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Rucker R. Ч Mind Tools. The Five Levels of Mathematical Reality
Rucker R. Ч Mind Tools. The Five Levels of Mathematical Reality

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Ќазвание: Mind Tools. The Five Levels of Mathematical Reality

јвтор: Rucker R.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1987

 оличество страниц: 339

ƒобавлена в каталог: 30.07.2013

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
"Number of the Beast"      87
$\mathcal{C}$ (size of set of points on real-number line)      252Ч253 261Ч264 267 278
Absolute Infinity      252 253 258Ч261
Absolute Infinity and nonstandard numbers      268
Absolute Infinity, vanishing point as      274 275
al-Khuwarizmi      30
Alef-one $(\aleph_{1})$      260Ч262 267
Alexander's Horned Sphere      160 161
Algebra      11Ч12
Algebra in logic world view      32
Algebra of logic      207Ч209
Algebraic curves      119Ч140
Algebraic curves vs. fractals      167
Algebraic curves, caustics      141Ч142
Algebraic curves, conics      124Ч128 129 see "Ellipse" "Hyperbola" "Parabola"
Algebraic curves, cubic      128 130Ч132 135
Algebraic curves, graphing of      133Ч140
Algebraic curves, higher-order      132Ч133 137
Algebraic curves, quartic      128 130 132 136
Algebraic surfaces      157Ч158
Algorithm      30 282
algorithmic complexity      See "Complexity algorithmic"
Algorithmic information theory      284
Alice's Adventures in Wonderland (Carroll)      199Ч200
Alienation, and modern culture      34 35
AM radio      143Ч144
Analog activities      See "Digital-analog distinction"
Analog bit      119 121 137 139Ч140 264
Analog computer      8
Analog information      116 119 122Ч125 137 145 183Ч184
Anderson, Laurie      280
Archetypal mathematical patterns      3Ч5 See
Archetypes      20 21 23
Archetypes and numbers      50
Archetypes, quaternity as      17
Archimedean spiral      145 148 150Ч151
Archimedes, large numbers named by      77Ч78 83
Aristotelian logic      11 32 197
Aristotelian logic and medievals      202 205Ч206
Aristotelian logic and Organon      205
Aristotelian logic and propositional calculus      201
Aristotelian logic and syllogism      202
Aristotelian logic and symbolic logic      207Ч209
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      20Ч21
Arithmetic, one-to-two step in      260 268
Arms race and numberskulls      76
Astronomy in quadrivium      20Ч21
Astronomy, universe of      253
Atomic properties      212
Atomism, logical      185 214Ч216
Automata, cellular      See "Cellular automata"
Base-ten (decimal) numeration system      40Ч42 49 91 92
Base-two numeration system      See "Binary numeration system"
Beaver function      302
Bennett, Charles      303Ч306
Big Bang and TV flea circus      307
Binary (base-two) numeration system      42Ч45
Binary (base-two) numeration system and information measurement      47Ч49 91
Binary (base-two) numeration system, zeros-and-ones code in      280Ч282
Binary point fractions      118Ч120 188 261 262 271Ч272
Binary tree      162 164 262 264 265 278 See
Bit strings and algorithmic complexity      279Ч286
Bit strings and Chaitin's theorem      286Ч290
Bit strings and dimensional location      188Ч194
Bit strings, conceivability/inconceivability of      292 296Ч300
Bit strings, logical depth of      303Ч305
Bit strings, run time for      302
bits      27 44Ч45 47 See
Bits and information measurement      47Ч49 51
Bits of precision      118 120 188Ч194 277
Bits, analog and digital      119 121 137 139Ч140 183 186
Bits, communication as exchange of      185Ч186
Bits, infinite $(\omega)$      159 264Ч267
Body number      93Ч95
Bohr, Niels      7 185 218
Bohr, Niels, coat of arms      7 8
Boole, George      34 197 198 201 208Ч209
Border, length of      164Ч168 See
Brain and number of thoughts      81Ч83
Brain, computer as model of      34Ч35
Brain, conceivability limit of      290Ч291
Brain, left-right division of      8Ч9 13 183
Branches      141 162Ч163 See
CA      See "Cellular automata"
Calculators and logarithms      47
Calculators, Turing machines as      231Ч232
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 209Ч212 216
Calculus and infinitesimals      13 268
Calculus in infinity world view      32
Calculus, curve sketching through      133Ч135
CAM (Cellular Automaton Machine)      307Ч309
Canetti, Elias      77
Cantor's theorem      263Ч264 266
Cantor, Georg      34 251Ч252 261 268
Carroll, Lewis (Charles Lutwidge Dodgson)      199Ч200 213
Cartesian coordinates      119Ч120 142 150
Catastrophe theory      130 132 133
Causation, and logical implication      210
Caustics      141Ч142
Cells in game of Life      111Ч114 116 307
Cells, hierarchy in levels of      313
Cellular automata (CA's)      113Ч116 307 309
Cellular automata (CA's), Turing machine as      309Ч311
Cellular automata (CA's), Wolfram's 1-D rules for      311
Cellular automata (CA's), world as      313Ч314
Cellular Automaton Machine (CAM)      307Ч309
Centered cube      54 60
Centered squares      55 58 62 63 66 70
Chaitin's theorem      284 286Ч290 302 305
Chaitin, Gregory      225 284 306
Change, and space      99
Channel, for information transmission      29
Chemistry and number      73Ч74
Church's Theorem      237Ч239 245Ч247
Church, Alonzo      225 237 245Ч247
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      85Ч89 222 223
Coding system, numerical      84Ч85 89 90Ч95
Cohen, Paul      262
Communication and analog-digital distinction      184Ч186
Communication and information      30
Communication and knowledge      26
Communication theory      27
Communication, through L27 system      87Ч89
Communication, through zeros-and-ones code      280Ч282
Commutative law and infinity      254
Complementarity      6Ч8
Complementarity and brain-half functions      8Ч9 13
Complementarity and digital-analog distinction      185
Complexity and fractals      103 160 167 174Ч175
Complexity and inconceivability      292Ч301
Complexity and information      25Ч26 35
Complexity and logical depth      303Ч306
Complexity and simple explanations      289Ч290 313Ч314
Complexity and the world      314
Complexity as inconceivable      290Ч292
Complexity of 1-D CA      312
Complexity of CAM      309
Complexity of Penrose tessellations      110
Complexity of physical world      156Ч157 164Ч166
Complexity of programs vs. internal states      235
Complexity, algorithmic      279Ч288
Complexity, Godel's theorem demonstrates      226
Complexity, limit on understanding of      214 225 287
Complexity, mathematical approach to      157Ч160
Computability and runtime      302
Computability and Turing machine      226 243 244
Computability as absolute      236
Computability of properties of numbers      243Ч244
Computability vs. listability      243Ч247
Computations, irreducible      313
Computer      See also "Information processing"
Computer and brain      34Ч35
Computer and Church's theorem      237Ч238
Computer and halting program      238Ч241
Computer and infinity      25
Computer and information measurement      4
Computer and logical systems      200
Computer and physics      35
Computer and Turing machine      228Ч236 283 see
Computer in information world view      32
Computer revolution      31
Computer, cellular automaton as      114Ч115
Computer, curve calculation on      136 139 140
Computer, digital vs. analog      8
Computer, fractal landscapes generated by      175 176
Computer, life fractal on      178Ч182
Computer, Life game on      112
Computer, operation of      226Ч228
Computer, polygons generated by      103Ч104
Computer, random numbers from      198
Computer, runtime of      219 301Ч306
Computer, serial vs. parallel      307
Computer, transfinite      258
Concepts, grouping of      16Ч17 See "Tetrads" "Triads"
Cone      158
Conies      124Ч129
Conies, circle      124 125 127 141 161 251
Conies, ellipse      124 125 127 137 141
Conies, hyperbola      124 126 127 141
Conies, parabola      12 124Ч127 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      12Ч13
Continuous vs. discrete patterns of magnitudes and number vs. space      14Ч15
Continuum problem      261Ч267
Contraposition, law of      211 212
Conway, John Horton      109 111Ч113 116 268Ч269 311
Coordinates, Cartesian      119Ч120 142 150
Coordinates, polar      150Ч151
Corkscrew pattern (helix)      141 142 145 154 155 157
Crowds, experience of      76Ч77
Crowds, reciprocal size comparisons of      271
Crystal and complexity      304
Crystal, archetype compared to      21
Cube as number pattern      54 58Ч62 67Ч69 71 72
Cube as regular      63
Cubic curves, general      130Ч132 135
Cubic curves, polynomial      128 130 131
Curve(s)      100
Curve(s), algebraic      119Ч124 see
Curve(s), fractal      161Ч170 173Ч175
Curve(s), nonalgebraic (transcendental)      142Ч155
Curve(s), power-series      158Ч159
Curve(s), Sierpinski carpet as      173
Curve(s), with corners      159Ч160
Curve-fitting      138
Darshan      76Ч77
Death of humans vs. bacteria or crabs      147
Decimal (base-ten) numeration system      40Ч42 49 91 92
Decimal point fractions      117Ч118
Decision problem (Entscheidungsproblem)      228 237 242
Decoding      See also "Coding system"
Decoding of hit string as location      189Ч191
Decoding, mathematics as      30
Degenerate conies      127Ч128 130
DeMorgan's laws      211 212
Depth, logical      See "Logical depth"
Derivatives, in calculus      134Ч135 138
Descartes, Rene      119
Devil, and pentagram      56
Dialogue(s)      See also "Communication"
Dialogue(s) of Plato      200Ч201 290
Dialogue(s), knowledge through      26
Dictionary as code book      85
Digital computer      8
Digital-analog distinction      8 117 183Ч184 See logical" "Bits" "Continuous
Digital-analog distinction and brain      8Ч9 13 183
Digital-analog distinction and communication      184Ч186
Digital-analog distinction and compact disc      292
Digital-analog distinction and division of line      117Ч119
Digital-analog distinction and joke-telling      84
Digital-analog distinction and physical reality      116Ч117
Digital-analog distinction and writing vs. speech      89
Digital-analog distinction in bits      119 121 137 139Ч140 183Ч184 186
Dimensionality      100 102Ч103
Dimensionality and Hilbert space      186Ч188 194
Dimensionality as information      188Ч194
Dimensionality in fractal curves      167Ч173
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)      199Ч200 213
Dust, fractal      176Ч177
Dyads      5Ч8
Dyads as archetype      21 50
Dyads as opposition      16 51
Dyads, number-space      5Ч7
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      255Ч256
Endlessness infinity as      15 see
Endlessness of sine wave equation      144Ч145
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      289Ч290 306 313Ч314 See
Exponential curve      145Ч147 158
Feeling      18 20
Fermat's spiral      150
Fermat, Pierre      119
Five-cell      23 24
Five-conceivability      300Ч301
Flea circus, TV      307
FM radio      144
FORM      See "Mathematical patterns" "Patterns"
Forms, spatial      100 156Ч157 177 See "Curves" "Fractals" "Polygons" "Sphere" "Surfaces"
Fourth dimension      186Ч187
Fourth dimension and number sixteen      63
Fourth dimension, logarithmic spiral in      154
Fractals      103 160Ч177
Fractals vs. parallels      274
Fractals, combination of different sorts of      177
Fractals, dimension value of      167Ч173
Fractals, life as      178Ч182
1 2 3 4
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