Rudy Rucker - 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

530.11dc23

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

WHEN I WAS GROWING UP in the 1950s, my main sources of esoteric information were mail-order paperbacks from Dover Books. I devoured Dovers volumes on mazes, the fourth dimension, infinity, and language gamesall 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. Im 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.

Im glad to have had the fourth dimension in my life for so many years. And Im 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.

Ruckers 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 Hintons writings about the fourth dimension, and writing a popular account of four-space and relativity, Ruckers 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 Cantors Continuum Problem? The subtitle is the exact title of a paper by the eminent logician Kurt Gdel, 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 Ruckers 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 systems 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 Ruckers 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 Ruckers 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 Abbotts 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, Ive learned a lot more about the fourth dimension. In writing