PRINT December 1978

Malevich and Khlebnikov: Suprematism Reinterpreted

To man’s actual existence there belongs a surrounding world, just as the statues of a god have a temple. This is the reason why we must mention the manifold threads which link the ideal (or the beauty of art) to externality and are drawn through it. . . .
—G.F. Hegel, Lectures on Fine Art

IN JUNE 1915, FOR THE occasion of the last Futurist exhibition in St. Petersburg, Kasimir Malevich published a treatise entitled From Cubism and Futurism to Suprematism: The New Pictorial Realism, which asserted that “. . . all painting past and present before Suprematism was reduced to servitude to the forms of nature and is looking forward to its liberation in order to speak its proper language. . .” Later, in the Non-Objective World (1928) Malevich wrote: “Art no longer cares to serve the state and religion. It no longer wishes to illustrate the history of manners. It wants to have nothing further to do with the object as such and believes that it can exist in and for itself . . . in the pure art of Suprematism.” More than 60 years later, in a totally different cultural and socioeconomic context, Michael Heizer gives an equally uncompromising viewpoint as an annotation to his piece Cement Slot, 1969, in Bern: “The cathedral personifies much that corrodes art. Art has been subjected to thousands of years of utility (magic), justification (religion) and decoration (architecture). Art fits into this environment like a subservient bauble. Utilitarian nuances pervade the contemporary dialogue . . . ”

The juxtaposition of these corresponding statements by Malevich and Heizer could be supported by visual material. Not that the visual resemblances between their (and many others’) works should be construed in terms only of stylistic affinities. On the contrary, these visual similarities suggest intriguing parallels between Russian art of the ’teens and 1920s and some American art of the 1960s, if one looks at works by Altmann, Stepanova, Rodchenko, Tatlin and others as compared with Reinhardt, Tony Smith, LeWitt, Andre, Morris, Serra and others. It is thus especially important in comprehending developments in more recent art that the work and artistic milieu of Malevich be accurately understood.

Visiting Richard Serra in his studio in 1973, I recall his remark about one of his black-and-white charcoal drawings being “. . . too much like Malevich . . .” However, I consider a simple formal comparison of this nature as being problematic, almost irrelevant, with regard to the understanding of specific artistic intentions and, hence, general cultural significance. Any analytical examination of the artistic meanings of Malevich and American artists of the 1960s should consider the proper cultural frames of reference. For once art moves in the direction of an analytical, conceptual or, philosophically speaking, an epistemological path—as in the case of Malevich—esthetic theories of style and preconceptions of art as an autonomous entity collapse.

Analogous are the ways which lead to the construction of artistic truth in painting and poetry: color, lines, planes—the end itself in painting: the conception of the artist; the word, its graphic form, its phonetic aspect, myth, symbol—the conception of the poet.
—Vladimir Mayakovsky, Speech at the Union of Youth, November 1912

Contemporaneous with the growing reflection on language (the work of deSaussure, Wittgenstein, Sapir, Whorf, et al.) Kasimir Malevich (as opposed to the abstractions of Kandinsky or Mondrian, for example) made in his work a fundamental attempt to reflect on images and painting per se, and their relation to nature and reality. Here, and not, as is often claimed, with Duchamp, the self-reflection on painting as such, and on painterly values, begins.

Usually, the artistic development of Malevich is explained by way of formal steps, from Italian Futurism to French Cubism and gradually increasing toward an abstraction of mimetic images up to his final break with the mimesis of Occidental art in the Black Square on White Ground. This is described as an evolutionary process, one which is familiar to us from the formally consistent evolution of French art, particularly in the Cubist developments of Picasso and Braque. Yet the case of Malevich, I intend to show, follows an essentially different path, the origins of which have to be sought not in an internal consistency of a formal genesis (as with Mondrian for example) but in extra-pictorial stimulations, in the context of his fellow poets and in their poetic theories. For the generally philosophical, partly epistemological interests of the Russian avant-garde appear not only in the writings by artist-authors like Burliuk, Shevchenko, Markov-Matvejs and Matyushin, among many others, but also specifically in Malevich’s artistic development and his essays. That Malevich’s sudden step into the nonobjective world, into pure geometrical forms, should be explained by more than its formal development Malevich himself asserted in his essay Suprematism as Pure Cognition: “Suprematism developed neither out of Cubism nor out of Futurism. . . . since nonobjectivity is not something that can develop out of anything else; always the sole and only question is, whether something is cognized or not.” Precisely this question is relevant to the following discussion of possible “cognitions” around 1913 that may have contributed to the creation of nonobjective formulations in Malevich’s work.

Up to now, “the question, whether something is cognized or not” has rarely been dealt with in the literature on Malevich—and then only in metaphysical terms. The critics’ complementary interpretations, differing only in details, represent Malevich’s development, in typical neo-Kantian fashion, either through purely formal deductions (geometrical tendencies toward “total abstraction”) or through delicate exegeses of Malevich’s texts, interpreting them simply metaphysically, textual explications placing Malevich in the philosophical traditions of Plato, Kant, Hegel, Berdiaev (the Russian scientist and mystic), Bergson, et al., and even—post festum—of Heidegger. Critics have been nearly unanimous in stressing the influence of the theosophically oriented philosopher Peter D. Ouspensky, a monarchist sympathizer, and, specifically, of his neo-Kantian metaphysical scientific speculations on the “Fourth Dimension” as the “Highest Intuition.” These efforts to explain Malevich’s Suprematistic creations on a formalistic level even go so far as to refer to the irrelevant, simply formally corresponding, geometrical illustrations and theories of American scholars like Hinton and Bragdon. Only the art historian Andersen opposed the influence of the books on the “Fourth Dimension” by Hinton, Bragdon, etc.: in connection with Malevich’s Black Square, he refers, if aphoristically, to the formulations of Einstein on the new axiomatic geometry and mathematics in his book Geometry and Experience, which was not even published until 1921. Hardly any account is taken of the specifically national situation in the natural sciences, geometry and mathematics,1 although this would have obvious relevance to the world of Malevich’s forms, which is so closely related to that of scientific geometry. Nor has any comparative analysis been done of the work and poetic theory of the eminent artist and friend of Malevich, Velimir Khlebnikov, himself a former student of mathematics, although his name is often mentioned.

Actually, one of the means to a better understanding of Suprematism may be sought in Malevich’s immediate cultural environment: in the widely respected personality of Khlebnikov, a dominating figure of these years, and in the relationship between art and science as manifest specifically in the relation of Khlebnikov’s poetry to mathematics, which he articulated with uncharacteristic thoroughness.

This relation between science and art was later to be common, too, in the fine arts, in Constructivism and especially with Lissitzky, the pupil and colleague of Malevich.

Recently I have come to number-writing; this is an art which develops out of the scraps of modern science, just as the customary sort of painting, accessible to all, is qualified to absorb the natural science.
—Velimir Khlebnikov, My Own

L’idée de l’espace comme une convention picturale, du temps ideéographique, s’infiltre dans la science de l’art. Mais le problème du temps et de l’espace comme formes du langage poétique est encore étranger à la science.
—Roman Jakobson, On Khlebnikov, 1919

The relation between art and science on the one hand and to Khlebnikov on the other finds an echo as early as 1913 in Malevich’s pictorial oeuvre. Only two obvious graphic examples from 1913 will be discussed here: the lithographs Simultaneous Death of a Man in an Airplane and on a Railway and a hardly noticed work bearing the title (written on the stone itself) Arithmetic—the Science of Numbers, a title undoubtedly connected with the ideas and concepts of Khlebnikov.

While a few of Malevich’s illustrations printed in the course of 1913 display a thematic and stylistic relation to his paintings, this subject is completely new to the visual arts. Iconographically one notices in the otherwise nonobjective picture an only partly visible house (whose smoking chimney probably indicates its familial state) and a series of mostly half-hidden numbers and letters not arranged in any obvious compositional order. The number “7,” set conspicuously in the center of the page, and the primary letter “A” strike the eye immediately against a background of geometrical radial constructions (“linée-force”), together with other arithmetical signs. In the March edition of the journal Union of Youth, Khlebnikov had just recently written in his “Conversation between Two Persons”: “The seven stages of the moon’s ascent to earth recall the seven heavens and much else with ‘seven.’ But it is precisely in the numeric names that we recognize the ancient face of man. Is not ‘seven’ (sem’) the truncated word for ‘family’ (semya)?” The use of the numeric word or name occurs often in Khlebnikov’s work as well as the conception of a semantic meaning of the alphabet, which might ultimately establish a “new way of seeing.”

Malevich’s lithograph Arithmetic is an interesting example of a stage in his development toward nonobjectivity. The choice of pictorial elements like numbers, mathematical signs and letters cannot be explained by traditional iconography, but we do find these thematic elements in the publications of Khlebnikov.

Also revealing in this context is Malevich’s print Simultaneous Death of a Man in an Airplane and a Railway, which, though likewise thematically unique, nonetheless recalls in its formal execution the Universal Landscape from the same year. The theme is suggested first in the contemporary discussions of Italian futuristic conceptions of technique, velocity and simultaneity, but is related as well to Russian discussion of space/time, as we will see.

With this quite unusual title, Malevich addresses the mathematical-physical problematic of most recent times—the problematic of the relative relationship of space and time, the space/time-continuum (which was also a favorite theme of Khlebnikov), and the simultaneity of events at different, mobile locations. This problematic and its epistemological background were treated by Khlebnikov’s former teacher, Alexander Vasilyev, an eminent mathematician and influential champion of the discoveries of Lobachevsky, who discussed this matter at the latest in his book New Ideas in Mathematics (1913). Vasilyev’s writings contributed significantly to the popularization of Lobachevsky’s ideas and the problematic of Einstein’s Special Theory of Relativity (1905). Thus, for example, Vasilyev quoted Lobachevsky: “The motion of one body, if it is taken as the measure of the motion of another body, is called time”—an understanding of space and time that Vasilyev rediscovered in Einstein’s Special Theory of Relativity: “The objects of our perception invariably include places and times in combination. Nobody has ever noticed a place except at a time, or a time except at a place.” He described Einstein’s new and fundamental perception in these words: “Two events which appear simultaneous to one observer will appear nonsimultaneous to the other,” and contrasted this with Newton’s traditional conception of time, “which flows uniformly without any relation to any outside object.” The title of Malevich’s painting can refer only to this issue of space and time as formulated by Einstein in 1905 and by Minkowski three years later.2 Its combination of “simultaneity” (time) with objects moving at different rates (space) becomes meaningful only against the background of these scientific findings.

Yet another often-cited event had brought Malevich into close contact with his poetic colleagues Khlebnikov, Kruchenykh, Mayakovsky, Guro, and others: the production of the opera Victory over the Sun, with music by Matyushin, a libretto by Kruchenykh, an introduction by Khlebnikov and costumes and scenery by Malevich. However, the idea that in the costume sketches (especially in light of the recently discovered drawing shown) one could already perceive the beginnings of Suprematism is based on an inadequate notion of the conception of Suprematism’s nonobjectivity. Even though a sharply reduced geometrical form can be seen in the torso of the figure, this form must still be seen in the closest connection with figural representation and has, therefore, to be understood as mere reduction of forms observed in nature following the tradition of Cubism. One look at Picasso’s Farmer’s Wife, 1908, from the Shchukin Collection in Moscow (with which Malevich was surely acquainted), shows Malevich’s stylistic origin and obligation still in this Cubist period: feet, arms and individual parts of the body were already conceived as somewhat flat surfaces to a similar degree by Picasso around 1908, and even the unity of the figure itself, despite the more drastic geometrical reduction by Malevich, is comparable to Picasso.

The earliest rudiments of the nonobjective compositions of Suprematism can be seen rather in some of the sketches for the scenery of this opera. However, all the plans for the scenery are based on a foreshortened schematization of the box-stage; diagonal lines lead from the outer boundaries of the stage, in the form of a square, to the stage backdrop, which is not schematized by a square (as is always claimed), but by a vertical rectangle. The proportions, which are given on the lower line of the rectangle (10 to 8) in most of the sketches, thus probably correspond to the actual dimensions of the stage.

In the present context two sketches are particularly interesting. The first, which separates the background into a black and white triangle, is often taken to be the first manifestation of Suprematism. But it can rather be seen as the representation of a part of the sun against the dark universe, especially since, as has been correctly noted, the diagonal before the left angle actually touches the bottom line, and thus, strictly speaking, forms only one triangle, that of the sun. Far more instructive, however, is the sketch, also recently discovered, of scene i of the first act. This is the drawing that comes closest to the world of Suprematism: nonobjective formal elements like parallelograms and trapezoids, such as appeared already in the work Untitled, are arranged in such a way within the scheme of the stage, and are so related to each other, that they counteract the illusionistic space of the stage. The resulting two-dimensional effect breaches the dictum of representational space (of representing “objects of nature”—Malevich). That the beginnings of the Suprematistic world of forms could be seen in one of these sketches was later intimated by Malevich in a letter to Matyushin: “This drawing will have great significance for painting. What had been done unconsciously is now yielding extraordinary results” (May 27, 1915). And the phrase “unconsciously” is worthy of note: not the “unconsciously” created forms for the decor and costumes of the opera, but only a subsequent act of “cognition” was thus responsible for those “extraordinary results”—Suprematism. So, too, Malevich wrote to Matyushin in 1913: “ . . . a different kind of reason has arisen within us . . . it also has its own law, construction and meaning, and only when we have cognized it will our works be founded on the truly new law of transrationalism.”

I am thinking of a complex work “Diagonally through the times,” where the rules of logic, time and space are broken as often as the drinker regularly reaches for his glass of liquor.
—Velimir Khlebnikov, Letter to Kamensky, 1909

Chez Khlebnikov, les comparaisons ne sont presque jamais justifiées par une impression réelle de ressemblance entre les objets, mais apparaissent en fonction de la composition.
—Roman Jakobson, 1919

In the literature on Khlebnikov one finds numerous references to his intensive relationship to science, to mathematics and numbers in particular. So, for example, he is aptly characterized by Luda Schnitzer, who has been translating his prose and poetry since 1967:

. . . in short, the passion for numbers and the veneration of the first non-Euclidean mathematician Nikolai Lobachevsky. Like all those who were born on the banks of the Volga, Khlebnikov had a passionate attachment for the great river, the route from the Indies taken by Russian navigators and symbol of liberty: “Volga where at night they sing Razine.” He never forgot the boats of the “free folk” and their revolutionary ataman. Khlebnikov loved and admired both Stepan Razine, the force of nature fighting for his people’s freedom, and Nikolai Lobachevsky, the force of science, who shattered the hold of Euclidean law. ‘I am Razine hoisting the standard of Lobachevsky,’ said Khlebnikov. That is what he wanted to be for poetry: a liberator. And that is what he was.

Biographical data reinforce this description of Khlebnikov: he was born in 1885 in a village of the Ukraine; in 1903 he began the study of mathematics at Kazan University, where Lobachevsky had taught and where the Lobachevsky Congress was held annually from 1893 on. In 1904 Khlebnikov also began to study the natural sciences and remained with the physics/mathematics department until 1908. Khlebnikov’s early interest in mathematical and scientific problems continued through his life. Thus, in his essay “Contention for Priority” (1914), he spoke of Lobachevsky and Chebyshov, another eminent Russian mathematician: “Space is more objective than numbers. Lobachevsky tried to construct a second nonexistent objective world, and Chebyshov gave a more beautiful structure not to the objective, but to the already existing world of numbers.” In one of his earliest prose pieces (dated to 1904, the time of his studies in Kazan), we read: “He found the true qualification of the sciences, he linked time with space, he created the geometry of numbers . . .”

Brief reference has been made to the influence which Khlebnikov had not only on the poets, but also on the painters of his time, through his own poetical practice and, above all, through the often epistemologically oriented statements to be gleaned from his works. In this sense Mayakovsky and others called Khlebnikov a “poet for producers,” a “poets’ poet.” Just as mathematicians like Poincaré, Jouffret and others—besides such well-known authors as Apollinaire, Bergson, Mallarmé and Denis—had a significant influence on the development of French Cubists, so Khlebnikov played an analogous role for the Russian avant-garde. His poetic preoccupation with the “autonomous value” of the word as such—the “autotelic word,” as he himself termed it, the “zaum-language” or “transrational language”—could be explained, as it often is, from the tradition of Rimbaud, Mallarmé, French and Russian symbolism, or of Potebnya, the famous Russian linguist. But we must also take into account analogous developments in mathematics, geometry and arithmetic—an area to which Khlebnikov devoted particular attention in his utilization of numbers as semantic unities and, thus, as a means for poetic language.

In the course of the 19th century, mathematicians like Hamilton and Lobachevsky had determined and gradually realized that mathematics—arithmetic as well as geometry—was not a science that could be verified in the physical world by experiments alone; rather it must be understood as an axiomatic, purely intellectual discovery of the human mind. The development of an “abstract geometry” (Lobachevsky), which is consistent in and for itself, the development of an “abstract algebra” (Hamilton et al.) and an “axiomatic arithmetic” (David Hilbert) was typical of the 19th century. Bertrand Russell’s remark in 1901 characterized this movement at the threshold of the 20th century: "The nineteenth century, which prides itself on the invention of steam and evolution, might have derived a more legitimate title to fame from the discovery of pure mathematics.

This trend toward axiomatic mathematics, i.e. abstract theory which by definition is consistent only in itself, can be noted increasingly in Khlebnikov’s prose and lyric poetry, although his awareness of history and nearly encyclopedic knowledge prevented his use of the “autotelic” word from solidifying into a dogmatic principle of style, as it had for Kruchenykh. Far more essential to Khlebnikov’s poetry was the historical and evolutionary development of the human mind and its products, like language and culture. Thus in the dialogue “Teacher and Pupil” he gives to the pupil the following programmatic speech on the relation of science to culture and language: “Only the development of science will enable us to decipher the total wisdom of language, which is wise because it was itself a part of nature.”

The degree of Khlebnikov’s familiarity with the latest developments in science is revealed clearly in the quotations cited earlier about the logic of space and time and his understanding of the space/time-continuum—an insight which he also brings to expression in his essay “Time, Measure of the World” (1915): “If two twin concepts exist, then they are space and time . . . some [Hamilton] consider algebra to be the theory of a possible time. The primary truths of time should not speak about how it could be, but how it is.” With his comprehension of the physical world, Khlebnikov stood at the forefront of a scientific discussion whose philosophical consequences imply the rejection of Kant’s category of the “synthetic a priori,” which, in any event, followed necessarily from the breakthrough in physics, at least since Lobachevsky’s non-Euclidean geometry. In a prose work published in 1913 Khlebnikov called Kant a “cobbler”: “That is all that remains of a thinker, of this thinker.”

Khlebnikov’s preoccupation with science coincides with an increase in his literary production, which at first remained within the framework of the Symbolist tradition. As early as 1910, however, he caused a stir in literary circles with the publication of the famous poem “Incantation by Laughter,” which consisted of neologisms. In this poem we perceive for the first time the tendency toward the “autotelic word,” the “word as such,” as it was called in the proclamation of 1913—or zaum-language, “transrational” language, as it was later conceptually defined.

Dealing with words often from linguistic aspects, and interpreting them as esthetic unities, is characteristic of Khlebnikov’s work in particular. The following discussion will focus on four aspects of the “autotelic” word which form the cornerstone of a cubo-futuristic “esthetic” and its application, and which are especially interesting with regard to the artistic development and practice of Malevich.

(1) The formation of neologisms: in contrast to Kruchenykh, who was rarely interested in linguistic problems, the alteration of words in Khlebnikov’s poetic diction occurs not on a lexical but on a grammatical level, to emphasize the “inner form of the word.” This technique should not be considered primarily as an esthetic isolation of the word; rather it signifies the self-reflection of language, “meta-language,” the examination of linguistic material and its syntactic and semantic dimensions. As the linguistic theorist Boris Eichenbaum remarked in 1923, “The interest of the Futurists in the meaningless word, the ‘transrational’ (or zaum) language, lay in their efforts to create a new, namely oral-semantic element of the word—and not the word as symbolic sound, but the word as a direct articulation of real meaning.” Thus the numerous attempts to place Khlebnikov in the tradition of the Russian and French Symbolists are to some extent imprecise and misleading: they were principally interested in an esthetic formation and utilization of language, while the striving for a semantic analysis of linguistic material can be seen first in Khlebnikov: “To create words is to burst linguistic silence, the deaf mute layers of language.”

As Jakobson remarked in his 1919 article on Khlebnikov, we are to see in his semantic as well as phonetic deformation of words “nonobjectivity” (bespredmietnost) as “an important possibility of poetic neologism”; in Khlebnikov’s poetry, according to Jakobson, words first lose their objectivity, then their inner, and finally even their outer form: “The law of poetic etymology still holds, the inner and outer forms of the word are experienced, but what Husserl calls the ‘objective reference’ is lacking. An example of the realization of a ‘nonobjective’ neologism: ‘The fairy has peaceing shores. Peacelings grew here and there, white amidst the raven’s nest. Beneath however it was overgrown with woefuls . . .’”

This sort of poem, which might make clear the tendency toward nonobjectivity, was already published in works like “A Slap in the Face to Public Taste” (1912) and “Croaked Moon” (1913). It is not difficult to draw obvious analogies in the artistic application of neologism to the later works of Malevich, to his alogical paintings of 1913/14 (e.g. The Englishman in Moscow) as well as, in tendency at least, to the nonobjective works of Suprematism.

The Paris drawing Woman serves as a good example of this: it is one of the few known instances where Malevich supplies a Suprematist drawing with an object name for a title, which is handwritten on the paper. With this work it becomes possible to give the reader a better understanding of zaum—pictorial language, of the “transrational” language of painting.

(2) Besides the deformation of syntax and the creation of neologisms, zaum language, or “transrational” language, was of special significance. In this regard, too, Khlebnikov and Kruchenykh represented two essentially different concepts in their artistic praxis.

Critics have often ascribed the invention of the concept zaum and its application to Kruchenykh, from whom stem the widely published proclamatory definitions and manifestoes. Khlebnikov had indeed added his signature to these works, but it is unlikely that he had actually drafted them. While in Khlebnikov the zaum formations never appear in isolation, but always in a coherent context (if only by association)—“subconscious,” “transmental,” “intuitive”—Kruchenykh follows another direction: the total destruction of conventional reality, without offering anything at all as a meaningful substitute. This is destruction for its own sake, without indicating an alternative on any level of significance, a fundamental attack without an attempt at a fundamental reply. In an essay on Khlebnikov, Osip Brik rejected Kruchenykh’s “poetry” as “pure estheticism” and “nominalism”—a new name for an old thing—the flower “lily” receives the name “euy”—while Khlebnikov’s verbal creations correspond to a “new phenomenon” or a “newly discovered subtlety of a phenomenon”: “He communicated a new reality through his new words. Khlebnikov never imagined anything, never ‘invented.’ He discovered.”3

Kruchenykh thought to achieve “freedom from meaning” through relatively meaningless word-combinations, as for example, in this poem that consists entirely of vowels, from his “Declaration of the Word as Such”:

a e u
e e u
iii e

Khlebnikov, on the other hand, practiced zaum-language with the idea, forgotten since the days of Romantic linguistics, that individual sounds carry specific semantic functions:

Since exactly these words do not make us conscious of anything (are worthless for the puppet-show), these free combinations are called zaum-language. . . .

But there is a way to render the zaum-language intelligible. If one takes a word—“shell,” for example—we do not know what meaning each individual sound has for the entire word . . . [We can assume, however:] Sh means “cover.” And in this way zaum-language ceases to be zaum—beyond reason. It becomes a play on the alphabet as we have explained it [italics added]—a new art, on whose threshold we stand.

In these definitions Khlebnikov clearly reveals his training and experience in modern mathematics and physics, which operate—analogous to his notion of an “alphabet as we have explained it”—on the basis of axiomatic postulates. Bertrand Russell, the protagonist of logical mathematics, defines this phenomenon in his Introduction to Mathematical Philosophy:

Mathematics is a study which . . . may be pursued in either of two opposite directions. The more familiar direction is constructive, towards gradually increasing perplexity. . . . The other direction . . . proceeds, by analyzing, to greater and greater abstractness and logical simplicity; instead of asking what can be defined and deduced from what is assumed to begin with, we ask instead what more general ideas and principles can be found, in terms of which what was our starting point can be defined or deduced.

The classical conflict between Man and Nature begins to move on a self-reflecting, abstract level, for which the self-reflection of language represents a fundamental presupposition.

(3) Phonetic deformation runs parallel to the semantic—the “sound-picture,” for the purpose of introducing a semantic factor through “rhythm”4 or alliteratior . . . This, too, is essentially distinct from the Symbolists’ use of “sound pictures” for basically ornamental purposes.

(4) An anti-esthetic conception, to some extent almost militant, in lyric as well as prose, can be noted throughout Khlebnikov’s works, and is often designated as “hard texture” (tugaja faktura). In a manifesto published in 1913 Khlebnikov and Kruchenykh spoke of “‘roughing up’ language.”

One can also see anti-esthetic tendencies in Malevich’s oeuvre, which he discusses in his essay “From Cubism . . .” (1916), and whose conceptual significance and analogues to Khlebnikov’s poetic theory have as yet hardly been recognized.

Malevich’s intensive preoccupation with the art of poetry is sufficiently noticed and can be dated at the latest to the time of his participation in the publication of Troe (The Three). It is also apparent in the relatively unusual drawings of 1913. The title is Fight on the Boulevard; the words are selected according to a “sound picture” principle and arranged visually. The inflected suffix of the word for “Boulevard” is separated from the stem, so that the first three words end in “a.” In January 1916 Malevich led a public discussion on the occasion of the exhibition “0.10,” whose program lists “Alogism in Poetry” as the final point of discussion. Malevich’s recently published letters to Matyushin (1913–1916) reveal the intensity and insight which Malevich brought to his study of poetic techniques and concepts already at a relatively early date. In June of 1916 he wrote with unusual thoroughness of his opinions about poetry and Kruchenykh in particular—informative opinions that to date have been largely ignored.

Malevich unequivocally rejects Kruchenykh’s attempt to connect zaum-poetry with mystical sects and theosophic conceptions: “The poet (Kruchenykh) justified himself by exile to the sect of Shishkov, to the nervous system, to religious ecstasy, and by means of this he wanted to prove his case of the existence of ”dyr bul“ [a famous zaum-poem by Kruchenykh]. But this exile led the poet into a blind alley, knocking him down to the same core, to the same point as before. The poet has not succeeded in explaining the reasons for the liberation of the letter.” A few paragraphs later Malevich speaks of the “sound picture” of the word, taking up the ideas and concepts of Khlebnikov: “In the beginning there was no letter, there was only sound. By sound they determined this or another thing. Then they divided the sound into separate tones and these divisions they represented with signs. Thus they could convey their ideas and descriptions to others.”

A comparative juxtaposition of Malevich’s pictorial world, as in Englishman in Moscow of 1914, with selected poems or prose pieces of Khlebnikov also yields interesting analogies. The following scene from Khlebnikov’s “Flight from the Grave Mount of the Dead Son” (1913), with its composite, alogical pictorial conception, finds, as Jakobson pointed out, a correspondence in the similarly conceived Englishman in Moscow:

She wears a white straw hat with a sky-blue border. A bicycle that bends the grass. There he is. Laughing, nodding their heads, they sit down. Through the window of the brightly lit house one can perceive how they step through the glass doors without disturbing the living, a friendly welcome, exchanging polite words of greeting. Lofty, a collar with sharply bent ends projects upwards.

In his study of Khlebnikov, Markov called attention to the characteristic “absurd contrasts, nonsense and irrelevance” with a certain underlying humor, and saw in this an emphasis of their “secondary shades of meaning.” Next to poetic clichés, Markov points out, Khlebnikov juxtaposed word plays of an incomparable sort, and this drastic combination of different levels (achieved through “nonsensical contrast”) is often termed sdvig (shift/alienation): “Venus is juxtaposed to a witch doctor; poetic and colloquial levels are combined.” Tomashevsky spoke of the “scrap structure” in Khlebnikov’s work, stating: “It freely combines lines which satisfy different metrical norms, but combines them in such a way that the metrical norm of each line is discernible.” In Malevich’s Englishman in Moscow the separation of words like zatmenie (“darkening” [of the sun]) and chas-tich-noye (“partly”; chas also means “hour”) recalls the poetic principle of sdvig. Through their nonsensical alogical confrontation with iconographic content of the painting the words take on a completely different purpose from the scraps of words in paintings by Braque or Picasso from 1910–11, where the words are associated with pictorial elements. Further, the constant change in the metrical norm finds an unprecedented pictorial correspondence in Malevich’s reversal and dissolution of normal proportions: a man’s face stands in the same undimensional relation to the image of the cathedral as the sword does to the ladder, etc.—a literary allusion to the dogma of the illusionistic, three-dimensional perspectival perception of nature that had dominated painting since the Renaissance.

The same problems were already addressed in the work Cow and Violin, 1913. On the reverse of this oil painting the artist later stated: “The alogical collusion of two forms, the violin and the cow, illustrates the moment of struggle between logic, natural law, bourgeois meaning, and prejudice.” Certainly this work marks a decisive step in Malevich’s development: the cow, illusionistically painted, is simultaneously a symbol for nature (so often invoked by Malevich) as it appears to the old “common sense” view of the world and its values, and for the anecdotal sujet and naturalistic perspectival form. The cow is combined in a sort of collage with the two-dimensional representation of a violin, a product of refined Western civilization since the Renaissance, against a background composition reminiscent of Cubism. Thus, in exemplary fashion, Malevich has taken up and posed for us (in form as well as content) the problem of “human consciousness vs. nature” which crops up frequently in his early writings and which he addressed once more in the Composition with Mona Lisa.

In addition to this iconographically oriented exposition of the two figures (cow/violin) as symbols, their individual significance is also broken down: the meaning of a notion—so many linguists assert—is not merely tied to the notion itself, but is constituted through the context of the notion. An alogical contrast between notions—or images—destroys, or at least disturbs, association with the original meaning that each element previously possessed. The four illusionistic nails in the corners stress the tableau-objet character of the painting as a flat surface; the imitative faux-bois of the violin, as a quote from the formal repertoire of French Cubists, functions in this context rather as a critical comment on what Malevich was to characterize two years later as “the esthetic trap of Cubism.” The bias toward the anecdotal nature of the mimetic picture, toward romantic sujets, is significantly connected to the formal dead-end of Cubism.

Thus not only does the composition Cow and Violin correspond to the numerous assertions in Malevich’s manifesto of 1916 (e.g. “. . . the Futurists, who destroyed the old habits of thought . . . and spat in the face of ‘common sense’”), but also to the breakdown of traditional meaning through alogical contrast—unlike in the works of the Cubists and Futurists—which was also reflected in the formal arrangement of the work, and realized for the first time programatically: the cow/violin pair is contrasted not only semantically, but also through the infringement of traditional proportion. Malevich wrote: “The scale of each form is arbitrary . . . which justifies the appearance of parts of real objects in places which do not correspond to nature.”

These artistic principles—the confrontation of images whose dimensions do not correspond to convention (as determined by tradition and traditional geometry), the removal of the metrical norm—seem to reflect the artist’s knowledge of the essentials of the latest scientific hypotheses and their results (e.g. non-Euclidian geometry, the Special Theory of Relativity, the time/space-continuum), and these correspond in turn to Malevich’s declaration of 1915: “Form is convention; in reality form does not exist.”5

Absolute space, absolute time and even geometry are not conditions upon which mechanics are based . . . All these things no more existed before mechanics than the French language logically existed before the truths which had to be formulated in French. . . . Principles of geometry are merely conventions.
—Henri Poincaré, Science and Hypothesis, 1902

As in France, so too in Russia the popularity of the new discoveries in physics and mathematics was so great that even Kruchenykh, after meeting with Matyushin and Malevich in Finland, could not avoid mentioning the new physical laws in his “Declaration of the Word as Such,” published as a pamphlet in the summer of 1913: “The limitation of time, space, etc. Here I agree with Kulbin, who discovered the Fourth Dimension: gravity; the Fifth: motion; and the Sixth or Seventh: time.” In a letter of reply to Matyushin (1914), Khlebnikov spoke about the Fourth Dimension and Poincaré’s Science and Hypothesis and strongly advised him to read the Lobachevsky publications of the mathematics department at Kazan. One can also find statements by Malevich that undoubtedly imply knowledge and understanding of mathematical and physical laws: “Hence, beyond purely conditional relationships, it is impossible to establish an object as something delimited,” Malevich noted in his journal. He spoke of “the relative precision of movement of objects—movement of objects existing objectively for everyone—and, in turn, the objects themselves existing objectively and relatively. . . . The movement of a point becomes something objective even though, in essence, this point does not exist. . . . So the modern artist is a scientist.”

If, as Marcadé rightly demands, the first version of Malevich’s essay (which Matyushin presumably did not revise) “From Cubism to Suprematism—The New Pictorial Realism,” published in June 1915, is compared with the third edition of 1916, one notices immediately the use of scientific terms in a text which is otherwise contradictory in its philosophical tendencies. Malevich prefixed a motto: “Space is the receptacle without dimension into which reason deposits its creation.” And later we read in the text: “The discovery of these points could be made in arbitrary fashion, independently of the physical law of the natural and of perspective.” In the edition of 1916, he wrote: “And art is knowing how to create a structure which proceeds not from the basis of esthetic taste about the prettiness of the structure’s composition, but from the basis of weight, of velocity and of the direction of motion” (italics by Malevich). Further, in the second part of this essay Malevich asserted: “Objects have within them a multitude of temporal moments.”

In “A. and Pangeometry,” published by El Lissitzky in 1925, Malevich and his Black Square on White Surface are again connected with mathematical ideas and with Lobachevsky, who “burst the absolute of Euclidian space:” “Thus A. [Arts] is an invention of our mind, a complex that links the rational with the imaginary, the physical with the mathematical . . .”

Again and again we run across the name Lobachevsky (1793–1856) and his non-Euclidian geometry. In the years around the turn of the century Lobachevsky and his mathematical and philosophical legacy were rediscovered and popularized throughout the country. On the occasion of the centennial celebration in Lobachevsky’s honor at the University of Kazan in 1893, Alexander Vasilyev called him “the Copernicus of our time.” Vasilyev’s most interesting remarks, however, concerned Lobachevsky’s philosophical views, which were most clearly elucidated in the brief tract “New Principles of Geometry” (1835). There Lobachevsky appears as a convinced supporter of Bacon’s “sensualism” and, consequently, a decisive opponent of Kant’s interpretation of space and time as “pure categories” independent of experience. Vasilyev also established the annual Lobachevsky Prize at Kazan University, which achieved international prominence in 1904, when the winner, Henri Poincaré, published in the university journal an article on the mathematical and philosophical influence of non-Euclidian geometry on modern science. Poincaré’s essay was mainly concerned with the influence of non-Euclidean geometry on the presentation of complex numbers, the introduction of hypercomplex numbers into arithmetic, and Georg Cantor’s conception of infinite quantities. According to Poincaré, the principal achievement of non-Euclidean geometry was the legitimizing of the concept of spatial relativity (to which Einstein referred in his “General Theory” of 1916); moreover, it argued for “mathematics of intuition”—that most important source of modern mathematical thought—to stand beside analytical mathematics. In 1904 Poincaré’s Science and Hypothesis (1902), already translated into Russian, certainly aroused attention in Russian artistic circles, since Poincaré’s significance for the French Cubists was generally known. Khlebnikov too, as we already noted, recommended this book to Matyushin in reference to the Fourth Dimension.

Poincaré begins his foreword with these lines:

For the superficial observer scientific truth is incontrovertible, the logic of science is infallible. . . . Mathematical truths clan be derived from a few obvious hypotheses—with the aid of a series of flawless conclusions; these are forced not only on us, but even on nature itself.

In his chapter on non-Euclidean geometries, Poincaré speaks of the geometry of “irnaginary beings” that define space only in two dimensions: “For these, a straight line will be the shortest distance from one point on a sphere to another—thus, an arc of a great circle.” In the chapter “Space and Geometry” he described the essential difference between “representative space in its tripartite form—visual, tactile and kinetic”and “geometric space,” stating: “Our pictorial conceptions (représentations) are merely the reproduction of our sensory impressions, hence they must be placed within the same frame of reference—i.e. in representative space. It is thus just as impossible for us to represent external objects in geometrical space as it is for an artist to paint three-dimensional objects on a flat surface.” A quotation from Malevich attests to his essential agreement with this view: “If his [the painter’s] conception is spatial then he transforms it into a flat surface on his canvas. In so doing, he does not notice that his conception of objects has forfeited its physical qualities on the painting’s surface.” Poincaré follows the above statements with a chapter on the Fourth Dimension (Le monde a quatre dimensions), to which Khlebnikov referred in his letter to Matyushin, discussing sensory impressions, which may allow us to conceive of the world in four dimensions: “. . . these sensory impressions would be precisely those experienced by a being which has a retina for two dimensions, and which had entered a space of four dimensions. In this sense we could say that we could imagine the Fourth Dimension.” While Poincaré designated the Third Dimension as a fictive one, to depict “geometric space” (“Thus the Third Dimension seems not to play the same role for us as the two others do”), he explained how our senses can comprehend the Second and Fourth Dimension.

In this context one is better able to understand the titles Malevich gave to his paintings at the “0.10” exhibition: Movement of Painterly Masses in the 4th Dimension, Lady: Color Masses of the 4th and 2nd Dimension, Painterly Masses in Movement, Painterly Masses in Two Dimensions in a State of Rest, Self-portrait in Two Dimensions6, etc. The fact that in these titles The Third Dimension is conspicuously absent leads us to believe that Malevich knew of Poincaré’s text. The predominant use of physical concepts like “masses,” “movement” or “state of rest” strengthens this assumption. In order to conceptualize the Fourth Dimension, critics have referred almost exclusively to Ouspensky’s Tertium Organum, in which the author speaks of the necessity of a “cosmic consciousness” and a “higher intuition.” But this approach appears speculative and misguided in view of the facts discussed above. If one were to attempt a summary description of Poincaré’s views of physical reality as presented in Science and Hypothesis, one could say that Poincaré has shown how physical theories are capable of expressing not objects themselves, but merely the relationships between them, or between phenomena.

But Poincaré was certainly not needed to introduce to the Russian intelligentsia the revolutionary ideas of their compatriot Lobachevsky. Especially in the first decade of the 20th century, Russian scientists like Lodan, Chebyshov, Tinger, Shiller, Umov, Bachinsky and Khvolson devoted themselves increasingly to the implication of non-Euclidean geometry and the latest scientific theories, which were circulated in a growing number of popular scientific journals. Thus, for example, Hermann Minkowski’s celebrated essay on the four-dimensional world (1908) was already available in a Russian translation by 1911. Most of these scientists were markedly inclined toward a general philosophical explication of their scientific views. They divided into the most disparate camps: idealists, mystics, spiritualists and theosophers, materialists and empiricists, Marxists, and many other groups.

One of the dominant Russian mathematicians and physicists was A.V. Vasilyev, already mentioned, who earned special recognition for his popular philosophical interpretations of the latest mathematical/physical developments and their historical classification. He edited a two-volume work entitled New Ideas in Mathematics published in St. Petersburg in 1913.

The theories of non-Euclidean geometry, in which mathematicians like Gauss, Bolyai, Riemann and others also played a decisive role, had to find recognition in all fields of science and culture. Finally it was shown, as Halsted, an eminent American mathematician and translator of Lobachevsky, wrote: “that the riddle of the universe is an indeterminate equation capable of entirely different sets of solutions. It shows that our universe is largely manmade, and must be often remade to be solved.” A large portion of these “new ideas” was inspired by, and based upon, Nikolai Lobachevsky’s New Principles of Geometry, which, in the history of science, marks the beginning of abstract arithmetic or axiomatic mathematics—a tendency that would reach its high point with Russell and Whitehead’s Principia Mathematica (1910–1913).

Of special interest to us here are the ideas which Lobachevsky presents in his near philosophical work New Principles of Geometry. They may be summarized as follows: In contrast to Euclidean geometry, Lobachevsky calls the system he devised “imaginary geometry.” After an opening mathematical section, in which he rejects the existing theories about parallels and their axioms as inadequate and, above all, arbitrary, he declares: “We cognize directly in nature only motion, without which all the impressions our senses receive become impossible.”

Lobachevsky continues this thought, adding another idea that is essential for our purposes: “All other ideas, for example geometric, though tied up implicitly in the properties of motion, are artificial products of our minds; and consequently space, by its own self, abstractly, for us does not exist.” A few pages later he repeats: “Surfaces, lines, points, as geometry defines them, exist only in our imagination,” and “From another side, lines straight or curved, planes and curved surfaces do not exist in nature; we encounter only bodies, so that all the rest, created by our imagination, exist only in theory.” These few sentences, logically and meaningfully embedded in the overall context, must have evoked far-reaching thoughts in the reader of that time. And these ideas, “cognitions,” can be clearly connected to the pictorial world of Malevich.

Represented volumes, planes and lines exist only on the pictorial surface, but not in reality.
—Kasimir Malevich

Hors de l’intention (terme de la psychologie), hors du style (terme de l’histoire de l’art), it n’y a pas de representation de l’objet.
—Roman Jacobson, Futurism, 1919

Examining the works in the extant photo of the exhibition “0.10” one notes that the forms depicted there, and even their individual elements, are all taken from the scientific field of what Poincaré terms “metrical geometry.” Geometric signs like lines, triangles, quadrangles, squares, circles, trapezoids and various sorts of parallelograms—reflecting Lobachevsky’s “complete theory of parallels”—are arranged in arbitrary relationships to each other, showing an attempt to create a new vocabulary for pictorial language. Only in this context can one understand the explanations Malevich supplied for the catalogue of this exhibition: Painterly Masses in Movement and in Two Dimensions in a State of Rest. “In naming some pictures, I do not want to suggest that one should look for their forms in the titles, but I do mean to indicate that I consider the real forms to be like piles of pictorial masses without form, from which has been created a pictorial scene that has nothing to be seen in nature.”

In this light one can understand why Malevich said “Form is convention, in reality form does not exist”; why he repeatedly polemicized against “the representation of the small corners of nature, of madonnas or immodest Venuses”; and why he called for “pictorial masses, without repeating and without modifying the primary forms of the objects of nature,” and for a “new Realism” in painting. It also becomes apparent that Malevich saw creativity not in the “interdependence of form and color, nor on the basis of an esthetic taste for beauty in composition,” but merely “on the basis of mass, velocity and direction movement” (italics by Malevich). This repeats quite closely Lobachevsky’s observation that we can perceive only “the movement” of bodies, and “all other ideas, for example geometric, are only artificial products of our imagination.” As we have already noted, the problems of relativity were much discussed in the circles of the avant-garde, and this too is echoed in many of the sometimes metaphorical statements of Malevich:

Science has proved the different oscillating intensities and wave lengths of rays of color. Red rays move more slowly, yellow rays faster, and the white fastest of all. Yet these differences are purely relative and tell us nothing about their real motion. . . . Nature, whose reality lies beyond reason, is nonobjective, and if it were possible for a human being to travel beyond the earth’s domain, he would realize what irrationality surrounds him. . . . The world is nonobjective, and it is only man who wants to objectify it and force it into real forms . . .

In light of the ideas manifested in these texts, one can understand how Malevich could designate as “alogical” the graphic conception of Composition with Mona Lisa, in which the two irreconceivable levels of objective and nonobjective art encounter each other, and where word and language (zatmenie/chastichnoye)7 are confronted with the pictorial potential of icons (Mona Lisa, programmatically crossed out with red lines) and symbols (the “S” of the violin). His conception becomes obvious if we contrast it with a work of the “old logic,” of “common sense,” Picasso’s Clarinet and Violin of 1912, which by 1913 at the latest was on display in the Shchukin Collection in Moscow as an outstanding example of the collage-type of Cubist composition. Here, as opposed to Malevich’s alogical principle, each individual sign (“S” of the sound-hole) and each form (imitative faux bois) is arranged according to the overall context, and can be explained only in those terms: the “old logic of the objective world” is communicated to the observer through selected symbols. In Malevich we find a different state of affairs. Not only is the surprising, iconographically unusual, combination of different pictorial elements conceived as “alogical”; also alogical is the confrontation of two imagistic structures (an objective and nonobjective) which are mutually exclusive in their logic—two languages, one of which is supposed to represent the world of mimetic illusionism (representation of objects in perspective), the other “the world of nonobjectivity,” of modern scientific perceptions. In Malevich’s development, this painting represents the unique confrontation of the “old” and “new” patterns of thought, and at the same time it is a programmatic rejection of tradition.

The aspect of linguistic structure explored therein acquires a wider context: the phenomenon of the space/time-continuum and its adequate linguistic expression. Linguistics has established that European languages perceive the concept of time spatially, and circumscribe it metaphorically with spatial concepts (“The day is long”), while North American Indian cultures, for example, express time and duration literally and without metaphors, “which seem to analyze reality predominantly in the conceptual framework of events.”

A similar attempt on the level of an imagistic vocabulary for the fine arts can be seen in the Suprematist paintings of Malevich, which expand our repertoire of forms (limited by convention) by means of isolation and new structures, and redefine these forms semantically. The title of the Suprematist work of 1915, Football Game, refers to the objective world—a theme which implies the factor of time as well as space, and is characteristic of the new understanding of Malevich’s world of forms. Also in the carefully executed drawing Suprematis, to be dated 1914, one can recognize Malevich’s new formulations: above an “arc of a circle,” which according to Poincaré represents a straight line for the two-dimensional being, are geometric forms like rectangles and lines (the arbitrary inventions of human mind, according to Lobachevsky) arranged in an interrelationship that determines the composition of the work.

These are the works that recall Velimir Khlebnikov’s ground-breaking essay “To the Painters of the World”:

_The goal is—to create a common written language, common to all peoples of the third planet from the sun, to construct written symbols that can be understood and accepted by the entire population of this star. . . . Painting has always spoken in a language accessible to all. . . . The mute geometric signs will reconcile to each other the multiplicity of languages. . . . The task of the artist of color is to offer geometric signs as the fundamental units of comprehension. . . . The alphabet already contains a world-wide network of sound pictures for different types of space; now a second network should be created, from written characters—mute money in the markets of discourse.

Rainer Crone



This article is an abbreviated version of a book-length essay with extensive references, appearing in Wallraf-Richartz-Jahrbuch 1978 and in my forthcoming book Kasimir Malevich and the Meaning of Non-objective Art.

This article must be seen as employing traditional art historical methods, a first toward a more comprehensive understanding of Malevich’s nonobjectivity—and abstract imagery in general—within the context of semiotic theory, a step toward transcending the traditional dichotomy between iconic and noniconic art (see for this Charles Morris, Sign, Language and Behavior, New York 1938; Charles Sanders Peirce, Collected Papers, Cambridge, Mass. 1931–1935: Louis Hjemslev, Prolegomena to a Theory of Language, University of Wisconsin 1961; and in particular Umberto Eco, A Theory of Semiotics, Bloomington, c. 1976).

Acknowledgment should go to Roman Jakobson and to my colleagues at Yale University; Victor Erich, Robert L Herbert, Martin J. Klein, James Marrow, and to John E. Bowlt. Susan Korb and Matthew Dillon for their help and cooperation.

1. See in this context Linda Henderson, The Artist, “The Fourth Dimension,” dissertation, Yale University 1975; Linda Henderson, “The Merging of Time and Space: ‘The Fourth Dimension’ in Russia from Ouspensky to Malevich,” The Structurist 15/16, 1975/1976, pp. 87–108; Andrei B. Nakov, Malévitch Ecrits, Paris 1975, p. 85; Susan Compton, “Malevich and the Fourth Dimension,” Studio International, April 1974, pp. 190–195; Susan Compton, “Malevich’s Suprematism—The Higher Intuition,” Burlington Magazine 118, August 1976, pp. 577–585; and Charlotte Douglas, Swans of Other Worlds: Kasimir Malevich and the Origins of Suprematism: 1908–1915, dissertation, University of Texas, Austin 1975.

The integral relationship between mathematics and art is not new to Khlebnikov or even to 20th-century art in general. We see this interest in work as early as that of Novalis in German Romanticism (see for example Kate Hamburger, Novalis und die Mathematik, Halle 1929). I am presently preparing an essay tracing the changes abstraction undergoes from early Romanticism to 20th-century art

2. That at this time, in 1913, Einstein’s “Special Theory of Relativity” of 1905 was already discussed even in semipopular magazines of Russia, is referred to by Alexander Vucinich, Science in Russian Culture 1861–1917, Stanford 1970, p. 369. The physicist Khvolson, for example, known for his publications in textbooks, discussed the ideas of Einstein’s “Special Theory of Relativity” in an article Principle of Relativity, published in the popular magazine Nature of 1912 (No. 11, pp. 1275–1316). It is exactly from this article by Khvolson that Roman Jakobson quoted in Futurism of 1919—Jakobson’s essay disputing problems of contemporary paintings: “‘Therefore, our spatial dimensions, in tact, are situated not within a three-dimensional, but in a four-dimensional space.’” See Roman Jakobson, Questions de poétique, Paris 1973, p.28

3. Victor Erlich, Russian Formalism, History-Doctrine, Paris 1965, p. 157, noted that Kruchenykh here confuses the terms “meaning” and “referent.” Incidentally, “freedom from meaning” is, in terms of linguistics, impossible: see for example Benjamin L. Whorl, “Language, Mind and Reality,” in: Language, Thought and Reality, Boston 1956, p. 256

4. To what extent mistaken interpretations result from the artificial restriction to strictly artistic developments can be demonstrated—pars pro toto—by the statements of E. Martineau on the topic “Rhythm”: “The question remains open as to the exact meaning of the word ”rhythm“—for the Greeks and for Malevich . . .” (Catalogue Suprematisme, Galerie Chauvelin, Paris 1977, p. 90). Kant’s “grandeur infinie” is cited by way of explanation, but no mention whatever is made of the exhaustive discussion of rhythm by the group OPOJAZ and by the Russian Formalists; see for example Osip Brik, “Rhythmus und Syntax,” or Boris Tomashevsky, “Vern und Rhythmus,” in Wolf-Dieter Stempel (ed.), Texte der Russischen Formalisten, Munich 1972.

5. In From Cubism and Futurism to Suprematism, quoted from Jean-Claude Marcadé (ed.), De Cézanne au Suprématisme, Ecrits I, Lausanne 1974, p. 17. The sometimes quite substantial diversities in translating the original Russian version (there are now three diferent translations: Troels Andersen, Essays I, II and III; Marcadé, Ecrits I and II. and Andrei B. Nakov, Malévitch Ecrits, Paris 1975) demand a bilingual edition of the essayistic oeuvre by Malevich. For example, in Andersen, Essays I, 190, the above quoted sentence is translated as- “. . . form is condition and that in reality form does not exist,” whereas both Marcadé and Nakov, Ecrits, 329, translated: “la forme . . . est une convention, que dans la réalité, la forme n’existe pas.” Even within the same translation one finds difering translations of the same sentence: e.g. Nakov, Ecrits, 104 “Les couleurs ont mûri sans que leur forme ait mûri en consequence.” and the same sentence on p. 196 “Les couleurs ont mûri, sans que leur forme ait mûri dans la conscience.” I took Marcadé’s translation as the most adequate and reliable.

6. Troels Andersen, Catalogue Malevich, Stedelijk Museum Amsterdam 1970, pp. 162–63, listed ten such titles, but which cannot be attributed to specific paintings. Ouspensky’s statements (on space for example), insofar as they do not reproduce the concepts of other scientists, are plainly in opposition to Malevich’s admittedly metaphorical conception of space—and especially these picture titles of 1915, which contain no reference to a sort of “cosmic intuition” or “mysterious fourth perpendicular.” A quote from Ouspensky, entirely dominated by the Euclidian conception of space, when contrasted with a quote from Malevich, may make clear their incompatibility: “There is physical existence . . . and there is metaphysical existence. . . . In addition to the three known to us, a mysterious fourth perpendicular is possible. This assumption is practically founded on the consideration that there are things and phenomena in the world undoubtedly really existing, but quite incommensurable in terms of length, breadth and thickness, and lying as it were outside of three-dimensional space” (Ouspensky, Tertium Organum, 23). Besides Ouspensky, who is generally the only one of the mystics referred to in the literature on Malevich (probably because his writings are more accessible to the Western world), there are a number of other mystics, who were in fashion around the turn of the century, especially in the aristocratic circles of Petersburg, to whom Matyush in had access (see Vucinich, Science, pp. 145–147). But, contrary to the views of these mystics, is Malevich’s ever-recurring thesis “Nature, whose reality lies beyond reason, is nonobjective.” In addition to the contrary conception of “nature.” one further matter may be cited against the determining influence of Ouspensky recently Susan Compton (“Malevich’s Suprematism . . .,” Burlington Magazine, August 1976), following Henderson, has reviewed the thesis that Malevich’s drawings for The Victory over the Sun, schematizing the box-stage, are comparable in form to a two-dimensional projection of a cube into a plane, such a formal configuration appeared in a diagram from the book A Primer of Higher Space, New York 1913, by the American theosopher C. Bragdon. She alleged that this book was known to the mystic Peter Ouspensky in 1913, who then supposedly passed it on to Malevich. Two points may be cited to the contrary: (1) Regarding the inner quadrangle in this schematic representation of a stage, we are not concerned with a correspondence of the outer square, but with a rectangle the dimensions 10 by 8 inches, as is noted on the lower line of most of the drawings (2) Even a general connection between Malevich and the notorious mystic and theosopher Peter Ouspensky, who was not prominent and a rather unimportant figure among his contemporaries (see e.g. the account of mystic sectarians by George Ivask. “Russians Modernist Poets and the Mystic Sectarians,” Russian Modernism. Culture and Avant-Garde, 1900–1930, ed. by George Gibian and H.W. Tjasma, Ithaca and London 1973, 85–106, and Karl Konrad Grass, Die russischen mystischen Sekten, Leipzig 1914) is—because of the latter’s close association with mysticism—highly doubtful, as I was able to show through letters by Malevich. Even beyond this factual data—the preoccupation of the Symbolist poets with mysticism (see e.g. Ivask, “Sectarians,” pp. 90–100) was well known, as the opposition to symbol became a dominant attitude among the Cubo-Futurists in general and Khlebnikov and Malevich in particular.

7. Malevich had used the same combination of words in an entirely different iconographic context, in “Englishman in Moscow.” This fact demonstrates how programmatically Malevich understood and used language in pictorial contexts.