Gödel, Escher, Bach: An Eternal Golden Braid (142 page)

board evaluation: static and dynamic, 604-5, 611;

Strange Loops in. 604-5

Bodhidharnta, 232, 238, 245. 252, 625 Bolvai, Farkas, 92

Bolyai, Janos, 91-92 Bongard, M., 646

Bongard problems, 646-62, 664. 669, 674; uni

versality of, 661-62

Boole, Geo., 20, 404, 600 Boolean Buddhism, 577 boomerangs, 75, 84, 267, 472

bootstrapping, 24, 293-94, 524, 548

bottom (recursion), 139-40; see also skeletons bottom-up vs. top-down, 48-49

bottoming out, 133-35, 151, 259, 301, 650

boustrophedonic writing, 168-69, 176

boxed systems, 469-70, 543

Boyle's law, 308; see also gases

brains: ant colonies and, 315-16, 318, 324-25, 350, 358-59; as ATN-colonies, 359; as mathematical objects, 559; Epimenides paradox and, 584-85; formal systems and, 337-38, 559-62, 569-79, 584-85, 676, see also Church-Turing Thesis, formal vs. informal systems, brains and rules; frame and outer messages and, 170-71; mappings between, 341-42, 345-46, 369-82; music and, 163; operating systems and, 296; programmability of, 302; rules and, 26-27, 676, see also brains and formal systems; suborgans of, 340-41; thoughts and, 337-65; vs. minds, 576; see also minds, intelligence, etc.

Breton, Andre, 700

"British Grenadiers, The", 607

Brouwer, Luitzen E. J., 404

Buddha-nature, 233, 234, 238-44

Butterflies (Escher), 147-48

Buxtehude, Dietrich, 335

Byrd, Donald, see SMUT

Byron, Lord, 25

C-svstem, 65-67, 71-72

CAGE (acrorn.m), 174-75 C-A-G-E (melody), 156-57

Cage, John, 156-57, 163-64, 167, 174-75, 556,

Contents

VII

699-700, 704

calculating prodigies, see idiots savants Canon by Intervallic Augmentation, 525

"Canon per augmentationem et contrario motu"

(Bach), see Sloth Canon

,,Canon per Tonos" (Bach), see Endlessly Rising Canon

canons: copies and, 8-9, 146; Dialogues and, 665-69, 738; Escher drawings and, 15; in Goldberg Variations, 392; in Musical Offering 7-10, 726-27; polyribosomes and, 526-28; self-refs and, 501-3; structure of, 8-10; two-tiered,

527-28; see also individual canons, fugues

Cantor, Georg, 20, 216, 418, 421, 422-24

Cantor set, 142 .Cantorcrostipunctus", 424

Capitalized Essences, 29

car radio. 670-71

cardinalitv, intuitive sense of, 567

Carroll, John B., 630

Canon, Lewis, 20, 28, 46, 192, 372, 681; material by, 43-45. 366-68

Carroll paradox: 28, 43-45, 681; evidence ver

sion, 693-94; message version, 170: problem

po4ed by, 46. 181; proof version, 192-93; Sam

uel's argument and, 684-85; symbolized, 193; see also infinite regress cascades, 224, 529, 626, 664

caste distribution: encoding of knowledge in, 319,

324-28, 359; meaning of, 321-24; updating of,

318-19, 324

catalogues of programs (Blue, Green, Red), 419,

427-28

catalysts, 528-29

cats, 313, 343-46, 532 causality, types of, 709-10 CCrab, see ATTACCA ceilings, see loops, bounded: BlooP celestial mechanics, 353-54 CELLS (BIooP), 410-11

cellular processes, as models for All, 663-64 Central Crabmap, 667

Central Dogma: of Mathematical Logic, 271,

532-34; of the MIC-system, 513; of Molecular

Biology, 504-5, 514, 532-34, 536, 667; of Ty

pogenetics, 513; of Zen strings, 238, 239, 240,

243

Central Dogmap, 532-34, 545, 547, 672, 709 Central Pipemap, 701-2 central processing unit, 288, 289 Central Proposition, 264, 269 Central Slothmap, 702

Central Xmaps, 702, 716; see also individual en

tries

centrality, 374-75 centromere, 668 cerebellum, 341 Chadwick, John, 50 chain letters, 546

Champernowne, David, 595 Champollion, Jean Fransois, 165 channeling, 299, 376-77

chaos in number theory, 137-38, 152, 557; see also

order and chaos

chauvinism, 171-73

checkers programs, 573, 604-5 Chekhov, Anton, 642

Contents

VIII

chess: chunking and, 285-87, 604; grand masters in, 286-87; round-the-house, 595; self-modifying, 687-88

chess boards, hierarchy of, 687 chess players, cycle of, 94-95

chess programs: Babbage and. 25, 729-31, 736;

choice and, 711-12; Crab and, 721, 729-31; difficulty of, 151-52, 605; jumping out of the system and, 37-38, 678; knowledge representation in, 618; recursive structure of 150-52; strengths and weaknesses of, 151-52, 285-87, 573, 603-4, 611; Turing and, 595, 596, 736: varieties of, 601; without look-ahead, 604

chests of drawers, nested, 644-45

children's stories and Al, 675-76

Chiyono, 256

choice, 711-14

Chopin, Frederic, 70, 257, 677 chords and analogies, 673-74 chromosomes, homologous, 668

chunked versions of this book: jacket,

viiixiii, 370, 758-77

chunking: ant colonies and, 326-27; brains arid, 381-84, 559; computer languages and, 290-92, 381, 412-13; defined, 285-88; determinism and, 306-8, 363, 522; of DNA, 531-32; intuitive world-view and, 305-6, 362-63; of music, 160, 164, 525; of one's own brain, 382; probabilistic,

384; scientific explanation and, 305-6; super conductivity and, 305; trade-offs in, 326; vision and, 348

Church, Alonzo, 428, 476, 561

Church-Turing Thesis, 428-29, 552, 561-79; Al Version, 578-79, 580, 581; Hardy's Version 566; Isomorphism Version, 567-68; Microscopic Version, 572; Public-Processes Version, 562, 568, 574, 580; Reductionist's Version, 572, 574; Soulist's Version, 574; Standard Version, 561-62, 579; Tautological Version, 561; The odore Roszak Version, 574-75; unprovability of, 562

Church's Theorem, 560--61,574,579-81,609, 697 cigars, 199, 201, 383, 481, 651

classes vs. instances, 351-55, 360-61; see also prototypes, intensionality and extensionality, analogies, conceptual skeletons, etc.codes: art and, 703-4; familiar and unfamiliar,82, 158. 267; see also decoding, Gödel Code,

Genetic Code, etc.

"coding" of sentences, 583-84

codons, 519-20, 524, 533, 535; see also Gödel

codons, duplets

Colby, K., 599 columns in brain, 346 Comenius, Johann Amos, 625 comments in programs, 297 Common Sense (Magritte), 700-1 common sense and programs, 301

communicability of algorithms, 562 commutativity, 55-56, 209, 225-27, 453, 639

compelling inner logic, 161-62, 163-64 competing theories, and nature of evidence, 695

compiler languages, 292-95 compilers, 292-95, 297, 503 compiling, reverse of, 381

Complete List of All Great Mathematicians, see List

completeness, 100-2, 417-18, 422, 465; see also incompleteness, consistency complexity of world, 569

composite numbers, 64, 65-66, 73; see also prime

numbers

compound sentences, in TNT, 214 compound words, 665

Contents

IX

computer chess, see chess programs

computer languages: analogues in cell, 547; dialects of, 503; flexibility and, 298-99; high level, 292-93, 297-300; message-passing, 662-63; power of, 299, 428-29; presented, 289-99, 406-30, 498-99; in SHRDLU, 629-32 computer systems, 287-302 computers: assembled by computers, 504, 684; crying, 675-76; determinism and, 25-27, 306-7, 684-86; fallibility of, 575, 578, 678; learning by, 603-5; origins of, 24-26; in phonographs, 78, 484, 486-88; see also programs, Al, Al programs

concept network, 651-54; see also semantic networks

conceptual dimensions, 670-71

conceptual mapping. 668-72

conceptual nearness, 371-73, 614, 651-56 conceptual revolutions, 660-61, 673 conceptual skeletons, 381, 514. 666-72, 674 connotations and culture, 372-73, 379-80 consciousness: causality and, 709-10; source of,

384-85, 387-88: understanding of, 82, 680,

708-10

conservation of complexity, 60, 195

consistency: defined, 94; of extended TNT, 223, 459; hypothetical worlds and, 95-100; interpretations and, 88, 94-101; Lucas and, 477; oath of, in TNT, 450; proofs of, 23-24, 191-92, 229-30, 449-50; of Propositional Calculus, 191-92, 229; of TNT, 229-30, 449-50; varieties of, 94-96; see also (o-consistency

constants, parameters, variables, 643-44, 669

context: necessity of, 1614, 173-76; restoring of, 115-16, 128, 133, 161-64, 173-76

context-free sums, 520-22

contexts, nested, 643-46, 672, 674

continued fractions, 140, 277, 563, 565

continuous vs. discrete processes, 598

Contracrostipunctus, discussed, 82-85, 267, 270-71, 406-7, 424, 467-70, 483-84, 534-37, 608, 721

contradictions: between levels, see level-conflicts; caused by impossible cycles, 94-96; coexisting in same brain, 383, 697-98; diagonal argument and, 420-22; in mathematics, 17-24, 196-97, 223, 580-81; so-consistency and, 453; personal nonexistence and, 698; in pq-system, 87, 88; in Propositional Calculus, 191-92, 196-97; in selfimage, 696; Tortoise's shell and, 177-80; two levels of, 581, 584; visual, 97-99; Zen and, 99, 235, 246-56, 698; see also paradoxes, inconsistency, Epimenides paradox, etc.

Contrafadus, 641, 643, 669

Convex and Concave (Escher), 105-9, 348 Cooper pairs, 304-5

copies: canons and, 8-9, 527-28; in code, 517, 527-28; complementary to originals, 70, 501, 506-7, 517, see also inversion; DNA and, 529-31; inexact, 500-3, 546; nature of, 146-49; self-reps and, 500-4, 512-13; television and, 489; viruses and, 542-43; visually nested, 138-40; see also sameness, isomorphisms

copper, 173

Cops Silva and Could, 405

Copy mode (Typogenetics), 506-8

cortex: areas of, 344; cerebral, 340-48; visual, 343-48

counterfactual parameters, 639

Contents

X

counterfactuals, 634-40, 641-44 counterpoint, see canons, fugues, Bach, etc. counting, 55-57, 228, 364

court system, 692, 693

covalent bonds, 514

cows, 312, 346, 351

CPU, see central processing unit

Crab: entertains Achilles, 480-94; genes of,

200-1, 204. 507;' hikes and plays flute, 549-58;

intelligence of. 549, 558, 733; jukebox of,

154-57; meets Achilles, 200; musical evening

chez, 720-42; origin of, 666-68; plight of, 281,

383-84; questionable behavior of, 560, 562,

573-74, 579-81; receives presents and enter

tains guests, 275-84, 311-36; subjunctive afternoon chez, 633-40; Theme of, 729, 732.

740, 742; vs. Tortoise, 75-78, 406, 493-88,540, 543 Crab Canon (Bach), 202-3, 666 Crab Canon (Dialogue), 204, 355-56, 665-69, 672, 723-25, 738

Crab Canon (Escher), 198-99, 667

crab canons, 9, 198-203, 204, 355, 501. 665-69; in DNA, 200-1

crab programs, 500-1

creativity, mechanizability of. 25, 26, 571, 620, 673; see also originality, paradox of Al, non programmability, etc.

Crick, Francs, 505, 532, 533, 534, 617 Crime and Punishment i'Dostoevskvl, 379-80

Cristofori, Bartolommeo, 3 critical mass, 228, 317, 389, 417, 470 crossing-over, 665-68

crystal in magnetic field, 140-43 crystallization metaphor, 347 C"f-Thesis, see Church-Turing Thesis Cube with Magic Ribbons (Escher), 281-82 cursively drawable figures, 67-68, 72 cytoplasm, 517, 518, 522-24 cytosine, see nucleotides

da Vinci, Leonardo, 641

Dali, Salvador, 700

Dase, Johann Martin Zacharias, 567 data base, 618 daughter programs, 503, 546 David, Hans Theodore, 3, 28, 719 Day and Night (Escher), 252, 255, 667 Dboups, Hfpsh, 515, 533 De Chirico, Giorgio, 700 De Morgan, Augustus, 20, 404, 600 decidable strings, 417

decimal system, 262-64, 269

decipherment of texts, 50, 164-65, 173-74, 583 decision procedures: for alienness, 487-88, 540-41; for axiomhood, 41, 48, 470; for beauty, 552-58, 560, 579, 581-82, 583-84; as BlooP puzzles, 415-17; for Buddha-nature, 234, 239, 272; defined, 39-41; for Diophantine equations, 559-60; for dreamable themes, 384; for end of Dialogue, 402-3; for genuineness of koans, 234, 239; for Goldbach property, 400, 414; for Granny, 344-45, 347-48; for halting, 425-29; for intelligence, see Turing test; for Mozart pieces, 649; no guarantee of existence of, 72; for number-theoretic truths, 228-29, 426, 551-58, 560. 573-74, 579-81; for primality, 64, 149, 413; for proof-pair-ness, 416, 439-41; for sameness, 146-49, 158-59; for sorting numbers into two classes, see Church-Turing Thesis; for termination, 425-29; for "the Way" in Zen, 250-51, 253, 254; for theoremhood, 39-41, 47-49, 72-73, 190-91, 408, 416, 560, 579-80, 582; for theorem-numbers, 440-41, 580; topdown vs. bottom-up, 48-49; for Tortoise-pairness, 441; for Tortoise property, 396-97, 415, 441; for truth, 213, 228-29, 417, 552-58, 560-61, 579, 581; for validity of derivations, 194, 416, 439-41, 470; for well-formedness, 182, 269, 416, 582; for Contents

XI

wondrousness, 402, 425

d coding: of DNA, 159-62, 175-76, 201, 231, 531-32, 538; of formal systems, 50-51, 54; of fortune, 154; via Gtidel isomorphism, 267; of nature. 409; of records, 154-57, 158-59, 161-64, 172, 174-75; as revelation, 160-61; of Russian text, 380; see also isomorphisms, translation, information, chunking

decoding mechanisms: complexity of, 158-62, 172-76, 582-84; innate, 170-71; nature of, 158-76; record players as, 83, 154-57; transparency of, 267, 501; for Tripitaka, 257; see also isomorphisms, etc.

L)eduction Theorem, 186

default options, 352-53, 386, 411, 645, 674 defects and expectations, 77, 86, 102, 222, 476 demidoublets, 633-34, 669

demons, 663-64 deoxyribonucleic acid, see DNA derivations: alleged, 439-40; defined, 35-36: fallacious, 220, 439; in MIU-system, 35-36, 262, 264, 439; in Propositional Calculus, 184, 185, 188, 189-90, 196; supernatural, 454-55; in

TNT, 217, 218, 219, 224-27, 269; in tq-system,