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about the author Clifford A. Pickover received his Ph.D. from Yale University's Department of Molecular Biophysics and Biochemistry. He graduated first in his class from Franklin and Marshall College, after completing the four-year undergraduate program in three years. He is author of the popular books The Science of Aliens (Basic Books, 1998), Strange Brains and Genius (Plenum, 1998), Time: A Traveler's Guide (Oxford University Press, 1998), The Alien 7Q Test (Basic Books, 1997), The Loom of God (Plenum, 1997), Black Holes: A Traveler's Guide (John Wiley & Sons, 1996), and Keys to Infinity (Wiley, 1995). He is also the author of numerous other highly acclaimed books including Chaos in Wonderland: Visual Adventures in a Fractal World (1994), Mazes for the Mind: Computers and the Unexpected (1992), Computers and the Imagination (1991) and Computers, Pattern, Chaos, and Beauty (1990), all published by St. Martin's Press—as well as the author of over 200 articles concerning topics in science, art, and mathematics. He is also coauthor, with Piers Anthony, of Spider Legs, a science-fiction novel recently listed as Barnes & Noble's second best-selling science-fiction title. Pickover is currently an associate editor for the scientific journals Computers and Graphics, Computers in Physics, and Theta Mathematics Journal, and is an editorial board member for Odyssey, Speculations in Science and Technology, Idealistic Studies, Leonardo, and YLEM. He has been a guest editor for several scientific journals. He is the editor of Chaos and Fractals: A Computer-Graphical Journey (Elsevier, 1998), The Pattern Book: Fractals, Art, and Nature (World Scientific, 1995), Visions of the Future: Art, Technology, and Computing in the Next Century (St. Martin's Press, 1993), Future Health (St. Martin's Press, 1995), Fractal Horizons (St. Martin's Press, 1996), and Visualizing Biological Information (World Scientific, 1995), and coeditor of the books Spiral Symmetry (World Scientific, 1992) and Frontiers in Scientific Visualization (John Wiley & Sons, 1994), Dr. Pickover's primary interest is finding new ways to continually expand creativity by melding art, science, mathematics, and other seemingly disparate areas of human endeavor. The Los Angeles Times recently proclaimed, "Pickover has published nearly a book a year in which he stretches the limits of computers, art and thought." Pickover received first prize in the Institute of Physics' "Beauty of Physics Photographic Competition." His computer graphics have been featured on the covers of many popular magazines, and his research has recently received considerable attention by the press—including CNN's "Science and Technology Week," The Discovery 233
234 about the author Channel, Science News, the Washington Post, Wired, and the Christian Science Monitor—and also in international exhibitions and museums. OMNI magazine recently described him as "Van Leeuwenhoek's twentieth-century equivalent." Scientific American several times featured his graphic work, calling it "strange and beautiful, stunningly realistic." Pickover has received numerous U.S. patents, including Patent 5,095,302 for a 3-D computer mouse, 5,564,004 for strange computer icons, and 5,682,486 for black-hole transporter interfaces to computers. Dr. Pickover is currently a Research Staff Member at the IBM T. J. Watson Research Center, where he has received sixteen invention achievement awards, three research division awards, and four external honor awards. Dr. Pickover is also lead columnist for the brain-boggier column in Discover magazine. Dr. Pickover's hobbies include the practice of Ch'ang-Shih Tai-Chi Ch'uan and Shaolin Kung Fu, raising golden and green severums (large Amazonian fish), and piano playing (mostly jazz). He is also a member of the SETI League, a group of signal-processing enthusiasts who systematically search the sky for intelligent, extraterrestrial life. Visit his web site, which has received over 200,000 visits: http://sprott.physics.wisc.edu/<strong>pickover</strong>/home.htm. He can be reached at P.O. Box 549, Millwood, New York 10546-0549 USA.
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surfing through hyperspace
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surfing through hyperspace Understa
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This book is dedicated to Gillian A
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An unspeakable horror seized me. Th
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X contents Appendix E Four-Dimensio
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xii preface I first became excited
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XIV preface problems—from a four-
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XVI preface My soul is an entangled
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XVIII preface I've attempted to mak
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The trouble with integers is that w
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XXII introduction cal and national
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xxiv introduction snaps a few photo
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surfing through hyperspace
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degrees of freedom FBI Headquarters
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DEGREES OF FREEDOM 5 Figure 1.1 A f
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DEGREES OF FREEDOM 7 Figure 1.3 A f
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DEGREES OF FREEDOM -9 1800s. Howeve
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DEGREES OF FREEDOM -11 Although phi
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DEGREES OF FREEDOM 13 angles and lo
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DEGREES OF FREEDOM 15 with other my
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DEGREES OF FREEDOM 17 Figure 1.4b K
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DEGREES OF FREEDOM 19 Figure 1.5 An
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DEGREES OF FREEDOM 21 time-like cha
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the divinity of higher dimensions F
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THE DIVINITY OF HIGHER DIMENSIONS 2
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Figure 2.9 A ball being pushed thro
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satan and perpendicular worlds Wash
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SATAN AND PERPENDICULAR WORLDS 55 a
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SATAN AND PERPENDICULAR WORLDS 57 S
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SATAN AND PERPENDICULAR WORLDS 59 F
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Figure 3.5 A "hyperspace" blood tra
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SATAN AND PERPENDICULAR WORLDS 63 t
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SATAN AND PERPENDICULAR WORLDS 65 "
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SATAN AND PERPENDICULAR WORLDS 67 E
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SATAN AND PERPENDICULAR WORLDS 69 T
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SATAN AND PERPENDICULAR WORLDS 71 S
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Figure 3.13 Chess played on a Mobiu
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SATAN AND PERPENDICULAR WORLDS 79 d
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hyperspheres and tesseracts FBI Hea
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HYPERSPHERES AND TESSERACTS 83 simp
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Figure 4.2 Strange universes, (a) T
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HYPERSPHERES AND TESSERACTS 87 runn
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HYPERSPHERES AND TESSERACTS 89 Poin
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HYPERSPHERES AND TESSERACTS 91 "Sal
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Figure 4.8 The Crucifixion {Corpus
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HYPERSPHERES AND TESSERACTS 95 Figu
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HYPERSPHERES AND TESSERACTS 97 Hint
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HYPERSPHERES AND TESSERACTS 99 Next
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Figure 4.10 Slices of a hypercube a
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Figure 4.13 Embryonic 5-D cube in F
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HYPERSPHERES AND TESSERACTS 105 Fig
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HYPERSPHERES AND TESSERACTS 107 Fig
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HYPERSPHERES AND TESSERACTS 109 4-D
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Figure 4.21 Volume of a radius 2 sp
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HYPERSPHERES AND TESSERACTS 113 How
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HYPERSPHERES AND TESSERACTS 115 ans
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HYPERSPHERESANDTESSERACTS 117 Figur
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mirror worlds FBI Headquarters, Was
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MIRROR WORLDS 121 "I've designed a
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MIRROR WORLDS 123 Sally puts her he
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MIRROR WORLDS 125 Figure 5.4 A stri
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MIRROR WORLDS 127 "Me too." She pla
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MIRROR WORLDS 129 Zollner Experimen
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MIRROR WORLDS 131 not possible; per
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MIRROR WORLDS 133 Rotate Figure 5.6
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MIRROR WORLDS 135 To get a better u
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MIRROR WORLDS 137 Figure 5.9 Comput
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MIRROR WORLDS 139 Figure 5.11 A mor
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the gods of hyperspace The White Ho
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THE GODS OF HYPERSPACE 143 Sally tu
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THE GODS OF HYPERSPACE 145 "What's
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THE GODS OF HYPERSPACE 147 Figure 6
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Figure 6.2 The cross section of 4-D
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THE GODS OF HYPERSPACE 151 Figure 6
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THE GODS OF HYPERSPACE 153 You take
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THE GODS OF HYPERSPACE 155 "Let's d
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Figure 6.4 Cross-sections of higher
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THE GODS OF HYPERSPACE 159 The mana
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THE GODS OF HYPERSPACE 161 Kindling
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concluding remarks This completes o
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CONCLUDING REMARKS 165 If intellige
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CONCLUDING REMARKS 167 swered. I ho
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appendix a mind-bending four-dimens
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MIND-BENDING FOUR-DIMENSIONAL PUZZL
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Figure A.3 (right). The capture of
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appendix b higher dimensions in sci
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HIGHER DIMENSIONS IN SCIENCE FICTIO
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Page 210 and 211: HIGHER DIMENSIONS IN SCIENCE FICTIO
Page 212 and 213: appendix c banchoff klein bottle It
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Page 216 and 217: QUARTERNIONS 189 Figure D.I author.
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Page 220 and 221: SMORGASBORD FOR COMPUTER JUNKIES 19
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Page 224 and 225: EVOLUTION OF FOUR-DIMENSIONAL BEING
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Page 230 and 231: CHALLENGING QUESTIONS FOR FURTHER T
Page 240 and 241: HYPERSPACE TITLES 213 tinctly diffe
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Page 244 and 245: notes Only God truly exists; all ot
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Page 252 and 253: notes 225 less mass, the universe e
Page 254 and 255: notes 227 Appendix C 1. For more in
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Page 258 and 259: further readings 231 Ehrenfest, P (
Page 262 and 263: addendum As this book goes to press
Page 264 and 265: index 10-D universe, 15 Abbott, Edw
Page 266: Index 239 Slade, Henry, 123, 129 So
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