Books: Dr Milner struggles with Malevich's relationship with geometry

This study of the Suprematist artist fails to recognise that his mathematical games were metaphorical, not computational


Dr Milner’s book on Malevich deserves to stand as a prime source book for years to come, with its rich detective work and its Franco-Russian cross-fertilisation. The illustrations are superb and are placed exactly at the point where they are discussed in the book. But geometry?

The problem with Malevich is that he approached geometry as mysticism, as well as blending it with influences from astrology, Blavatsky, Egyptian mystery religion and Bergson’s time-flux, the fourth dimension and communism. The question is: how do we assess the relation between an artist’s theory and his work? For example, Dr Milner says, “The square is not a subconscious form. It is the creation of intuitive reason.” So to what degree is complex geometrical insight to be discovered in Malevich’s painting?

In attempting to examine the connection, two fallacies can lead us astray: the genetic fallacy—confusing an effect with its cause—and the Socratic fallacy—(falsely) insisting that one needs to define a thing to understand it.

On the “genetic” fallacy: Malevich’s use of mathematics does not always result in converting geometry into an aesthetic feature in his paintings. According to Dr Milner, Malevich’s painting is “a form of art based upon geometries” and it uses an archaic Russian measurement consisting of the arshin: “Without recognising the arshin (and its division into sixteen vershok) it is impossible to grasp the simplicity and grandeur of the mathematical ratios involved in the work of this period.”

Really “impossible”? Even Dr Milner finds himself trying (unsuccessfully) to explain Malevich’s use of the archaic Russian measurements by recourse to the Fibonacci series.

With regard to the Socratic fallacy, one may counter that we can understand a work of art without defining an artist’s formal techniques. This is the perennial problem of treating art as propaganda for aesthetic theories. If art has been produced by a substantial input of geometry—painting by numbers, so to speak—is geometry internal to, and a defining criterion of, the art?

It is incredible to read that Khlebnikov, with Malevich vigorously assenting, said, without a trace of irony, “I have begun writing numbers, as Number-Artist of the eternal head of the Universe.” Dr Milner lets such claims pass without comment.

Although Dr Milner acknowledges Malevich’s hermetic leanings, he seems to have discounted their distorting influence on Malevich’s mathematical ideas. Malevich’s belief in the connection between geometry and mysticism was extreme. Dr Milner notes, “The Black Square is the simplest and therefore the primary ‘generator,’ but all other Suprematist canvases have this potential for harmonic organisation of the infinite variety.”

Current mathematics and logic make terms like “simplest” difficult, but even so, as every school boy knows, a one-dimensional point is simpler—and “infinite variety” is an awful lot of variety. To us at the end of the twentieth century, who have been made humbler by our awareness of technical complexity, Malevich’s claims seem embarrassingly inflated.

Which brings us to the central problem. Dr Milner champions and describes Malevich’s claim to use geometry as the basis of his painting, but he does not explain or assess it. Malevich’s “geometry” is actually a metaphor, not a computation or mathematical function. Another book needs to be written on the boundary between the rhetorical or metaphorical use of “geometry” and the spatial projection of geometry in Malevich’s art.

Wonderful though Male-vich’s paintings are, his theoretical games were crude and should not therefore be confused with mathematics nor regarded as synonymous with his art.

o John Milner, Kazimir Malevich and the art of geometry, (Yale University Press, New Haven, 1996), 236 pp, 293 b/w ills, 27 col. ills, £40 $50 ISBN 0300064179

Originally appeared in The Art Magazine as 'Painting by numbers—(arshins and vershoks)'