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HIGHER DIMENSIONS IN SCIENCE FICTION 181 36. Pohl, F. (1987) The Coming of Quantum Cats. New York: Bantam. A parallel worlds story. 37. Pohl, F. and Williamson, J. (1987) The Singers of Times. New York: Ballantine. A parallel worlds story. 38. Schachner, N. (1938) "Simultaneous Worlds." All 3-D matter extends into a higher dimension. A machine images these higher worlds that resemble Earth. 39. Shaw, R. (1967) Night Walk. New York: Banner Books. A hyperspace universe has a fiendishly complicated shape. 40. Shaw, B. (1986) The Two-Timers. A man who lost his wife inadvertently creates a parallel world in which she still exists. 41. Shaw, B. (1987) A Wreath of Stars. New York: Baen Books. Two worlds made of different kinds of matter coexist until the approach of a star shifts the orbit of one of them. 42. Silverberg, R. (1972) Trips. Transuniversal tourists wander aimlessly <strong>through</strong> worlds with varying similarities. 43. Simak, C. (1992) Ring Around the Sun. New York: Carroll & Graf. (Originally published in 1953.) Describes a series of Earths, empty of humanity and available for colonization and exploitation. 44. Simak, C. (1943) Shadow of Life. Martians learn to shrink themselves to subatomic size by extending into the fourth dimension, causing them to lose mass and size in the other three dimensions. 45. Smith, E. E. (1939) Grey Lensman. A crew feels as though they "were being compressed, not as a whole, but atom by atom . . . twisted . . . extruded . . . in an unknowable and non-existent direction. . . . Hyperspace is funny that way. . . ."A weapon known as a "hyperspatial tube" is used. It is described as an "extradimensional" vortex. The terminus of the tube cannot be established too close to a star due to the tube's apparent sensitivity to gravitational fields. 46. Smith, M. (1949) The Mystery of Element 117. Describes how our universe extends a short distance into a fourth spatial dimension. Because of this, it is possible to rotate matter completely out of three-space by building a 4-D translator. Element 117 opens a portal into this new dimension inhabited by humans who have died. They live in a neighboring world to ours, slightly shifted from ours along the fourth dimension. "Our 3-space is but one hyperplane of hyperspace." Succeeding layers are linked together like pages in a book.
182 appendix b 47. Tenneshaw, S. (1950) "Who's That Knocking at My Door?" A honeymooning couple's hyperdrive breaks down near a white dwarf star. 48. Upson, W. (1958) "A. Botts and the Moebius Strip," in Fantasia Mathematica, C. Fadiman, ed. New York: Simon and Schuster. A simple demonstration in topology saves the lives of several Australian soldiers. 49. van Vogt, A. E. (1971) "M 33 in Andromeda," in M33 in Andromeda, A. E. van Vogt. New York: Paperback Library. (Originally published in 1943.) Humans receive mental messages from an advanced civilization in the Andromeda galaxy. Earthlings use "hyperspace" in planet-to-planet matter transmission. Focusing a hyperspace transmitter on a spaceship moving faster than light requires specifying coordinates in a 900,000-dimensional space. 50. Wandrei, D. (1954) "The Blinding Shadows," in Beachheads in Space, August Derleth, ed. New York: Weidenfeld Nicolson. (Story originally published in 1934.) An inventor named Dowdson builds a machine that sucks energy into the fourth dimension. In a speech to his colleagues, Dowdson remarks: Gentlemen, there was a time long ago when objects were considered to have two dimensions, namely, length and breadth. After Euclid, it was discovered that length, breadth, and thickness comprised three dimensions. For thousands of years, man could visualize only two dimensions, at right angles to each other. He was wrong. Now, for more thousands of years, man has been able to visualize only three dimensions, at right angles to each other. May there not be a fourth dimension, perhaps at right angles to these, in some fashion that we cannot yet picture, or perhaps lying altogether beyond our range of vision? Objects emitting infra-red rays, and lying in such a four-dimensional world, might easily be past our ability to see and our capacity to understand, while existing beside us, nay, in this very hall. The audience pays deep attention to Dowdson as he reaches the main point of his paper: A three-dimensional object casts a two-dimensional shadow. If such a thing as a two-dimensional object existed, doubtless it would throw a one-dimensional shadow. And should a fourdimensional solid be extant, its shadow would be three-dimensional. In other words, gentlemen, it is entirely conceivable
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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
Page 158 and 159: MIRROR WORLDS 131 not possible; per
Page 160 and 161: MIRROR WORLDS 133 Rotate Figure 5.6
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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
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Page 176 and 177: Figure 6.2 The cross section of 4-D
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Page 184 and 185: Figure 6.4 Cross-sections of higher
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Page 190 and 191: concluding remarks This completes o
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Page 194 and 195: CONCLUDING REMARKS 167 swered. I ho
Page 196 and 197: appendix a mind-bending four-dimens
Page 198 and 199: MIND-BENDING FOUR-DIMENSIONAL PUZZL
Page 200 and 201: Figure A.3 (right). The capture of
Page 202 and 203: appendix b higher dimensions in sci
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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
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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
Page 242 and 243: HYPERSPACE TITLES 215 meaningfully
Page 244 and 245: notes Only God truly exists; all ot
Page 246 and 247: notes 219 4. Unfortunately, there a
Page 248 and 249: notes 221 tiny discrete units. To q
Page 250 and 251: notes 223 less universes could be v
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
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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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