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DEGREES OF FREEDOM 17 Figure 1.4b Kabala. Another representation of the sephiroth, the central figure for the size of a proton to the size of the solar system, this is the same ratio that describes the relative size of a superstring to a proton. John Horgan, an editor at Scientific American, recently published an article describing what other researchers have said of Witten and superstrings in ten dimensions. One researcher interviewed exclaimed that in sheer mathematical mind power, Edward Witten exceeds Einstein and has no rival since Newton.
18 surfing through hyperspace So complex is string theory that when a Nobel Prize—wining physicist was asked to comment on the importance of Witten's work, he said that he could not understand Witten's recent papers; therefore, he could not ascertain how brilliant Witten is! 6 Recently, humanity's attempt to formulate a "theory of everything" includes not only string theory but membrane theory, also known as M-theory. 7 In the words of Edward Witten (whom Life magazine dubbed the sixth most influential American baby boomer), "M stands for Magic, Mystery, or Membrane, according to taste." In this new theory, life, the universe, and everything may arise from the interplay of membranes, strings, and bubbles in higher dimensions of spacetime. The membranes may take the form of bubbles, be stretched out in two directions like a sheet of rubber, or wrapped so tightly that they resemble a string. The main point to remember about these advanced theories is that modern physicists continue to produce models of matter and the universe requiring extra spatial dimensions. Hypertime In this book, I'm interested primarily in a fourth spatial dimension, although various scientists have considered other dimensions, such as time, as a fourth dimension. In this section, I digress and speak for a moment on time and what it would be like to live outside the flow of time. Readers are encouraged to consult my book Time: A Traveler's Guide for an extensive treatise on the subject. Einstein's theory of general relativity describes space and time as a unified 4-D continuum called "spacetime." The 4-D continuum of Einstein's relativity in which three spatial dimensions are combined with one dimension of time is not the same as hyperspace consisting of four spatial coordinates. To best understand this, consider yourself as having three spatial dimensions—height, width, and breadth. You also have the dimension of duration—how long you last. Modern physics views time as an extra dimension; thus, we live in a universe having (at least) three spatial dimensions and one additional dimension of time. Stop and consider some mystical implications of spacetime. Can something exist outside of spacetime? What would it be like to exist outside of spacetime? For example, Thomas Aquinas believed God to be outside of spacetime and thus capable of seeing all of the universe's objects, past and future, in
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 42 and 43: DEGREES OF FREEDOM 15 with other my
Page 46 and 47: DEGREES OF FREEDOM 19 Figure 1.5 An
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 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 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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