The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion

The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion THE NEW GEOMETRIES IN ART AND THEORY 1900-1930 During the first three decades of the twentieth century, the fourth dimension was a concern common to artists in nearly every major modern movement: Analytical and Synthetic Cubists (as well as Duchamp, Picabia, and Kupka), Italian Futurists, Russian Futurists, Suprematists, and Constructivists, American modernists in the Stieglitz and Arensberg circles, Dadaists, and members of De Stijl. While the rise of Fauvism and German Expressionism preceded the first artistic application of higher dimensions by the Cubists, Matisse himself later demonstrated a passing interest in the subject. And, even though the German Bauhaus was not an active center of interest in the fourth dimension, it, too, was touched by the idea through the propagandizing of Van Doesburg, Kandinsky’s own awareness of the idea, and the growing interest in Germany in the space-time world of Einstein. Although by the end of the 1920s the temporal fourth dimension of Einsteinian Relativity Theory had largely displaced the popular fourth dimension of space in the public mind, one further movement was to explore a fourth spatial dimension (and non-Euclidean geometry): French Surrealism. While acknowledging Einstein’s theories, AndrC Breton and various Surrealist painters during the 1930s and 1940sretained many ofthe preEinsteinian implications of ‘the fourth dimension’ and non-Euclidean geometry. Non-Euclidean geometry never achieved the widespread popularity of the fourth dimension, which possessed many more nongeometric associations. As a result, the list of artists and critics actively interested in non-Euclidean geometry was considerably smaller. In addition to Duchamp and the Cubists Metzinger and Gleizes, the main advocates of nonLinda Dalrymple Henderson is a teacher. Art Department, University of Texas, University Station, Austin, TX 78712. U.S.A. From Linda Dalrymple Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Arf. Copyright 0 1983 by Princeton University Press. Excerpts, pp. 339-352, reprintedby permission of Princeton University Press. Linda Dalrymple Henderson Euclidean geometry were the Russian poet Khlebnikov and the painter El Lissitzky, and rebel spirits such as Benjamin de Casseres, Dada founder Tristan Tzara, and, later, the Surrealists. For all of these individuals, whether they explored its principles or not, nonEuclidean geometry signified a new freedom from the tyranny of established laws. Codified in PoincarYs philosophy of conventionalism, this recognition of the relativity of knowledge was a powerful influence on early twentiethcentury thought. Thus, even artists who concentrated on the fourth dimension alone owed something to the nonEuclidean geometries that had prepared the way for the acceptance of alternative kinds of space. Like non-Euclidean geometry, the fourth dimension was primarily a symbol of liberation for artists. However, the notion of a higher dimension lent itself to painterly applications far more easily than did the principles of non-Euclidean geometry. Specifically, belief in a fourth dimension encouraged artists to depart from visual reality and to reject completely the one-point perspective system that for centuries had portrayed the world as three-dimensional. The late nineteenth-century resurgence of idealist philosophy provided further support for painters to proclaim the existence of a higher, four-dimensional reality, which artists alone could intuit and reveal. Among those who subscribed to this view of the fourth dimension were the Cubists, Kupka, the Futurists Boccioni and Severini, Max Weber, Malevich and his Russian colleagues, and Mondrian and Van Doesburg. For the artists of this group whose distrust of visual reality was most deep-seated, belief in a fourth dimension was an important impetus to create a totally abstract art. Malevich’s ‘objectless’ style was the most directly indebted to the fourth dimension, but both Kupka and Mondrian accepted the idea as a supplement to their Theosophical beliefs. And, even though the term the fourth dimension does not figure in Kandinsky’s early writings, the belief of his era in the possibility of higher dimensions stands, along with Steiner’s Christian Theosophy, behind his antimaterialist philosophy. Two last figures who were less inclined toward otherworldly beliefs, Picabia and Larionov, also identified total abstraction in art with the fourth dimension. The fourth dimension also supported bold experimentation by those painters who did not reject visual experience entirely...