In the 19th century, interest in the fourth dimension began to emerge as an alternative to Euclidian geometry. Challenges to Euclidean geometry suggested the existence of curved space, rather than linear, and the possibility of change in the shape of forms as they moved through space. In addition to these challenges, the rise of science fiction helped pave the way for philosophical considerations of the idea of the fourth dimension.
One of the chief writers to promote a philosophy of the fourth dimension was the Russian philosopher, Uspensky, whose writing was dominated by a belief in the evolution of consciousness, an evolution which enabled the eventual comprehension of the fourth dimension. He proposed that art and music were the paths to this evolved consciousness.
According to Uspensky, the only way we could understand infinity was to understand it as an endless illogicality. The illogicality lay in the awareness that in the fourth dimension, everything from the third dimension was reversed: reality and unreality of the third dimension changed places in the fourth.
Further, in the fourth dimension, time and motion are recognized as illusions. Consequently, to truly understand the fourth dimension required not only a new logic but also a new language. In this respect, the radically unfamiliar artistic languages of Kandinsky, Mondrian, and Malevich might be seen as direct responses to the philosophy of the fourth dimension, and as attempts to get past the third dimension to depict a gravity-free, directionless space.
Another fourth dimension concept, and one which connects fourth dimension thinking to theosophy, is that of monism. Monism referred to the unity of all things, to a spiritual and material unity which could be explained in the fourth dimension and only in the fourth dimension, because in the third dimension, dualities and separations continued to exist.
Theosophy, founded by Blavatsky, was an alternative way of thinking about spirituality and art. According to theosophy, the universe originally contained atoms and a vacuum. The vacuum was a latent force or deity, which could become organized into a willful force, meaning that out of nothingness, eventually the will would emerge. Duality became a positive concept for theosophy because it represented the union of the latent, which could not be known, and a living force or spirit, which could be known.
The connection to art was made in at least two ways: one was through the belief that color had a vibrating spiritual property which would awaken the dormant spirituality within a person. Another was the belief that art should begin in nature and that the apocalypse would lead to the future new world.
The eventual union of symbolist thought with theosophy fostered a belief in the communicative properties of color separated from form, in the goal of involving the viewer in a pathway or process of deciphering the meaning of hidden imagery, in the use of apocalyptic imagery, and in the belief that a painting of the confused order of reality would, like the apocalypse, lead to a new spiritual order.
One of the best books to explore the connections between late 19th and early 20th century
abstraction and the 4th dimension is by Linda Dalrymple Henderson, The Fourth Dimension and
Non-Euclidean Geometry in Modern Art (Princeton: Princeton University Press, 1983).
Edwin Abbot’s book, Flatland, is not specifically about the 4th dimension but it’s a lot of fun.