Shattering the Boundaries of Three Dimensional Figures
Perhaps the most influential ideas to the Russian Avant-garde regarding higher dimensionality were Peter Ouspensky's theories on the fourth dimension. Dubbed a "hyperspace philosopher," Ouspensky asserted that the concept of a fourth dimension must be approached psychologically as well as physically or geometrically. He argued that our inability to perceive dimensions above the third is a psychological barrier, that our perception of space is distorted, and that we "see everything as unlike what it really is." Ouspensky maintained that a higher spatial dimensionality is a basic characteristic of the fourth dimension, though his later descriptions suggest temporal properties as well. This spatial quality as well as the relation to human psychology and perception are perhaps the most notable aspects of the fourth dimension represented in Russian Avant-garde pieces.
Kazimir Malevich's Smert cheloveka odnovre menno na aeroplane i zhel. doroge incorporates Ouspensky's ideas on the fourth dimension using typical motifs of the art-style. As in Malevich's Morning in a Village after a Snowstorm, Smert cheloveka uses bold, intersecting lines to form highly geometrical figures throughout the page. In this piece, however, the geometry is much sharper, reminiscent of a shattered mirror or broken glass. The scene is chaotic; bits and pieces are recognizable, but are often themselves somewhat ambiguous. Malevich's work can be thought of as two simultaneous spatial realities, connected by some imperceptible higher domain which provides our viewpoint. The shattered appearance of the piece could represent an attempt of the human consciousness to perceive these three dimensional spaces and the fourth dimensional connection between them. The title lends itself to this interpretation with its literal meaning; there are two realities, one in which the man perishes on the plane and one in which he meets his fate on the railway. Additionally, in accordance the image, the title is oddly fragmented and cut short. Odnovremenno (simultaneously) is typically a single word, and zhel. doroge is an abbreviation of zheleznoi doroge (iron railway).
A much subtler example of Malevich incorporating fourth dimensionality in his work follows Smert cheloveka in Alexei Kruchenyk's book Vzorval'. The piece is titled simply Molitva (Prayer), and again features sets of bold, intersecting lines and resulting geometric figures. Comparing the work to its preceding piece (forgive the Gutenbergian perspective), a few key distinctions can be made. Fragmentation around the "face" of the figure in Molitva is very apparent, but the image as a whole is relatively clear. The titles are also quite dissimilar: one is explicit and fragmented while the other is simple and whole. Molitva can be viewed as a simultaneous representation of two (or perhaps many more) very similar realities in contrast to the very different realities of Smert cheloveka. When considering the close relation of hyperspace philosophy to spirituality as well as the stylistic similarities between the two pieces, the connection between Molitva and the fourth dimension becomes clear.
