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1. 1 2017-02-22T17:37:42-08:00 Stephen Heim 7069d17c035042745c96bc6c7619096cd7b33da4 Shattered Image - Similar Realities Stephen Heim 3 Broken images, similar scenes plain 2017-02-22T17:41:39-08:00 Stephen Heim 7069d17c035042745c96bc6c7619096cd7b33da4
2. 1 2017-02-22T17:32:59-08:00 Stephen Heim 7069d17c035042745c96bc6c7619096cd7b33da4 Simple Title - Directed Perception Stephen Heim 2 plain 2017-02-22T17:40:54-08:00 Stephen Heim 7069d17c035042745c96bc6c7619096cd7b33da4
3. 1 2017-02-22T17:41:47-08:00 Stephen Heim 7069d17c035042745c96bc6c7619096cd7b33da4 Many Faces - One Face Stephen Heim 2 Fragmented face formed of intersecting lines plain 2017-02-22T17:45:17-08:00 Stephen Heim 7069d17c035042745c96bc6c7619096cd7b33da4

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1. 1 2017-03-01T14:14:13-08:00 Craig Dietrich 2d66800a3e5a1eaee3a9ca2f91f391c8a6893490 Timeline Craig Dietrich 2 timeline 2017-03-01T14:16:58-08:00 Craig Dietrich 2d66800a3e5a1eaee3a9ca2f91f391c8a6893490

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• 1 2017-02-23T10:45:45-08:00 Shattering the Boundaries of Three Dimensional Figures 17 An analysis of Malevich's representation of fourth-dimensionality plain 2017-04-16T21:01:46-07:00 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. 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.
  
  By the early 20th century the popular concepts of hyperspace (or higher dimensionality) and non-Euclidean geometry had migrated from Europe to Russia. Writings by Riemann, Helmholtz, and Poincare revived the ideas of Russia's own Lobachevsky, inspiring a slew of popular scientific articles within the country. Within the first decade of the 20th century, far more Russian scholarly works featured discussions of non-Euclidean geometry than of higher dimensionality. The idea of higher dimensions, however, was much more prevalent in the art of the Russian Avant-garde, influencing the works of several artists including Velimir Khlebnikov and in particular Kazimir Malevich. 
  
  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 describes the forms of Suprematism as a series of "flat surfaces [...] expressing through themselves the plans of future three dimensional bodies". This notion can easily be extended to dimensions beyond the third, and considering the artist's interest in Ouspensky's theories and ideas the parallels in several of his works become clear. 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.