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The Fourth Dimension and Non-Euclidean Geometry in Modern Art, Revised Edition

by Linda Dalrymple Henderson
The MIT Press, Cambridge, MA, 2013
740 pp., illus. 140 b &w. Trade, $54.00 USD
ISBN: 978-0-262-58244-5.

Reviewed by Rob Harle


I think I can say without fear of contradiction that this book is the definitive work on the relationship of non-Euclidean geometry, the fourth dimension, however conceived, and modern art.

It was first published in 1983 from Dalrymple Henderson's 1975 original doctoral dissertation. This 2013 substantially revised edition is at the very least a goldmine of detailed information for historians, artists, scientists, spiritual practitioners and teachers alike.

The Fourth Dimension and Non-Euclidean Geometry in Modern Art is well written and quite accessible to both scholars and lay readers. The book is one of the Leonardo Book Series and offers a Foreword by Roger Malina and an extensive, comprehensive Reintroduction. This is followed by the original Introduction together with six chapters and the Conclusion. Chapters are as follows:

1 -The Nineteenth-Century Background
2 - Cubism and the New Geometries
3 - Marcel Duchamp and the New Geometries
4 - The Fourth Dimension and Non-Euclidean Geometry in America
5 – Transcending the Present; The Fourth Dimension in the Philosophy of Ouspensky and In Russian Futurism and Suprematism
6 – The New Geometries during World War 1 and the Postwar Period in France and Holland; Reevaluation and Transformation

There are Appendices, extensive notes, Bibliography and Indexes to both the Reintroduction and the 1983 Edition.

One thing this study really highlights is how scientific 'truths' are subject to change without notice! And how they become accepted totally by the public and, then, some time later rejected or at least forgotten. Prior to Einstein's theories of relativity, the fourth dimension was generally conceived of as a spatial dimension, invisible to normal human perception. With the discoveries of X-rays, wireless telegraphy, and demonstrations of electromagnetic principles the idea of an invisible something or “ether” existing could no longer be denied. “Contemporary periodicals, for example, provided instructions for wiring an antenna to one's apartment balcony in order to pick up the time signals sent out from the top of the Eiffel Tower” (p. 15).

It took some time after Einstein published his relativity theories before they would supplant the spatial fourth dimension with that of time as the fourth dimension. There has been a major resurgence in the latter part of the twentieth century in the belief that the fourth dimension (once again) is a spatial dimension. This is partly due to the introduction of super string theory and computer demonstrations that were not possible prior to its introduction. “By definition, it is extremely difficult to imagine worlds outside of our experience. For that, we are as likely to receive guidance from our artists and philosophers, as from our mathematicians and scientists” (p. 96). Anyone who doubts the possibility of dimensions more than our three obvious ones should read and/or watch Flatland, which this book discusses at length. See also my review of Flatland: A Romance of Many Dimensions (The Movie Edition) by Edwin A. Abbott - Leonardo Reviews, July 2008.

The exciting part of this book for me is the extensive discussion concerning how various artists adopted, intuited, and utilised the scientific discoveries in their artwork. Artists such as Picasso, Braque, Duchamp, Dali, Moholy-Nagy, Malevich, to name just a few, were all intrigued by the fourth dimension and their works from the second and third decades of the twentieth century were extraordinary examples of how science and art can form a mutually beneficial symbiotic relationship.

This book is an excellent example to illustrate Leonardo and ISAST’s mission, especially it's first aim: “To document and make known the work of artists, researchers, and scholars interested in the ways that the contemporary arts interact with science and technology” (p. xxi). The book weighs in at a hefty 740 pages, is extensively illustrated with black and white images of our very favourite masterpieces of modern art, and by any account is a veritable intellectual tour de force.

Dalrymple Henderson's historical investigation and exposition leaves very few stones unturned––and those that she does, she explains why. Some sections of the book are a little dry, a bit long-winded, and repetitive, but these are made palatable by the exciting tasty portions of little known connections and influences of a huge number of artists, scientists, mathematicians and occultists, such as Ouspensky, Blavatsky, Tesla, Poincaré, Steiner, Weber and Fuller, together with sections on mysticism, Theosophy and certain Russian paranormal investigations.

As this book clearly shows, the reverberations of different incarnations of the fourth dimension traverse artistic, scientific, cultural, and national boundaries, and humanity is enriched immensely by this cross-fertilisation. A must have book for historians, artists, cultural theorists, scientists and the general reader interested in the history of ideas.

Last Updated 3 June 2013

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