Gödel, Escher, Bach: An Eternal Golden Braid (143 page)

65; in Typogenetics, 507, 509; vs. proofs,

35-36, 193-94, 195

Descartes, Rene, 263, 340, 677 description-schemas, 650; see also templates descriptions: calculus of, 338; restructuring of,

649-53, 659-61, 672; tentative, 646-49 descriptors, 647

detachment, rule of, 185-86, 577 determinism, 54; see also free will Devil, 685

Dewdrop (Escher), 249, 256 Di of Antus, 333

diagonal method, Cantor's, 418-24, 426, 427-29,

438, 446, 469

Diagram G, 135-37 dialogicians, 81

dialogues, miniature, 191-92, 193, 408-9, 431,

560, 565, 595-96, 598, 599

Dialogues: origin of, 28, 665-69; as self-refs,

84-85, 129, 204, 502-3, 667, 738-39

Dickens, Charles, 326, 328, 380 Difference Engine, 25 differentiation, cellular, 543-46

digestion, 306

digits, shunting of, 264 Diophantine equations, 279, 459-60 Diophantus of Alexandria, 275 directory of real numbers, 421-24 disambiguation, 586-93, 603, 629-32 distance to goal, 611-13 divisor-freeness, 74

djinns, 113-15, 216-17, 223, 224; see also Genie DNA: as aperiodic crystal, 167; as carrier of genetic information, 159; compared to computer languages, 290-91; composition and structure of, 514-15; covalent backbone of, 514-15; as declarative knowledge, 616-17; double strands, 514-15, 530-31; isomorphism with organism,

146-48; mode of self-replication, 529-30; in outer space, 167, 175-76; as program, language,data, 290-91, 547; quining and, 531; recombinant, 665; relation to mRNA, 517; self-destroy

ing, 536; unusual interpretation of, 231 DNA endonudease, 530, 531 DNA ligase, 530, 531

DNA polymerise, 530, 531

Contents

XII

DNA Rapid Transit Service, 505. 517 Doctor program, 599-600. 608 dog-and-bone problem, 611-13 .doGma 1, doGma II, 532-33

dogs, 233, 234, 354, 383, 569, 570, 611-12, 679 Doko, 250, 698

Dostoevsky, Feodor, 379-80 double negation, 183, 545, 554 Double Nodulation, law of, 243 Dragon (Escher), 473-74, 524, 698

Drawing Hands (Escher), 15, 21, 133, 689-92, 710, 716, 737

dreams, 378, 379, 384, 725 Dreyfus, Hubert, 574

dualism, 251-55, 698-99; see also subject vs. object Dumpty, H., 332

duplets (Typogenetics), 510, 512 Dvoi£k, Antonin, 163

E. coli bacterium, 176, 537-41

Earrwig, Dr. Tony, 586-93. 627

earth chauvinism, 171-72

Earth-Moon-Sun system, 353-54

earthworm(s), 341-42

Eccles, John, 574

Edifying Thoughts of a Tobacco Smoker (Bach), 482

Edifying Thoughts of a Tobacco Smoker (Dialogue), 543

eggs, 192, 360, 383

Einstein, Albert, 100

electrons, 140-46, 258, 30.3-5

ELIZA, see Doctor program

embedding of formal systems, 97, 207, 215

emergent phenomena, 708-9, 714

emotions: brains and, 83; counterfeit, 599-600; dependence of intelligence upon, 573, 597-98; as epiphenomena, 677; music and, 83, 160, 163-64, 174-75, 383-84, 626-27, 676-77, 699; potential, 281, 383-84, 583; programs and, 573, 597-600, 626-27, 675-77; universality of, 163, 174-75

emulation, 295

Endlessly Rising Canon (Bach), 10-11, 15, 46, 130, 717-19, 742

ENIUQ (procedure), 498-99

enlightenment, 232, 237, 243, 246, 251, 254-55, 479, 567

Enlightenment 'Yond Enlightenment, 237, 239, 243, 244

End, 232, 252

enzymes: function of, 520-22, 528-30, 543-45; as models for AI, 663-64; rules of inference and, 509-10, 513, 531; structure of, 519-21, 525; synthesis of, 517-19, 522-25, 527-29, 538-45, 547; versatility of, 529; vs. typoenzymes, 529; see also proteins, typoenzymes

epigenesis, 159-60, 161-62, 531-32, 665

Epimenides, picture of, 496

Epimenides paradox: connection with G6del's Theorem, 17-18; Escher and, 716; expanded version, 21, 22; fear of, 23; French-English version, 501; indirect recursion and, 134; molecular version, 536-37; neural version, 584-85; Quine version, 431-37, 445, 446, 449. 497-99, 531, 537; subtlety of, 495-98; Tarski version, 580-81, 584-85; two levels of, 581, 584-85; Whitely's version, 476-77

epiphen9mena, 308-9, 363, 577, 596, 677-79

Contents

XIII

errors in programs, 295, 297-98. 596

Escher, Maurits Cornelis: Bach and, 201, 666-67; contradictions and, 97-99; copies and, 146-48; drawings of, see List of Illustrations (xiv-xviii); figure and ground in, 67-68; flat vs. spatial and, 473-74, 689; incompleteness and, 716-17; Magritte and, 480; as prime mover, 689-92, 710; on subbrains, 387; Strange Loops and, 10-15, 737; Zen and, 255-57

Escherization, repeatability of, 473-74, 689; see also 2-D vs. 3-D, Godelization 1.SP, 598-99, 693-95

essential incompleteness: of Achilles' birthday, 462-64, 475-76, 688; of Al, see Tesleis Theorem; of list of reals, 423-24, 469; of phonographs, see Todelization; of self-engulfing process, 493; of TNT and related systems, 468-71; see also Godelization, Tlidelization, Escherization, nonprogrammahility, etc.

Eta Oin, 586-93, 674

ETAOIN SHRDLU, 628,630

Euclid, 19, 43, 58-60, 88-89, 216

Euclid's prime number Theorem, 35, 58-60, 228 Euler, Leonhard, 3, 394

Fume, Max. 605

evidence, nature of, 633-36

evolution, 321-22

existential quantifiers. see quantifiers

exotic styles of thought, 552, 563-64, 566-67 expanding nodes, 134-36

explanatory power on high level, 321, 326, 707-10 expressibility and expressive power, 101, 417,

441-43, 444-45, 450, 454, 465-70, 580-81 extrasensory perception, see ESP

extraterrestrial intelligence, 162-64, 167, 172-76,

341, 646, 661-62

eyes, 237, 248, 260, 308, 311, 313, 477, 633, 715

Fair Captive, The (Magritte), 489 FANCY NOUN, 132-34

Fantasia and Fugue in G minor (Bath), 719 fantasy rule, 183-85, 187

faucet, mental, 364-65

faultlessly functioning machines, 575-78 Faure, Gabriel, 163

feedback and feedforward, 544-45 Fermant, Johant Sebastiant, 332-35 Fermant's Last Fugue, 335

Fermat, Pierre de, 275-77, 278; confused with Bach, 331-35

fermatas, 275, 329, 332, 333

Fermat's Last Theorem: 275-79, 332, 416; coun

terexample to, 277, 279, 460; inverted, 333-34;

parodied, 335, 551; proof of, 277, 279, 460 Feynman diagrams, 144-46

Fibonacci (Leonardo of Pisa), 136, 246

Fibonacci sequence, 136, 138, 139, 152, 173-74, 265, 416

fiddles, see violins

fifth postulate (Euclid), 90-93, 222, 451-52 50 (fifty), 338, 557, 564

figure and ground: 61-63, 64-74, 731; in music, 70-71

FIGURE-FIGURE figure (Kim), 68-70, 73

filters: for abstraction, 286, 407-9, 648, 657-60,

663, 673; for Pools, 418, 427

Contents

XIV

finitistic methods of reasoning, 24, 230 Fishes and Scales (Escher), 146-47

fission and fusion (of concepts), 338, 352-56, 438,

470, 664-65

5-D space, 640

flags, 29-32, 188

flashcards, fee tRNA

flat vs, spatial, see 2-D vs. 3-D flattened look-ahead, 604-5

flattened roles of inference, see theorems vs. rules flexibility and inflexibility, 26-27, 296-302, 611-14, 657, 673-75, 686

flights of fancy, 378

FlooP, 406, 424-30, 567-68; fed into itself,

425-26; power of, 428-29. 561-62

fluency, 376-77

flutes, 3-5, 27, 528, 552-58, 720, 726 F(n) and Min), 137, 142, 359 focusing, 657-59

folding-up of enzymes, 511-12, 519, 521, 525 football, 44, 303, 353, 634-40, 643, 644, 645, 672 footraces, 29-32, 43, 594-95, 681-83 forced matching, 670-72 forgetting, 577, 578, 619 Forkel, Johann Nikolaus, 4. 86 form, 47. 66-67, 68, 73. 190-91, 370-71; syntactic

vs. semantic, 581-84, 631

form and content, 84-85, 204, 279, 581-84,

667-68, 740

formal systems, presentations of: C-system,

64-65; MIU-system, 33-41; P-system, 73-74:

pq-system, 46-60;

Propositional Calculus,

181-97; TNT, 204-30; tq-system, 64-65; Typogenetics. 504-13

formal systems vs. reality, 53-58

formal vs. informal reasoning, 193-97, 228-29,

271-72. 449-50, 614-15, 618-19

formal vs. informal systems, 26-27, 559-85, 598,

684-86; see also brains, minds, etc.

formalist philosophy of mathematics, 458 formula: closed, see sentence; open, 207-8

formulas of TNT, 206, 207-15 Four-color Theorem, parodied, 550 4-D space, 638-39

four-postulate geometry, see geometry, absolute 4'33" (Cage), 156

Fourmi, Lierre de, 333-34 frame effect, 704

frame messages, 162, 166-67, 176 frames, 373, 644-46, 662-63, 672 framing devices, 478

Frank, Philipp, 642

Frederick the Great, King of Prussia, 3-8, 27, 394, 729

free will, 388, 680, 708, 710-14, 720-16, 734-35, 739; see also jumping out of the system Frege, Gottlob, 20

French fries, 636-38, 683

French Suite no. 5, Gigue (Bach), 130 frequencies, of words and letters, 377, 630 friend, mental model of, 386-87 fringe science, 693-94

fugues, 335, 634, 730, 736; in the Art of the Fugue,

79-81, 86; devices in, 314, 322-23, 329-30,

737-40; Dialogues and, 28; in the Musical Offering, 4-9; nature of, 9, 281-84, 737

Fundamental Facts 1 and 2. 440-42 fundamental jukebox-axiom, 155 funneling, 346-48

Contents

XV

G (Godel's string), 18, 271-72, 285, 447-55, 459-60. 502, 580, 608, 667, 707-8 G', G" G"'

Gu, 466-68 -G, 272, 449, 451-55, 458-59, 542 Galileo, 478-79

games played by Al programs, 601

Ganto, 189-90, 256, 407

gases and molecules, 307-8, 317, 693 Gateles.s Gate, see Muvtonkan Gauss, Karl Friedrich, 92, 100 Gebstadter, Egbert B., 94-95, 402-3, 484 Gelemter, E.. 606-7

general recursivity, 406, 430, 470

genes, 200-1, 507, 512, 524-25, 531, 544-45, 668 Genetic code, 160. 519-20, 522-24, 533-34, 536,

538; origins of, 231, 548

genetics, 504-48

(.enie, Meta-Genie, etc., 109-16, 216-17, 223, 224,

610; see also djinns

genie, symbol-manipulating. 39-40, 48

genotype and phenotype, 159-62, 167, 173-74,

175-76, 295, 531-32, 667-68

Gentzen, Gerhard, 195

Geometric Code. 235-37, 241, 626

geometry: absolute, 91, 93, 97, 222, 407, 451-52;

elliptical, 93; Euclidean, 19-20, 88-92, 100, 222, 451, 456, 606-7, non-Euclidean, 19-20, 91-93, 98-99, 100,222-23, 451, 455-56; "true" version of, 88-94, 99-100, 456-57

German professor, proverbial, 130-31 Giant Electronic Brains. 25, 601 glia, 339

GlooP, 406, 428-29 G(n), 137

goals and subgoals, 227, 589, 590-91, 609-14, 618-19, 629, 632

Goblet G, 79, 81, 83-85, 267

God, 216, 400, 478, 482, 533, 567, 597, 711; picture of, 142-43

GOD (acronym), 110-15, 133, 134, 216, 223, 224,

722; see also djinns, Genie

Gddel, Kurt, 15-19, 24, 28, 738, 740, 742 G6del Code, 18, 268, 533-35 Godel codons, 268, 425, 533-35

Godel isomorphism, 261-71, 439, 442-46,

738-39; likened to reflection of world in brain, 502, 570

Godel-numbering, 18, 438, 738-39; of FlooP programs, 425-26, 502; of MIU-system, 261-64; of TNT, 268-70, 579

Godel questions, Lucas on, 389, 390 Godelization, 270; programmability. of, 471-73; repeatability of. 424, 465-76, 688; see also

Escherization, Todelization, jumping out l of the system

Godelizing operator, 472-73, 475-76, 543 Godel's argument, summarized, 18, 272, 448

Godel's article. 17, 24, 438 Godel's construction, illustrated, 84

Godel's method, underlying causes of, 204, 407, 465, 468-71

Godel's Second Theorem. 230, 449-50, 696 Godel's Theorem: All and, 388-90, 471-77, 706-7, 714; analogue of in molecular biology, 534, 536-37; brief mentions, 72, 74, 78, 100, 486; consequences of, 450-60, 469-76; Contracrosttpunctus and, see Contracrosttpunctus: Diophantine equations and, 459-60; LISP and, 738-39; proof of, 18, 265-72, 438-49; stated, 17, 101, 272

Godel's Theorems and human introspection, 450, 696-98

Contents

XVI

Goffman, Erving, 478 gold, 173

Gold Box, Very Asian, 404-5

Goldbach, Christian, 394, 395

Goldbach Conjecture, 394-96, 400, 404, 557-58, 615; parodied, 551

Goldbach property, 395-97, 400, 414, 418 Goldbach Variation, 395-98. 400, 426, 441

Goldberg, Johann Theophilus, 391-92 Goldberg Variations (Bach), 392-93, 395

Goodfortune, Hexachlorophene J., 103-4, 115, 128-29, 130

Goso, 248

Gplot, 138, 140-43, 146-47, 159, 503, 661 grammar: for computer languages, 297, 408-15; for Feynman diagrams, 142. 145; high-level, 625-27; for koans, 625-26; for music, 626-27; for natural languages. 130-34, 150, 363,

588-93, 619-21, 630-32; for thought, 627 Grand Tortue, 237, 243-44 grandmother cell, 344, 345

grandmothers, perception of, 344, 345, 347-48. 349

graphics, 728 grass roots, 693

Great Tutor, 237, 239, 244 Green Programs, 427 Greendiag [NJ, 427

Grelling's paradox, 20-21, 22 Groot, Adriaan de, 286 grounds, excellent, 731 guanine, see nucleotides

guaranteed termination, 41, 396-98, 399, 403 guitars, 62, 200

gullibility, 75-76, 106, 309, 461, 600, 701 Gutei, 237

G0025, white stony, 626

HACKER, 664

haiku, 153-54, 525, 619-20

halting problem, 74, 425-29, 594, 697 hamburger-confusion, 577 Hammurabi, 169

Hardy, Godfrey Harold, 562-66

harmonic tension, 122-23; see also tension and resolution

harpsichords, 3, 391, 502 Harrison, Lawrence, 657 Haussmann, Elias Gottlieb, 2 HE-HE

puzzle, 62-63, 669 headache, 62-63 hearing by computer, 602 "heart", in an All program, 679 Heisenberg uncertainty principle, 455, 698 Helen of Troy, 110