Gödel, Escher, Bach: An Eternal Golden Braid (145 page)

look-ahead trees, 151, 604-5, 611, 712

loops: bounded, 149, 410-14, 418, 440-41, 444; free, 149, 424-25; in music, 150; in programming, 149-50, 410-14, 424-25, 503, 632 lottery, 639-40

Lovelace, Lady Ada Augusta, 25, 307, 598

lower levels, see substrate, mental

lowest-level rules embodied in hardware, 685-86 Lucas, J. R. 388-90, 471-73, 475, 476, 477, 574,

577-78, 597

Lucas' argument: counterarguments to, 475-77, 577-78; merits of, 472; summarized, 471-73 Lucas sequence, 139, 152, 174

M-mode, see Mechanical mode

MacGillavry, Caroline, 667

machine dependence and independence, 294 machine language, 289-300, 306, 381, 547

machines: not the sum of their parts, 389-90;

reflecting on themselves, 288-89; self-assem

Contents

XXII

bling, 160, 486, 504, 543, 545

MacLaine, Shirley, 285

macroscopic effects from micros

307

copic causes, MACSYMA, 615

Madstop, 727

magnetic field and crystal, 140-43 Magnficat in D (Bach), 549, 552, 558 hfagn#iicrab, Indeed, 560, 574, 581

Magritte, Rene, 480-81, 489, 493-94, 627, 700-2,

705-6; paintings by, see List of Illustrations (xiv xviii)

Mahalanobis, P. C., 565

main theses of book, 26, 46, 559, 714 Majotaur, 119-21, 123-25 malaphors, 657

Mandelbrot, Benoit, 71 manifestations of symbols, 351 Mao Tse-tung, 433

mappings: charted, 85, 449, 533, 536; induced, 668-69, 671-72

marbles, rolling, 711-12 Margie-balloon story, 675 Materialism, champions of, 27, 729

mathematical logic, history of, 19-24 mathematical view of brains, 559 mathematicians, 458-59, 559, 566, 614 mathematics: done by computers, 573, 602,

614-15; foundations of, 19-24; reality and, 54-58, 456-59

Mathews, Max, 607-8 McCarthy, John, 293 McCulloch, Warren, 134

meaning: built on triggering-patterns of symbols, 325, 327, 350; carried only on symbol level, 324-27, 330, 330, 709-10, codes and, 82, 158-62, 164-67, 267; of Contracrostipunctns, 82-85; of DNA, 160, 531-32, 665; explicit vs. implicit, 82-85, 158-76, 495-500, 583; in formal systems, see interpretations; intelligence and, 158, 162-64, 170-76, 501, 661-62; intrinsic, see meaning, explicit vs. implicit; location of, 153-57, 158-76, 408-9, 582-84; as multidimensional cognitive structure, 582-84; multiple, 8, 10, 52-53, 82-85, 94-102, 153-57, 158, 172, 266-67, 271, 409, 447-48, 524, 532, 666, see also disambiguation; in music, 83, 160, 161, 162-64, 167, 172, 174-75, 227, 582-84, 626-27, 676-77, 699-700, 704; objective, see meaning, explicit vs. implicit; as optional highlevel feature, 571; passive vs. active, 51-52, 94, 97, 100, 102, 191-92, 266, 267, 271, 456; purpose and, 321-32; rooted in isomorphisms, 49-53, 87-88, 94, 267, 337, 350; unnecessary on evolutionary time scale, 321-22

meaningless vs. meaningful interpretations, 51, 88

meaninglessness, in art and music, 699-700, 704-3

meat grinders, 414

Mechanical mode, 38-39, 65, 194, 221, 613-14

mechanization of thought processes, see Al, formal systems, etc.

meiosis, 665, 672

melodies: recall of, 363-64; time-shared, 385

memory, in computers, 288-89, 546, 616

memory dump, 381

men vs. women, 477, 595-96

Mendel, Arthur, 3, 28

Mental Arithmetic (MagrittO, 627

mention, see use vs. mention

Menzel, Adolph von, 4-5

Meredith, Marsha, 625

Mergenthaler, Otto, 630

Contents

XXIII

message-L

sing languages, 662-63

messages, 154, 158-76: in ant colonies, 350; in bottles, 167-69, 524; layers of, 166-71, 524, 703-4; from nature, 408-9; see also frame message, inner message, outer message messenger, for koans, 235-36, 238 messenger RNA, see mRNA meta, 216-17, 224 metaagnosticism, 114 rneta-analogy, 673-74 meta-answer-schema, 463 meta-author, 607-9, 726 metabook, 22

meta-descriptions, 656-57, 674 meta-evidence, etc., 693-94 Meta-Genie, see Genie meta-hiccups, 726 meta-intuition, 605 META-JOSH1-), etc., 443 metaknowledge, 364

metalanguage, 22, 184, 194. 248, 270, 514 metalogic, 23, 676

metanrathematics, 23, 579; reflected inside TNT,

449-50

Metamorphosis (Escher). 14-15 metaphase, 666-57 metaphor, 672 meta-proteins, 533-34

metarules, etc.: in chess, 687-88; in intelligence,

26-27, 559, 684-85

meta-search, 397 meta-symbols, 560 metatheorems, 193-94 metatheorv, formalized, 194

meta-TNT, etc., 442-43, 533-34 meta-wishes, see wishes meteorites, 167, 172

methylation, 540-41

metric, mental, 613, 614; see also conceptual nearness

Meyer, Leonard B., 167, 704 Michelangelo, 642 microprogramming, 295

minds: overlap of, 376; programmability of. 302, 679, see also Al, paradox of All, Tesler's The

orem, nonprogrammability; thoughts and,

369-90; two ways of creating. 390; vs. brains,

309, 575-77; see also brains, intelligence, etc. mini-vocabulary, 647

Minsky, Marvin, 373, 388, 644, 679, 722 mirroring, see isomorphisms, representation misspelling and computers, 297-98 MIU-numbers, 264-67; see also theorem-numbers MIU-system, 33-41, 46, 47, 48, 52, 191, 260-67;

as model for TNT, 439-42, 466; table of rules of, 260

MIU+MU-system, 466 Mobius Strip I (Escher), 29-30 Mobius Strip II (Escher), 276

modes of fugue-listening, 282-84

modularity, 149-50, 615-18, 628, 677-78; see also

localization, local vs. global properties modulation, 10, 121-23, 129-30, 466, 501, 717, 739

modules in brain, see symbols Modus Ponens, see detachment molecular biology, 504, 514-48 Mondrian, Piet, 700

monkeys, vision of, 345-4b

Monod, Jacques, 161 morphogenesis, 539, 543-44 Mosaic II (Escher), 61-63

mountain-car wreck story, 338-39, 361, 365 Mozart, W. A., 649, 702

mRNA, 517-20, 522-25, 527-28, 530-33, 536,

545, 547, 662, 663

MU, as possible theorem of MIU-system, 33-41,

229, 259-61, 265-67, 271, 708

MU, Zen word, 233, 241, 246, 254, 259, 272, 311,

312-313, 328

MU-LOOP (Floc P), 424-25, 441 Mu Offering, A, 272, 628 muoperator, 424

MU-picture, 283-84, 310-13, 327, 328-29,

Contents

XXIV

525-26

MU-puzzle, 33-41, 259-61, 509-10, 613-14 multifurcation of TNT, 467

multiple representations, 616-18, 670-71, 674 multiplication, 54-56, 64-65, 206, 409, 455, 566, 567

Mumon, 242, 246, 248-49, 253, 259, 260, 272;

commentaries by, 246-49, 252; poems by,

246-49, 252, 272

MUMON, string of TNT, 265-67, 271, 441-42 Mumonkan, 246

music: composed by computer, 25, 595, 597, 603,

607-9, 626-27, 676-77; dimensions of, 175;

mathematics and, 227, 555, 560; modern,

156-57, 163-64, 174-75, 699-700, 704; notation

of, 552-59, see also SMUT; semantics of, 83,

162-64, 167, 174-75, 582-84, 626-27, 676-77;

superhuman comprehension of, 172, 679; syntax of, 121-23, 129-30, 227, 626-27, 737; to break phonographs by, 75-78; to infiltrate phonographs by, 487-88; see also fugues, canons, pianos, flutes, etc.

music box, preprogrammed, 677

Musical Offering, The (Bach), 4-10, 86, 665, 666,

719, 720, 724, 727, 739-42 mutations, 295

N, see number theory

Najunamar, Z., 549-52 Nansen, 248-49, 253, 255

natural language utterances as programs, 629 natural numbers: defined, 54, 204; generalized;

453-56; postulates for, 216-17; see also number

theory, numerals, TNT, prime numbers, etc. near misses, see "almost"-situations nearly decomposable systems, 303-6 negation, 70, 71, 183, 191-92, 210-11, 214, 545 negative space, 62-63, 66-68, 72; see also figure and ground

nested movies, 184-85

nested works of art, 15, 106, 700-1, 705-6 nesting, 127, 138-41, 184-85, 660; see also recursion

neural networks, see symbols Neuroneater, 382

neurons: compared with ants, 315, 325, 339-40;

described, 339-40; Eudid's, 60; faultless func

tioning of, 575-77; firing of, 83, 340, 316,

343-45, 347, 350, 357; as an inviolate level, 302, 677, 686, 691-92, see also inaccessibility; not controllable consciously, 302, see also inaccessibility; on-center and off-center, 343-44; in

retina, 343-44; simple, complex, hypercomplex,-

neurons (continued)

344-45, 346, 347; as summing inputs, 316, 340, 575-77, 677

neurosurgery, 309, 313-14, 618. 678 New Yorker, The, 641-42

nickelodeon, 500; see also jukeboxes nodes and links, 370-71, 652-54 noise in vacuum, 82

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XXV

nondivisibility, 73-74

nonequilibrium thermodynamics, 693 Noneudid, 91-92

nonexistence, 254-55, 698, 725; see also Tumbolia nonproducible numbers, 265

nonprogrammability: of creativity, 570-71, 620, 673; of emotions and will, 677, 684-86; of Godelization, 472-76; of intelligence, 26-27, 471-73, 597-99, 601; of irrationality, 575-77; of jumping out of the system, 37-38, 477-78, 674-75; of ordinal names, 476; of soul, 574-75; of world chess champion, 151-52, 674; see also people vs. machines, essential incompleteness, Todeization, paradox of Al, TC-battles, 2-D vs. 3-D, etc.

non-self-assembling viruses, 542-43 non-self-descriptive adjectives, see heterological adjectives

nonsense: based on sense, 378-79; computer-generated, 620, 621-22, 625-26; human-generated, 621-22

nontermination, 408, 425-30; see also potentially endless searches, Hoop nontheorems, see theorems vs. nontheorems normal science, 660-61

nouns, most common in English, 630

novelty, and jumping out of the system, 475

nuclei: atomic, 303-4; cellular, 514, 517, 518

nudeotides, 514-17, 519, 522-24, 530, 540-41; first letters of, 231, 517, 666

number theory: applications of, 278-29; core of, 100, 407; Crab and, 551-58, 560, 562, 573-74, 579-81; demise of, 228-29, 426; formalized, see TNT; informal (N), 54-660, 204, 228; nonstandard, 100, 452-59; primitive notions of, 204-9; as scaled-off mini-world, 569; soothing powers of, 391-404; "true" version of, 458-59; typical sentences of, 204-5; typographical, see TNT; as universal mirror of formal systems, 260-65, 270; used and mentioned, 458

numbers, nature of, 54-58, 452, 458

numerals, 205-6, 213; vs. numbers, 264

object language, 22, 184, 248

objectivity, quest after, 479, 693-96 Oborin, Lev, 162

octopus cell, 345

Oin, Eta, see Eta Oin

Oistrakh, David, 162

Okanisama, 232, 234, 237, 238, 239, 241, 242 Old Ba. Ch., 726

Old Bach, 4, 28, 460, 481-83, 738, 739 ca-consistency, 459; see also or-inconsistency cs-incompleteness, 221-22, 421, 450-51 co-inconsistency, 17, 223, 453-55, 458-59 1-D vs.

3-D, 519-21, 616-17

open-ended searches, see potentially endless

searches, nontermination, unpredictable but

guaranteed termination, loops, free, FlooP, etc. operating systems, 295-96, 300-31, 308

operators and operons, 544-45 oracles, 567

orchard analogy, see information, depth from surface order and chaos: in ant colonies, 316-17; in number theory, 393, 395, 398-402, 406. 408-9, 418;

self-awareness and, 406

Order and Chaos (Escher), 399 ordinals, 462-64, 475-76 organ point. 329-30 origin of life, 548

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XXVI

original (as opposed to copies), 504 originality and machines, 25-26, 606-9 ORNATE

NOUN, 131-33 outcome, 184

outer messages, 166-71, 174-76, 501, 524, 704 OUTPUT (BlooP), 410, 411 overlapping genes, 524-25

overview capacity, 613-14, 678; see also jumping out of the system P-system, 64, 73-74

padding, 402-3

pages, in computers, 289

palindromes, in molecular biology, 201, 667 Palindromi, 353-54, 634-37, 643, 644

Pappus, 606-7

paradigm shifts, 660-61

paradox: of Al, 19, 26-27, 620, 673, see also Tesler's Theorem; in an, see Escher, Magritte,

Cage; of credibility through fallibility, 564; of God and the stone, 478; in mathematics, 17-24, 580-81; of motion, see Zeno's paradoxes; near misses, 612, 691; resolutions of, 116, 196-97,

245, see also MU, Tumbolia, jumping out of the system; of self-consciousness, 389; of the Typeless Wish, 115-16; in Zen, 249-55; see also contradictions, inconsistency parallel postulate, see fifth postulate PARRY, 300-301, 599-600, 677

parsing of natural languages, 588-93, 630-32; see also grammar, language partial recursivity, 430

particles, elementary, 54, 140-46, 258, 303-5, 309,522

partitions, mental, 671

parts, 303-5; see also reductionism Pascal, Blaise, 24, 25, 600

pathways: in ATN's and RTN's, 131-34, 150;

chemical, 528-29, 544-45, 663-64; conditional on circumstances, 383-84; goal-oriented choice of, 227, 609-15; as incorporating knowledge,

beliefs, 378-79; morphogenetic of T4, 539;

plausible vs. implausible, 383; potential, in

brain, 281

pattern recognition, see Bongard problems, conceptual skeletons, vision by computers patterns on all levels, 674 Peano, Giuseppe, 20, 216-17 Peano arithmetic, 100 Peano postulates, 216-17, 224 pearl and oyster, 17, 438 Penfield, Wilder, 342-43 Penrose, Roger, 15

people vs. machines, 25-27, 36-38, 151-52,

388-90, 471-73, 475-77, 559-62, 567-75,

577-79, 595-99, 606-9, 621-23, 680, 684-86 peptide bonds, 523

perception: visual, 97-98; and Zen, 251 Perfect items, 3, 75-79, 85, 406, 424, 486, 536

perfect numbers, 416, 418

phages, see viruses

phenotype, see genotype and phenotype 0(174, 176, 524-25