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Figure 3.13 Chess played on a Mobius band, (a) Possible starting configuration, (b) In Mobius chess, either Knight can attack the pawn, (c) In this configuration, the pawn does not necessarily protect the Knight, because the Rook may travel in the opposite direction and end up beneath the Knight. (Drawing by Brian Mansfield.)
78 <strong>surfing</strong> <strong>through</strong> hyperspace Figure 3.14 Extending Monopoly games into higher dimensions. The Free Parking square acts as a wormhole between parallel universes. (Drawing by Brian Mansfield.) learn in Chapter 5, a Mobius strip is created by twisting a strip of paper 180 degrees and then taping the ends together. The resultant object has only one side.) Now that chessmaster Gary Kasparov has been beaten by an IBM computer, perhaps chess variants such as these would provide an infinite reservoir for new matches and theories. 3 When I was young, I played hyperdimensional Monopoly games by aligning two or more boards, side by side (Fig. 3.14). The Free Parking square acted as a "wormhole" between parallel universes. In other words, if a playing piece lands on Free Parking, it has the option of moving to an adjacent board. Try this mind-boggling variant. I'd be interested in hearing from readers who have experimented with hyperdimensional Monopoly. Rubik's Tesseract Many of you will be familiar with Erno Rubik's ingenious cubical puzzle and its variations that include a 4 X 4 X 4 cube and puzzles shaped like tetrahedra. One natural variation that never appeared on toy store shelves is the 4-D version of Rubik's cube—Rubik's tesseract. Dan Velleman (Amherst College)
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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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Page 62 and 63: Figure 2.9 A ball being pushed thro
Page 80 and 81: satan and perpendicular worlds Wash
Page 82 and 83: SATAN AND PERPENDICULAR WORLDS 55 a
Page 84 and 85: SATAN AND PERPENDICULAR WORLDS 57 S
Page 86 and 87: SATAN AND PERPENDICULAR WORLDS 59 F
Page 88 and 89: Figure 3.5 A "hyperspace" blood tra
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Page 94 and 95: SATAN AND PERPENDICULAR WORLDS 67 E
Page 96 and 97: SATAN AND PERPENDICULAR WORLDS 69 T
Page 98 and 99: SATAN AND PERPENDICULAR WORLDS 71 S
Page 106 and 107: SATAN AND PERPENDICULAR WORLDS 79 d
Page 108 and 109: hyperspheres and tesseracts FBI Hea
Page 110 and 111: HYPERSPHERES AND TESSERACTS 83 simp
Page 112 and 113: Figure 4.2 Strange universes, (a) T
Page 114 and 115: HYPERSPHERES AND TESSERACTS 87 runn
Page 116 and 117: HYPERSPHERES AND TESSERACTS 89 Poin
Page 118 and 119: HYPERSPHERES AND TESSERACTS 91 "Sal
Page 120 and 121: Figure 4.8 The Crucifixion {Corpus
Page 122 and 123: HYPERSPHERES AND TESSERACTS 95 Figu
Page 124 and 125: HYPERSPHERES AND TESSERACTS 97 Hint
Page 126 and 127: HYPERSPHERES AND TESSERACTS 99 Next
Page 128 and 129: Figure 4.10 Slices of a hypercube a
Page 130 and 131: Figure 4.13 Embryonic 5-D cube in F
Page 132 and 133: HYPERSPHERES AND TESSERACTS 105 Fig
Page 134 and 135: HYPERSPHERES AND TESSERACTS 107 Fig
Page 136 and 137: HYPERSPHERES AND TESSERACTS 109 4-D
Page 138 and 139: Figure 4.21 Volume of a radius 2 sp
Page 140 and 141: HYPERSPHERES AND TESSERACTS 113 How
Page 142 and 143: HYPERSPHERES AND TESSERACTS 115 ans
Page 144 and 145: HYPERSPHERESANDTESSERACTS 117 Figur
Page 146 and 147: mirror worlds FBI Headquarters, Was
Page 148 and 149: MIRROR WORLDS 121 "I've designed a
Page 150 and 151: MIRROR WORLDS 123 Sally puts her he
Page 152 and 153: 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
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BANCHOFF KLEIN BOTTLE 187 Figure C.
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QUARTERNIONS 189 Figure D.I author.
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FOUR-DIMENSIONAL MAZES 191 graph. T
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SMORGASBORD FOR COMPUTER JUNKIES 19
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SMORGASBORD FOR COMPUTER JUNKIES 19
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EVOLUTION OF FOUR-DIMENSIONAL BEING
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appendix h challenging questions fo
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Figure H.2 An artist's renditions o
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CHALLENGING QUESTIONS FOR FURTHER T
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HYPERSPACE TITLES 213 tinctly diffe
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HYPERSPACE TITLES 215 meaningfully
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notes Only God truly exists; all ot
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notes 219 4. Unfortunately, there a
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notes 221 tiny discrete units. To q
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notes 223 less universes could be v
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notes 225 less mass, the universe e
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notes 227 Appendix C 1. For more in
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notes 229 Ben Brown suggests that 4
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further readings 231 Ehrenfest, P (
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about the author Clifford A. Pickov
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addendum As this book goes to press
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index 10-D universe, 15 Abbott, Edw
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Index 239 Slade, Henry, 123, 129 So
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