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Figure 4.2 Strange universes, (a) Tapping yourself on the back in a small, closed universe. (Drawing by Clay Fried.) (b) Like bubbles floating in the air, many separate n- dimensional worlds could exist if the universe were n+/-dimensional. Could our universe be one of many separated in 4-D space? If these spaces were to touch at some point, would we be able to communicate with an adjacent world? (c) Your "inside-out" friend in a small, hyperspherical universe. (Drawing by Clay Fried.)
86 surfing through hyperspace "That's a good question. 1 I have no answer, but now it seems that the Omegamorphs are changing all that." Sally tosses the tennis ball to you. "If we lived on a hyperspherical universe and you traveled to a point in the universe that was furthest from me, I would still be able to see you with a telescope in no matter what direction I looked." "That's true if the sphere were not too large." "If I could see you no matter where I looked, would you seern infinitely big to me?" You place the tennis balls back in the cabinet. "Yes. Even stranger, I would be 'inside out.' In other words, instead of my skin and hair forming a surface around my guts, it would seem that my guts were on the outside, and my hair and skin would be surrounding you! Of course, I wouldn't notice anything strange. I wouldn't be about to die. To me, you would look infinitely large arid inside out" (Fig. 4.2c). You toss a basketball to Sally. "Next lesson. If you cut this sphere with a plane, you'd produce a circle. If you cut a hypersphere with a 3-D hyperplane, the cross section is a sphere." Sally looks at the basketball. "What happens if you try to cut a hypersphere with an ordinary 2-D plane?" "Sally, you can't slice a hypersphere into two pieces with a 2-D plane. A hyperbasketball, sliced down the middle by a plane, remains in one piece, just like a sphere pierced with a line does not fall apart into two separate pieces. This means that a guillotine for a hyperbeing would be a 3-D object like a cube, not a plane." You take the basketball from Sally's hands and deflate it with a pin. "If I asked you to turn this basketball inside out, could you?" Sally studies it for a moment. "I don't think so, not without cutting it." You nod. "Correct. However, a flexible sphere of any dimension can be turned inside out through the next-highest dimension. For example, we 3-D beings can turn a rubber ring inside out so that its outer surface becomes the inner, and the inner becomes the outer. Try it with a rubber band. Similarly, a hyperbeing could grab this basketball and turn it inside out through his space." "Does this mean that a hyperbeing could turn a human inside out?" "From a practical standpoint, we're not quite as flexible as a rubber ball. We're also not spheres. We're more like a sphere with a digestive tube
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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
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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
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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
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Page 104 and 105: Figure 3.13 Chess played on a Mobiu
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Page 108 and 109: hyperspheres and tesseracts FBI Hea
Page 110 and 111: HYPERSPHERES AND TESSERACTS 83 simp
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
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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
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Page 138 and 139: Figure 4.21 Volume of a radius 2 sp
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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
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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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