Surfing through Hyperspace: Understanding Higher Universes in Six Easy Lessons

266 Pages·1999·16.95 MB·English

by  Clifford A. Pickover

surfing through hyperspace
Previous Works by Clifford A. Pickover
The Alien 7Q Test
Black Holes: A Traveler's Guide
Chaos and Fractals: A Computer-Graphical Journey
Chaos in Wonderland: Visual Adventures in a Fractal World
Computers and the Imagination
Computers, Pattern, Chaos, and Beauty
Fractal Horizons: The Future Use of Fractals
Frontiers of Scientific Visualization (with Stu Tewksbury)
Future Health: Computers and Medicine in the 21st Century
The Girl Who Gave Birth to Rabbits
Keys to Infinity
The Loom of God
Mazes for the Mind: Computers and the Unexpected
Mit den Augen des Computers
The Pattern Book: Fractals, Art, and Nature
The Science of Aliens
Spider Legs (with Piers Anthony)
Spiral Symmetry (with Istvan Hargittai)
Strange Brains and Genius
Time: A Traveler's Guide
Visions of the Future: Art, Technology, and Computing in the 21st Century
Visualizing Biological Information
surfing through hyperspace
Understanding Higher Universes in Six Easy Lessons
Clifford A. Pickover
New York Oxford
OXFORD UNIVERSITY PRESS
1999
Oxford University Press
Oxford New York
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Copyright © 1999 by Clifford A. Pickover
Published by Oxford University Press, Inc.
198 Madison Avenue, New York, NY 10016
Oxford is a registered trademark of Oxford University Press
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means,
electronic, mechanical, photocopying, recording, or otherwise,
without the prior permission of Oxford University Press.
Library of Congress Cataloging-in-Publication Data
Pickover, Clifford A.
Surfing through hyperspace : understanding higher universes in six
easy lessons / by Clifford A. Pickover.
p. cm.
Includes bibliographical references and index.
ISBN 0-19-513006-5
1. Cosmology.
2. Hyperspace.
3. Fourth dimension.
4. Science—Philosophy
5. Mathematics—Philosophy.
I. Title.
QB981.P625 1999
523.1—dc21 98-48660
1 3 5 7 9 8 6 42
Printed in the United States of America
on acid-free paper

This book is dedicated to
Gillian Anderson, David Duchovny, and Chris Carter
acknowledgments and disclaimers
Dost thou reckon thyself only a puny form
When within thee the universe is folded?
—Baha'u'llah quoting Imam Ali, the first Shia Imam
I owe a special debt of gratitude to mathematician Dr. Rudy Rucker for his won-
derful books and papers from which I have drawn many facts regarding the fourth
dimension. I heartily recommend his book The Fourth Dimension for further
information on higher dimensions in science and spirituality. I also thank Dr.
Thomas Banchoff, author of Beyond the Third Dimension, for his pioneering work
in visualizing the fourth dimension. Among his many talents, Dr. Banchoff is also
an expert on the nineteenth-century classic Flatland, which continues to be an
excellent introduction to the interrelationship between worlds of different dimen-
sions. The various works of Martin Gardner, listed in the Further Readings sec-
tion, have also been influential in my formulating an eclectic view of the fourth
dimension. I thank Kirk Jensen, my editor at Oxford University Press, for his con-
tinued support and encouragement, and Brian Mansfield, Lorraine Miro, Carl
Speare, Arlin Anderson, Clay Fried, Gary Adamson, Ben Brown, Sean Henry,
Michelle Sullivan, Greg Weiss, and Dan Platt for useful advice and comments.
Brian Mansfield prepared many of the illustrations and April Pedersen drew the
wonderful small cartoons used in the chapter openings on pages 8, 43, 69, 96,
129, 155, and 163. Some of the drawings of Earthly animals, such as the seashells
and trilobites, come from the Dover Pictorial Archive; one excellent source is Ernst
Haeckel's Art Forms in Nature.
Many of the science-fiction books listed in Appendix B were suggested by Dr.
Sten Odenwald. The twisted bottle in Figure 5.10 is courtesy of artist/writer Paul
Ryan of the Earth Environmental Group and was drawn by Gary Allen. Figures 3.3,
3.8b, and 5.2 and are courtesy of the National Library of Medicine's Visible Human
Project. Don Webb is the author of the poem, "Reflections on aTesseract Rose."
The Chinese calligraphy in the Introduction was contributed by Dr. Siu-Leung
Lee, who has been practicing the art of calligraphy for more than forty years.
Capable of writing in many styles, Dr. Lee has created his own form evolving from
those of the Han and Jin dynasties. Roughly translated, his calligraphy is: "We surf
in higher dimensions." The calligraphy uses lettering that combines archaic struc-
ture and fluid movements to symbolize the dynamic nature of the universe.
This book was not prepared, approved, or endorsed by any entity associated
with the Federal Bureau of Investigation, nor was it prepared, approved, licensed,
or endorsed by any entity involved in creating or producing the X-Files TV show.
vii
An unspeakable horror seized me. There was a darkness; then a
dizzy, sickening sensation of sight that was not like seeing; I saw a
Line that was no Line; Space that was not Space; I was myself, and
not myself. When I could find voice, I shrieked aloud in agony,
"Either this is madness or it is Hell." "It is neither," calmly replied
the voice of the Sphere, "it is Knowledge; it is Three Dimensions;
Open your eye once again and try to look steadily."
—Edwin Abbott Abbott, Flatland
Even the mathematician would like to nibble the forbidden fruit,
to glimpse what it would be like if he could slip for a moment into
a fourth dimension.
—Edward Kasner and James Newman,
Mathematics and the Imagination
May I pass along my congratulations for your great interdimen-
sional breakthrough. I am sure, in the miserable annals of the
Earth, you will be duly inscribed.
—Lord John Whorfin
in The Adventures ofBuckaroo Banzai Across the 8th Dimension
A man who devoted his life to it could perhaps succeed in picturing
himself a fourth dimension.
—Henri Poincare, "L'Espace et la geometrie"
contents
Preface xi
Introduction xxi
1.
Degrees of Freedom 3
2. The Divinity of Higher Dimensions 23
3. Satan and Perpendicular Worlds 53
4. Hyperspheres and Tesseracts 81
5. Mirror Worlds 119
6. The Gods of Hyperspace 141
Concluding Remarks 163
Appendix A 169
Mind-Bending Four-Dimensional Puzzles
Appendix B 175
Higher Dimensions in Science Fiction
Appendix C 185
Banchoff Klein Bottle
Appendix D 188
Quaternions
ix