Fractals, scheme-generated numbers as 300
Fractals, skin surfaces as 4
Fractions, binary point 118—120 188 261 262 271—272
Fractions, decimal point 117—118
Fredkin, Edward 116
Freedom and space 99
Frege, Gottlob 208 209
Fuller, Buckminster 226
Galactic Survey Number 93—95
Galen 207
Galileo 32 33
gambling 74 See
Gender Number 93—95
Geometric patterns See also "Shapes"
Geometric patterns, numbers as 51—72
Geometrical inversion 270
Geometry and smooth magnitudes 5
Geometry in quadrivium 20—21
Geometry, Euclid's axioms in 12
God and number 51
God as infinity 11 251 253
God in the details 170
Godel's theorem 13—14 32 34 218—226 236 245—247
Godel's theorem and Chaitin's theorem 284 286
Godel's theorem and infinite bit 264
Godel's theorem and transfinite computer 258
Godel, Kurt 13—14 197 220 246—247 262
Goldbach's conjecture 241—242
Googol 73 79—80
Googolplex 80
Grains of sand as infinitesimal 278
Grains of sand, Archimedes' numbering of 77—78
Growth, natural and CA rules 313
Growth, natural, logarithmic spiral in 153—154
Halting problem 238—242 313
Halting problem and Penrose tile problem 110
Halting problem and runtime 302
Hand and base-ten system 41
Hand and number five 55
Hand, binary system on 43
Hand, mathematical patterns in 3—4
Hardware, content compared to 157
Hegel, G.W.F. 16—17 20
Helix/helices (corkscrew pattern) 141 142 145 154 155 157
Heptagon 56
Hexagon (six-sided figure) 53 56
Hexagonal grid 53 57 61 66 67 69—71
Hexagonal tessellation 104
Hilbert space 32 100 182 186—194
Hilbert space and quantum physics 102 187—188
Hilbert space, life as fractal in 182—183
Hilbert's tenth problem 242
Hilbert, David 197 208 216—218 220
History, helical pattern in 155
History, succession of mathematical concepts in 25 31—35
Hofstadter, Douglas 226
Hydrant (fractal surface) 171 172
Hyperbola 124 126 127 141
Hyperbolic paraboloid 158
Hyperspaces 100
Icosahedron as number pattern 54 62
Icosahedron as regular 63
Inconceivability 290—301
Inconceivable numbers 73 91
Indiscernibles, principle of 198
Industrial Revolution 25 32—34
Infinite (to) bit 159 264—267
Infinite binary tree 162 164 262 264 265 See
Infinitesimals 268—269
Infinitesimals and calculus 13 268
Infinitesimals and perspective 272—277
Infinitesimals and reciprocals 269—272
Infinitesimals, grains of sand as 278—279
infinity 10—13 15—16 251—252 See
Infinity and commutative law 254
Infinity and continuum problem 261—267
Infinity and Godel's theorem 13—14 221—223 225 264
Infinity and intuition 20
Infinity and number eight 59
Infinity and number seven 56
Infinity and real number line 13
Infinity and reflection principle 253 258 261
Infinity and simple explanations 289
Infinity and simplexes 23—24
Infinity and size 259—260
Infinity as God 11 251 253
Infinity as Modern 25 34
Infinity as transfinite processes 254—258
Infinity in fractional measurement 118
Infinity in notation of line 122
Infinity in parts of real world 157
Infinity of natural numbers 90
Infinity of one-dimensional number 188
Infinity, alef-one as 260—262 267
Infinity, Cantor's three types of 252—253
Infinity, hand as 4
Infinity, number and space connected by 25
Inflection, points of 134—135 138
information 3 25—27 29—30 35 See
Information and computer revolution 31
Information and dimensionality 188—194
Information and Godel's theorem 225—226
Information and mathematical form 177
Information and reciprocals 271
Information and simplexes 23—24
Information in Hilbert space 186—194
Information in notation of line 122
Information in parts of real world 157
Information mechanics 32 116
Information processing 30
Information processing by physical objects 35 306—307
Information theory 27—29 See
Information theory and continuum problem 263—267
Information theory and logarithms 45—47 49 91
Information theory and uncertainty/unpredictability 28—29 47
Information theory, algorithmic 284
Information theory, measurement of information in 4 27—29 47—49 51 91 279 282 285
Information, analog 116 119 122—125 137 145 183—184
Information, DNA as 4 155 303
Information, hand as 4
Information, levels of 25—26
Information, logical consequences as 212
Information, measurement of 4 27—29 47—49 51 91 279 282 285
Information, numerical coding of 73 84—95 222 243 280—282
Information, simple explanations behind 314
Instincts, and archetypes 21
Interpretation See "Decoding" "Numeration
Intuition 18 20
Jung, C.G. 17—21
Justice and Pythagoreans 50
Justice as number four 53
Kaluza — Klein theory 102
Kasner, Edward 79 80
Kleene, Stephen 226
Koch curve 167—169 174—175
Kolmogorov, A.N. 284
L27 system of numeration 85—89
L27 system of numeration and Godel's theorem 220 222 223
Labeling 31
Language and logical principles 212
Language, Leibniz's conception of 197 214
Language, logic inadequate to 201
Large numbers 73 92
Large numbers as inconceivable 293—296
Large numbers, naming of 77—83 92—95
Laws or principles of thought of contraposition 211 212
Laws or principles of thought of double negation 211
Laws or principles of thought of excluded middle 211
Laws or principles of thought of indiscernibles 198
Laws or principles of thought of noncontradiction 198 208 211 221
| Leibniz, Gottfried 116 197—198 208 214 216 268
Liar, Paradox of 221—222
Life as fractal 178—182
Life, game of (Conway's) 111—114 116 307 311
Life, logical depth in growth of 303
Life, Secret of 214 306
Line, as degenerate conic 128 130
Listability 243—247
Lo-shu (magic square) 52
Log log graph paper 148 149
Logarithmic spiral 150—154
Logarithms 45—47 49
Logarithms and fractal dimension 169
Logarithms and information 91
Logarithms and large numbers 81
Logarithms as transcendental function 147—148
Logic 11 15—16 197—200
Logic and Godel's theorem 13—14 34 223—225 236 see
Logic and Industrial Revolution 25 33
Logic and Lewis Carroll 199—200
Logic and Platonic dialogues 200—201
Logic and simplexes 23—24
Logic and space 12
Logic and thinking 20
Logic as relative 29
Logic in notation of line 122
Logic of mathematics 11
Logic, hand as 4
Logic, history of 197—198
Logic, limitation of 198 200 286
Logic, monadic-property sentences in 201—202
Logic, number and space connected by 25
Logic, predicate calculus in 209 210 216
Logic, propositional calculus in 201 209—212 216
Logic, syllogism in 202—207
Logic, symbolic 32 207—212
Logical depth 303
Logical depth and the world 314
Logical depth of 1-D CA 312
Logical depth of CAM 309
Logical space 213—217
Logical space and Godel's theorem 220—221
Lucas, J. Anthony 226
Luck See also "Gambling"
Luck and number eleven 61
Luck and number fourteen 63
Luck and number seven 56
Luck and number thirteen 63
Luzhin hypothesis 278—279
Magic square 52
Magnitudes, spotty vs. smooth 5 6 10 See "Digital-analog
Mandelbrot, Benoit 160 164—168 175
Mao Zedong on 1000 flowers 214
Margolus, Norman 308
Martin's Axiom 279
Marx brothers, on thinking 197
Master equation 313—314
Mathematical logic 11 See
Mathematical name 92
Mathematical pattern, infinity as 4 15—16 see
Mathematical pattern, information as 4 see
Mathematical pattern, logic as 4 15—16 see
Mathematical pattern, number as 3 15—16 see
Mathematical pattern, space as 3—4 15—16 see
Mathematical space 99—100
Mathematical space and perspective 273
Mathematical space vs. real space 100—103
Mathematics See also "Algebra" "Arithmetic" "Geometry" "Infinity" "Number" "Space"
Mathematics and Godel's theorem 220—226 see
Mathematics and halting problem 241—242
Mathematics and information 25 30 35 177
Mathematics and propositional calculus 201
Mathematics and reality 156—157 177
Mathematics and space-number gap 10
Mathematics as formal system 216—218 220
Mathematics, psychological roots of 14—16
Maxwell, James Clark 34
McLuhan, Marshall 33
Measurement and measuring unit (natural borders) 166
Measurement of information 4 27—29 47—49 51 279 282 285
Menger sponge 173—174
Metaphysics, and Boole's logic 208
Microcomputers 31 See
Middle Ages 25 31—33
Middle Ages and number five 55—56
Middle Ages, logic in 202 205—206
Mnemonic verse, on syllogisms 205—206
Modern Times 25 34
Modus Tollens 211 212
Monad and information mechanics 116
Monad as archetype 50
Motion and space 99
Motion, sine curve as describing 145
Mutual knowledge 254—255
Myhill, John 246
Names for large numbers 92—95
Nephroid 141 142
Nephroid of Freeth 132 137
Newton, Isaac 32—34 131—132 218 268
Noncontradiction, law or principle of 198 208 211 221
Nonstandard numbers 267—269
Notation, numerical See also "Numeration systems"
Notation, numerical for large numbers 80—81
Nuclear arms and numberskulls 76
NUMBER 15—16
Number and left brain 9
Number and Middle Ages 25 31 33
Number and power 99
Number and sensation 19
Number and simplexes 23—24
Number as objective 14—16 50 73
Number as patterns 49—72 91—92 293
Number as spotty magnitude 5
Number as unbreakable units 49
Number games (gambling) 74
Number in notation of line 122
Number vs. space 5—6 9 10
Number, Conway's view of 269
Number, hand as 3
Number-log lines 148 149
Numbers and crowds 76—77
Numbers and Godel's theorem 220
Numbers and infinite sets 259—260
Numbers and Pythagoreans 50—51 55 56 60 73—74
Numbers and real number line 13 261 268
Numbers, alef-one  260—262 267
Numbers, associations suggested by 50—65
Numbers, checking truth of sentences about 257—258
Numbers, Goldbach's conjecture on 241—242
Numbers, inconceivable 293—295
Numbers, infinitesimal 13 268—269 see
Numbers, information coded as 73 84—95 222 243 280—282
numbers, large 73 77—83 92—95
Numbers, nonstandard transfinite 267—269
Numbers, one 39—40
Numbers, perfect 56
Numbers, prime 56
Numbers, size ranges of 72—73 91—92
Numbers, tetrahedral 65 67—68 70
Numbers, transfinite 253—254 258 267—269 294—295
Numbers, triangular 56 60 63
Numbers, zero 39—40
Numberskulls 74—76
Numeration systems, base-ten (decimal) 40—42 49 91 92
Numeration systems, base-three through base-ten 42
Numeration systems, binary (base-two) 42—45 48 49 91 280—282
Numeration systems, L27 85—89 220 222 223
Numeration systems, power of 92
Numeration systems, Roman 40
Numeration systems, tally 40 43
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