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SATAN AND PERPENDICULAR WORLDS 59 Figure 3.4 The retina of a 4-D being's eye. edges, and distinguish between small gradations in intensity and color. In fact, there are many millions of cells to aid us in gaining insight about our world: 125 million rods and cones, several million intervening cells in the retina, and one million neurons in the lateral geniculate nucleus, the first major processing station for visual input. If we have 125 million rods and cones in our 2-D retina, I'd expect roughly 1.3 trillion cells in the 3-D retina of a 4-D being's eye." "Wow, how did you come up with that?" "You need to first take the square root of 125 million to estimate the number of cells in a single dimension, and then cube that. Because the retinas are one dimension less than the dimension of the creature, we could estimate the number of cells in all higher-dimensional retinas." You glance out the window and sense something moving nearby. You lift your head but see nothing unusual. You roll down the window, but that doesn't help. Should you step out of the car to look? And then he appears. An old man in a Santa Claus outfit. He seems to tower above the crowds, but strangely none of the police find him peculiar. Yet the man is clearly out of place. For some reason, you feel embar-
60 surfing through hyperspace rassed that the man is so obviously seeking attention. You wish the man would go away. He does not belong. It's a feeling you frequently have. You roll up the window. "Sally, I think I can help you understand how a 3-D retina can visualize a human, inside and out, at the same time. First consider a blood transfusion for 2-D creatures via a tube that goes up into the third dimension and back down again into the plane of the creature. As far as the creature is concerned, you are not breaking the skin, which might be represented as a line in a drawing. Can you visualize how 4-D creatures can transfuse us?" (Fig. 3.5). "Yes, they could transfuse a 3-D creature by using a transfusion tube that goes upsilon and delta into the fourth dimension without ever breaking the skin. The same concept applies to stealing objects in safes without ever breaking the safe wall. Your hand would materialize in the safe and then dematerialize as you withdrew it. But where does the transfusion tube really go?" (Fig. 3.6). "It goes upsilon where the operating room doesn't even exist! Similarly, a 4-D creature's 3-D retina can see all of your insides without breaking your skin. This assumes that light rays are reflected into the fourth dimension—we'll have to research that further. I've memorized Abbott's nice description of a 2-D creature lifted out of Flatland and looking down into his 2-D world from a 3-D world": I felt myself rising through space. It was even as the Sphere had said. The further we receded from the object we beheld, the larger became the field of vision. My native city, with the interior of every house and every creature therein, lay open to my view in miniature. We mounted higher, and lo, the secrets of the earth, the depths of mines and inmost caverns of the hills, were bared before me. Sally nods. "We've talked about how 4-D beings would look to us, but what would we really look like to them? "To answer that question, let's talk about the appearance of creatures living in worlds perpendicular to one another." "Perpendicular worlds?" "Yes, again I'll start with a 2-D analogy. Consider two planes on which thousands of intelligent insects live. Their two worlds intersect in a line. Along the line of intersection are many moving line segments changing size, disappearing and reappearing" (Fig. 3.7).
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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
Page 36 and 37: DEGREES OF FREEDOM -9 1800s. Howeve
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Page 44 and 45: DEGREES OF FREEDOM 17 Figure 1.4b K
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Page 48 and 49: DEGREES OF FREEDOM 21 time-like cha
Page 50 and 51: the divinity of higher dimensions F
Page 52 and 53: THE DIVINITY OF HIGHER DIMENSIONS 2
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 88 and 89: Figure 3.5 A "hyperspace" blood tra
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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
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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
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Page 120 and 121: Figure 4.8 The Crucifixion {Corpus
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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
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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
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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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