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Exploding Tongues: Language, Art, and the Russian Avant-garde

Malevich, K. "Death of a person simultaneously on an airplane and on a railroad"

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1. Malevich, K. "Death of a person simultaneously on an airplane and on a railroad"
Contents of this annotation:
1. Malevich, K. "Death of a person simultaneously on an airplane and on a railroad"
Contents of this annotation:
1. Malevich, K. "Death of a person simultaneously on an airplane and on a railroad"
Contents of this annotation:
1. Malevich, K. "Death of a person simultaneously on an airplane and on a railroad"
Contents of this annotation:
1. Malevich, K. "Death of a person simultaneously on an airplane and on a railroad"

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(Hyper)cubism Non-Euclidean geometry is the term given to geometries which oppose Euclid's parallel postulate, that is, in opposition to the postulate: "through a given point can be drawn only one parallel to a given line." In such geometries infinitely many lines through a given point may be parallel to a given line, and similarly the sum of angles of a triangle will be less than 180 degrees. The idea of non-Euclidean geometry was first hypothesized in 1824 by Karl Gauss and more formally in 1829 by Nikolai Lobachevsky, and was further developed throughout the late 19th century and beyond. The geometry of higher dimensions (greater than three) was gradually developed in the following decades, and is far less unified in its formulation than non-Euclidean geometry. Algebraically, the notion of higher dimensional geometry is relatively straightforward: variables are simply added to the typical x, y, and z. Visualizing dimensions beyond the third, however, is much more complex. Often, properties of higher dimensions will be analogous to their more familiar counterparts: rotation about a line in the three dimensions is analogous to rotation about a plane in four dimensions, and a four dimensional hypercube is bounded by cubes just as a cube is bounded by squares. This applies to any conceivable three dimensional shape; four dimensional objects can be formed by boundaries of tetrahedrons, octahedrons, etc. Beyond these analogues, however, n-dimensional geometry was often ascribed philosophical and almost mystical properties. It was perhaps due to these strange properties that it, along with the concept of non-Euclidean geometry, became not only a scholarly but also a cultural and literary phenomenon in Europe during the late 19th century.

As n-dimensional and non-Euclidean geometry began to take the world by storm - America and Russia were not isolated from this phenomenon - certain aspects of these ideas were incorporated into artistic movements, including the then-developing Cubist theories. The "freedom" of geometries not constrained by convention or Euclid's three dimensions was particularly appealing to Cubist artists. [such as...] Farther East, Russian mathematicians and scholars wrote prolifically on the subject of non-Euclidean geometry. It was the idea of a fourth dimension, however, that caught on and spread throughout popular culture and appeared in many art forms of the Russian Avant-garde. The philosophical and mystical - in addition to mathematical - elements of a spatial fourth dimension as described by the writings of Peter Ouspensky were extremely influential to several artists and styles of this movement. 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. We can track the influence and appearance of the cultural phenomenon that is the fourth dimension as it spreads through the Russian Avant-garde: in several of Kazimir Malevich's Futurist paintings and one of his earliest contributions to a Futurist book; in Mikhail Larionov and Natalya Goncharova's Rayist paintings; in El Lissitzky's Prouns, sketches, and diagrams; and finally in various works of (unrealized) Russian fantasy architecture. While Malevich was quick to abandon the physical (mathematical) elements of the fourth dimension in favor of the simpler, even more abstract style of Suprematism, its mystical and philosophical elements can be observed in his Suprematist writings and pieces.

The aforementioned contribution to a Futurist book by Kazimir Malevich, "Death of a man simultaneously on an airplane and the railway", and Rayist works by Mikhail Larionov and Natalya Goncharova, "Glass" and "Green and Blue Forest" respectively, exhibit particularly notable parallels to the fourth dimension and Ouspensky's ideas and writings. -Describe Ouspensky's ideas- Abstraction through highly geometrical, jagged, and acute lines are used to suggest a reconciliation of human perception and the unknowable fourth dimension - an intuition of new meaning and understanding from recognizable fragments. In the case of Malevich, his sketch exhibits many similar elements to his early oil-on-canvas pieces.

Upon examining these qualities within these early pieces of the Russian Avant-garde and similar ones in later works such as Vasily Kamensky's "Tango With Cows" and Ilia Zdanevich's "As Though Zga", it is clear that certain elements of fourth dimensionality persisted in bookmaking throughout the artistic movement. Tango With Cows exhibits qualities seen in Malevich's Futurist piece as well as qualities seen in Larionov and Goncharova's Rayist pieces. "As Though Zga" exhibits elements of simultaneity and fragmented realities seen in the fourth dimension through its countless possible readings.