Discovering Duchamp through the “Fourth Dimension” in 1971

As a first-year graduate student in a Yale seminar with Robert Herbert, I had followed his superb suggestion to explore early twentieth century usages of the term “fourth dimension” in artists’ and critics’ writings. By the 1940s a body of art critical writing had developed spuriously connecting that idea to Einstein’s Relativity Theory, where it signified time. By contrast, as I discovered, before 1919 the “fourth dimension” had signified a higher dimension of space of which our three-dimensional world would be merely a section or shadow. Recovering that forgotten extra spatial dimension, which had been eclipsed by Einstein’s rise to celebrity as of 1919, I wrote an MA qualifying paper on its importance for Cubist artists and published in it The Art Quarterly in 1971. But we wondered, could there possibly be enough in this topic for a dissertation?

A moment of synchronicity in 1970–71 brought revelations that made clear there would be. In 1970 the Stedelijk Museum’s first major Kazimir Malevich exhibition had revealed his use of “Fourth Dimension” in his titles. And, most importantly, there was a clue in the entry for Duchamp’s 1920 Rotary Glass Plates in the 1968 catalog of the MOMA exhibition The Machine as Seen at the End of the Mechanical Age. There Pontus Hultén, drawing on research by his friend Ulf Linde, had written: “Duchamp was very interested in the theories and speculations of two French mathematicians Poincaré and Jouffret, who had written about a non-Euclidean, fourth-dimensional geometry.”

In response to a query I sent to Linde at Hultén’s suggestion, I learned of the publication by the Cordier & Ekstrom Gallery of Duchamp’s deluxe A l’infinitif (The White Box) in 1967, which included his many notes on the fourth dimension. A visit to MOMA’s print room to view the notes made clear the extent of his engagement with popular ideas about higher dimensions and with four-dimensional geometry, for which he created his own playful postulates. In the contrast between four and three dimensions Duchamp found a means to create the insuperable divide he was seeking between the realms of the Bride and the Bachelors in his The Large Glass, The Bride Stripped Bare by Her Bachelors, Even (1915–23). During 1912–15, he had made hundreds of notes for that project. However, in his first major publication of notes, the 1934 Green Box, Duchamp excluded all of the fourth-dimension focused notes, undoubtedly because Einstein’s theories had superseded the spatial fourth dimension by that time. Happily, in 1973 the White Box notes, along with those of the Green Box, were published as Salt Seller: The Writings of Marcel Duchamp, easing access to the notes for scholars as well as contemporary artists.

It was work on the Duchamp chapter of the dissertation, which ultimately became The Fourth Dimension and Non-Euclidean Geometry in Modern Art (1983; new edition, MIT Press, 2013), that immersed me in the artist’s works and writings. There I discovered his brilliant mind and wit as well as his creative invention as an artist challenging traditional artmaking. But grappling with the fourth-dimension oriented notes was often difficult, since they were so complex: was this humor or had he misunderstood, for example, how two-dimensional lines would relate to four-dimensional space? After I’d written to the distinguished Yale historian of mathematics, Asger Aaboe, to ask which postulate of Euclid was pictured in the weathered geometry book in Duchamp’s Unhappy Readymade (1919), he wrote back a full explanation; he concluded his letter, “Anyway, what is a nice young lady like you doing with such a cuckoo fellow as Duchamp?” I kept that comment on my bulletin board, thinking that once the dissertation was finished, I probably wouldn’t work on Duchamp again.

But the artist had a surprise in store for scholars after his death in 1968. In 1980 the Centre Pompidou published a collection of 289 previously unpublished notes, the majority of which had been written in 1912–15. When in the mid-1980s I began research on X-rays, I took a look at those notes and was struck at the prevalence of references to chemistry and physics in them. Clearly, Duchamp had found there an important model for the impersonal execution and the content of his technoscientific allegory of quest in The Large Glass. Following his lead, I dove into the science and technology that had dominated the pre-World War I era—e.g., X-rays, radioactivity, electrons, the ether of space, and wireless telegraphy. By now I was hooked and had no hesitation about following Duchamp wherever he might lead me, resulting in my 1998 book Duchamp in Context: Science and Technology in the Large Glass and Related Works.

Now I am working on a book titled Ether and the Energies of Modernism: Art, Science, and Occultism in the Early 20th Century, and who is central to it? None other than Marcel Duchamp, who truly changed my life.