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MIRROR WORLDS 121 "I've designed a machine that will rotate me into the fourth dimension. I haven't figured out a way to entirely vault into the fourth dimension, but even if I have to keep a piece of me here all the time, I can do some marvelous tricks. But don't worry, the machine is perfectly safe." You place the device on the cement sidewalk and step on it. "This will turn me over in the fourth dimension so that I will be rotated into a mirror image of myself. The machine rotates me about a plane that cuts through my body from head to groin. Watch." Sally stuffs her fist into her mouth and gasps. "I am in complete control. Watch as my right half moves delta and my left half moves upsilon. When a Flatlander rotates, all you see is a line segment until his entire body fills the plane again. Similarly, you are now seeing a planar cross section of my body with all of my internal organs." "Stop it!" Sally says as she looks at wriggling splotches of crimson floating in the air. Occasionally, the white of bone appears. It's as if a torturer from the Spanish Inquisition had sliced you with a huge sharp razor from head to toe and proudly brandished the thin slice in front of Sally (Fig. 5.2). "Sally, as I rotate, all that remains is my cross section. Looks like sliced meat. An Omegamorph could turn us into our own mirror images by rotating us, in the fourth dimension, around planes that cut through our bodies. It's just like the Flatlander rotated about a line into the third dimension and then back down into the second dimension." Sally steps back. "This can't be safe. Rotate yourself back to normal this instant." "Sally, if you wanted to, you could move in close and tickle my kid- » neys. "You are sick." After a minute, you rotate back into the 3-D universe. You have returned to normal, except that you are your mirror image. "Pkool I od woH" "What did you say?" You stare uncertainly at Sally. Sally's eyes glisten like diamonds. For an instant you feel like light trapped within a shiny sphere. You peer at her corneas, your image many times reflected as if you are standing on the periphery of some gigantic crystal, alone in a field of darkness. One of her earrings has fallen into a puddle. The puddle shivers. You are mesmerized by the lovely play of light on the clear rippling surface.
122 surfing through hyperspace Figure 5.2 Rotating a 3-D person about a central plane. While the person is in the process of rotating, all that remains in our space is a cross section resembling microtomed meat. You need not move. There is enough motion from the lights. You feel like you can live forever, suspended in space. The light is reflected according to mathematical laws. Angles, polarizations, intensities, refractions, diffractions, interferences, geometrical optics, spherical aberrations. Such beauty from pure math. Sally snaps you from your reverie. "My God, when you rotated, you looked like a CAT scan or an MRI from a hospital. The fourth dimension would make the ultimate medical diagnostic tool." She pauses. "But now you look a little different." "Yes, my left and right sides are reversed. I couldn't do this without rotating in the fourth dimension." "Can we prove it?" "Listen to my heart. There's no way my heart could be on my right side without a rotation in the fourth dimension."
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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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satan and perpendicular worlds Wash
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SATAN AND PERPENDICULAR WORLDS 55 a
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SATAN AND PERPENDICULAR WORLDS 57 S
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SATAN AND PERPENDICULAR WORLDS 59 F
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Figure 3.5 A "hyperspace" blood tra
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SATAN AND PERPENDICULAR WORLDS 63 t
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SATAN AND PERPENDICULAR WORLDS 65 "
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SATAN AND PERPENDICULAR WORLDS 67 E
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SATAN AND PERPENDICULAR WORLDS 69 T
Page 98 and 99: SATAN AND PERPENDICULAR WORLDS 71 S
Page 100 and 101: SATAN AND PERPENDICULAR WORLDS 73 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
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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 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
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Page 168 and 169: the gods of hyperspace The White Ho
Page 170 and 171: THE GODS OF HYPERSPACE 143 Sally tu
Page 172 and 173: THE GODS OF HYPERSPACE 145 "What's
Page 174 and 175: THE GODS OF HYPERSPACE 147 Figure 6
Page 176 and 177: Figure 6.2 The cross section of 4-D
Page 178 and 179: THE GODS OF HYPERSPACE 151 Figure 6
Page 180 and 181: THE GODS OF HYPERSPACE 153 You take
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Page 184 and 185: Figure 6.4 Cross-sections of higher
Page 186 and 187: THE GODS OF HYPERSPACE 159 The mana
Page 188 and 189: THE GODS OF HYPERSPACE 161 Kindling
Page 190 and 191: concluding remarks This completes o
Page 192 and 193: CONCLUDING REMARKS 165 If intellige
Page 194 and 195: CONCLUDING REMARKS 167 swered. I ho
Page 196 and 197: 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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