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index 10-D universe, 15 Abbott, Edwin viii, 23-33, 44, 60, 167 Abdu'1-Baha, xi, An Episode of Flatland, 97 Ana, 99 Appearance (of 4-D beings), xxiv, 50, 69-71, 148, 157, 197 Aquinas, Thomas, 18 Aristotle, 9 Art, 199 Astrians, 98 Atomic stability, 203 Baha'i, vii, xi, 22, 38, 43 Baha'u'llah, vii, 22, 38, 43 Banchoff Klein bottle, 185-188, 225, 227 Banchoff, Thomas, vii, 49, 100, 225, 227 Beaty, William, 208 Bennett, Alan, 138, 225-226 Big Bang, 235 Blood transfusion, 61 Brains, 48-49, 65 Cages, 205-206, 217 Central projection, 100 Challenges of life, 202 Chemistry, 228 Chess games, 75-78 Circulatory system, 197 Closed timelike curves, 223 Communication, 204 Computer programs, 185—197 Cosmological constant, 235 Conference of the Birds, 68 Curved space, 13 Dali, Salvador, 91-93 Dead universes, 203 Degrees of freedom, 2-21 Delta, xvi, 99 Diffusion, 228 Digestion, 197 Digestive systems, 39—41 Distance, 107-108 DNA, 210 Dyson, Freeman, 9—10, 165 Earth, end of, 165—166 Einstein, Albert, 13 Enantiomorphism, 130, 134, 139 Eternitygram, 19 Euclid, 9, 11 Euclidean universe, 224 Evolution, 196-199 Exotic matter, 75 Extrinsic geometry, 12 Eyes, 57-59, 153, 196 FLttlarut, viii, 23-33, 44-48, 60, 167 women of, 47—48 Fleas, 205-206 Fractals, 10, 189 Fromm, Eric, 143 Games, 75—78 Gardner, Martin, vii, 49 Gauss, Carl, 13 Ghosts, 130 God, xi, xvi, 9, 18, 21-40, 51, 56, 127, 130, 133, 167, 217 Handedness, 134-135, 139 Hawking, Stephen, 222, 235 Heim, Karl, 10, 47, 130, 185, 192, 196 237
238 Index Heinlein, Robert, xiii, 72 Hendricks, John, 209-210 Hiding, 49 Hinton cubes, 97 Hyperbeings, xiv, 20, 135 Hyperbolic universe, 224 Hypercube, 81-118 rotating, 101 unfolding, 92 Hypersculpture, 51 Hyperseeing, 51 HyperSpace (journal), 191 Hyperspace, origin of term, xvi, 44 Hyperspheres, 81-118 packing of, 115 universe as, 13, 84—86 volume, 109-112 Hypertetrahedral numbers, 174 Hyperthickness, 130 Hypertime, 18 Ice, 205 Inflation theory, 219, 225 Intrinsic geometry, 11 Islam, 217 Kabala, 15-16 Kaku, Michio, 166, 218 Kant, Immanuel, 9, 97 Kata, 99 Klein bottle, 137-138, 185-188, 195, 225 Knots, 123-124 Lattices, 207 Lee, Siu-Leung, vii Leibniz, Gottfried, 133 Light, 199, 229 Linde, Andre, 222 Magic tesseract, 209-210 Many-worlds theory, 72, 223, 235 Mazes, 190 Membrane theory, 220 Miracles, 38, 125 Mirror worlds, 119-132 Miyazaki, Koji, 191 Mobius band, model of universe, 135-137, 186 Mobius worlds, 133-135 Monopoly, 78 More, Henry, 130 Morris, Richard, 202 Multiverse, 223, 235 Nonorientable space, 135, 186 Okasaki, Chris, 190 Optical aid, 208 Orbits, 203, Ouspensky, P., 127 Outer Limits, The, xii Packing, of hyperspheres, 115 Paradoxes, 204 Parallel universes, 71—72, 235 Perpendicular worlds, 62—64 Photons, 199, 229 Plato, 49 Poltergeist, xii Powers (of 4-D beings), xiv, 20, 30, 44 Puzzles, 169 Quantum foam, 65 Quantum theory, 73 Quaternions, 188-191, 227 Raedschelders, Peter, 106-108 Random walk, 169, 226 Religion, xi, xvi, 9, 18, 21-40, 51, 56, 127, 130, 133, 167 Retinas, 57-59, 153, 196 Riemann, Bernhard, 11—12 Rotating in higher dimensions, 120—122 Rubik's Tesseract, 78-79, 170-171, 226 Rucker, Rudy, vii, xiii, 65, 128 Science fiction, 175-178 Senses, 196, 229 Shelley, Percy, 160-161
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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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appendix c banchoff klein bottle It
Page 214 and 215: BANCHOFF KLEIN BOTTLE 187 Figure C.
Page 216 and 217: QUARTERNIONS 189 Figure D.I author.
Page 218 and 219: FOUR-DIMENSIONAL MAZES 191 graph. T
Page 220 and 221: SMORGASBORD FOR COMPUTER JUNKIES 19
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Page 224 and 225: EVOLUTION OF FOUR-DIMENSIONAL BEING
Page 226 and 227: appendix h challenging questions fo
Page 228 and 229: Figure H.2 An artist's renditions o
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
Page 246 and 247: notes 219 4. Unfortunately, there a
Page 248 and 249: notes 221 tiny discrete units. To q
Page 250 and 251: notes 223 less universes could be v
Page 252 and 253: notes 225 less mass, the universe e
Page 254 and 255: notes 227 Appendix C 1. For more in
Page 256 and 257: notes 229 Ben Brown suggests that 4
Page 258 and 259: further readings 231 Ehrenfest, P (
Page 260 and 261: about the author Clifford A. Pickov
Page 262 and 263: addendum As this book goes to press
Page 266: Index 239 Slade, Henry, 123, 129 So
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