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further readings 231 Ehrenfest, P (1917) Can atoms or planets exist in higher dimensions? Proceedings of the Amsterdam Academy. 20:200-203. Everett, H. (1957) Relative state formulation of quantum mechanics. Reviews of Modern Physics. 29 (July):454-62. Freeman, I. (1969) Why is space three-dimensional? American Journal of Physics. 37:1222-24. Friedman, N. (1998) Hyperspace, hyperseeing, and hypersculpture. Preprint available from Professor Nat Friedman, Mathematics Department, University of Albany SUNY, Albany, New York 12222. Gardner, M. (1990) The New Ambidextrous Universe, New York: Freeman. Gardner, M. (1982) Mathematical Circus. New York: Penguin. Gardner, M. (1969) The Unexpected Hanging. New York: Simon and Schuster. Gardner, M. (1965) Mathematical Carnival. New York: Vintage. Halpern, P. (1993) Cosmic Wormholes. New York: Plume. Heim, K. (1953) Christian Faith and Natural Science. New York: Harper and Row. (Reprinted in 1971 by Peter Smith, Glouchester, Mass.) Heinlein, R. (1958) "—And he built a crooked house." In Fantasia Mathematica, C. Fadiman, ed. New York: Simon and Schuster. (Story originally published in 1940.) Hendricks, J. (1990) The magic tesseracts of Order 3 complete. Journal of Recreational Mathematics. 22(l):16-26. Hendricks, J. (1962) The five-and six-dimensional magic hypercubes of Order 3. Canadian Mathematical Bulletin. May, 5(2):171—89. Henricks, J. (1995) Magic tesseract. In The Pattern Book: Fractals, Art, and Nature, C. Pickover, ed. River Edge. N.J.: World Scientific. H<strong>org</strong>an, J. (1991) The Pied Piper of superstrings. Scientific American. November 265(5):42-44. Kaku, M. (1994) Hyperspace. New York: Oxford University Press. Kasner, E. and Newman, R. (1989) Mathematics and the Imagination. New York: Ternpus. (A reprint of the 1940 edition.) Misner, C. W, Thome, K. S., and Wheeler, J. A. (1973) Gravitation. New York: Freeman. (Excellent comprehensive background for more technical readers. A megatextbook on Einstein's theory of relativity, among other things. Lots of equations.) Morris, M. S. and Thome, K. S. (1988) Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity. American Journal of Physics. 56:395. Morris, M. S., Thorne, K. S., and Yurtsever, U. (1988) Wormholes, time machines, and the weak energy conditions. Physical Review Letters. 61:1446. Morris, R. (1993) Cosmic Questions. New York: John Wiley & Sons. Pappas, T (1990) More Joy of Mathematics. San Carlos, Calif: Wide World Publishing/Tetra. Peterson, I. (1998) Circle in the sky: detecting the shape of the universe. Science News. February, 153(8): 123-35.
232 further readings Pickover, C. (1998) Black Holes: A Traveler's Guide. New York: John Wiley & Sons. Peterson, I. (1998) Evading quantum barrier to time travel. Science News. April 11, 153(19):231. Peterson, I. (1998) Loops of gravity: calculating a foamy quantum space-time. Science News. June 13, 153(24):376-77. Rucker, R. (1984) The Fourth Dimension. Boston: Houghton-Mifflin. Rucker, R. (1977) Geometry, Relativity, and the Fourth Dimension. New York: Dover. Stewart, I. (1998) Glass Klein bottles. Scientific American. 278(3):100-101. Tangherlini, F. (1963) Atoms in higher dimensions. Nuovo Cimento. 27:636—639. Tegmark, M. (1997) On the dimensionality of spacetime. Classical and Quantum Gravity. 14:L69-L75. Thorne, K. S. (1994) Black Holes and Time Warps: Einstein's Outrageous Legacy. New York: W. W. Norton. Velleman, D. (1992) Rubik's tesseract. Mathematics Magazine. February 65(1): 27-36. Visser, M. (1989) Traversable wormholes from surgically modified Schwarzchild spacetimes. Nuclear Physics. B328:203. Visser, M. (1989) Traversable wormholes: some simple examples. Physical Review. 39D:3182. Visser, M. (1990) Wormholes, baby universes, and causality. Physical Review. 41D: 1116.
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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
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SATAN AND PERPENDICULAR WORLDS 71 S
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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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HIGHER DIMENSIONS IN SCIENCE FICTIO
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Page 212 and 213: appendix c banchoff klein bottle It
Page 214 and 215: BANCHOFF KLEIN BOTTLE 187 Figure C.
Page 216 and 217: QUARTERNIONS 189 Figure D.I author.
Page 218 and 219: FOUR-DIMENSIONAL MAZES 191 graph. T
Page 220 and 221: SMORGASBORD FOR COMPUTER JUNKIES 19
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Page 224 and 225: EVOLUTION OF FOUR-DIMENSIONAL BEING
Page 226 and 227: appendix h challenging questions fo
Page 228 and 229: Figure H.2 An artist's renditions o
Page 230 and 231: CHALLENGING QUESTIONS FOR FURTHER T
Page 240 and 241: HYPERSPACE TITLES 213 tinctly diffe
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Page 244 and 245: notes Only God truly exists; all ot
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Page 248 and 249: notes 221 tiny discrete units. To q
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Page 252 and 253: notes 225 less mass, the universe e
Page 254 and 255: notes 227 Appendix C 1. For more in
Page 256 and 257: notes 229 Ben Brown suggests that 4
Page 260 and 261: about the author Clifford A. Pickov
Page 262 and 263: addendum As this book goes to press
Page 264 and 265: index 10-D universe, 15 Abbott, Edw
Page 266: Index 239 Slade, Henry, 123, 129 So
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