Gödel, Escher, Bach: An Eternal Golden Braid (148 page)

TTortoise, see ATTACCA

tuba, flaming, 488-89, 492, 735

Tumbolia, 116, 243, 255. 725; lavers of, 243 tuning an Al program, 678-79

Turing, Alan M., 26, 389, 425-26, 428-29.

594-99, 734-42; objections to Al, 597-99 Turing, Sara, 595

Turing machines, 390, 594, 735

Turing test, 595-99, 600, 677-78, 735-37;

arithmetic error in, 596; miniature, 621-23;

proposed revisions in, 600

Turtle's Theorem, see Todefs Theorem 2, as concept, 678

2-D vs. 3-D: in Escher, 57-58, 105-6, 125, 473-74, 524, 689-90, 698, 714-16; in Magritte, 480-81, 493-94, 700-1, 705-6; television screens and, 488-93, 737; trip-lets and, see triplets

Two Mysteries, The (Magritte), 701-2

Two-Part Invention, 28, 43-45, 684-86; see also Carroll paradox, Lewis Carroll 2 + 2 =

5,576

typeface metaphor, 541

Typeless Wishes, 111-15, 610-11 types, theory of, 21-23

typesetting machine, 608

typoenzymes, 505-13; binding-preferences of, 505-6, 511-12

Typogenctic Code, 510, 512, 513, 519 Typogenetics, 504-13, 514, 519, 520, 529; con trasted with MIU-system, 509-10, 514 Typographical Number Theory, see TNT

typographical operations, defined, 64 typos, 404

U, as nontheorem of MIU-system, 36, 39 U-mode, see Un-mode

Ulam, Stanislaw, 560, 621, 676 Un-mode, 39, 98, 254

Unamuno, Miguel de, 698

uncertainty principle, see Heisenberg uncertainty principle

Contents

XXXVIII

uncles, 446-48, 464, 466, 468, 541, 580 undecidability, 17, 222, 449, 451-55, 468; causes of, 707-8

undefined terms, 92-102, 216, 456; defined, 93, 97

understanding, nature of, 569, 675-76, 680 understanding minds/brains: meaning of, 697; possibility of, 697-98, 706-7

unicycle, tandem, 633, 669

units in Tvpogenetics. 505, 509 universal quantifiers, see quantifiers universal triggering power, 171, 175 Unmon, 254

unobservant machines, 36-37, 674

unpredictable but guaranteed termination, 400, 425

upper bounds, see loops, bounded, BIooP uracil, see nucleotides

use vs. mention, 434-37, 458, 531, 545, 699-700;

see also form, syntactic vs. semantic, programs

vs. data, syntax vs. semantics, structure vs. function variables in TNT, 206, 213-14; free, 207-9, 214; quantified, 208, 214, see also quantifiers

verb-at-the-end phenomenon, 130-31

Verbum (Escher), 257, 731-32

versus, see accessible vs. inaccessible knowledge, active vs. passive symbols, ants vs. ant colonies, arithmetical vs. typographical rules, Bach vs. Cage, beautiful vs. non-beautiful, bottom-up vs. top-down, classes vs. instances, continuous vs. discrete processes, deductive vs. analogical awareness, derivations vs. proofs, dissection vs. appreciation of Bach, distinct vs. similar levels, enzymes vs. typoenzymes, explicit vs. implicit knowledge, explicit vs. implicit meaning, explicit vs. implicit pruning, formal vs.

informal reasoning, formal vs. informal systems, formal systems vs. reality, genuine vs.

phony koans, high-fidelity vs. low-fidelity, holism vs. reductionism, improvisation vs.

introspection, instructions vs. templates, local vs. global properties, meaningless vs.

meaningful interpretations, men vs. women, minds vs. brains, nouns vs. verbs in triggering patterns, 1-D vs. 3-D, passive vs. active meaning, people vs. machines, plausible vs. implausible pathways, President v. Supreme Court, procedural vs.

declarative knowledge, programs vs. data, programs vs. programmers, purposeful vs.

purposeless behavior, rational vs. irrational, sanity vs. insanity, self-perception vs. self-transcendence, structure vs. function, subject vs. object, symbol vs. object, symbols vs.

neurons, symbols vs. signals, syntactic vs. semantic form, syntax vs. semantics, teleological vs. evolutionary viewpoint, theorems vs. nontheorems, theorems vs. rules, theorems vs. Theorems, theorems vs. truth, Tortoise vs. Crab, truth vs. beauty, truth vs.

commercials, truth vs. falsity, 2-D vs. 3-D, use vs. mention, weight vs. mass, womanseeing vs. seeing, words vs. letters, Zen vs. logic, Zen vs. words vibrations, 76-78, 82-85, 102, 270, 271, 469

Vice President, 670

Villon, Fransois, 369

Vinogradov, Ivan M., 394-95

Vinogradov property, 394-95

violins, 62, 63, 70, 81, 84, 162, 200, 257, 434, 502, 595, 681, 720, 724

viruses, 536-43; likened to Henkin sentences, 542-43

vision by computer, 602, 627

Contents

XXXIX

visual imagery: Bongard problems and, 661: faucets and, 364-65; inaccessible knowledge and, 365; lack of in programs, 623; mathematics and, 569, 678; necessitating layers of substrate, 570-71; power of, 338-39; role in

conceptual mapping. 668, 672; rubbing-off and.

361-62 es and canons, 28, 282-83, 314, voices in fugu

322-23, 335, 665-67, 669, 683, 737, 740 Voltaire, Francois Marie Arouet de, 3

vortices, 713-19

Vuillard, Edouard, 347 Wachter, F. L., 92 Warrin, Frank L., 366

-WASH ME", 608

Waterfall (Escher), 11-13, 99, 716 Watergate, 692

Watson, J. D.. 667 Weasel, 106 weather. 302-3 Weaver, Warren, 380 Weierstrass, Karl W. T., 404 weight vs. mass, 171-72 Weizenbaum, Joseph, 599-600. 675

well-formed strings: in Art of Zen Strings, 239, 242, 244; BIooP puzzle on, 416; defined.

53: in pq-svstem, 47; in Propositional Calculus, 181-83; in TNT, 213-15

Well-Te"ered Clavier (Bach), 7, 280-84, 327. 329,

335

Well-Tested Conjecture (Fourmi), 333-35 "When Johnny Comes Marching Home", 607

Whitehead, Alfred North, 18, 21, 23-24 Whitely, C. H., 477

wholes, see holism Wiener, Norbert, 684 Wiesel, Torsten, 343

will: free, see free will; mechanical, 684-86; roots

of, 684-86

Wilson, E. 0., 350 Winograd. Terry, 627-32 Winston. Patrick Henry, 299 wishes, metawishes, etc., 109-16 Wittgenstein, Ludwig, 680, 699

Wolff, Christoph, 392

womanseeing vs. seeing, womansee men vs. women wondrous and unwondrous numbers, 400-2, 408,

415, 418, 425

Wooldridge, Dean, 360

words: in computers, 288-90, 295, 411; as programs, 629-30; spelled backwards. 81, 418, 427, 498, 505, 533, 549, 727, 738, 740; thoughts, formal rules, and, see main theses: vs.

letters,

325-27, 570, 571; Zen attitude towards, 246, 249, 251-54

worker ants, 318

working inside the system, see Mechanical mode

yes-answers, 461-64 Yngve, Victor, 620 Young, LaMonte, 700

Zen Algebra, 577

Zen Buddhism: Achilles teaches the Tortoise about. 231-45; computers and, 625-26; Crab's refrigerator and, 406-7; Escher and, 255-58; holism vs. reductionism and, 312-13; inconsistencies and, see Zen vs. logic; introduction to, 246-59; jumping out of the system and, 233, 255, 479; music, art, and, 699, 704-6; Mystery of the Undecidable and, 272; nonexistence and, 254-55, 698; patriarchs of, 30, 232, 252, 259; quasi-, 625-26; U-mode and, 39, 98. 254; vs, logic, 99, 233-34, 249-51, 254; vs. words, 246, 248-49, 251-54; Zeno and, 30

Contents

XL

Zen Strings, Art of, see Art of Zen Strings

Zenfunny, Beethoven's Ninth, 634

Zeno of Elea, 28, 29-32, 94-95, 144, 146, 232, 610, 681, 704, 722

Zeno's paradoxes, 29-32, 35, 43, 146, 610

Zentences, 186-90

ZET-cycles, 94-96, 689

zooming in, 645, 671

i T

Contents

XLI