"Number of the Beast" 87
 (size of set of points on real-number line) 252—253 261—264 267 278
Absolute Infinity 252 253 258—261
Absolute Infinity and nonstandard numbers 268
Absolute Infinity, vanishing point as 274 275
al-Khuwarizmi 30
Alef-one  260—262 267
Alexander's Horned Sphere 160 161
Algebra 11—12
Algebra in logic world view 32
Algebra of logic 207—209
Algebraic curves 119—140
Algebraic curves vs. fractals 167
Algebraic curves, caustics 141—142
Algebraic curves, conics 124—128 129 see "Ellipse" "Hyperbola" "Parabola"
Algebraic curves, cubic 128 130—132 135
Algebraic curves, graphing of 133—140
Algebraic curves, higher-order 132—133 137
Algebraic curves, quartic 128 130 132 136
Algebraic surfaces 157—158
Algorithm 30 282
algorithmic complexity See "Complexity algorithmic"
Algorithmic information theory 284
Alice's Adventures in Wonderland (Carroll) 199—200
Alienation, and modern culture 34 35
AM radio 143—144
Analog activities See "Digital-analog distinction"
Analog bit 119 121 137 139—140 264
Analog computer 8
Analog information 116 119 122—125 137 145 183—184
Anderson, Laurie 280
Archetypal mathematical patterns 3—5 See
Archetypes 20 21 23
Archetypes and numbers 50
Archetypes, quaternity as 17
Archimedean spiral 145 148 150—151
Archimedes, large numbers named by 77—78 83
Aristotelian logic 11 32 197
Aristotelian logic and medievals 202 205—206
Aristotelian logic and Organon 205
Aristotelian logic and propositional calculus 201
Aristotelian logic and syllogism 202
Aristotelian logic and symbolic logic 207—209
Aristotle and Paradox of Liar 221
Aristotle on Pythagoreans 50
Aristotle, Lewis Carroll dedicates to 199
Arithmetic and commutativity under infinity 254
Arithmetic and spotty magnitudes 5
Arithmetic as digital 8
Arithmetic in quadrivium 20—21
Arithmetic, one-to-two step in 260 268
Arms race and numberskulls 76
Astronomy in quadrivium 20—21
Astronomy, universe of 253
Atomic properties 212
Atomism, logical 185 214—216
Automata, cellular See "Cellular automata"
Base-ten (decimal) numeration system 40—42 49 91 92
Base-two numeration system See "Binary numeration system"
Beaver function 302
Bennett, Charles 303—306
Big Bang and TV flea circus 307
Binary (base-two) numeration system 42—45
Binary (base-two) numeration system and information measurement 47—49 91
Binary (base-two) numeration system, zeros-and-ones code in 280—282
Binary point fractions 118—120 188 261 262 271—272
Binary tree 162 164 262 264 265 278 See
Bit strings and algorithmic complexity 279—286
Bit strings and Chaitin's theorem 286—290
Bit strings and dimensional location 188—194
Bit strings, conceivability/inconceivability of 292 296—300
Bit strings, logical depth of 303—305
Bit strings, run time for 302
bits 27 44—45 47 See
Bits and information measurement 47—49 51
Bits of precision 118 120 188—194 277
Bits, analog and digital 119 121 137 139—140 183 186
Bits, communication as exchange of 185—186
Bits, infinite  159 264—267
Body number 93—95
Bohr, Niels 7 185 218
Bohr, Niels, coat of arms 7 8
Boole, George 34 197 198 201 208—209
Border, length of 164—168 See
Brain and number of thoughts 81—83
Brain, computer as model of 34—35
Brain, conceivability limit of 290—291
Brain, left-right division of 8—9 13 183
Branches 141 162—163 See
CA See "Cellular automata"
Calculators and logarithms 47
Calculators, Turing machines as 231—232
Calculus 13
Calculus (logic) and Boole 198
Calculus (logic) and Leibniz 197
Calculus (logic) of monadic properties 201
Calculus (logic), predicate 209 210 216
Calculus (logic), propositional 201 209—212 216
Calculus and infinitesimals 13 268
Calculus in infinity world view 32
Calculus, curve sketching through 133—135
CAM (Cellular Automaton Machine) 307—309
Canetti, Elias 77
Cantor's theorem 263—264 266
Cantor, Georg 34 251—252 261 268
Carroll, Lewis (Charles Lutwidge Dodgson) 199—200 213
Cartesian coordinates 119—120 142 150
Catastrophe theory 130 132 133
Causation, and logical implication 210
Caustics 141—142
Cells in game of Life 111—114 116 307
Cells, hierarchy in levels of 313
Cellular automata (CA's) 113—116 307 309
Cellular automata (CA's), Turing machine as 309—311
Cellular automata (CA's), Wolfram's 1-D rules for 311
Cellular automata (CA's), world as 313—314
Cellular Automaton Machine (CAM) 307—309
Centered cube 54 60
Centered squares 55 58 62 63 66 70
Chaitin's theorem 284 286—290 302 305
Chaitin, Gregory 225 284 306
Change, and space 99
Channel, for information transmission 29
Chemistry and number 73—74
Church's Theorem 237—239 245—247
Church, Alonzo 225 237 245—247
circle 124 125 127 141
Circle and simplicity 161
Circle, infinite number of points on 251
Coding system See also "Numeration systems"
Coding system, L27 85—89 222 223
Coding system, numerical 84—85 89 90—95
Cohen, Paul 262
Communication and analog-digital distinction 184—186
Communication and information 30
Communication and knowledge 26
Communication theory 27
Communication, through L27 system 87—89
Communication, through zeros-and-ones code 280—282
Commutative law and infinity 254
Complementarity 6—8
Complementarity and brain-half functions 8—9 13
Complementarity and digital-analog distinction 185
Complexity and fractals 103 160 167 174—175
Complexity and inconceivability 292—301
Complexity and information 25—26 35
Complexity and logical depth 303—306
Complexity and simple explanations 289—290 313—314
Complexity and the world 314
Complexity as inconceivable 290—292
| Complexity of 1-D CA 312
Complexity of CAM 309
Complexity of Penrose tessellations 110
Complexity of physical world 156—157 164—166
Complexity of programs vs. internal states 235
Complexity, algorithmic 279—288
Complexity, Godel's theorem demonstrates 226
Complexity, limit on understanding of 214 225 287
Complexity, mathematical approach to 157—160
Computability and runtime 302
Computability and Turing machine 226 243 244
Computability as absolute 236
Computability of properties of numbers 243—244
Computability vs. listability 243—247
Computations, irreducible 313
Computer See also "Information processing"
Computer and brain 34—35
Computer and Church's theorem 237—238
Computer and halting program 238—241
Computer and infinity 25
Computer and information measurement 4
Computer and logical systems 200
Computer and physics 35
Computer and Turing machine 228—236 283 see
Computer in information world view 32
Computer revolution 31
Computer, cellular automaton as 114—115
Computer, curve calculation on 136 139 140
Computer, digital vs. analog 8
Computer, fractal landscapes generated by 175 176
Computer, life fractal on 178—182
Computer, Life game on 112
Computer, operation of 226—228
Computer, polygons generated by 103—104
Computer, random numbers from 198
Computer, runtime of 219 301—306
Computer, serial vs. parallel 307
Computer, transfinite 258
Concepts, grouping of 16—17 See "Tetrads" "Triads"
Cone 158
Conies 124—129
Conies, circle 124 125 127 141 161 251
Conies, ellipse 124 125 127 137 141
Conies, hyperbola 124 126 127 141
Conies, parabola 12 124—127 134 141
Consequentia mirabilis 211 212
Continuous vs. discrete patterns of magnitudes 10 13 See
Continuous vs. discrete patterns of magnitudes and algebra 12
Continuous vs. discrete patterns of magnitudes and infinity 12—13
Continuous vs. discrete patterns of magnitudes and number vs. space 14—15
Continuum problem 261—267
Contraposition, law of 211 212
Conway, John Horton 109 111—113 116 268—269 311
Coordinates, Cartesian 119—120 142 150
Coordinates, polar 150—151
Corkscrew pattern (helix) 141 142 145 154 155 157
Crowds, experience of 76—77
Crowds, reciprocal size comparisons of 271
Crystal and complexity 304
Crystal, archetype compared to 21
Cube as number pattern 54 58—62 67—69 71 72
Cube as regular 63
Cubic curves, general 130—132 135
Cubic curves, polynomial 128 130 131
Curve(s) 100
Curve(s), algebraic 119—124 see
Curve(s), fractal 161—170 173—175
Curve(s), nonalgebraic (transcendental) 142—155
Curve(s), power-series 158—159
Curve(s), Sierpinski carpet as 173
Curve(s), with corners 159—160
Curve-fitting 138
Darshan 76—77
Death of humans vs. bacteria or crabs 147
Decimal (base-ten) numeration system 40—42 49 91 92
Decimal point fractions 117—118
Decision problem (Entscheidungsproblem) 228 237 242
Decoding See also "Coding system"
Decoding of hit string as location 189—191
Decoding, mathematics as 30
Degenerate conies 127—128 130
DeMorgan's laws 211 212
Depth, logical See "Logical depth"
Derivatives, in calculus 134—135 138
Descartes, Rene 119
Devil, and pentagram 56
Dialogue(s) See also "Communication"
Dialogue(s) of Plato 200—201 290
Dialogue(s), knowledge through 26
Dictionary as code book 85
Digital computer 8
Digital-analog distinction 8 117 183—184 See logical" "Bits" "Continuous
Digital-analog distinction and brain 8—9 13 183
Digital-analog distinction and communication 184—186
Digital-analog distinction and compact disc 292
Digital-analog distinction and division of line 117—119
Digital-analog distinction and joke-telling 84
Digital-analog distinction and physical reality 116—117
Digital-analog distinction and writing vs. speech 89
Digital-analog distinction in bits 119 121 137 139—140 183—184 186
Dimensionality 100 102—103
Dimensionality and Hilbert space 186—188 194
Dimensionality as information 188—194
Dimensionality in fractal curves 167—173
Discrete magnitudes See "Continuous vs. discrete patterns or magnitudes" "Digital-analog
Divinity See "Absolute Infinity" "God"
Division, infinite See "Binary point fractions" "Binary "Continuum "Infinitesimals" "Precision
DNA 4 16 155 303
Dodecahedron as number pattern 57 67
Dodecahedron as regular 63
Dodgson, Charles Lutwidge (Lewis Carroll) 199—200 213
Dust, fractal 176—177
Dyads 5—8
Dyads as archetype 21 50
Dyads as opposition 16 51
Dyads, number-space 5—7
Electrons, Bohr's view of 7
ellipse 124 125 127 137 141
Ellipsoid 158
Endless decimals 261 See
Endless dimensions, Hilbert space as 187 See
Endless loops of Turing machines 230 232
Endless questions on any object 264
Endless regress in self knowledge 255—256
Endlessness infinity as 15 see
Endlessness of sine wave equation 144—145
Entscheidungsproblem (decision problem) 228 237 242
Euclid's axioms 12
Excluded middle, law of 211
Explanations and logical depth 303
Explanations and logical theorizing 214
Explanations, simple 289—290 306 313—314 See
Exponential curve 145—147 158
Feeling 18 20
Fermat's spiral 150
Fermat, Pierre 119
Five-cell 23 24
Five-conceivability 300—301
Flea circus, TV 307
FM radio 144
FORM See "Mathematical patterns" "Patterns"
Forms, spatial 100 156—157 177 See "Curves" "Fractals" "Polygons" "Sphere" "Surfaces"
Fourth dimension 186—187
Fourth dimension and number sixteen 63
Fourth dimension, logarithmic spiral in 154
Fractals 103 160—177
Fractals vs. parallels 274
Fractals, combination of different sorts of 177
Fractals, dimension value of 167—173
Fractals, life as 178—182
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