Gödel, Escher, Bach: An Eternal Golden Braid (140 page)

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Authors: Douglas R. Hofstadter

Tags: #Computers, #Art, #Classical, #Symmetry, #Bach; Johann Sebastian, #Individual Artists, #Science, #Science & Technology, #Philosophy, #General, #Metamathematics, #Intelligence (AI) & Semantics, #G'odel; Kurt, #Music, #Logic, #Biography & Autobiography, #Mathematics, #Genres & Styles, #Artificial Intelligence, #Escher; M. C

BOOK: Gödel, Escher, Bach: An Eternal Golden Braid
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(Feb. 24, 1977). An exciting presentation of the first laying-bare ever of the full hereditary material of any organism. The surprise is the double-entendre: two proteins coded for in an overlapping way: almost too much to believe.

Sayre, Kenneth M., and Frederick J. Crosson. The Modeling of Mind: Computers and Intelligence. New York: Simon and Schuster, Clarion Books, 1963. A collection of philosophical comments on the idea of Artificial Intelligence by people from a wide range of disciplines. Contributors include Anatol Rapoport, Ludwig Wittgenstein, Donald Mackay, Michael Scriven, Gilbert Ryle, and others.

* Schank, Roger, and Kenneth Colby. Computer Models of Thought and Language. San Francisco: W. H. Freeman, 1973. A collection of articles on various approaches to the simulation of mental processes such as language-understanding, belief-systems, translation, and so forth. An important Al book, and many of the articles are not hard to read, even for the layman.

Schrodinger, Erwin. What is Life? & Mind and Matter. New York: Cambridge University Press, 1967. Paperback. A famous book by a famous physicist (one of the main founders of quantum mechanics). Explores the physical basis of life and brain; then goes on to discuss consciousness in quite metaphysical terms. The first half, What is Life?, had considerable influence in the 1940's on the search for the carrier of genetic information.

Shepard, Roger N. "Circularity in judgments of Relative Pitch". Journal of the Acoustical Society of America 36, no. 12 (December 1964), pp. 2346-2353. The source of the amazing auditory illusion of "Shepard tones".

Simon, Herbert A. The Sciences of the Artificial. Cambridge, Mass.: M.I.T. Press, 1969.

Paperback. An interesting book on understanding complex systems. The last chapter, entitled "The Architecture of Complexity", discusses problems of reductionism versus holism somewhat.

Smart, J. J. C. "Godel's Theorem, Church's Theorem, and Mechanism". Synthese 13

(1961): 105. A well written article predating Lucas' 1961 article, but essentially arguing against it. One might conclude that you have to be Good and Smart, to argue against Lucas...

** Smullvan, Raymond. Theory of Formal Systems. Princeton, N. J.: Princeton University Press, 1961. Paperback. An advanced treatise, but one which begins with a beautiful discussion of formal systems, and proves a simple version of Godel's Theorem in an elegant way. Worthwhile for Chapter 1 alone. What Is the Name of This Book?

Englewood Cliffs, N. J.: Prentice-Hall, 1978. A book of puzzles and fantasies on paradoxes, self-reference, and Godel's Theorem. Sounds like it will appeal to many of the same readers as my book. It appeared after mine was all written (with the exception of a certain entry in my bibliography).

Index

XVII

Sommerhoff, Gerd. The Logic of the Living Brain. New York: John Wiley, 1974. A book which attempts to use knowledge of small-scale structures in the brain, in creating a theory of how the brain as a whole works.

Sperrv, Roger. "Mind, Brain, and Humanist Values". In John R. Platt, ed. .Vew Views on the Nature of Man. Chicago: University of Chicago Press, 1965, A pioneering neurophvsiologist here explains most vividly how he reconciles brain activity and consciousness.

* Steiner, George. After Babel: Aspects of Language and Translation. New York: Oxford University Press, 1975. Paperback. A book by a scholar in linguistics about the deep problems of translation and understanding of language by humans. Although Al is hardly discussed, the tone is that to program a computer to understand a novel or a poem is out of the question. A well written, thought-provoking-sometimes infuriating-book.

Stenesh, J. Dictionary of Biochemistry. New York: John Wiley, Wiley-Interscience, 1975. For me, a useful companion to technical books on molecular biology.

** Stent, Gunther. "Explicit and Implicit Semantic Content of the Genetic Information".

In The Centrality of Science and Absolute Values, Vol. 1. Proceedings of the 4th International Conference on the Unity of the Sciences, New York, 1975. Amazingly enough, this article is in the proceedings of a conference organized by the nowinfamous Rev. Sun Mvung Moon. Despite this, the article is excellent. It is about whether a genotype can be said, in any operational sense, to contain "all" the information about its phenotype. In other words, it is about the location of meaning in the genotype.

. Molecular Genetics: A Historical Narrative. San Francisco: W. H. Freeman, 1971. Stent has a broad, humanistic viewpoint, and conveys ideas in their historical perspective. An unusual text on molecular biology.

Suppes, Patrick. Introduction to Logic. New York: Van Nostrand Reinhold, 1957. A standard text, with clear presentations of both the Propositional Calculus and the Predicate Calculus. My Propositional Calculus stems mainly from here.

Sussman, Gerald Jay. A Computer Model of Skill Acquisition. New York: American Elsevier, 1975. Paperback. A theory of programs which understand the task of programming a computer. The questions of how to break the task into parts, and of how the different parts of such a program should interact, are discussed in detail.

** Tanenbaum, Andrew S. Structured Computer Organization. Englewood Cliffs, N. J.: Prentice-Hall, 1976. Excellent: a straightforward, extremely well written account of the many levels which are present in modern computer systems. It covers microprogramming languages, machine languages, assembly languages, operating systems, and many other topics. Has a good, partially annotated, bibliography.

Tarski, Alfred. Logic, Semantics, Metamathematics. Papers from 1923 to 1938.

Translated by J. H. Lot, New York: Oxford University Press, 1956. Sets forth Tarski's ideas about truth, and the relationship between language and the world it represents.

These ideas are still having repercussions in the problem of knowledge representation in Artificial Intelligence.

Taube, Mortimer. Computers and Common Sense. New York: McGraw-Hill, 1961.

Paperback. Perhaps the first tirade against the modern concept of Artificial Intelligence.

Annoying.

Index

XVIII

Tietze, Heinrich. Famous Problems of Mathematics. Baltimore: Graylock Press, 1965. A book on famous problems, written in a very personal and erudite style. Good illustrations and historical material.

Trakhtenbrot, V. Algorithms and Computing Machines. Heath. Paperback. A discussion of theoretical issues involving computers, particularly unsohable problems such as the halting problem, and the word-equisalence problem. Short. which is nice.

Turing, Sara. Alan M. Turing. Cambridge, U. K.: WW'. Hefter & Sons, 1959. A biography of the great computer pion4r. A mother's work of love.

* Ulam, Stanislaw. Adventures of a Mathematician. New York: Charles Scribner's, 1976.

An autobiography written by a sixty-five-year old man who writes as if he were still twenty and drunk in love with mathematics. Chock-full of gossip about who thought who was the best, and who envied whom, etc. Not only fun, but serious.

,A'aitson, J. D. The Molecular Biology of the Gene, 3rd edition. Menlo Park, Calif.: W.

A. Benjamin, 1976. A good book but not nearly as well organized as Lehninger's, in my opinion. Still almost every page has something interesting on it.

Webb, Judson. "Metamathematics and the Philosophy of Mind". Philosophy of Science 35 (1968): 156. A detailed and rigorous argument against Lucas, which contains this conclusion: "My overall position in the present paper may be stated by saying that the mind-machine-GOdel problem cannot be coherently treated until the constructivity problem in the foundations of mathematics is clarified."

Weiss, Paul. "One Plus One Does Not Equal Two". In G. C. Quarton, T. Melnechuk, and F. O. Schmitt, eds. The Neurosciences:.4 Study Program. New York: Rockefeller University Press, 1967. An article trying to reconcile holism and reductionism, but a good bit too holism-oriented for my taste.

* Weizenbaum, Joseph. Computer Power and Human Reason. San Francisco: W. H.

Freeman, Freeman, 19i6. Paperback. A provocative book by an early At worker who has come to the conclusion that much work in computer science, particularly in Al, is dangerous. Although I can agree with him on some of his criticisms, I think he goes too far. His sanctimonious reference to Al people as "artificial intelligentsia" is funny the first time, but becomes tiring after the dozenth time. Anyone interested in computers should read it.

Wheeler, William Morton. "The Ant-Colony as an Organism".Journal of Morphology 22, 2 (1911): 307-325. One of the foremost authorities of his time on insects gives a famous statement about why an ant colony deserves the label "organism" as much as its parts do.

Whitely, C. H. "Minds, Machines, and Godel: A Reply to Mr Lucas". Philosophy 37

(1962): 61. A simple but potent reply to Lucas' argument. Wilder, Raymond. An Introduction to the Foundations of :Mathematics. New York: John Wiley, 1952. A good general overview, putting into perspective the important ideas of the past century.

* Wilson, Edward O. The Insect Societies. Cambridge, Mass.: Harvard University Press, elknap Press, 1971. Paperback. The authoritative book on collective behavior of insects.

Although it is detailed, it is still readable, and discusses many fascinating ideas. It has excellent illustrations, and a giant (although regrettably not annotated) bibliography.

Winograd, Terry. Five Lectures on Artificial Intelligence. AI Memo 246. Stanford, Calif.: Stanford University Artificial Intelligence Laboratory, 1974. Paperback. A description of fundamental problems in At and new ideas for attacking them, by one of the Index

XIX

important contemporary workers in the field.. Language as a Cognitive Process.

Reading, Mass.: Addison-Wesley (forthcoming). From what I have seen of the manuscript, this will be a most exciting book, dealing with language in its full complexity as no other book ever has. . Understanding Natural Language. New York: Academic Press, 1972. A detailed discussion of one particular program which is remarkably "smart", in a limited world. The book shows how language cannot be separated from a general understanding of the world, and suggests directions to go in, in writing programs which can use language in the way that people do. An important contribution; many ideas can be stimulated by a reading of this book.

. "On some contested suppositions of generative linguistics about the scientific study of language", Cognition 4:6. A droll rebuttal to a head-on attack on Artificial Intelligence by some doctrinaire linguists.

* Winston, Patrick. Artificial Intelligence. Reading, Mass.: Addison-Wesley, 1977. A strong, general presentation of many facets of At by a dedicated and influential young proponent. The first half is independent of programs; the second half is LISP-dependent and includes a good brief exposition of the language LISP. The book contains many pointers to present-day At literature. ed. The Psychology of Computer Vision. New York: McGraw-Hill. 1975. Silly title, but fine book. It contains articles on how to program computers to do visual recognition of objects. scenes. and so forth. The articles deal with all levels of the problem, from the detection of line segments to the general organization of knowledge. In particular, there is an article by Winston himself on a program he wrote which develops abstract concepts from concrete examples, and an article by Minsky on the nascent notion of "frames".

* Wooldridge, Dean. Mechanical Man-The Physical Basis of Intelligent Life. New York: NJ McGraw-Hill, 1968. Paperback. A thorough-going discussion of the relationship of mental phenomena to brain phenomena, written in clear language. Explores difficult philosophical concepts in novel was, shedding light on them by means of concrete examples.

Index

XX

Credits

Figures: Fig. 1, Johann Sebastian Bach by Elias Gottlieb-Hart ssmann (1748), collection of William H. Scheide, Princeton, New Jersey; Fig. 2, Flute Concert in Saussouci, by Adolf von Menzel, Nationalgalerie, West Berlin; Figs. 3, 4, 152, "The Royal Theme" and the last page of the "Six-part Ricercar." from the original edition of Musical Offering by Johann Sebastian Bath, are reproduced courtesy of the Library of Congress; Figures of lithographs and woodcuts of M. C. Escher are reproduced by permission of the Escher Foundation, Haags Gemeentemuseum, The Hague, copyright © the Escher Foundation, 1979, reproduction rights arranged courtesy of the Vorpal Galleries, New York, Chicago, San Francisco, and Laguna Beach; Fig. 9, photograph of Kurt Godel by Orren J. Turner from Foundations of

Mathematics. Symposium Papers Commemorating the Sixtieth Birthday of Kurt Godel, edited by

Jack J. Bulloff, Thomas C. Holyoke, and S. W. Hahn, New York, Springer-Verlag, 1969; Figs. 17, 96, "Figure-Figure" and "A section of mRNA passing through a ribosome,"

drawings by Scott E. Kim; Figs. 19, 44, 133, 148, musical selections from the Musical Offering by J. S. Bach, music printed by Donald Byrd's program "SMUT"; Fig. 25,

"Cretan labyrinth" from W. H. Matthews, Mazes and Labyrinths: Their History and Development, New York, Dover Publications, Inc., 1970; Fig. 39, photograph of Rosetta Stone, courtesy of the British Museum; Fig. 40, A collage of scripts. Samples of cuneiform, Easter Island, Mongolian and Runic scripts from Hans Jensen, Sign, Symbol and Script, East Germany VEB Deutscher Verlag Der Wissenschaften; samples of Bengali and Buginese script from Kenneth Katzner, The Languages of the World, New York, Funk & Wagnalls, 1975; samples of Tamil and Thai from I. A. Richards and Christine Gibson, English Through Pictures, New York, Washington Square Press; Fig.

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