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HYPERSPHERES AND TESSERACTS 87 running down the middle. But you're right, topologically speaking, a hyperbeing could do weird things to us." Outside your window, you see the man in the Santa Glaus outfit. "Who is that?" Sally looks out. "No one special, I'm sure." You try desperately to glimpse his face, but there is not enough light. All you can see is a figure dressed in a red suit. Even though you can't observe the man's face, you recognize something familiar. On his left hand is a tattoo in the shape of a tesseract projected into two dimensions. Could he be an agent of the Omegamorphs? Worse, you sense that the man is looking for you. You are paralyzed; you are certain the Santa Glaus man knows you are there. Your body tenses, waiting—but for what? Outside on the street, the sounds blend in a cacophonous hiss. You hear voices, but can never identify sentences. There is some laughter. You blink and the man is gone. Just as many people are walking by on the sidewalk, but the sounds are softer, less tense. Sally taps you on your back. "It was no one. It's that time of year." You nod and withdraw a wooden cube from your cabinet. "Follow me to the blackboard. I want to talk about tesseracts, the 4-D analogs of a cube. You can get an idea about what they're like by starting in lower dimensions. For example, if you move a point from left to right you trace out a 1-D line segment." You place the tip of your chalk on the blackboard and move the tip to the right so that it produces a line. "If you take this line segment and move it up (perpendicularly) along the blackboard, you produce a 2-D square. If you move the square out of the blackboard, you produces a 3-D cube" (Fig. 4.3). Sally comes closer. "How can we move the square out of the black board?" "We can't do that, but we can graphically represent the perpendicular motion by moving the square—on the blackboard—in a direction diagonal to the first two motions. In fact, if we use the other diagonal direction to represent the fourth dimension, we can move the image of the cube in this fourth dimension to draw a picture of a 4-D hypercube, also known as a tesseract. Or we can rotate the cube and move it straight up in the drawing" (Fig. 4.4). "Beautiful. The tesseract is produced by the trail of a cube moving into the fourth dimension."
88 <strong>surfing</strong> <strong>through</strong> hyperspace Drag Drag Drag Figure 4.3 Lower-dimensional figures trace out higher-dimensional figures when the lower-dimensional figures are moved. Figure 4.4 A hypercube (right) produced by moving (left) a cube along the fourth dimension. "That's right, Sally. Our visual powers have a hard time moving the image of a cube, but we can assume that the cube is shifted a distance in a direction perpendicular to all three of its axes. We can even write down the number of corners, edges, faces, and solids for higher-dimensional objects." You write on the blackboard:
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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 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 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 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
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
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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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