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

(Dana P.) #1
associativity, 55-56, 207
assumptions, shaky, 420, 422, 429, 580, 581, 644,
672
ASU's: defined, 373-74: orientation in, 375; trips
in, 377-79, 383
ATN's, see Augmented Transition Networks
ATN-colony, 359
atoms: in physics, 303: in Propositional Calculus,
182, 186: in TNT, 207, 213, 214
ATTACCA, 176,284, 311,505
attachment and nonattachment, 232-33, 244
augmentation, 8, 9, 146, 503, 681--83, 738: inter-
vallic, 156-57
Augmented Transition Networks, 150, 258-59,
359, 621, 625-27, 630
Augustus II, Elector of Saxony, King of Poland,
461
Aunt Hillary, 314-33, 382, 630
Author, the, 3, 6, 204, 370, 689, 722, 724-42
authorship triangle, 94-95, 96, 689
autological adjectives, 20-21
automatic programming, 298-99
Avery, Oswald, 159, 161
awareness, deductive vs. analogical, 570-71, 619
axiom schemata, 47, 48, 65, 87, 468, 472-73, 543
axiomatic systems, see formal systems
axioms: defined, 35; lack of in Propositional Cal-
culus, 183; of MIU-system, 33, 35; of P-system,
73-74: of pq-system, 47; of pq-system, modi-
fied, 87; of 31O-system, 263: of TNT, 216; of
TNT, extended, 451-52, 466-68; of tq-system,
65
axons, 339-40
Babbage, Charles, 24-26, 598, 601, 726-42
Babbage test, 735-73
BACH (acronym), 174-75
B-A-C-H (melody), 79--81, 86, 102, 121, 155-57,
266, 719
Bach, Anna Magdalena, 482
Bach, C. P. E., 3, 4, 80
Bach, Joh and Seb., 633, 669
Bach, Joh. Seb.: AI and, 27, 677; as composer,
392, 461, 740-42; as glassblower, 79; as
harpsichordist, 275, 279, 280; as inspiration for
Dialogues, 28, 737; confused with Fermat,
331-35: depth of, 7--8, 9-10,27-28, 70-71, 677;
dissection vs. appreciation of, 680; Escher and,
199, 666-67: Forkel on, 4, 86; homage to, 81;
improvisation by, 3-7, 96, 719; in Leipzig, 383,
404; indirect self-reference of, 79--81, 86: life
and death of, 86; modulation and, 122-23, 130:
recursive qualities of music of, 70-71: Shepard
tones and, 719: squared, 679: vs. Cage, 157,
162-64, 174-75; see also Old Bach
Bach, Wilhelm Friedemann, 4, 6
background assumptions, 644
backtr*king, 97, 629, 632
backwards chaining, 618
bankers, 457
base-pairing, complementary, 433, 506-7, 514-16,
517, 523, 534
baseball, 637-38
bases (genetics): 514, see also nucleotides: in Ty-
pogenetics, 505--8, 510
Baso, 234
Bassui,255
beautiful vs. non-beautiful, 552-58, 560, 573-75,
581--82
beauty: computers and, 575; elusiveness of, 554,
555, 565, 574-75, 581, 583--84

760


bees, 360, 641, 720
Beethoven, Ludwig van, 6, 75, 163, 634
beliefs, catalogue of, 382, 384
Bell, A. G., 296
Belnap, Nuel, 197
Berio, Luciano, 704
bicentuplets, 540
bifurcations, 91-94, 100, 456-59, 467, 579
biojukeboxes, 160, 175
BirthtJay Can/ala (Bach), 461
BirtMo.y Cantatatata (Dialogue), 468, 475, 688
birthdays, 461-64
bits, 288--89, 290, 291
BLOCK (BlooP), 410-11
blocks world, 586-93, 627-32, 674
BlooP, 406, 409-30, 440, 441, 444: alphabet of,
419, 425; control structures in, 410; primordial
steps of, 409, 412-13: syntax of, 410-15
BlooP programs, 410-14
Blue Programs, 418-20, 422, 427
Bluediag [N), 42-44, 428
board evaluation: static and dynamic, 604-5, 611;
Strange Loops in, 604-5
Bodhidharma, 232, 238, 245, 252, 625
Bolyai, 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 mathe-
matical 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
Buttcrjlies (Escher), 147-48
Buxtehude, Dietrich, 335
Byrd, Donald, see SMUT
Byron, Lord, 25

C-system, 65-67, 71-72
CAGE (acronym), 174-75
C-A-G-E (melody), 156-57
Cage, John, 156-57, 163-64, 167, 174-75, 556,
699-700, 704
calculating prodigies, see idiots savants
Canon by Intervallic Augmentation, 525
"Canon per augmentationem et contrario motu"
(Bach), see Sloth Canon

Index

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