In the early years of the twentieth century, the striking scientific developments of the period included a great increase in popular and professional attention to non-Euclidean geometry. One of the leading scholars of the subject was Henri Poincaré, who was also a widely read theorist of the scientific discovery process, keenly concerned with the role of the intuition and the subconscious. His writings, and those of his interpreters, could well have increased the appeal of four-dimensional geometry for artists already attracted to the possibilities presented by these concepts. The working notes of one such artist, Marcel Duchamp, record directly his debt to ideas linked to Poincaré—an example of the interaction of greatly different parts of the wider culture.
An earlier version of this paper was presented on 5 November 1999 at the conference “Methods of Understanding in Art and Science: The Case of Duchamp and Poincaré,” at Harvard University Science Center, Cambridge, MA.