Gödel, Escher, Bach An Eternal Golden Braid by Douglas R. Hofstadter

(Dana P.) #1

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 pho-
nographs, 78, 484, 486--88; see also programs,
AI, AI programs
concept network. 651-54; see also semantic net-
works
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; inter-
pretations 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 w-consistency
constants, parameters, variables, 643-44, 669
context: necessity of, 161-64, 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,i467-70, 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; w-consistency and, 453; personal
nonexistence and, 698; in pq-system, 87, 88; in
Propositional Calculus, 191-92, 196-97; in self-
image, 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, inconsis-
tency, Epimenides paradox, etc.
Contrafactus, 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 Gould, 405
Copy mode (Typogenetics), 506--8
cortex: areas of, 344; cerebral, 340-48; visual,
343-48
counterfactual parameters, 639
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,


762


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 after-
noon chez, 633-40; Theme of, 729, 732, 740,
742; vs. Tortoise, 75-78, 406, 483--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 AI, non-
programmability, etc.
Crick, Francis, 505, 532, 533, 534, 617
Crime and Punishment (Dostoevsky), 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
CT-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; top-
down vs. bottom-up, 48-49; for Tortoise-pair-
ness, 441; for Tortoise property, 396-97, 415,
441; for truth, 213, 228-29, 417, 552-58,
560-61, 579, 581; for validity of derivations,

Index

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