Chapter 1 - 4th Dimension - Historical Perspective

[The forth dimension] along with non-Euclidean Geometry, played a vital role in the development of modern art and theory. […] once the artistic impact of he new geometries is understood, the art and critical literature of the early modern era regain a unity and a level of meaning that has long been lost.

Henderson, 1993, page 230

The fourth dimension during the 19th century was developed by mathematicians and used in literature such as in Abbott’s Flatland when it was just starting to be scientifically relevant:
Sphere. But where is this land of Four Dimensions?
I. I Know not: But doubtless my Teacher Knows.

Abbott, 1884, Chapter 19

In the first three decades of the 20thcentury the fourth dimension was present in almost every major modern movement. Cubists, Futurists, Constructivists, Dadaists and other artistic circles through out the world were investigating new geometries and properties of this concept.
In the 1920’s Einstein Relativity theory almost banished the spatial fourth dimension from the public imagination, replacing it by the temporal fourth dimension. Even so, one more artistic group was still to come and save this idea and non-Euclidean geometry’s presence in the art world, that movement was French Surrealism.
For many artists such as Metzinger, Gleizes, Duchamp, Dada founder Tzara and the surrealists (just to mention a few) non-Euclidean geometry meant new freedom from traditional ways of thinking. The 4th dimension was also a symbol of the liberation for artists until the 1930’s. It was used widely in painting allowing abstract artists to reject the one point perspective system that was used since the Renascence.
Although non-Euclidean geometries have always been strongly connected to the idea of forth dimension, they never achieved the popularity of this pre-Einstein concept which had many other non-geometric features. At first associated with cubist faceted forms and later on with gravity by Duchamp, the fourth dimension was also related to antigravity by Malevich, spirals by the futurists and even the Platonic realm by Synthetic Cubists. Many artists also added motion as an attribute of the fourth dimension (these included Duchamp, Kupka, Boccioni, Malevich and many others).
According to Lynda Henderson during the 1930’s the fourth dimension was not just limited by the Relativity Theory but also the “increase discouragement of deep space in modern painting” by a formalist art theory. Never the less the Manifeste Dimensioniste was published in Paris 1936. This document was signed by artists from all over the world and from different artistic tendencies, such as: Miró, Hans Arp, Moholy-Nagy, Duchamp, Picabia, Kandinsky, Ben Nicholson, Alexander Calder, Robert Delaunay, etc… A very impressive and extensive list of names approved this attempt to adapt previous viewpoints on the 4th dimension to Einstein’s Space-time.
In the 1940’s the 4th dimension was discussed by Breton, Dali, Dominguez and many other. In a very “surreal” way, time and the “initial 4D concept” were being merged and related to Freud, unconscious, mysticism and attacks on reason.
During the 1950’s and 1960’s very few were still interested in the fourth dimension of space, even amongst surrealists but in the 1970’s some individuals, artists and mathematicians, tried to give visual form to the concept again. A symposium, Hypergraphics: visualizing Complex Relationships in Art, Science and Technology (1978) started the new era of the fourth dimension: computer graphics (Fig.2) and programs were opening new doors to the visual and the mind.