plane. A picture could be a decoration, but icons were fraught with magic. Through icons, the holy being was in our very presence, where it could be prayed to or honored. Trivially, a square is a square, not a picture of one. Malevich created reality, rather than merely depicting it. And that in a sense is what the figure in an icon was believed to be–a reality rather than a picture.

After Malevich’s death, when he lay in state, a black square hung above his head. There was a black square on his tomb. As a kind of icon, it carried a religious power. In 1920, he wrote, “I had an idea that were humanity to draw an image of the Divinity after its own image, perhaps the black square is the image of God as the essence of his perfection on a new path for today’s fresh beginning.” He clearly identified himself with the black square: It served him as a kind of signature, appearing in the lower right-hand corner of his last painting, a self-portrait. In any case, it was not a proto-Dadaist hoot.

The original Black Square is perhaps the pièce de résistance in an elegant exhibition at the Guggenheim Museum given over entirely to Malevich’s Suprematist phase (until September 14; Menil Collection, Houston, October 3-January 11, 2004). It is the first time it has been allowed to travel, and one can see why. It’s in terrible shape, so blemished by cracks and fissures that one would give it a pass at a yard sale. Its ravaged condition conveys a sense of touching vulnerability, like a martyr’s relic. In fact, Malevich painted at least four Black Squares, and it occurs as a motif throughout his oeuvre, making its first appearance in 1913, in a small pencil study for the décor of the Futurist opera Victory Over the Sun, two years before he invented–or discovered–Suprematism.

There are several of these studies in the Guggenheim show, in deference to Malevich’s belief that they are proto-Suprematist works, though at the time he considered himself a Cubo-Futurist. After Cubo-Futurism, he went through a related style, making what he described as “alogical” or “transrational” works, hardly a year before the great breakthrough that Black Square represents. I wish I knew more about the moment when Malevich decided to paint a large black square, and realized that he had hit upon something that changed the meaning of art forever, not merely purging it of any pictorial elements but stultifying the impulse to see it as a picture of unrelieved blackness. Given the momentousness he ascribed to Suprematism, one can appreciate that Malevich looked for intimations of it in his earlier work, much in the way in which scholars pore over Pollock’s pre-1945 work in search of the drip.

Victory Over the Sun was a collaborative effort by three avant-garde figures, all friends–the composer Matiushin, the poet Kruchenykh and Malevich himself. It was given only two performances, at Luna Park in St. Petersburg. There were two acts. In Act I, the sun is captured and locked up in a concrete box. In Act II, the Strong Men of the Future produce a new social order, no longer dependent on the primitive source of light that had been worshiped for centuries. Music, words and of course the sets and costumes were radical and cutting-edge: The music was dissonant, the lyrics were basic sounds in an experimental discourse called Zaum. Only fragments of the music and language survive, but Malevich’s sketches for the costumes exist (you can see them on the Internet), and there are, as well, his set designs. The set that he later singled out as Black Square‘s first appearance in his work is, according to the Guggenheim catalogue, for Act II, Scene 5. Indeed, it shows a square, divided by a diagonal into two areas, one black, the other light.

The truth is that the drawing in question has the look of something seen through a square opening in some sort of optical instrument, like a segment of the sun against a dark sky. It really looks like a picture.

Here is a better way to look at the question. In one of Malevich’s studies for the opera’s décor, there is a black square and a number of black rectangles–a large vertical one, and then two sets of three black rectangles at various angles to one another on either side of it. But in the same drawing there are a number of other components–some large letters, some numerals, a foot, a hand holding what looks like a bomb, a cigarette with smoke–and a number of mere marks–circles, waves, hooks, indications of the edges of overlapping planes. It is an example of an “alogical” or “transrational” drawing, a drawing whose various components (some abstract, others representational) don’t cohere as a composition. The alogical drawings have something of the disorder of dreams, as Freud attempted to characterize them when he suggested that we approach them like rebus puzzles–concatenations of pictures that seem to have no rational connection with one another.

Now imagine laying a piece of transparent paper over Malevich’s drawing and simply tracing the black geometrical components, disregarding all the rest. The result will look like a Suprematist drawing of 1915, consisting of a number of free-floating rectangles together with a square. It is as though Malevich’s drawing had a Suprematist drawing inscribed within itself. But this would have been invisible until Suprematism was invented two years later. Suprematism consists in getting rid of all the objects other than the geometrical ones. When that has been done, one is left with a nonobjectivist work, and Suprematism is virtually synonymous with what came to be called Non-Objective art.

The term was first used by Rodchenko in connection with his Black on Black Painting (1918), but Malevich made the concept his own, and published a book, The Non-Objective World, in 1927. It is worth mentioning that the Guggenheim Museum was originally called the Museum of Non-Objective Painting when it was located on East 54th Street in Manhattan, and one really felt as if one were entering a nonobjective world when one visited it. Most of the paintings consisted of shapes floating in empty space, many of them by Rudolph Bauer, the lover of the director, the Baroness Hilla Rebay, who used to sit at the reception desk, eagerly discussing the philosophy of nonobjectivity with anyone interested. There were a lot of Kandinskys and perhaps some Mirós and Mondrians. I don’t know if there was anything by Malevich, but there were some at the Museum of Modern Art, including the famous White on White. It was a great place to take someone one felt moony about, and hold hands on the round gray velvet settees.

Very little of Malevich’s Cubo-Futurist work of 1914, with which the Guggenheim show begins, or the alogical drawings and paintings of the following year, is especially rewarding unless you think of Suprematism as struggling to emerge from the early avant-garde clutter. But when one enters the gallery of 1915 masterpieces, there is a sense of liberation that must, one is certain, recapture Malevich’s own feeling when he broke free and entered what he regarded as unoccupied territory. The paintings convey a feeling of utter glee. One feels as if one were witnessing the beginning a new era, where the history of art has been left behind forever. The Russian avant-garde was obsessed with the idea of the fourth dimension, which its members read about in the mystical writings of Pyotr Demianovich Ouspensky. The fourth dimension was not an extra parameter in some dry equations but rather a living reality that one could hope to enter, like a new world. Ouspensky, a Theosophist, believed that artists were uniquely capable of making the fourth dimension vivid for individuals who are otherwise locked in their three-dimensional perception of the world. That is what the great Suprematist paintings convey–the optimism and generosity that defined the art of the Russian avant-garde at the dawn of Modernism, when it saw its mission as bringing art into life, and contributing, through art, to the creation of a new social reality, a vision initially embraced by the Russian Revolution before the perversions of Stalinism.

The smooth geometries and whitish spaces of Suprematist painting, using brilliant colors and jaunty compositions, were a vocabulary of hope and idealism. They could symbolize all the bright modernities for which the art stood–syncopated rhythms; the fourth dimension as a field of infinite explorations; the radical redesign of contemporary clothing, housing and cities–and above all, they could express speed and flight. “I have torn through the blue lampshade of color limitations,” Malevich wrote in 1919, “and come into the white. After me, comrade aviators sail into the chasm–I have set up the semaphores of Suprematism!”

All the Suprematist compositions lift the spirit. Let’s just consider Airplane Flying. It is, of course, not a picture, so don’t bother to look for the airplane. What it captures, rather, is the feeling of flight. The flight begins at the bottom-right corner, with a tilted black square. Along the diagonal that its angle defines are two black rectangles, one larger than the other, with two thin whiz lines on either side, marked by thin black rectangles. At the upper edge of the largest black rectangle, direction changes–we get a flight of yellow rectangles, heading for the upper-right corner, crossing a long, nearly horizontal thin red rectangle as it goes. “My new painting does not belong to the earth exclusively,” Malevich said in 1916. “The earth has been abandoned like a house eaten up with worms. And in fact in man and his consciousness there lies the aspiration toward space, the inclination to ‘reject the earthly globe.'”

This is how the future used to look. Then came the Depression, Stalinism, fascism, the two world wars, the cold war. The poor mangled Black Square shows how that once-bright future looks now. It is like the ashes of hope, and in its way a memorial to Malevich himself, as the future collapsed around him. He died a poor man, disgraced and erased from the history of art according to the Soviet Union.