I recently had the honor of winning an award for my book "Cosmic Catastrophes" from my university. One of the unanticipated benefits of that was meeting Linda Henderson at the award banquet. Professor Henderson is an art historian who wrote a remarkable book that I am enjoying. It is called "The Fourth Dimension and Non-Euclidian Geometry in Modern Art," (Princeton University Press, 1983). The book will be reprinted by MIT Press and she is working on a new essay for that which will address the topic in the latter half of the 20th century. I had vaguely understood that cubism was an attempt to throw off the shackles of Renaissance perspective and view things, figures, from different orientations simultaneously. Picasso and Braque may not have been directly affected, but Henderson makes a persuasive case that many of the cubists were, in fact, attempting to view things, not just from different three-dimensional perspectives, but from a fourth spatial dimension.

The background to this begins with Nikolai Ivanovich Lobachevsky and Janos Bolyai in the 1820s and their explorations of non-Euclidian geometry and to Georg Friedrich Berhhard Riemann's exposition of differential geometry around 1860. One can study the geometry of curved space in the confines of the dimensionality of that space, but there is a strong instinct to ask about the space, that of higher dimensions, into which the curved space curves. The idea that there was a space of four dimensions in which our normal perceptual space of three dimensions is embedded gained considerable popular currency after the mathematical work of these pioneers. Notions of the fourth dimension provided the stimulus for work by Charles Howard Hinton, inventor of the word "tesseract" and related notions in the 1880s, and for E. A. Abbott's delightful "Flatland," published in 1884. By the end of the 19th century and the beginning of the 20th, such thinking was popularized in France by Poincare. The notion of the fourth dimension became part of many people's philosophy and world view.

One of the interesting characters in this development, unknown to me until I delved into Henderson's history, was Maurice Princet. Princet was an insurance actuary by trade, but being mathematically inclined, he knew something of four-dimensional geometry. More to the point, he ran with the crew of cubists in Paris in the early 20th century. It is not clear that he had a direct influence on Picasso, who may have been pursuing his own fiercely independent motivations, but there is no doubt that "la quatrieme dimension" was in the air at the time and that some cubists, like Jean Metzinger, credited Princet for influencing their thinking. With this background in mind, one can see intimations of tesseracts and more in the work of Duchamp, Gris, and others.

This parallel development of mathematics and art was interrupted by Einstein and Minkowski. With their work came the notion that time was the fourth dimension. The work of Einstein has had a powerful effect on popular culture, but the influence of a fourth spatial dimension on popular culture and art shrank from the limelight. There are still pockets of activity. These parallel worlds of art, science and popular culture are explored in Steve Martin's charming play, "Picasso at the Lapin Agile." Some artists are still striving to capture the richness of a fourth dimension. Check out work by Marcos Novak and a book by Tony Robbin, "Fourfield: Computers, Art, and the Fourth Dimension" (Little Brown, 1992). There is also the new "Flatterland" by Ian Stewart and the recently published "Einstein, Picasso" by Arthur Miller, a new exploration of Henderson's theme.

What is really new, however, is the vision arising from string theory with its 10 dimensions of space and one of time, its folded Calabi-Yau geometries, and, most recently, considerations of brane worlds and the higher dimensional "bulk" in which they are embedded. String theorists refer to a five-dimensional bulk in which our Universe may float, but they are working with a space of four spatial dimensions plus time. The fourth dimension is back! The radical ideas of string theory are beginning to permeate into popular consciousness, especially among people who are stimulated by new scientific ideas, for instance fans of SPACE.com who with great acumen recently voted "nothing" as the most exciting development in outer space, a reference to the mysterious dark energy that may accelerate the Universe and have its origin in stringy things.

A fascinating prospect will be to see whether the parallel worlds of art and science converge again in the fourth dimension as they did one hundred years ago.