A mathematician I once knew used to take an impish pleasure in pretending not to understand what artists meant by “geometric form.” All forms, he tirelessly observed, were indifferently geometric. And he explained, with aggressive patience, the uncontested facts of analytic geometry to the sullen painers in his company. In point of pedantry, he was infuriatingly right. every point in a plane has a unique pair of real numbers as coordinates, and since every form is a locus of points, any form, however loopy to the eye, can be represented by an equation. No form, accordingly, is especially more geometric than any other so far as algebraic method is concerned. So why especially paint squares and bars and circles when the lush presences of the visible world–young girls, flowers, the surging sea, grazing cows, and dancers at the Bal Tabarin–are no less geometric? Why, in the name of geometry, cut oneself off from the myriad shapes of the world as it is?
The artists before whom he laid these impeccable reasonings were uncomfortable and finally unimpressed, and they were right to be so. It would be perverse to designate the “Last Judgment” of Michelangelo or Turner’s “The Slave Ship” as geometric paintings, even if one could point to hidden trapezoids and obvious diagonals. The term “geometry” invokes, in even the most modestly informed, austere scenarios enacted by circles and spheres, by polyhedrons and polygons of unimpeachable regularity, which chastely intersect one another or submit to the bloodless martyrdoms of being cut by planes or inscribed by lines. The etire lore of cones, cubes and cylinders, triangles and pyramids, parallelograms and rhombohedrons had assumed mythic status in Western consciousness long before the introduction of coordinate analysis by Descartes in 1637. The use of pyramids to house the preserved bodies of pharaohs, the fact that the altar of Apollo at Athens had the form of a cube or that the heavens were believed composed of crystalline spheres in harmonic relationship to one another, were not semiotically innocent choices. They were comprehensible in terms of a language of forms which Kepler drew upon only a few decades before Descartes’s discovery, when he exulted, alas without foundation, at having found the key to the solar system in the five regular Euclidian solids that marked the spaces between the planets. Only such a geometrically ordered universe would be worthy of a Perfect Designer, Kepler supposed; he was disgusted to discover not long afterward that the planetary orbits were ellipses rather than the circles celestial perfection would recommend.
Confronted by such facts, my friend would raise his circumfex eyebrows in mock surprise. “Oh,” he would say through the perfect circle his lips formed on such occasions. “But I thought geometrical art was supposed to be modern.” And there he would have a point. There truly is a paradox in the fact that once liberated by the possibilities of abstraction from the need for perceptual replication, painters reverted to forms they had learned to constrct as schoolchildren with tin compasses and ink-stained rulers. Why should geometric forms carry the cachet of modernism from the first decade of the twentieth century down to the present? Why should postmodernism seem to consist in postgemetricism?
There is no single answer to the first question, since succeeding geerations og geometric painters responded to very different artistic imperatives. The Russian Constructivist Aleksandr Rodchenko, for example, programmatically empoyed geometric forms generated by such instruments as compass and straightedge specifically to obliterate personality. A circle executed by a compass and another executed freehand by an artist with the exquisite reflexes Giotto is said to have possessed might be perfectly congruent, or at least indistinguishable to the unaided eye–but the circumstances of their execution carry an invisible meaning. The submersion of personality, in that overheated period of artistic utopianism in Russia, went with a natural celebration of the community, of the mass, of what anyone with the right tools could draw. rodchenko meant to present himself as subservient to this. But for Giotto the circle was a signature, almost a gesture or arrogance, declaring that no one but he could have made it.
consider some further examples. There is a drawing of about 1922 by El Lissitzky showing Rodchnko’s great contemporary, Vladimir Tatlin, working on his visionary–and unrealized–Monument to the Third International. Tatlin’s face is featureless, but there is a compass protruding from his right eveysocket, his head is framed by a circular arc suspiciously like a halo and he holds a straightedge with the authority of Prospero displaying his staff. The Monument to the Third International rejects figuration as roundly as Rodchenko rejects personality. Tatlin would have been agonized to see the heroized worker-and-soldier monuments that came to dominate the open places of Soviet cities. He instead favored an impersonal ordering of geometric solids almost like that of the universe according to Kepler: the lowest story of his monument was to have been a cube, the second a pyramid, the third a cylinder topped by a hemisphere. The stories were given over to different functions and were to rotate at different velocities; the whole complex was encased in a scaffolding reminiscent of a powerful telescope. It was to be a place not of contemplation but of agitation, and you, as visitor, should “be mechanically taken up, carried away against your will.” It was a lesson in submission to forces as overwhelming as social metaphysics could imagine.
The famous “Black Square,” shown by Kasimir Malevich in a turbulent exhibition in St. Petersburg in 1915, carries another meaning. That simple shape was dese with the intended erasure of the whole of Western art. It went beyond represetation, since it was in fact a square, not the representation of one. It went beyond illusion, since it was not in pictorial space but coextensive with the canvas. It was hung across a corner rather than conventionally on a wall, declaring a whole new concept of exhibition. The black could have been a gesture of defiant mourning for the death of all previous art. It was conceived as a radical beginning, and as such conveys an altogether different meaning from any we might ascribe to squares done by Josef Albers or Ad Reinhardt, or by some more recent Minimalist. It was an icon of revolutionary consciousness, not a symbol of artistic distillation.
The Russian Modernists are featured in a show of seven decades of geometric abstraction called Contrasts of Form, on view at the Museum of Modern Art until January 7. The exhibition is in acknowledgment of a generous donation to MOMA of the extensive and deep Riklis Collection of the McCrory Corporation. This collection is, according to its curator, Celia Ascher, largely constructivist in spirit. MOMA has responded by placing it in the format of a chronicle of geometric art from 1910 to 1980, augmenting it with examples of relevant art already in the museum’s collection and prefacing the whole with certain Cubist and Futurist works from which the Russians made their severe projections and reductions. I was not happy with the format, nor for that matter with the title, since it is not the forms that contrast so much as the meanings of forms, which may themselves be quite similar. Befoe offering some argumets for critical disquiet, however, I want to return to the sort of historical concerns that constructivism and its immediate predecessor, Suprematism, express.
Standing in the gallery where these fragile, small, somewhat empty and faded objects hang in their protective light, looking almost like specimens of tissues preserved for an obscure scientific purpose, I could not but wonder what the casual visitor, Unaware of the passionate social and esthetic controversies which brought them into being, might see in them. They were, in effect, the product of an antiesthetic esthetic, a repudiation of beauty and pleasure, of grace and elegance, os suavity and feeling. The traditional values of art were held at bay by works that were almost constituted by the tension of not yielding to them. Painting as it was known was declared obsolete. Inevitably monochrome, deliberately dulled, the little works took on the puritan drabness, the antidecorative utilitarian blankness, of communist architecture and city design–or even costume, as in the blue work-clothes of Chinese. The materials are as consistently countertraditional as possible: a scrap of burlap, some wrapping paper, a bit of tin, some string. This was not in the exuberant spirit of French collage, which inspired Apollinaire to write, “One can paint with whatever one likes, with pipes, postage stamps, postcards or playing cards, candlesticks, pieces of oilcloth, detachable collars, wallpaper, newspapers.” Nor was it in the spirit of redeeming base materials for artistic transifugration, as in the work of Kurt Schwitters. My mathematician friend might, consistent with his position on form, have observed that since any material could be used, why not gold leaf, marble or bronze? And the answer is that it was precisely such materials that had to be rejected as bourgeois: one professed proletarian solidarity by using the simplest of industrial materials to constitute the most mechanical of forms in the most modest compositions on the least prepossessing scales.
Everything that gives these eviscerated objects force and structure is present by exclusion, but it is invisible to the historically uninformed eye. It is a mockery of their intensity of artistic purpose to treat them formalistically, or as exercises in pure design, to be graded by criteria students at the Bauhaus had to meet. It is demeaning to see them as other than allegories of a hopeless revolutionary consciousness, destined to be blown sky-high by forces those who created them could not have anticipated. The galleries here are suffused with the weight of political tragedy and, if you like, artistic exalatation. It is against the doctrinaire condesations of this advanced art that we can, finally, appreciate the early Chagall, whose boisterous colors, vivid fantasy, poetry, wit and opulence constitute a gesture of defiance as fragrant as, say, Marilyn Monroe in full glamorous regalia at a workers’ meeting of the hydroelectric plant of Tientsin. In the willed desert of principled Constructivism, Chagall was magnificent.
And this is what bothers me about the exhibition. Only at the most superficial evel is there much community between these works and those which, in a formal or material way, influenced them or were influenced by them. The efficient and final causes of history are missing here. The linear chronology dissolves the meaning of geometry by treating the works merely as stages in the steady stream of abstraction. But Mondrian’s geometrizing arises out of different passions from Tatlin’s, Moholy-Nagy’s forms arise out of a different theoretical atmosphere from those of Sol Lewitt, Kandinsky’s out of a conception of spirit alien to van doesburg. The exhibition could only have been illuminating had it broken the continuity and related the impulses to geometry to the different domains of though that produced them.
The catalogue, by Magadalena Dabrowski, is immeasurably better than the exhibition it illuminates, just because it does furish the kind of information the works cry out for. Walking amid the circles, rectangles, grids, diagonals and squares, I flet like Odysseus among the bodiless spooks of the nether world. Odysseus is able to communicate with them only by giving them blood he has brought along for the purpose. The thirsty spirits, momentarily transfused, revert to something like their former vibrant selves. Some of the blood these paintings and constructions so desperately require is furnished by Dabroski’s exemplary text. In the rooms devoted to “The Paris-New York Connection: 1930-1959,” filed with paintings that seem robust by comparison with the withered membranes of Construcivist art, it is useful to know that “for the generation of the 1930s, geometric abstraction became a style rather than a philosophy.” Had this been printed in large letters on the wall, the differences would have come to life. all modern painting before the 1930s was held erect by philosophical belief defended with nearly religious enthusiasm and intensity. It was the age of manifestoes, and the idea that painting was something one might do independently of a fervent and utopian project was all but unthinkable. In 1925 Mondrian broke with De Stijl because of van Doesburg’s insistence on the diagonal. Diagonalists, if I may characterize them thus, differed from Perpendicularists as Catholics differ from Protestants on the topic of communion. Here is the way van doesburg preaches the diagonal:
The purest and, at the same time, the most direct means of expression of the human spirit, which recognizes neither right nor left, neither symmetry, nor statics, nor the exclusively horizontal-Vertical but is always in revolt, in opposition, to nature.
It is a standard criticism of laboratory science that the world beyond the sterile walls of experimental space is so rich and complex that what is found within them can rarely be projected outward. Such criticism is most convincing in connection with living things, and the injunction to study them ethologically, in their natural atmospheres, becomes more compelling as their behavior becomes more nuanced and reflective. Something like this should be true of works of art as well. It is a premise of formalism that they stand on their own, containing in temselves all the information we equire to understand them. An exhibition of geometric abstraction is a crucial test for such views, just because the works seem most amenable to formalistic analysis. But this is an illusion. The current show fails to comply with the simple direction laid down in Celia Ascher’s prefatory remark: “Collecting should follow a defined path of exploration and scholarship, rather than the willy-nilly road of the eclectic contemporary.” This show, for all its marvelous contents, is willy-nilly eclectic. all a work needs to get in is some sort of geometric credential, plus the right date and place of birth. The curatorial mind is fixated on chronology and influence but blind to the philosophy that animates art and ought to animate its intelligent display.
Riklis believes, rightly, that his collection is “of significant esthetic and educational value.” But the esthetic access is blocked by educational negligence, and if it were not for Dabrowski’s catalogue, the show would have been a failure. Without it, the scraps and bits of geometry are puzzling and mute–scarcely the bare beauty on which Euclid is said to have looked.