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DEGREES OF FREEDOM 19 Figure 1.5 An eternitygram for two colliding discs. one blinding instant. An observer existing outside of time, in a region called "hypertime," can see the past and future all at once. There are many other examples of beings in literature and myth who live outside of spacetime. Many people living in the Middle Ages believed that angels were nonmaterial intelligences living by a time different from humans, and that God was entirely outside of time. Lord Byron aptly describes these ideas in the first act of his play Cain, A Mystery, where the fallen angel Lucifer says: With us acts are exempt from time, and we Can crowd eternity into an hour, Or stretch an hour into eternity. We breathe not by a mortal measurement— But that's a mystery.
20 surfing through hyperspace A direct analogy involves an illustration of an "eternitygram" representing two discs rolling toward one another, colliding, and rebounding. Figure 1.5 shows two spatial dimensions along with the additional dimension of time. You can think of successive instants in time as stacks of movie frames that form a 3-D picture of hypertime in the eternitygram. Figure 1.5 is a "timeless" picture of colliding discs in eternity, an eternity in which all instants of time lie frozen like musical notes on a musical score. Eternitygrams are timeless. Hyperbeings looking at the discs in this chunk of spacetime would see past, present, and future all at once. What kind of relationship with humans could a creature (or God) have who lives completely outside of time? How could they relate to us in our changing world? One of my favorite modern examples of God's living outside of time is described in Anne Rice's novel Memnoch the Devil. At one point, Lestat, Anne Rice's protagonist, says, "I saw as God sees, and I saw as if Forever and in All Directions." Lestat looks over a balustrade in Heaven to see the entire history of our world: . . . the world as I had never seen it in all its ages, with all its secrets of the past revealed. I had only to rush to the railing and I could peer down into the time of Eden or Ancient Mesopotamia, or a moment when Roman legions had marched through the woods of my earthly home. I would see the great eruption of Vesuvius spill its horrid deadly ash down upon the ancient living city of Pompeii. Everything there to be known and finally comprehended, all questions settled, the smell of another time, the taste of it. . . . If all our movements through time were somehow fixed like tunnels in the ice of spacetime (as in the eternitygram in Fig. 1.5), and all that "moved" was our perception shifting through the ice as time "passes," we would still see a complex dance of movements even though nothing was actually moving. Perhaps an alien would see this differently. In some sense, all our motions may be considered fixed in the geometry of spacetime, with all movement and change being an illusion resulting from our changing psychological perception of the moment "now." Some mystics have suggested that spacetime is like a novel being "read" by the soul — the "soul" being a kind of eye or observer that stands outside of spacetime, slowly gazing along the time axis. Note 8 describes the metamorphosis of time into a spatial dimension during the early evolution of our universe. At the point when time loses its
Page 2 and 3: surfing through hyperspace
Page 4 and 5: surfing through hyperspace Understa
Page 7 and 8: This book is dedicated to Gillian A
Page 9 and 10: An unspeakable horror seized me. Th
Page 11 and 12: X contents Appendix E Four-Dimensio
Page 13 and 14: xii preface I first became excited
Page 15 and 16: XIV preface problems—from a four-
Page 17 and 18: XVI preface My soul is an entangled
Page 19 and 20: XVIII preface I've attempted to mak
Page 21 and 22: The trouble with integers is that w
Page 23 and 24: XXII introduction cal and national
Page 25 and 26: xxiv introduction snaps a few photo
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Page 30 and 31: degrees of freedom FBI Headquarters
Page 32 and 33: DEGREES OF FREEDOM 5 Figure 1.1 A f
Page 34 and 35: 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 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 86 and 87: SATAN AND PERPENDICULAR WORLDS 59 F
Page 88 and 89: Figure 3.5 A "hyperspace" blood tra
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SATAN AND PERPENDICULAR WORLDS 69 T
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SATAN AND PERPENDICULAR WORLDS 71 S
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SATAN AND PERPENDICULAR WORLDS 73 t
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SATAN AND PERPENDICULAR WORLDS 75 t
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Figure 3.13 Chess played on a Mobiu
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SATAN AND PERPENDICULAR WORLDS 79 d
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hyperspheres and tesseracts FBI Hea
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HYPERSPHERES AND TESSERACTS 83 simp
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Figure 4.2 Strange universes, (a) T
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HYPERSPHERES AND TESSERACTS 87 runn
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HYPERSPHERES AND TESSERACTS 89 Poin
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HYPERSPHERES AND TESSERACTS 91 "Sal
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Figure 4.8 The Crucifixion {Corpus
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HYPERSPHERES AND TESSERACTS 95 Figu
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HYPERSPHERES AND TESSERACTS 97 Hint
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HYPERSPHERES AND TESSERACTS 99 Next
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Figure 4.10 Slices of a hypercube a
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Figure 4.13 Embryonic 5-D cube in F
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HYPERSPHERES AND TESSERACTS 105 Fig
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HYPERSPHERES AND TESSERACTS 107 Fig
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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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