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HYPERSPHERES AND TESSERACTS 95 Figure 4.9 As the cubical prison moves down, corner-first, through Flatland, the Flatlanders first see a point, then a series of growing triangles, then hexagons, then triangles, then a point. (After Banchoff.) You nod. "Sally, if Satan were a 4-D being, it might be possible to confine him in a tesseract prison. If it were an ordinary cube, Satan could flee into the fourth dimension. However, if the cube in our world was really part of a hypercube, he would be trapped. As he leaped upsilon into the fourth dimension, he'd just hit his head on a cubical ceiling. Similarly, a Flatlander having the ability to leap into the third dimension would bang himself on a cubical prison that spanned his world." You and Sally are quiet as you gaze outside at the street lights. They cast shadows that spring up about you as if they are living creatures. Suddenly most of the lights go out. Others flicker like fireflies. You turn to Sally. "Must be an electrical problem." She comes closer to you. "Spooky." / want to fly, you think as you stare into the dim room. Fly into the fourth dimension, like a bird. To fly, to feel the surge of your body as it lifts into the higher universe. Breathless. You imagine a force that moves you gently but purposefully upward. Voices float around you like the breaking of ocean waves on rocks.
96 surfing through hyperspace You look out the window, occasionally seeing fantastically bright birds alighting on the hoods of cars. Could they be birds from the fourth dimension? Perhaps "bird" is not the right word. Their gossamer wings quiver on bodies resembling balls of twine. Some of the animals have more slender bodies. Speckles on their skin glow like neon lights. Then the speckles fade in the evening drizzle. The only illumination comes from the green and red lights emitted by the bioluminescent bacteria coating the trees. It reminds you of Christmas. The Science Behind the Science Fiction The rift between belief and natural science can today be bridged only if it is possible to transpose the concept of space, which has acquired a position of primary significance in modern physics, in a higher connotation to the world-picture of belief. —Karl Heim, Christian Faith and Natural Science Theoretical physics seems to becoming more and more like science fiction. -Steven Weinberg, The First Three Minutes
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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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Page 72 and 73: THE DIVINITY OF HIGHER DIMENSIONS 4
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
Page 90 and 91: SATAN AND PERPENDICULAR WORLDS 63 t
Page 92 and 93: SATAN AND PERPENDICULAR WORLDS 65 "
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 104 and 105: Figure 3.13 Chess played on a Mobiu
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
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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 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
Page 154 and 155: MIRROR WORLDS 127 "Me too." She pla
Page 156 and 157: MIRROR WORLDS 129 Zollner Experimen
Page 158 and 159: MIRROR WORLDS 131 not possible; per
Page 160 and 161: MIRROR WORLDS 133 Rotate Figure 5.6
Page 162 and 163: MIRROR WORLDS 135 To get a better u
Page 164 and 165: MIRROR WORLDS 137 Figure 5.9 Comput
Page 166 and 167: MIRROR WORLDS 139 Figure 5.11 A mor
Page 168 and 169: the gods of hyperspace The White Ho
Page 170 and 171: 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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