Journal Article

Velimir Khlebnikov and the Fourth Dimension

Weststeijn, Willem G.

2026

Overview

The developments in mathematics in the nineteenth century, in particular non-Euclidean geometry, which was not concerned with flat space, but with curvature, led at the end of the century and the beginning of the next one to much discussion of and experiments with the fourth dimension. The idea of a fourth dimension played a major role in the arts. In literature the Symbolists were convinced that there existed a “higher” reality behind the visible one and tried to suggest it in their poetry. In pictorial art and sculpture completely new forms emerged that distorted reality and in that way showed that one had to look at the world in a different way; there was something beyond the usual three dimensions. Many artists consciously tried to visualize this “beyondness”, the fourth dimension. The followers of the idea of a higher reality considered the fourth dimension as time, most artists as space. Much influence in the discussion about the fourth dimension had Charles Howard Hinton and, especially in Russia, Pyotr Ouspensky; both wrote a book entitled The Fourth Dimension (1904 and 1909, respectively), in which they propagated their ideas. The Futurist poet Velimir Klebnikov did not explicitly mention the fourth dimension in his work, but in view of his scientific interests (he studied mathematics at the University of Kazan, one of whose most celebrated scientists was Nikolai Lobachevsky, the founder of non-Euclidean geometry) and his close ties with the avant-garde painters, he was undoubtedly aware of the ideas about the fourth dimension in his time. Khlebnikov compared himself with Lobachevsky and used his geometry in his own description of the cities of the future. With his experiments with language and numerals he tried to find a new meaning behind the usual ones, and he made endless calculations to determine the laws of time: there must be some principle that rules the continuous stream of events. Establishing this principle, one might transcend history and ultimately find a solution for fate and death. His entire work is devoted to the search of a new dimension.

• Publisher: MDPI AG
• Subject: Fourth dimension / Geometry / Geometry, Non-Euclidean / Gharles Howard Hinton / Khlebnikov, Velimir (1885-1922) / Khlebnikov, Viktor Vladimirovich / Mathematicians / Mathematics / Mysticism / Nikolai Lobachevsky / non-Euclidian geometry / Philosophers / Poetry / Poets / Portrayals / Pyotr Ouspensky / Russian literature / the fourth dimension / Theory of relativity / Velimr Khlebnikov / Wells, H G (1866-1946) / Works