Gödel, Escher, Bach: An Eternal Golden Braid (137 page)

3 E. O. Wilson,
The Insect Societies
, p. 226.

2 Steven Rose,
The Conscious Brain

4 Dean Wooldridge,:
Mechanical Man
, p. 70.

English French German Suite

1 Lewis Carroll. The Annotated Alice (
Alice's

versions. The original sources for the French and

Adventures in Wonderland
and Thr
ough the

German texts are given below.

Looking-Glass
). Introduction and Notes by Martin

2 Frank L. Warrin,
The Vew Yorker
, Jan. 10, 1931.

Gardner (New fork: Meridian Press, New American

3 Robert Scott, "The Jabberwock Traced to Its True

Library, 1960). This source contains all three

Source",
Macmillan's Magazine
, Feb. 1872

.

1 Warren Weaver, "Translation

in Machine

2 C. H. MacGillavrv.
Symmetry Aspects of the

Translation of Languages, Wm. N. Locke and A.

Periodic Drawings of M C. Escher
, p. viii,

Donald Booth. eds. (News fork: John Wiles and

3 J. R. Lucas, "Minds, Machines, and Gödel", in A.

Sons, and Cambridge, Mass,: SLI. F. Press, 1955),

R. Anderson, ed., Minds and Machines, pp. 57-9.

p. 18.

Chapter XIII: BlooP and FlooP and GlooP

1 J . M. Jauch, Are Quanta Real?, pp. 63-65.

1 The title of Gödel’s 1931 article included a Roman the difficult arguments. However, the first paper was numeral "I" at the end, signifying that he intended to so widely acclaimed that a second one seas rendered follow it up with a more detailed defense of some of

superfluous, and it was never written

Chapter XV: Jumping out of the System

1 Lucas in Anderson, p. 43.

4 M. C. Escher, The
Graphic Wash of M. C Escher

2 Ibid., p. 48.

(New York: Meredith Press. 1967), p. 21.

3 Ibid., pp. 48-9.

5 Ibid., p. 22.

6 E. Goffinan.
Frame Analysis
, p. 475.

Edifying Thoughts of a Tobacco Smoker

This translation of Bach's poem is taken from Day id and Mendel,
The Bach Reader
, pp. 97-8.

Chapter XVII: Church, Turing, Tarski, and Others

1 Stanislaw Ulam,
Adventures of a Mathematician
,

5 Newman, p. 375.

p. 13.

6 Ibid., p. 375.

2 James R. Newman, "Srinivasa Ramanujan°, in

7 Ibid., p. 375-6.

James R. Newman, ed.,
The World of Mathematics

8 Ibid., p. 376.

(New York: Simon and Schuster, 1956), Vol. 1, pp.

9 Lucas in Anderson, p. 44.

372-3.

10 Ibid., p. 54.

3 Ibid., p. 375.

11 Ibid., p. 53.

4 S. R. Ranganathan,
Ramanujon
, pp. 81-2.

SHRDLU, Toy of Alan's Designing

1 This Dialogue is adapted front 'terry Winograd, "A
Thought and Language
, pp. 155-66. Only the names Procedural Model of Language Understanding", in

of two characters have been modified.

R. Schank and K.Colby, eds., Computer
Models of

1 Alan M. Turing, "Computing Machinery and

Intelligence", Mind, Vol. LIX, No. 236

(1950). Reprinted in A. R. Anderson, ed.,
Minds and

Machines
.

2 Turing in Anderson, p. 5. 3 Ibid, p. 6

4 Ibid., p. 6.

5 Ibid., P. 6.

6 Ibid., pp. 13-4.

7 Ibid., pp, 14-24.

8 Ibid., p. 17

9 Vinton Cerf, "Parry Encounters the Doctor", p. 63.

10 Joseph Weizenhaum,
Computer Power and

Human
Reason, p. 189.

11 Ibid., pp. 9-10

12 M. Mathews and L. Rosier, "A Graphical

Language for Computer Sounds" in H. vn Foerster

and J. W. Beauchamp, eds.,
Music by Computers
, p.

96.

13 Ibid., p. 106.

14 Carl Sagan,
Communication with Extraterrestrial

Intelligence
, p. 52.

15
Art-Language
, Vol. 3. No. 2, May 1975.

16 Terry Winograd, "A Procedural Model of

Language Understanding", in R. Schank and K.

Colbc, eds..
Computer Models of Thought and

Language
, p. 170.

17' Ibid., p. 175.

18 Ibid..- p. 175.

19 Terry Winograd,
Understanding Natural

Language
, p. 69.

20 Winograd, "A Procedural Model", pp. 182-3.

21 Ibid., pp. 171-2.

1
The New Yorker
, Sept. 19, 1977, p. 107.

2 Ibid., p. 140.

3 George Steiner,
After Babl
(, pp. 215-227.

4 David E. Rumelhart, "Notes on a Schema for Stories", in D. Bobrow and A. Collins, eds.,
Representation
and Understanding
, p. 211.

5 Stanislaw Ulam, Adventures of a Mathematician, p. 183.

6 Marvin Minsky, "Steps Toward Artificial Intelligence", in E. Feigenbaum and J. Feldman, eds.,
Computers and Thought
, p. 447.

7 Ibid., p. 446.

Chapter XX: Strange Loops, Or Tangled Hierarchies

1 A. L. Samuel, "Some Moral and Technical Consequences of Automation-A Refutation",
Science
132

(Sept. 16, 1960), pp. 741-2.

2 Leonard B. Meyer,
Music, The Arts, and Ideas
, pp. 161, 167.

3 Suzi Gablik, Magritte, p. 97.

4 Roger Sperry, "Mind, Brain, and Humanist Values", pp. 78-83.

5 H T. David,
J. S. Bach's Musical Offering
, p. 43.

Index

VI

Bibliography

The presence of two asterisks indicates that the hook or article was a prime motivator of my book. The presence of a single asterisk means that the book or article has some special feature or quirk which I want to single out.

I have not given many direct pointers into technical literature; instead I have chosen to give "meta-pointers": pointers to books which have pointers to technical literature.

Allen, John. The Anatomy of LISP. New York: McGraw-Hill, 1978. The most comprehensive book on LISP, the computer language which has dominated Artificial Intelligence research for two decades. Clear and crisp.

Anderson, Alan Ross, ed. Minds and Machines. Englewood Cliffs, N. J.: PrenticeHall, 1964. Paperback. A collection of provocative articles for and against Artificial Intelligence. Included are Turing's famous article "Computing Machines and Intelligence" and Lucas' exasperating article "Minds, Machines, and Godel".

Babbage, Charles. Passages from the Life of a Philosopher. London: Longman, Green, 1864. Reprinted in 1968 by Dawsons of Pall Mall (London). A rambling selection of events and musings in the life of this little-understood genius. There's even a play starring Turnstile, a retired philosopher turned politician, whose favorite musical instrument is the barrel-organ. I find it quite jolly reading.

Baker, Adolph. Modern Physics and Anti-physics. Reading, Mass.: Addison-Wesley, 1970. Paperback. A book on modern physics-especially quantum mechanics and relativity-whose unusual feature is a set of dialogues between a "Poet" (an antiscience

"freak") and a "Physicist". These dialogues illustrate the strange problems which arise when one person uses logical thinking in defense of itself while another turns logic against itself.

Ball, W. W. Rouse. "Calculating Prodigies", in James R. Newman, ed. The World of Mathematics, Vol. 1. New York: Simon and Schuster, 1956. Intriguing descriptions of several different people with amazing abilities that rival computing machines.

Barker, Stephen F. Philosophy of Mathematics. Englewood Cliffs, N. J.: Prentice-Hall.

1969. A short paperback which discusses Euclidean and non-Euclidean geometry, and then Godel's Theorem and related results without any mathematical forms lism.

* Beckmann, Petr. A History of Pi. New York: St. Martin's Press, 1976. Paperback.

Actually, a history of the world, with pi as its focus. Most entertaining, as well as a useful reference on the history of mathematics.

* Bell, Eric Temple. Men of Mathematics. New York: Simon & Schuster, 1965.

Paperback. Perhaps the most romantic writer of all time on the history of mathematics.

He makes every life story read like a short novel. Nonmathematicians can come away with a true sense of the power, beauty, and meaning of mathematics.

Benacerraf, Paul. "God, the Devil, and Godel". Monist 51 (1967): 9. One of the most important of the many attempts at refutation of Lucas. All about mechanism and metaphysics, in the light of Godel's work.

Benacerraf, Paul, and Hilary Putnam. Philosophy of Mathematics-Selected Readings.

Englewood Cliffs, N. J.: Prentice-Hall, 1964. Articles by Godel, Russell, Nagel, von Index

VII

Neumann, Brouwer, Frege, Hilbert, Poincare, Wittgenstein, Carnap, Quine, and others on the reality of numbers and sets, the nature of mathematical truth, and so on.

* Bergerson, Howard. Palindromes and Anagrams. New York: Dover Publications, 1973.

Paperback. An incredible collection of some of the most bizarre and unbelievable wordplay in English. Palindromic poems, plays, stories, and so on.

Bobrow, D. G., and Allan Collins, eds. Representation and Understanding: Studies in Cognitive Science. New York: Academic Press, 1975. Various experts on Artificial Intelligence thrash about, debating the nature of the elusive "frames", the question of procedural vs. declarative representation of knowledge, and so on. In a way, this book marks the start of a new era of Al: the era of representation.

* Boden, Margaret. Artificial Intelligence and Natural Man. New York: Basic Books, 1977. The best hook I have ever seen on nearly all aspects of Artificial Intelligence, including technical questions, philosophical questions, etc. It is a rich book, and in niv opinion, a classic. Continues the British tradition of clear thinking and expression on matters of mind, free will, etc. Also contains an extensive technical bibliography.

. Purposive Explanation in Psychology. Cambridge, Mass.: Harvard University Press, 1972. The book to which her Al book is merely- "an extended footnote", says Boden.

* Boeke, Kees. Cosmic View: The Universe in 40 Jumps. New York: John Day, 1957.

The ultimate book on levels of description. Everyone should see this book at some point in their life. Suitable for children.

** Bongard, M. Pattern Recognition. Rochelle Park, N. J.: Hay den Book Co., Spartan Books, 1970. The author is concerned with problems of determining categories in an ill-defined space. In his book, he sets forth a magnificent collection of 100 "Bongard problems" (as I call them)-puzzles for a pattern recognizer (human or machine) to test its wits on. They are invaluably stimulating for anyone whoo is interested in the nature of intelligence.

Boolos, George S., and Richard Jeffrey. Computability and Logic. New York: Cambridge University Press. 1974. A sequel to Jeffrey's Formal Logic. It contains a wide number of results not easily obtainable elsewhere. Quite rigorous, but this does not impair its readability.

Carroll, John B., Peter Davies, and Barry Rickman. The American Heritage Word Frequency Book. Boston: Houghton Mifflin, and New York: American Heritage Publishing Co., 1971. A table of words in order of frequency in modern written American English. Perusing it reseals fascinating things about out- thought processes.

Cerf, Vinton. "Parry Encounters the Doctor". Datamation, July 1973, pp. 62-64. The first meeting of artificial "minds"-what a shock!

Chadwick, John. The Decipherment of Linear B. New York: Cambridge University Press, 1958. Paperback. A book about a classic decipherment-that of a script from the island of Crete-done by a single man: Michael Ventris.

Chaitin, Gregory J. "Randomness and Mathematical Proof"'. Scientific American, May 1975. An article about an algorithmic definition of randomness, and its intimate relation to simplicity. These two concepts are tied in with Godel's Theorem, which assumes a new meaning. An important article.

Cohen, Paul C. Set Theory and the Continuum Hypothesis. Menlo Park, Calif.: W. A.

Benjamin, 1966. Paperback. A great contribution to modern mathematics-the demonstration that various statements are undecidable within the usual formalisms for Index

VIII

set theory-is here explained to nonspecialists by its discoverer. The necessary prerequisites in mathematical logic are quickly, concisely, and quite clearly presented.

Cooke, Deryck. The Language of Music. New York: Oxford University Press, 1959.

Paperback. The only book that I know which tries to draw an explicit connection between elements of music and elements of human emotion. A valuable start down what is sure to be a long hard road to understanding music and the human mind.

* David, Hans Theodore.J. S. Bach's Musical Offering. New York: Dover Publications, 1972. Paperback. Subtitled "History, Interpretation, and Analysis". A wealth of information about this tour de force by Bach. Attractively written.

** David, Hans Theodore, and Arthur Mendel. The Bach Reader. New York: W. W.

Norton, 1966. Paperback. An excellent annotated collection of original source material on Bach's life, containing pictures, reproductions of manuscript pages, many short quotes from contemporaries, anecdotes, etc., etc.