The Fourth Dimension and Non-Euclidean Geometry in Modern Art

by Linda Dalrymple Henderson

The long-awaited new edition of a groundbreaking work on the impact of alternative concepts of space on modern art. In this groundbreaking study, first published in 1983 and unavailable for over a decade, Linda Dalrymple Henderson demonstrates that two concepts of space beyond immediate perception—the curved spaces of non-Euclidean geometry and, most important, a higher, fourth dimension of space—were central to the development of modern art. The possibility of a spatial fourth dimension suggested that our world might be merely a shadow or section of a higher dimensional existence. That iconoclastic idea encouraged radical innovation by a variety of early twentieth-century artists, ranging from French Cubists, Italian Futurists, and Marcel Duchamp, to Max Weber, Kazimir Malevich, and the artists of De Stijl and Surrealism. In an extensive new Reintroduction, Henderson surveys the impact of interest in higher dimensions of space in art and culture from the 1950s to 2000. Although largely eclipsed by relativity theory beginning in the 1920s, the spatial fourth dimension experienced a resurgence during the later 1950s and 1960s. In a remarkable turn of events, it has returned as an important theme in contemporary culture in the wake of the emergence in the 1980s of both string theory in physics (with its ten- or eleven-dimensional universes) and computer graphics. Henderson demonstrates the importance of this new conception of space for figures ranging from Buckminster Fuller, Robert Smithson, and the Park Place Gallery group in the 1960s to Tony Robbin and digital architect Marcos Novak.

Genres: Art, Nonfiction, Science, Mathematics, Art History, Geometry

729 pages, Hardcover

First published August 1, 1983

Reviews

[Sean Flinchpaugh · Rating 3 out of 5]

Would probably rate higher if I had a more in-depth background on Cubism and art movements circa 1910-1920. Reads as an addendum, or cultural critique, and if you don't come into the party with a certain level of knowledge, well hell, it's not gonna be a good party. It did help with visualizing the 4th dimension a bit and I both understand/appreciate what Cubists were trying to convey, so at the very least if you come away with a new appreciation of Cubism it won't be a total loss.

[John · Rating 4 out of 5]

Skipped chapters on America and Duchamp.

[A L]

An epic work of art history that helps to make the sequence of modernist art more coherent in the light of its summaries of contemporary science & superstitious trends.

[Tom Schulte · Rating 4 out of 5]

This revised edition of a work first published in 1983 details the impact and spread of non-Euclidean geometry and the idea of a fourth dimension into, mainly, early Twentieth Century art and thought. Henderson covers the gamut from philosophy topainting, literature to the plastic arts, and beyond. Along with a new index, there is an extensive hundred-page “Reintroduction” serving as the author’s reappraisal, history, and synopsis of this impressive work. Looking back on the three decades since publishing, Henderson considers the further impact of these concepts on art and culture in the late Twentieth Century. The work is well illustrated and it would have been nice had at least some of the numerous black and white plates been upgraded to color ones. This work is strongly persuasive that interpreting the fourth dimension theories and related topics was fundamental to the development of modern art...

[See my full review at MAA Reviews]

[Fraser Sherman · Rating 4 out of 5]

I actually read the recent second edition of this book but they're both impressive. Henderson looks at popular perceptions of the fourth dimension back when it was seen as a dimension of space rather than time and how some artists embraced that and attempted to capture a fourth dimension in their work (it played a part in Cubism's approach to art for instance). For others it was more of a mystical element, the dimension where the intensity and passion of art resided. Quite fascinating, with the obvious caveat that it's pretty specialized (there were some bits I just skimmed over).

[katie luisa borgesius]

Holy shit, seriously?