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DEGREES OF FREEDOM 15 with other mysterious particles that exist only in all ten dimensions, such as the hypothetical graviton, which conveys the force of gravity. Think of the universe as the music of a hyperdimensional orchestra. And we may never know if there is a hyperBeethoven guiding the cosmic harmonies. Whenever I read about string theory, I can't help thinking about the Kabala in Jewish mysticism. Kabala became popular in the twelfth and following centuries. Kabalists believe that much of the Old Testament is in code, and this is why scripture may seem muddled. The earliest known Jewish text on magic and mathematics, Sefer Yetzira (Book of Creation), appeared around the fourth century A.D. It explained creation as a process involving ten divine numbers or sephiroth. Kabala is based on a complicated number mysticism whereby the primordial One divides itself into ten sephiroth that are mysteriously connected with each other and work together. Twenty-two letters of the Hebrew alphabet are bridges between them (Fig. 1.4). The sephiroth are ten hypostatized attributes or emanations allowing the infinite to meet the finite. ("Hypostatize" means to make into or treat as a substance—to make an abstract thing a material thing.) According to Kabalists, by studying the ten sephiroth and their interconnections, one can develop the entire divine cosmic structure. Similarly, physical reality may be the hypostatization of these mathematical constructs called "strings." As I mentioned, strings, the basic building blocks of nature, are not tiny particles but unimaginably small loops and snippets loosely resembling strings—except that strings exist in a strange, 10-D universe. The current version of the theory took shape in the late 1960s. Using hyperspace theory, "matter" is viewed as vibrations that ripple through space and time. From this follows the idea that everything we see, from people to planets, is nothing but vibrations in hyperspace. In the last few years, theoretical physicists have been using strings to explain all the forces of nature—from atomic to gravitational. Although string theory describes elementary particles as vibrational modes of infinitesimal strings that exist in ten dimensions, many of you may be wondering how such things exist in our 3-D universe with an additional dimension of time. String theorists claim that six of the ten dimensions are "compactified"—tightly curled up (in structures known as Calabi-Yau spaces) so that the extra dimensions are essentially invisible. 4 As technically advanced as superstring theory sounds, superstring theory could have been developed a long time ago according to string-theory guru Edward Witten, 5 a theoretical physicist at the Institute for Advanced Study in
16 surfing through hyperspoce Figure 1.4a Zohar. The Sephiroth Tree, or Tree of Life, from an old manuscript of the Princeton. For example, he indicates that it is quite likely that other civilizations in the universe discovered superstring theory and then later derived Einsteinlike formulations (which in our world predate string theory by more than half a century). Unfortunately for experimentalists, superstrings are so small that they are not likely to ever be detectable by humans. If you consider the ratio of the
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
Page 46 and 47: DEGREES OF FREEDOM 19 Figure 1.5 An
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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
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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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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
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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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