Gödel, Escher, Bach: An Eternal Golden Braid (141 page)

59, "Intelligence built up layer by layer" (Fig. 9.8) adapted from Patrick Henry Winston.

Artificial Intelligence, Reading, Mass., Addison-Wesley Publishing Company, reprinted by permission; Figs. 63, 69, photographs of an ant bridge by Carl W. Rettenmeyer and construction of an arch by termite workers by Turid Hdlldobler, from E. O. Wilson, The Insect Societies, Cambridge, Mass., Harvard University Press, 1979; Fig. 65, schematic drawing of a neuron adapted from The Machinery of the Brain, by Dean Wooldridge, copyright © 1963, McGraw-Hill, Inc. used with permission of McGraw Hill Book Company, and from Fig. 11-6, page 26, Speech and Brain-Mechanisms, by Wilber Penfield and Lamar Roberts, copyright © by Princeton University Press, reprinted by permission of Princeton University Press; Fig. 66, "the human brain, seen from the left side," from Steven Rose, The Conscious Brain, copyright © 1973 by Steven Rose, reprinted by permission of Alfred A. Knopf, Inc., New York, and John Wolfers, London; Fig. 68, "overlapping neural pathways," from John C. Eccles, Facing Reality, New York, SpringerVerlag, 1970; Figs. 77, 78, 80, 82, 117, 137, 138, 141, The Shadows, State of Grace, The Fair

Captive, The Air and the Song, Mental Arithmetic, Common Sense, The Two Mysteries, and The

Human Condition I by Rene Magritte, copyright © by ADAGP, Paris, 1979; Figs. 79, 95,

"Tobacco Mosaic Virus" and "Secondary and Tertiary Structure of Myoglobin" from Albert Lehninger, Biochemistry, New York, Worth Publishers, 1975; Figs. 91, 92, "The Index

XXI

four constituent bases of DNA" and "The ladder-like structure of DNA" from Arthur Kornberg, "The Synthesis of DNA," Scientific American, copyright © October 1968, all rights reserved; Fig. 93, "Molecular model of the DNA double helix," reprinted by permission, from V. M. Ingram, Biosynthesis of Macromolecules, Menlo Park, California, The Benjamin/Cummings Publishing Company, 1972; Fig. 97,

"Polyribosome" from The Proteins, edited by R. E. Dickerson and H. Neurath, page 64, New York, Academic Press; Fig. 98, "A two-tiered molecular canon" from O. L. Miller, Jr., "Visualization of Genes in Action," in Scientific American, copyright © March 1973, all rights reserved; Figs. 101, 102, 103, "The T4 bacterial virus," "Infection of a Bacterium by a virus," and "The morphogenetic pathway of the T4 virus," from William B. Wood and R. S. Edgar, "Building a Bacterial Virus" in Scientific American, copyright

© July 1987, all rights reserved; Fig.

105, photograph of Srinivasa Ramanujan from S. R. Ranganathan, Ramanujan, the Man and the Mathematician, New York, Asia Publishing House, 1967; Figs. 110, 111, 112, from Terry Winograd, Understanding Natural Language,New York, Academic Press, 1972; Fig. 113, Photograph of Alan Turing by Mssrs. C. H. O. Trevelyan from Sara Turing, Alan M. Turing, Cambridge, England, W. H. Heffer and Sons, Ltd., 1959; Fig.

116, "a meaningful story in Arabic" from Abdelkebir Khatibi and Mohammed Sijelmassi, The Splendor of Islamic Callizrabhl, New York, London, Thames & Hudson, copyright

© by Qarawiyne Library in Fez. Fig 118, Procedural representation of “red cube which supports a pyramid,” adapted from Computer Models of Thought and Language, edited by Roger C. Schank and Kenneth Mark Colby. W. H. Freeman and Company, copyright 1973; Figs. 119, 122, 124, 130, Bongard problems from M. Bongard, Pattern Recognition, Rochelle Park, New Jersey,

Hayden Book Company, Spartan Books, 1970

Grateful acknowledgment is made to the following publishers for permission to quote excerpts from the following material: The Bach Reader. A Life of johann Sebastian Bach in Letters and Documents, edited by Hans T. David and Arthur Mendel, Revised, with the permission of W. W. Norton & Company, Inc., copyright (~) 1966, 1945 by W. W.

Norton & Company, Inc. copyright renewed 1972 by Mrs. Hans T. David and Arthur Mendel; J. S. Bach's Musical Offering, page 179, edited by Hans T. David, New York, copyright 1945 by G. Schirmer, Inc., used by permission; Gyomay Kubose, Zen Koans, Chicago, Regnery, 1973; Pauls Reps, Zen Flesh, Zen Bones, Tokyo, Japan, Charles E.

Tuttle Co., Inc. 1957; J. R. Lucas, "Minds, Machines, and Godel," and Alan M. Turing,

"Computing Machinery and Intelligence," from ,finds and Machines, edited by A. R.

Anderson, Englewood Cliffs, New Jersey, Prentice-Hall, 1964, and Philosophy, vol. 36, 1961; J. M. Jauch, Are Quanta Real? Bloomington, Indiana, Indiana University Press, 1973; James R. Newman, "Srinivasa Ramanujan," in The World of Mathematics, edited by James R. Newman, New York, Simon & Schuster, reprinted by permission of Simon

& Schuster, a division of Gulf & Western Corporation, 1956; Terry Winograd, "A Procedural Model of Language Understanding," from Computer Models of Thought and Language, edited by Roger C. Schank and Kenneth Mark Colby, San Francisco, W. H.

Freeman and Company, copyright © 1973; Joseph Weizenbaum, Computer Power and Human Reason: From judgment To Calculation, San Francisco, W. H. Freeman and Company, copyright © 1976.

Index

XXII

INDEX

AABB form, 130, 227

history of, 19, 24-27, 594-97, 600-9;

Abel, Niels Henrik, 404

leveltranslation and, 285; outline of, 601-3;

ABORT (BlooP), 412

relation

to

mathematics,

559-60;

abortion, 176 levels of, 651-53, 656-57, stratification of, 299-300

660,

Al programs: compared with people, 679-

abstraction, ti66-72, 674

80; curiosity of, 679; Lucas' argument and,

Achilles: answer-schemas and, 475; Carroll 577-78

paradox and, 46, 170, 181, 193; Crab Al Thesis, 579

Canon and, 204 666-67; heel of, 389, 484; Air and the Song, The (Magritte), 494

image of GOD, 223; inaccessible neurons Air on G's String, 445, 446, 497

of, 328. 686; initial letter of, 231, 507, 667; airplane-haystack story, 675

innocence of, 406, 408, 424; mapped onto aleatoric music, 163, 174, 700

ant colony, 318, 324; mentioned 84, 272, Algol, 292, 293, 381, 630

525, 573, 669; mystified by Crab, 560; algorithms, 292, 410, 412, 413, 414, 440, orchard analogy and, 427; origin of, 28, 29; 459, 567 all 60

picture of, 42; problem reduction and, 610-

"almost"-situations, 634-40, 641-43, 649

11; recursion and, 128-31, 149; as violin, alpha helix, 521, 525

502

Alternative Structures of the Union, see

Achilles property, 396-98, 415

ASU's

acoustico-retrieval, 278-80, 460

ambiguity: computer languages and, 297-

acronyms, 31-32, 113, 174, 176, 204, 237, 98; in translation into TNT, 209-11

272, 374, 606, 684, 727, 736, 738, 740

amino

acids,

518-25,

533-34;

in

acrostics, 7, 81

Typogenetics,

active site, 528-29, 544

508, 510-11

actor formalism, 662-64

analogical thinking: by computer, 603;

,,Actually Intelligent" programs, 676

underpin

addition: Al programs and, 677-78; ning of, 570-71

commutativity, associativity of, 55, 225-

analogies, 668-74

26; in BlooP, 409; noncommutative, 222-

Analytical Engine, 25, 598, 727 anaphase,

23, 639; pqsystem and, 49-53, 417; 667

representability of, 417; of supernaturals, anarchy, 693

455; TNT notation for, 206-7; triple, 101, "and", 177-80, 181, 186, 630 Anderson, 206-7

Alan Ross, 197 Announcer, 633-40

addresses (in memory), 289, 290

anomalies, 44, 96, 208, 435, 723 Another

adenine, see nucleotides

World (Escher), 250, 255 answer-schemas,

advertisements, 478

462-14, 475, 688 ant bridge, 334

Al: applied to mathematics, 573, 614-15; ant

colonies:

artificial,

359;

caste

arguments

against,

597-99;

attitudes distribution in,

against, see anti-Al attitudes; computer 318-28; castes in, 317-18; communism in, languages and, 299-300, 548; converging 318,

towards brains, 579; defined, 26; difficulty 330-31; compared with brains, 315-16, of, 26-27, 573, 740; evidence and, 695; 318,

faith underlying, 572, 578-79; G6del's 324-25, 350, 358-59; contrasted with gases, Theorem and, 388-90, 471-77, 706-7;

Index

XXIII

317; freedom and control in, 315-16, 327; Aria with Diverse Variations (Bach), 392-intel

93, 395 Aria with Diverse Variations

ligent,

310-36;

levels

in,

319-27; (Dialogue), 408 Aristotle, 19

mechanisms of

arithmetization, 262-65, 268-69, 533-34

teams and signals, 317-21; order and chaos arithmoquining, 445-54, 466-68, 497, 502, in,

541,

316-17; regrouped, 332-33; signals in, 320-

580-81

28;

arms, mutually washing, 691

symbol level in, 324-28, 330; teams in, art: identity crisis of, 699-700, 703-6; 317,

modern,

319-27; thresholds in, 316-17, 319-21; 699-706; by computer, 603, 619-20 Art-trails of,

Language, 622

315-17; see also caste distribution, Aunt Art of the Fugue (Bach), 79-81, 86, 671

Hillary,

Art of Zen Strings, 237, 239-42, 244, 626

Fermant, job. Seb., Fourmi, Lierre de, Artificial Imagery, 560 Artificial Intuition, teams,

560 Artificial Ism, 625

signals, symbols

artificial "thinking", 337, 601

Ant Fugue, 337, 349, 350, 382, 570, 686, Ascending and Descending (Escher), 12-737-39 "Aid Fugue" (Escher), 322-23 13, 15, 21,

Anteater, 275-84, 311-36, 382, 570, 722 716

anti-AI

attitudes.

27,

470-72,

628 Asian Box, Very Gold, see Gold Box, Very

anticodons, 522-24

Asian assemblers, 291, 294

ants: dispensability of, 326; nest of, 359; assembly language, 290-95; compared to vs. ant

DNA,

colonies, 314, 315, 319, 321, 326, 330 290-91

aperiodic crystals, 167-69, 174-76 arch of assembly lines, cellular, 528-29, 544-45

termites, 358-59

Appearances of Achilles and the Tortoise in Dialogues are not indexed, but those of less frequent characters are. The reader is encouraged to consult the figure on page 370 for possible help in crossreferences.

Index

24

associativity, 35-56, 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 Saxons, 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 Avers, 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 Calculus, 183; of MIU-svstern, 33, 35; of P-system, 73-74; of pq-system, 47; of pq-system, modified, 87; of 310-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.; Al 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-t7; 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, 1624, 174-75; see also Old Bach Bach, Wilhelm Friedemann, 4, 6

background assumptions, 644

backtracking, 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 Tvpogenetics, 505-8, 510

Baso, 234

Bassui, 255

Contents

VI

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

bees, 360, 641, 720

Beethoven, Ludwig van. 6. 75, 163, 634 beliefs, catalogue of. 382, 384 Bell, A. G., 296

Belnap, Nuel, 197 Beno, Luciano, 704 bicentuplets, 540

bifurcations, 91-94, 100, 456-59, 467, 579 biojukeboxes, 160, 175 Birthday Cantata (Bach), 461

Birthday 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