Page 48 - Studio International - April 1974

engineering than Malevich at the time they élémentaire de géometrie a quatre dimensions' the 'square on the hypotenuse' and here there
first knew each other in Vitebsk (where (Paris 1903), and it is very interesting to look are both a triangle and a rectangle—the
Lissitsky was head of Architecture and up the book and find that although Jouffret triangle has certainly changed its shape, because
Malevich, at first, of Painting), Lissitsky seems does quote Hinton, nowhere does he mention another, red triangle, which was not isosceles,
to have been convinced by what at first sight Lobachevsky, and indeed his diagrams show shows under the white paint. Both forms may
would appear to be an 'unscientific' approach — quite another approach to the 'fourth have changed their shape and shifted in
even to the extent of turning to painting dimension', namely the opening out of three- `irrational space', the black rectangle now
himself. dimensional, four-sided figures in order to representing the black square of the original
Undoubtedly Malevich's own approach had show all parts of them simultaneously.25 theorem. (see diagram 7.)
changed between 1913 and 1916. In a letter to It looks very much as though one of the Because Suprematism is the analogy or model
Sophie, Lissitsky described the great reasons that Malevich only understood of a totally different kind of spatial world,
difficulty he was experiencing in trying to French Cubism up to a point and no further is equally credible, but to be reached only by
translate Malevich's ideas into German in 1924. that he did not have access to Jouffret's book, efforts to transcend normal comprehension of
He says that he will have to omit some of the because in 1913 Matiushin jumped immediately three-dimensional space, only pure geometric
writings that date from 1915 because they are far to the conclusion that the term the 'fourth forms can survive in its 'ultimate illusion of
too 'mystical.' 21 dimension' used by French theorists in 1912-13 irrational space, with its infinite extensibility
I have already shown that Lissitsky still referred to that postulated by Hinton and into the background and foreground' (Lissitsky).
adhered to quite a substantial part of Uspensky. He thus perverted the course of A glance at the lithographs which Lissitsky
Malevich's suprematist theory which in its development of abstract art in Russia — or gave himself made for 'Victory over the Sun' show
sources in Hinton seem to be quite 'mystical' it its individual character, according to how one that an attempt to combine 'legibility' with the
or at least fantastical. But the modern looks at it. abstract forms of Suprematism is as unfortunate
assumption that they are quite beside the point Hinton himself, though devoting so much as Van der Leck's attempts to make 'readable'
leaves out of account the importance attached neo-plastic forms.
space to `Metageometry' admitted that
in Russia to the theories of Lobachevsky. Finally it may be argued that for Malevich
`although Lobachevsky's geometry has
`Lobachevsky has already exploded the evidently nothing to do directly with the 'additional' form which led from Cubism to
absoluteness of Euclidean space' wrote four-dimensional space' Practically . . . Suprematism was not the square, but a straight
Lissitsky in his 'Art and Pangeometry'. 22 metageometry had a great influence in bringing line. Perhaps this again refers to Hinton: 'now
Markov mentions that the poet Velimir the higher space to the front as a working as any three axes will be in our space, let us
Khlebnikov had studied Lobachevsky as a hypothesis'. send the white axis out into the unknown, the
student.23 When in 1913 Khlebnikov wrote the To Hinton the fourth dimension could be fourth dimension, and take the blue axis into our
introduction to 'Victory over the Sun' it would represented in model form by using coloured known space dimension.' Lissitsky said
be fascinating to know whether he discussed cubes which could be moved through space in `Suprematism has advanced the ultimate tip of
Lobachevsky with Matiushin and Malevich, time, and thus reveal to our consciousness the the visual pyramid of perspective into infinity.
since Matiushin would have known Hinton's existence of a fourth dimension in three- It has broken through the "blue lampshade of
exposition of the theory of Lobachevsky in a dimensional space : the demonstration the firmament" '27 and his diagram shows the
section of a chapter headed `Metageometry' in required the use of real, constructed, coloured originality of Suprematism's apparently utterly
`The Fourth Dimension' and references to him cubes, and their physical movement over a simple approach to picture-making. (diag. 5)
by Uspensky. real period of time. Naturally that But this language is simple only superficially.
It is necessary to realize that Lobachevsky's demonstration could not be a part of a painting It is to lead three-dimensional man towards
contribution to mathematical thought and it would seem that it took Malevich quite cosmic consciousness. Uspensky says: 'Cosmic
consisted in his pioneering of an attempt to a long period to work out how to represent consciousness is also possible of attainment
apply Euclid's laws of plane space to quite `irrational space' on a canvas, even though through the emotion attendant upon creation —
other conceptions of space — Lobachevsky's French Synthetic Cubism had shown him the in painters, musicians and poets. Art in its
own work according to Hinton being devoted formal way to make `alogical' paintings by 1914. highest manifestations is a path to cosmic
to proving that more than one line can be One of the earliest group of suprematist consciousness.' This is the way of the 'Fourth
drawn through a point, parallel to another line paintings consists of a black rectangle on a form. Beginning of the understanding of four-
(diag: 6). Later this theory was rationalized by white ground overlaid by an ultramarine dimensional space. A new concept-of time. The
mathematician called Beltrami who pointed out triangle; above it can be traced, under the possibility of more prolonged se 1f-consciousness.
that Lobachevsky's geometry was that of the white paint of the background, the letter 'B' Flashes of cosmic consciousness. The idea and
`shortest lines drawn on certain curved and its inclusion makes a likely date for sometimes the sensation of a living universe. A
surfaces'. However, it is not really the exact this painting close to other paintings including striving toward the wondrous. Sensation of
theories, correct or incorrect, which probably this letter, and probably close in date to the infinity. Beginning of self-conscious will and
interested Khlebnikov, Malevich or even moments of cosmic consciousness. Possibility of
exhibition 'Tramway B'.26
Lissitsky but the fact that here was a respectable This is the only known example of an personal immortality'.28 So the concept of 'the
mathematician who had proved that some of abstract painting by Malevich which included fourth dimension' is contrasted to the mundane
man's most cherished assumptions about a purely representational element, though of `third dimension' and perhaps explains the
describing the space in which he lives could be course French cubist synthetic paintings complete absence of the term 'in three
apparently turned upside down. could include letters without disrupting the dimensions' in the suprematist vocabulary. q
It could be argued that this was the case for credibility of the painting. Many of Malevich's
Frenchmen as well, since the cubists talked earlier paintings include words, parts of words
about 'The Fourth Dimension' endlessly. and even numbers and letters. Such an element
But Linda Dalrymple Henderson has written a was admissible in an `alogical' painting but it For a full account of the Russian futurist movement
masterly exposition of what the references appears to have seemed unsuitable in a painting in all its complexity see Vladimir Markov,
`Russian Futurism', London, 1969.
made by Apollinaire as well as by Gleizes and of 'irrational space'. The subject of this painting The quotations are from the English translation of
Metzinger and also, later, by Duchamp, seems even more relevant to the present thesis the second edition (London, 1970) where the author's
really referred to. 24 She traces the usage by since Hinton's description of metageometry name is transliterated Ouspensky, pp. 300, 73.
3 See further Andrei B. Nakov 'The show must go on'
the French cubists of Jouffret's `Traité includes a long passage on the theorem about 7.
Studio International, February 1974, Review pp 6,
194