The Fourth Dimension: Toward a Geometry of Higher Reality PDF
Preview The Fourth Dimension: Toward a Geometry of Higher Reality
The Fourth Dimension Toward a Geometry of Higher Reality Rudy Rucker Foreword by Martin Gardner Illustrations by David Povilaitis Dover Publications, Inc. Mineola, New York Copyright Copyright © 1984, 2014 by Rudy Rucker All rights reserved. Bibliographical Note The Fourth Dimension: Toward A Geometry of Higher Reality, first published by Dover Publications, Inc., in 2014, is an unabridged republication of The Fourth Dimension: A Guided Tour of the Higher Universes, originally published in 1984 by Houghton Mifflin Company, Boston. The author has provided a new Preface for this edition. Library of Congress Cataloging-in-Publication Data Rucker, Rudy, v. B. (Rudy von Bitter), 1946- The fourth dimension: toward a geometry of higher reality / Rudy Rucker; foreword by Martin Gardner; illustrations by David Povilaitis. p. cm. Originally published: Boston: Houghton Mifflin, 1984. Includes bibliographical references and index. eISBN-13: 978-0-486-79819-6 1. Fourth dimension. 2. Hyperspace. 3. Quantum theory. I. Title. QA699.R79 2014 530.11—dc23 2014015296 Manufactured in the United States by Courier Corporation 77978501 2014 www.doverpublications.com For A Square, on his hundredth anniversary Contents Preface to the Dover Edition Foreword by Martin Gardner Preface I. The Fourth Dimension 1. A New Direction 2. Flatland 3. Pictures of the Gone World 4. Through the Looking Glass 5. Ghosts from Hyperspace? II. Space 6. What We’re Made Of 7. The Shape of Space 8. Magic Doors to Other Worlds III. How To Get There 9. Spacetime Diary 10. Time Travel and Telepathy 11. What Is Reality? Puzzle Answers Bibliography Index Preface to the Dover Edition WHEN I WAS GROWING UP in the 1950s, my main sources of esoteric information were mail-order paperbacks from Dover Books. I devoured Dover’s volumes on mazes, the fourth dimension, infinity, and language games—all of these to become lifelong interests. My Fourth Dimension has been one of my best-selling books, with translations appearing in France, Israel, Italy, Japan, Korea, Germany, the Netherlands, Portugal, and spain. I’m very pleased that Dover is republishing it in paperback and ebook editions. The fourth dimension is a universal skeleton key, applicable to any number of conundrums. I always start with the hallowed Flatland analogy: 4-D is to 3-D as 3-D is to 2-D. By now, good old A Square feels like a friend of mine, or perhaps an eccentric cousin. Eventually I went so far as to write a novel called Spaceland, featuring a man named Joe Cube. He begins in our normal world, encounters a four-dimensional being, and travels into higher space. It was an interesting challenge for me to visualize what he saw there. As usual, my starting point was Flatland. I’m glad to have had the fourth dimension in my life for so many years. And I’m happy to share this higher knowledge with you. Welcome to The Fourth Dimension! Rudy Rucker June 22, 2014 Foreword by Martin Gardner As WRITERS, mathematicians are notoriously inept. There are happy exceptions, of course, and at least one teacher of mathematics, Lewis Carroll, wrote immortal fantasy fiction. Eric Temple Bell not only wrote colorfully about mathematics for laymen, but under the pseudonym John Taine he churned out a raft of science fiction novels. In more recent times, several professional mathematicians have written science fiction with strong mathematical underpinnings. Now along comes Rudolf von Bitter Rucker — mathematician, novelist, cartoonist, rock music buff, and a thinker with the courage to explore dark and unfamiliar territory in what he likes to call the mindscape. Rucker’s major mathematical interests are transfinite sets (he has a doctorate in mathematical logic from Rutgers) and spaces of higher dimensions. After editing a selection of Charles Hinton’s writings about the fourth dimension, and writing a popular account of four-space and relativity, Rucker’s first big success came in 1982 with the publication of Infinity and the Mind. Science fiction fans had earlier known him for his wild, funny, sexually outrageous novels and stories in which higher spaces often play essential roles. His best-known novel, White Light, actually has the subtitle What Is Cantor’s Continuum Problem? The subtitle is the exact title of a paper by the eminent logician Kurt Gödel, with whom Rucker had the privilege of many stimulating conversations. The Fourth Dimension: Toward a Geometry of Higher Reality will be eagerly read by writers and readers of science fiction, but anyone with even a minimal interest in mathematics and fantasy will find the book as informative and mind- dazzling as Rucker’s book on infinity. After exploring the whimsical underworld of Flatland, he plunges into spaces above three with a zest and energy that is breathtaking. The book is interspersed with clever problems for the mathematically competent, and finally, in a grand Carrollian climax, Rucker boldly invades the infinite dimensions of Hilbert space. Science fiction? In part, yes, and Rucker pauses frequently to quote from some of his bizarre tales. But without the tool of infinite-dimensional spaces, modern physics would be almost impossible. Older books on quantum mechanics talk about how the measurement of particles and quantum systems “collapses the psi function.” More recent books prefer the language of a complex Hilbert space, an approach adopted by John von Neumann in his classic work on quantum theory. When you measure a quantum system you are said to “rotate the state vector,” an abstract line of precisely defined length and orientation that represents the system’s state in a set of coordinate systems that constitute a Hilbert space. Are such spaces “real”? Or are they no more than convenient fictions used by physicists to simplify their calculations? It is with such deep ontological questions that Rucker concerns himself throughout this book and especially in the final chapters. Here I am unable to go along with his “All is One” philosophy. He seems to have inherited a genetic fondness for the Absolute from his great-great-great-grandfather, the famous philosopher Hegel. Like William James, I do not know if ultimate reality is One or Many. Nor can I accept Rucker’s views on synchronicity, taken over from Jung and Koestler, and his seeming belief that consulting the I Ching is more likely to produce meaningful “coincidences” than consulting say, Homer, the Bible, or the works of Isaac Asimov. But no matter. We are each entitled to what fames called our “over beliefs.” Whether you agree or disagree with Rucker’s Tao-tinged metaphysics, you will find his speculations twisting your mind toward fundamental questions that refuse to go away no matter how hard pragmatists and positivists try to banish them. Preface IN 1958, the Louisville Free Public Library had a single shelf of science fiction books. My friend Niles Schoening and I used to read and discuss them, wondering about time travel, wondering about the fourth dimension. This is where it all began. When I went off to college in 1963, my father, Embry Rucker, gave me a copy of Edwin Abbott’s Flatland. As an Episcopal priest, my father had already realized that the fourth dimension can serve as a symbol for higher spiritual realities. In the ensuing years, I puzzled over the relationship between the fourth dimension as higher reality, and the fourth dimension as time. When I got my first teaching job, at SUNY Geneseo, I began working out these connections in my lectures for a course on higher geometry. These lectures were published by Dover Publications in 1977, under the title Geometry, Relativity and the Fourth Dimension. In the seven years since then, I’ve learned a lot more about the fourth dimension. In writing The Fourth Dimension: Toward a Geometry of Higher Reality, I’ve tried to present a definitive and popular account of what the fourth dimension means, both physically and spiritually. I am grateful to Martin Gardner for lending me a number of rare books on the fourth dimension; to Thomas Banchoff for his help with the more technical research; to my editor, Gerard Van der Leun, for his encouragement; and to my illustrator, David Povilaitis, for his wit and weirdness. Most of all, I would like to thank my family, my friends, my students, and my correspondents. Enjoy the book!
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