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notes 229 Ben Brown suggests that 4-D beings would be solar powered. In three dimensions one photon contains 10 7 ergs; this energy would be significantly higher in four dimensions, due to a possible added oscillation. This means that one photon could be a more significant source of energy. In our 3-D world, it seems impractical for a mobile, warm-blooded creature to use solar energy; however, in four dimensions, it may be practical for beings to absorb light and turn it directly into a storable form of energy. Any such stored energy might reside as tissues deep inside the creature, shielding vital organs such as the brain. Appendix H 1. Obviously it is quite difficult to predict how particles will behave in different dimensions. This means that it is difficult to predict what senses would evolve in 4-D beings. In three dimensions, light oscillates in a 2-D fashion while moving forward through the third dimension (the electrical and magnetic fields oscillate at right angles to one another). In four dimensions, would light somehow oscillate in three dimensions while moving forward through a fourth? Of course this is quite speculative, but it may mean that "3-D light" would not be visible to a 4-D being, and that 2-D light may not be visible to us. If "light" could exist in two dimensions, "light" might oscillate through one dimension and move forward through a second. Does this mean that Flatland might not be visible to us as we stood above Flatland and looked down? Perhaps this implies that 4-D creatures would have difficulty seeing us. What would we see if our eyes were level with Flatland? (Would we be able to see a Flatlander if we illuminated him with a 3-D light source?) If we were able to see Flatlanders, movement and energy stored on the 2-D surface might somehow be translated into the energy levels of 3-D particles. Arlin Anderson believes that sound (vibrational energy) seems to dissipate all its energy within our 3-D world. This implies that a 4-D being can't hear (or see) us with our sound or light until the being puts his ear or eye on our level. However, if 4-D photons and phonons are possible, the being could use these to observe us.
further readings Higher space can be viewed as a background of connective tissue tying together the world's diverse phenomena. —Rudy Rucker, The Fourth Dimension The identification of the omnipresence of space with the omnipresence of God leads to a serious difficulty. —Max Jammer, Concepts of Space Abbott, E. (1952) Flatland. New York: Dover. [The original publication was in 1884 (Seeley & Co.), and the most recent Dover Thrift Edition appeared in 1992.1 Apostol, T. (1969) Calculus, Volume II, 2d. Edition. New York: John Wiley & Sons. Banchoff, T. (1996) Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions, 2d Edition. New York: Freeman. Banchoff, T. (1990) From Flatland to Hypergraphics. Interdisciplinary Science Reviews. 15:364-72. Berlinghoff, W. and Grant, K. (1992) Mathematics Sampler: Topics for Liberal Arts. New York: Ardsley House Publishing. Bond, N. (1974) "The monster from nowhere," in As Tomorrow Becomes Today, Charles W. Sullivan, ed. New York: Prentice-Hall. (Originally published in Fantastic Adventures, July 1939.) Buchel, W. (1963) Why is space three dimensional? (in German) Physikalische Blatter. 19:547-48. Cowen, R. (1998) Cosmologists in Flatland: Searching for the missing energy. Science News. February 28, 153(9):139-41. Deser, S., Jackiw, R., and 'tHofft, G. (1984). Three-dimensional Einstein gravity: dynamics of flat space. Annals ofPhyics. 152:220—35. Dewdney, A. (1984) The Planiverse: Computer Contact with a Two-Dimensional World. New York: Poseidon. Dorling, J. (1969) The dimensionality of time. American Journal of Physics. 38:539—42. Duff, M. (1998) The theory formerly known as strings. Scientific American. February, 278(2):64-69. (Discusses membrane theory.) Dyson, F. (1978) Characterizing irregularity. Science. May 12, 200(4342):677-78. Dyson, F. (1979) Time without end: physics and biology in an open universe. Reviews of Modern Physics. 51(3):447-60. 230
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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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Page 240 and 241: HYPERSPACE TITLES 213 tinctly diffe
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Page 260 and 261: about the author Clifford A. Pickov
Page 262 and 263: addendum As this book goes to press
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Page 266: Index 239 Slade, Henry, 123, 129 So
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