Hofstadter D.R. — Godel, Escher, Bach: An Eternal Golden Braid :: Электронная библиотека попечительского совета мехмата МГУ

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Hofstadter D.R. — Godel, Escher, Bach: An Eternal Golden Braid

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Название: Godel, Escher, Bach: An Eternal Golden Braid

Автор: Hofstadter D.R.

Аннотация:

Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.

Язык:

Рубрика: Математика/Популярные издания/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 757

Добавлена в каталог: 30.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Mumon: commentaries by      246—249 252
Mumon: poems by      246—249 252 272
Mumonkan      246
Music box, preprogrammed      677
Music: composed by computer      25 595 597 603 607—609 626—627 676—677
Music: dimensions of      175
Music: mathematics and      227 555 560
Music: modern      156—157 163—164 174—175 699—700 704
Music: notation of      552—559 (see also “SMUT”)
Music: semantics of      83 162—164 167 174—175 582—584 626—627 676—677
Music: superhuman comprehension of      172 679
Music: syntax of      121—123 129—130 227 626—627 737
Music: to break phonographs by      75—78
Music: to infiltrate phonographs by      487—488 (see also “Fugues” “Canons” “Pianos” “Flutes” etc.)
Musical Offering, The (Bach)      4—10 86 665 666 719 720 724 727 739—742
Mutations      295
N      see “Number theory”
Najunamar, Z.      549—552
Nansen      248—249 253 255
Natural language utterances as programs      629
Natural numbers: defined      54 204
Natural numbers: generalized      453—456
Natural numbers: postulates for      216—217 (see also “Number theory” “Numerals” “TNT” “Prime etc.)
Near misses      see ““Almost”-situations”
Nearly decomposable systems      303—306
Negation      70 71 183 191—192 210—211 214 545
Negative space      62—63 66—68 72
Nested movies      184—185
Nested works of art      15 106 700—701 705—706
Nesting      127 138—141 184—185 660
Neural networks      see “Symbols”
Neuroneater      382
Neurons as an inviolate level      302 677 686 691—692
Neurons as summing inputs      316 340 575—577 677
Neurons in retina      343—344
Neurons: compared with ants      315 325 339—340
Neurons: described      339—340
Neurons: Euclid's      60
Neurons: faultless functioning of      575—577
Neurons: firing of      83 340 316 343—345 347 350 357
Neurons: not controllable consciously      302 (see also “Inaccessibility”)
Neurons: on-center and off-center      343—344
Neurons: simple, complex, hypercomplex      344—345 346 347
Neurosurgery      309 313—314 618 678
New Yorker, The      641—642
Nickelodeon      500 (see also “Jukeboxes”)
Nodes and links      370—371 652—654
Noise in vacuum      82
Non-self-assembling viruses      542—543
Non-self-descriptive adjectives      see “Heterological adjectives”
Nondivisibility      73—74
Nonequilibrium thermodynamics      693
Noneuclid      91—92
Nonexistence      254—255 698 725
Nonproducible numbers      265
Nonprogrammability of creativity      570—571 620 673
Nonprogrammability of emotions and will      677 684—686
Nonprogrammability of Goedelisation      472—476
Nonprogrammability of intelligence      26—27 471—473 597—599 601
Nonprogrammability of irrationality      575—577
Nonprogrammability of jumping out of the system      37—38 477—478 674—675
Nonprogrammability of ordinal names      476
Nonprogrammability of soul      574—575
Nonprogrammability of world chess champion      151—152 674 “Essential “Toedelizalion” “Paradox “TC-battles” “2-D etc.)
Nonsense: based on sense      378—379
Nonsense: computer-generated      620 621—622 625—626
Nonsense: human-generated      621—622
Nontermination      408 425—430 “FlooP”)
Nontheorems      see “Theorems vs. nontheorems”
Normal science      660—661
Nouns, most common in English      630
Novelty, and jumping out of the system      475
Nuclei: atomic      303—304
Nuclei: cellular      514 517 518
Nucleolides      514—517 519 522—524 530 540—541
Nucleolides: first letters of      231 517 666
Number theory as sealed-off mini-world      569
Number theory as universal mirror of formal systems      260—265 270
Number theory: applications of      278—229
Number theory: core of      100 407
Number theory: Crab and      551—558 560 562 573—574 579—581
Number theory: demise of      228—229 426
Number theory: formalized      see “TNT”
Number theory: informal (N)      54—60 204 228
Number theory: nonstandard      100 452—459
Number theory: primitive notions of      204—209
Number theory: soothing powers of      391—404
Number theory: typical sentences of      204—205
Number theory: typographical      see “TNT”
Number theory: used and mentioned      458
Number theory: “true” version of      458—459
Numbers, nature of      54—58 452 458
Numerals      205—206 213
Numerals vs. numbers      264
Object language      22 184 248
Objectivity, quest after      479 693—696
Oborin, Lev      162
Octopus cell      345
Oistrakh, David      162
Okanisama      232 234 237 238 239 241 242
Old Ba.Ch.      726
Old Bach      4 28 460 481—483 738 739
Open-ended searches      see “Potentially endless searches” “Nontermination” “Unpredictable “Loops” “Free” “FlooP” etc.)
Operating systems      295—296 300—331 308
Operators and operons      544—545
Oracles      567
Orchard analogy      see “Information depth
Order and Chaos (Escher)      399
Order and chaos: in ant colonies      316—317
Order and chaos: in number theory      393 395 398—402 406 408—409 418
Order and chaos: self-awareness and      406
Ordinals      462—464 475—476
Organ point      329—330
Origin of life      548
Original (as opposed to copies)      504
Originality and machines      25—26 606—609
ORNATE NOUN      131—133
Outcome      184
Outer messages      166—171 174—176 501 524 704
OUTPUT (BlooP)      410 411
Overlapping genes      524—525
Overview capacity      613—614 678
p-system      64 73—74
padding      402—403
Pages, in computers      289
Palindromes, in molecular biology      201 667
Palindromi      353—354 634—637 643 644
Pappus      606—607
Paradigm shifts      660—661
Paradox in art      see “Escher” “Magritte” “Cage”
Paradox in mathematics      17—24 580—581
Paradox in Zen      249—255 (see also “Contradictions” “Inconsistency”)
Paradox near misses      612 691
Paradox of AI      19 26—27 620 673
Paradox of credibility through fallibility      564
Paradox of God and the stone      478
Paradox of motion      see “Zeno's paradoxes”
Paradox of self-consciousness      389
Paradox of the Typeless Wish      115—116
Paradox: resolutions of      116 196—197 245 “Tumbolia” “Jumping
Parallel postulate      see “Fifth postulate”
PARRY      300—301 599—600 677
Parsing of natural languages      588—593 630—632 “Language”)
Partial recursivity      430
Particles, elementary      54 140—146 258 303—305 309 522
Partitions, mental      671
PARTS      303—305 (see also “Reductionism”)
Pascal, Blaise      24 25 600
Pathways as incorporating knowledge, beliefs      378—379
Pathways in ATN's and RTN's      131—134 150

Pathways: chemical      528—529 544—545 663—664
Pathways: conditional on circumstances      383—384
Pathways: goal-oriented choice of      227 609—615
Pathways: morphogenetic of T4      539
Pathways: plausible vs. implausible      383
Pathways: potential, in brain      281
Pattern recognition      see “Bongard problems” “Conceptual “Vision
Patterns on all levels      674
Peano arithmetic      100
Peano postulates      216—217 224
Peano, Giuseppe      20 216—217
Pearl and oyster      17 438
Penfield, Wilder      342—343
Penrose, Roger      15
People vs. machines      25—27 36—38 151—152 388—390 471—473 475—477 559—562 567—575 577—579 595—599 606—609 621—623 680 684—686
Peptide bonds      523
Perception and Zen      251
Perception: visual      97—98
Perfect items      3 75—79 85 406 424 486 536
Perfect numbers      416 418
Phages      see “Viruses”
Phenotype      see “Genotype and phenotype”
Phonographs      see “Record players”
Phonons      304
Photocopy machines      499
photons      142—146 258
Physics, laws of: as base for choosing between rival mathematical theories      100 456—457
Physics, laws of: as blocking infinite regress      170 685
Physics, laws of: as formal system      53—54
Physics, laws of: inconsistency and      95—96 99 584—585
Physics, laws of: intuitive      362—363 711
Physics, laws of: levels and      303—305 307—308 693
Physics, laws of: no escape from      477 575
Physics, laws of: Reductionist's Dilemma and      522 709
Physics, laws of: underlying consciousness      575 685 710
Piano postulates      552—553
pianos      3—4 302 305 633—634 700 726
Pianos: inverted      681—683
Pickwick Papers, The (Dickens)      24 326 595 598
Pinball machine      307
Pipe dream      703
Pipes      480—482 486 488 493—494 521 638 701—703
Planets and satellites      353—354
PLANNER      629—632
Plurals      354
Pocket calculators      568—570 616 678 710
Pointers in computers      289—90 619
Points (geometrical)      19—20 90 92—93 100 207 222 452 456
Polanyi, Michael      574
Polarons      304—305
Polypeptides      523 525 528
Polyribosomes      526—528
Pons Asinoium proof      606—607 669
Pool B.      418
Pool F.      427
Popcorn      104 124—125
Popping      127—135 184—185
Popping-tonic      105—106 116—117 125
Porridge      431
Ports of access      670—671
Post, Emil      33
Post-ending endings      392 403
Postal system metaphor      663
Postulates of geometry      90—91 92—93 407
Potentially endless searches      396 400—402 425 400—401 444 582—583
pq-system: completeness and consistency of      101
pq-system: decision procedure for      47—49
pq-system: expressive weakness of      101 221—222 407 417
pq-system: horse-apple-happy interpretation of      51 88 215
pq-system: isomorphisms and      49—53 158 625
pq-system: modified      87—88 92—93 102
pq-system: surprise interpretation of      52—53 94
Predicate calculus      609
Predicates, number-theoretical      208—209
Predictable termination      400 407 409—418 420 441 582 “Terminators”)
Prelude      337 383 460 686 737 739
Preludes and fugues      280—284 335 “Well-Tempered
Premise      184
Preprocessing      647 650 659
President v. Supreme Court      692
Primary structure of proteins      519—522
Primary structure of typoenzymes      511 512
Prime numbers      58—59 64—67 72—74 149 211—212 413 551—558 615
Prime numbers: differences of      393 395—398 400 416
Prime numbers: sums of      393—396 400 414
Primitive recursive truths      407
Primitive recursivity      406 407 414—420 422 424 429—430 440 441 444 451 466 472
Principia Mathematica      18—19 21 23—24 228 618—619
Print Gallery (Escher)      15 714—717
Printer of computer      301 307
Problem reduction      609—613
Problem reduction: self applied      613
Problem spaces, representation of      611—613
Procedures      132—134 150—151 292 410—415 418—420 424—428
Procedures: chains of      413—414 415 418
Processors (computers)      504 513 547
Producible numbers      264—265 269—270
Program space      299
Programs as data      293 692
Programs for determining enzyme function      521—522
Programs for determining phenotype      532
Programs for determining tertiary structure      521—522
Programs for generating theorems      471—473 578 615 617—618
Programs for naming ordinals      476
Programs for translating programs      291—294
Programs in Analytical Engine      25
Programs in BlooP and FlooP      410—415 424—426
Programs vs. data      499 513 531 546—548 616—617 630
Programs vs. programmers      306 734—737 “Computer “AI etc.)
Programs: chess-playing      see “Chess programs”
Programs: constructed by programs      589 629—632 664
Programs: families of      503 546
Programs: high-level comparison of      380—381
Programs: recursive structure of      149—150
Programs: secondorder, third-order, etc.      476
Programs: self-modifying      152 692
Programs: self-reproducing      498—504 547
Prokofiev, Sergei      150
Pronoun reference      587 591 592
Proof-pairs      416 438—443 446—447 450—451 452—454 466 468 469
Proofs of proofs      192—193
Proofs vs. derivations      35 193 194—195
Proofs: as never absolute      191—194
Proofs: nature of      18—24 58—60 88—93 192—197 227—228 458—459 578 707—708
Prophase      665—666
Propositional calculus      181—197
Propositional Calculus as an epiphenomenon      578
Propositional Calculus: embedded in TNT      195 197 207 215—217
Propositional Calculus: interpretations of symbols of      186 189 191—192
Propositional Calculus: rules of inference, justified      188—189
Propositional Calculus: rules of inference, presented      181—187
Propositional Calculus: rules of inference, table of      187
Propositional Calculus: streamlined      193—194
Propositional Calculus: variants of      195
Propositional Calculus: ways to improve      193—194 196—197
Propositional Calculus: weaknesses of      195—197 578
Propositional Calculus: well-formedness in      181—183
Proteins      517—518 544—545
Proteins as procedural knowledge      616—617
Proteins as programs, data, interpreters, processors      547 (see also “Enzymes”)
Prototype principle      352
Provability      18 101
Prudence and Imprudence      191—192 229
Pruning, explicit vs. implicit      286
Pseudo-epigenesis      531—532
Psychic powers      693 (see also “ESP”)
Ptolemy V Epiphanes      165
Puddle (Escher)      256
Pulling-oul (mechanisms)      see “Decoding (mechanisms)”
Punctuation      33 268 440 510 512 520 524—525

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