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HYPERSPACE TITLES 215 meaningfully presenting hyperdimensional models that occur whenever four or more variables exist simultaneously.) 19. Lowen, R. (1983) Hyperspaces of fuzzy sets. Fuzzy Sets and Systems. 9(3): 287-311. 20. Condurache, D. (1981) Symbolic representation of signals on hyperspaces. II. The response of linear systems to excitations representable symbolically. Buletinul Institutului Politehnic din lasi, Sectia III (Electrotehnica, Electronica, Automatizari). 27(3-4): 49-56. (Describes conditions in which multiplication, raising to a power, and inversion modify the partition class of the elements entering those operations. The results are useful in studying the response of linear systems to symbolically representable excitations.) 21. Cerin, Z. T. and Sostak, A.-P. (1981) Fundamental and approximative uniformity on the hyperspace. Glasnik Matematicki, Serija III. 16(2): 339-59. [Introduces the fundamental uniformity 2(f,V) and the approximate uniformity 2(a,V) on the hyperspace 2(x) of all nonempty compact subsets of a uniform space (X, V) that reflect space properties of elements of 2(x).] 22. Condurache, D. (1981) Symbolic representation of signals on hyperspaces. I. Symbolic representation of modulated signals. Buletinul Institutului Politehnic din lasi, Sectia III (Electrotehnica, Electronica, Automatizari). 27(1-2): 33-42. (Discusses the notion of symbolic representation of a real, derivable function of a scalar argument by means of a finite dimension algebra element on the real number field.) 23. Burton, R. P. and Smith, D. R. (1982) A hidden-line algorithm for hyperspace. SIAMJournal on Computing. 11(1): 71-80. (The authors design an object-space hidden-line algorithm for higher-dimensional scenes. Scenes consist of convex hulls of any dimension, each compared against the edges of all convex hulls not eliminated by a hyperdimensional clipper, a depth test after sorting, and a minimax test. Hidden and visible elements are determined in accordance with the dimensionality of the selected viewing hyperspace. The algorithm produces shadows of hyperdimensional models, including 4-D space-time models, hyperdimensional catastrophe models, and multivariable statistical models.) 24. Goodykoontz, J. T, Jr. (1981) Hyperspaces of arc-smooth continua. Houston Journal of Mathematics. 7(1): 33-41. (Discusess the hyperspace of closed subsets.) 25. Nadler, S. B., Jr., Quinn, J. E., and Stavrakas, N. M. (1977) Hyperspaces of compact convex sets, II. Bulletin de I'Academie Polonaise des Sciences. Serie des Sciences Mathematiques, Astronomiques et Physiques. 25(4): 381-85. [The
216 appendix! authors show that cc(R(n)) is homeomorphic to the Hilbert cube minus a point.] 26. Kuchar, K. (1976) Dynamics of tensor fields in hyperspace, III. Journal of Mathematical Physics. 17(5): 801-20. (Discusses hypersurface dynamics of simple tensor fields with derivative gravitational coupling. The spacetime field action is studied and transformed into a hypersurface action. The hypersurface action of a covector field is cast into Hamiltonian form. Generalized Hamiltonian dynamics of spacetime hypertensors are discussed; closing relations for the constraint functions are derived.) 27. Kuchar, K. (1976) Kinematics of tensor fields in hyperspace, II. Journal of Mathematical Physics. 17(5): 792-800. (Differential geometry in hyperspace is used to investigate kinematical relationships between hypersurface projections of spacetime tensor fields in a Riemannian spacetime.) 28. Kuchar, K. (1976) Geometry of hyperspace, \.JournalofMathematical Physics. 17(5): 777-91. (The author defines hyperspace as an infinitedimensional manifold of all space-like hypersurfaces drawn in a given Riemannian spacetime.) 29. Shu-Chung Koo (1975) Recursive properties of transformation groups in hyperspaces. Mathematical Systems Theory. 9(1): 75-82. [Let (X,T) be a transformation group with compact Hausdorff phase space Xand arbitrary acting group T. There is a unique uniformity Omega of X that is compatible with the topology of X.) 30. Whiston, G. S. (1974) Hyperspace (the cobordism theory of spacetime). International Journal of Theoretical Physics. 11(5): 285—88 (A compact space- and time-orientable spacetime is cobordant in the unoriented sense—that is, it bounds a compact five-manifold. The bounding property is a direct consequence of the triviality of the Euler number.) 31. Tashmetov, U. (1974) Connectivity of hyperspaces. Doklady Akademii Nauk SSSR. 215(2): 286—88. (Results regarding connected and locally connected compacts in a hyperspace are extended to the case of arbitrary, full metric spaces.) 32. Caywood, C. (1988) The package in hyperspace. School Library Journal. 35(3): 110-11. 33. Easton, T. (1988) The architects of hyperspace. Analog Science Fiction- Science Fact. 108(5): 182-83. 34. Boiko, C. (1986) Danger in hyperspace (play). Plays. 45: 33-40.
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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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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 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
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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