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CHALLENGING QUESTIONS FOR FURTHER THOUGHT 211 "string" of information in the DNA. This information can be considered one dimensional, like a sequence of letters in a sentence. After transcription into RNA and translation into proteins, a final folding of the protein structure in three dimensions is necessary for the protein to function properly. With four-dimensional living cells, a similar process includes transcription and translation into a protein folded in the fourth dimension. In order to correctly form the four-dimensional protein, the original information may be conveyed by a molecule one dimension higher than the one-dimensional DNA sequence. Perhaps this hyper- DNA would exist as a 2-D "DNA sheet" which could be schematically represented as an array or matrix of letters. A closed circular surface would offer more combinations or possibilities for DNA information, but this would require more accurate and sophisticated start and stop codons to specify the boundaries of the DNA used for coding a particular protein. In conceiving a two-dimensional information storage molecule, I search for a shapes that can maximize information storage on a minimal surface as well as make the processes of maintenance and transfer of information (replication) more efficient. For pedagogical reasons, let us imagine a hyperDNA molecule with the same number of information molecules. In our world, DNA contains the basic hereditary information of all living cells and consists of a four-letter code: G, C, A, and T. The letters represent chemical "bases." In a higher universe, we would have a much larger set of possible codons (clusters of bases that code for an amino acid) resulting from the higher-dimensional DNA and the various arrangements of adjacent bases in two dimensions. The coding system would be much more rich. Highly evolved four-dimensional creatures would have extraordinarily developed nervous systems due in part to the increased number of possible neuronal synapses. Therefore the beings would be superintelligent. I would expect new and "higher" senses to be present. For example, "propioception," or pressure sensing, would probably not occur perpendicular to a 2-D creature's plane of existence. Similarly, four-dimensional creatures would have senses and sensory receptors that would make little sense to us.
appendix i hyperspace titles Suppose I somehow gain access to a 2-D world, and I convince the 2-D people I am their one true deity. From their point of view, there is only one God. But from my point of view, I am only one of many people who could appear as a God to these people. If God is a multidimensional being, is he alone in his dimension? Could he be only one of many Gods in his realm? If God moved parts of his body in and out of our dimensional realm, could he appear as a pillar of fire or a burning bush? —Darren Levanian, personal communication That Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love, May be able to comprehend with all saints what is the breadth, and length, and depth, and height; And to know the love of Christ, which passeth knowledge, that ye might be filled with all the fullness of God. Ephesians 3:17-19 While writing this book, I performed a computer search of the scientific literature mostly for articles with "hyperspace" in their titles, but also for some with "hyperspace" in the subject matter. A few titles were suggested by colleagues. Consider the following list a random walk <strong>through</strong> hyperspace to show a variety of applications in physics, mathematics, and computer science. 1. Carter,], and Saito, M. (1998) Knotted Surfaces and their Diagrams (Mathematical Surveys and Monographs, No 5). New York: American Mathematical Society. (Extends the methods of 3-D topology to 4-D topology.) 2. Devchand, C. and Nuyts, J. (1997) Supersymmetric Lorentz-covariant hyperspaces and self-duality: equations in dimensions greater than four. Nuclear Physics B. 503(3): 627-56. (The authors generalize the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore.) 3. Bordley, R. F. (1997) Discrete-time general relativity and hyperspace. Nuovo Cimento B. 112B(4): 561-74. (The author describes two popular, but dis- 212
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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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Page 190 and 191: concluding remarks This completes o
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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
Page 204 and 205: HIGHER DIMENSIONS IN SCIENCE FICTIO
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
Page 222 and 223: SMORGASBORD FOR COMPUTER JUNKIES 19
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
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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
Page 258 and 259: further readings 231 Ehrenfest, P (
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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