Fourfield

Computers, Art & the 4th Dimension

by Tony Robbin

foreword by Rudy Rucker

Bullfinch, 1992, First Edition, 082121909X, Hardcover, Dust Jacket, Fine/Fine condition, remainder mark on page ends, no underlining, no highlighting, 199 pages.

24 color and 73 black-and-white illustrations

Although a fascination with the fourth dimension and the search for ways of depicting it have engage( artists for more than a century, only the computer makes such depiction truly possible. Using the computer as a tool, painter and sculptor Tony Robbin has devoted his life as an artist to this quest Fourfield is both a record of that quest and an eloquent testament to the value of its fulfillment.

The understanding and appreciation of space as presented in works of art have changed over the centuries, and Robbin suggests that the time is ripe for our perception of space to undergo another radical shift. He makes clear that "seeing" space in three dimensions is merely a culturally based assumption, no more and no less valid than apprehending space in any other way. This realization frees us to understand space much as a computer might—as fluid, ever changing, and dynamic. It has also freed Robbin to create exhilarating and amazing works, derived from his original blending of art, science, and mathematics.

Fourfield is a firsthand account of the artist's visual, intellectual, and philosophical evolution, which has taken him from paintings in a traditional two-dimensional format to those in which rods extending from the canvas and the shadows they produce present a visual experience of four dimensions. Most recently, Robbin has created sculpture that incorporates quasicrystals ("crystals" made up of nonrepeating patterns) and whose appearance varies with the viewer's position and the orientation of light. This experimentation is suggesting startling new directions in architecture as well.

To assist the reader in comprehending this seemingly magical world, Fourfield comes with an image of a pattern of four-dimensional cubes, known as hypercubes, and special glasses through which to view it. Also included is an order form for a diskette containing a number of the computer programs developed by Robbin as he explored the world of computers and art.

Written with a voice of eloquence and clarity for anyone interested in art, science, mathematics, computers, or philosophy, Fourfield is, however, not for the timid. Just as Douglas Hofstadter's Godel, Escher, Bach and Robert Pirsig's Zen and the Art of Motorcycle Maintenance altered their readers' perceptions, readers of Fourfield will find their way of seeing the world changed forever.


Tony Robbin's paintings and sculpture have been exhibited in numerous museums and galleries in the United States and Europe, including solo exhibitions at New York's Whitney Museum of American Art and the Tibor de Nagy Gallery. Robbin, who lives in New York with his wife and son, has written many articles for such publications as ARTnews, Arts, and Leonardo. Fourfield is his first book.

Rudy Rucker is a mathematician who is well known for his books on mathematics and science, including The Fourth Dimension: A Guided Tour of the Higher Universes and Mind Tools: The Five Levels of Mathematical Reality. He is also the author of many works of science fiction.

Linda Dalrymple Henderson is Associate Professor of Art History at the University of Texas at Austin. Recognized as a leading authority on modern artists who have been influenced by science and mathematics, she is the author of The Fourth Dimension and Non-Euclidean Geometry in Modern Art.

Jacket design by Rick Horton

 

CONTENTS

Acknowledgments
Foreword by Rudy Rucker
Introduction by Linda Dalrymple Henderson

Prologue
1. Einstein's Cave
For a hundred years mathematicians have been drawing pictures of figures in four-dimensional space. It is now recognized by art historians that these esoteric drawings are one of the three or four main sources for the invention of modern art. Now, with the use of computers, it is possible for all to see the fourth dimension directly and to perceive it as real.
2. Emotional Equations: Space in Mathematics and Art
Space in art has always developed parallel to space in mathematics and science, because "space" is a cultural concept. Looking at the concept of space in ancient Greece, in the Renaissance, and at the beginning of the twentieth century makes this claim clear. What our culture is now telling us about space is not that it is a field (a concept from Van Gogh's time, still called modern), but that it is a network of wormholes.
3. Chinese Boxes and Shadows from Heaven
The geometry of four spatial dimensions teaches us to distinguish between slices and projections of geometric figures. This distinction' helps us to understand relativity as well as leading to a new strategy of making four-dimensional works of art.
4. Patterns in the Ether
Humans have a special biology that enables us to see and make sense of patterns. "Space" is really the functioning of the right brain. Four-dimensional space means patterns of four-dimensional figures. A wholly new class of patterns — quasicrystals, which are nonrepeating patterns in three-dimensional space -- behave as though they were four-dimensional. Quasicrystals can be exploited for a marvelous new architecture of rich ambiguity, flux, and subtle order.

5. Curvature: Lobofour and Nonclid
The most dramatic breakthroughs in contemporary geometry are in topology. Computers applied to curved and strangely connected three-dimensional spaces are causing a revolution in seeing. Such new spaces will inevitably enrich our pictorial arts.
6. Time in Space: Three Enigmas of Space
In spite of all these new spaces seen, the concept of space is still full of paradox: how quantum effects can occur in space, whether empty space has any substance, and how space makes time be an arrow.
All these questions are now considered legitimate concerns of geometry that mathematicians and physicists are beginning to address.
7. Exebar Speaks!
Artists are applied mathematicians, and thus mathematicians can learn about mathematical creativity from them. My generation was captivated by Oriental art, which embodies spatial concepts we intuit to be relevant to our own culture and to the completion of our personalities. The emotional satisfaction of these new geometries is discussed.
Black-and-white Plates
Appendix 1: Vincent Van Gogh's Letter
Appendix 2: Hardware and Software Notes
Notes
Glossary
Bibliography
Index

 

 

 

nthdegree books