Gödel, Escher, Bach: An Eternal Golden Braid (139 page)

* Kim, Scott E. "The Impossible Skew Quadrilateral: A Four-Dimensional Optical Illusion". In David Brisson, ed. Proceedings of the 1978 A.A.A.S. Sym osium on Hypergraphics: Visualizing Complex Relationships in Art and Science. Boulder, Colo.: Westview Press, 1978. What seems at first an inconceivably hard idea-an optical illusion for four-dimensional "people"-is gradually made crystal clear, in an amazing virtuoso presentation utilizing a long series of excellently executed diagrams. The form of this article is just as intriguing and unusual as its content: it is tripartite on many levels simultaneously. This article and my book developed in parallel and each stimulated the other.

Kleene, Stephen C. Introduction to Mathematical Logic. New York: John Wiley, 1967. A thorough, thoughtful text by an important figure in the subject. Very worthwhile. Each time I reread a passage, I find something new in it which had escaped me before.

. Introduction to Metamathematics. Princeton: D. Van Nostrand (1952). Classic work on mathematical logic; his textbook (above) is essentially an abridged version. Rigorous and complete, but oldish.

Kneebone G. J. Mathematical Logic and the Foundations of Mathematics. New York: Van Nostrand Reinhold, 1963. A solid book with much philosophical discussion of such topics as intuitionism, and the "reality" of the natural numbers, etc.

Koestler, Arthur. The Act of Creation, New York: Dell, 1966. Paperback. A wide-ranging and generally stimulating theory about how ideas are "bisociated" to yield novelty. Best to open it at random and read, rather than begin at the beginning.

Koestler, Arthur and J. R. Smythies, eds. Beyond Reductionism. Boston: Beacon Press, 1969. Paperback. Proceedings of Yr conference whose participants all were of the opinion that biological systems cannot be explained reductionistically, and that there is something "emergent" about life. I am intrigued by books which seem wrong to me, yet in a hard-to-pin-down way.

** Kutbose, Gyomay. Zen Koans. Chicago: Regnerv, 1973. Paperback. One of the best collections of koans available. Attractively presented- An essential book for any Zen library. Kuffler, Stephen W. and John G. Nicholls. From Neuron to Brain. Sunderland, deals Mss.: Smauer Associates, 1976. Paperback. A book which, despite its title, deals mostly with microscopic processes in the brain, and quite little with the way people's thoughts come out of the tangled mess. The work of Hubel and Wiesel on visual systems is covered particularly well.

Index

XIII

Lacey Huh, and Geoffrey Joseph. "What the Godel Formula Says". Mind 77 (1968)- 7~.

A useful discussion of the meaning of the Godel formula, based on a strict separation of three

levels:

uninterpreted

formal

system,

interpreted

formal

system,

a

metamathematics. Worth studying. Latos Imre. Proofs and Refutations. New York: Cambridge University Press, 1976. Paperback. A most entertaining book in dialogue form, discussing how concepts are formed in mathematics. Valuable not only to mathematicians, but also to people interested in thought processes.

** Lehninger, Albert. Biochemistry. New York: Worth Publishers, 1976. A wonderfully readable text, considering its technical level. In this book one can find many ways in which proteins and genes are tangled together. Well organized, and exciting.

** Lucas, J. R. "Minds, Machines, and Godel". Philosophy 36 (1961): 112. This article is reprinted in Anderson's Minds and Machines, and in Sayre and Crosson's The Modeling of Mind. A highly controversial and provocative article, it claims to show that the human brain cannot, in principle, be modeled by a computer program. The argument is based entirely on Godel's Incompleteness Theorem, and is a fascinating one. The prose is (to my mind)

incredibly infuriating-vet for that very reason, it makes humorous reading. "Satan Stultified: A Rejoinder to Paul Benacerraf". Monist 52 (1968): 145.

Anti-Benacerraf argument, written in hilariously learned style: at one point Lucas refers to Benacerraf as "self-stultifyingly eristic" (whatever that means). The Lucas-Benacerraf battle, like the Lucas-Good battle, offers much food for thought.

. "Human and Machine Logic: A Rejoinder". British Journal for the Philosophy of Science 19 (1967): 155. An attempted refutation of Good's attempted refutation of Lucas' original article.

** MacGillavry, Caroline H. Symmetry Aspects of the Periodic Drawings of M. C.

Escher. Utrecht: A. Oosthoek's Uitgevermaatschappij, 1965. A collection of tilings of the plane by Escher, with scientific commentary by a crystallographer. The source for some of my illustrations-e.g., the Ant Fugue and the Crab Canon. Reissued in 1976 in New York by Harry N. Abrams under the title Fantasy and Symmetry.

MacKay, Donald M. Information, Mechanism and Meaning. Cambridge, Mass.: M.I.T.

Press, 1970. Paperback. A book about different measures of information, applicable in different situations; theoretical issues related to human perception and understanding; and the way in which conscious activity can arise from a mechanistic underpinning.

• Mandelbrot, Benoit. Fractals: Form, Chance, and Dimension. San Francisco: W. H.

Freeman, 1977. A rarity: a picture book of sophisticated contemporary research ideas in mathematics. Here, it concerns recursively defined curves and shapes, whose dimensionality is not a whole number. Amazingly, Mandelbrot shows their relevance to practically every branch of science.

• McCarthy, John. "Ascribing Mental Qualities to Machines". To appear in Martin Ringle, ed. Philosophical Perspectives in Artificial Intelligence. New York: Humanities Press, 1979. A penetrating article about the circumstances under which it would make sense to say that a machine had beliefs, desires, intentions, consciousness, or free will.

It is interesting to compare this article with the book by Griffin.

Meschkowski, Herbert. Non-Euclidean Geometry. New York: Academic Press, 1964.

Paperback. A short book with good historical commentary.

Index

XIV

Meyer, can. ' Essai d'application de certains modeles cybernetiq ues it la coordina_ Lion c1Jei les insectes sociaux". Insertes Sociaux XI11, no. 2 1966 : o which ch aws some parallels between the neural organization in the( brain, and the organiz ae lion of an ant colon%.

Meyer, Leonard B. Emotion and Meaning in Music. Chicago: University of' Chicago Press, 1956. Paperback. A book which attempts to use ideas of Gestalt svcholo theory of perception to explain why musical structure is as it is. One of the more unusual the books on music and mind.

. Music, The Arts, and Ideas. Chicago: University of Chicago Press, 1967. Paperback. A thoughtful analysis of mental processes involved in listening to music, and of hierarchical structures in music. The author compares modern trends in music with Zen Buddhism.

Miller, G. A. and P. N. joint son-Laird. Language and Perception- Cambridge, Mass.: Harvard University Press, Belknap Press, 1976. A fascinating compendium of linguistic facts and theories, hearing on Whorl 's hypothesis that language is the same as worldviesv. A typical example is the discussion of the weird "mother-in-law" language of the Dyirbal people of Northern Queensland: a separate language used only for speaking to one's mother-in-law.

Minsky, Marvin L. "Matter, Mind, and Models". In Marvin L. Minskv, ed. Son antic Information Processing. Cambridge, Mass.: M.I.T. Press, 1968. Though merely a few pages long, this article implies a whole philosophy of consciousness and machine intelligence. It is a memorable piece of writing by one of the deepest thinkers in the field.

Minsky, Marvin L., and Seymour Papert_ .92-t cial Intelligence Progress Report.

Cambridge, Mass.: M.I.T. Artificial Intelligence Laboratory, Al Memo 252, 1972. A survey of all the work in Artificial Intelligence done at M.I.T. up to 1972, relating it to psychology and epistemology. Could serve excellently as an introduction to Al.

Monod, Jacques. Chance and Necessity. New York: Random House, Vintage Books, 1971. Paperback. An extremel fertile mind writing in an idiosyncratic way about fascinating questions, such as how life is constructed out of non-life: how evolution, seeming_ to violate the second law of thermodynamics, is actually dependent on it. The book excited me deeply.

* Morrison, Philip and Emil, eds. Charles Babbage and his Calculating Engines. Nesv York: Dover Publications, 1961. Paperback. A valuable source of information about the life of Babbage. A large fraction of Babbage's autobiography is reprinted here, along with several articles about Babbage's machines and his "Mechanical Notation".

Mvhill, John. "Some Philosophical Implications of Mathematical Logic". Review of Metaphysics 6 (1952): 165. An unusual discussion of ways in which Godel's Theorem and Church's Theorem are connected to psychology and epistemology. Ends up in a discussion of beauty and creativity.

Nagel, Ernest. The Structure of Science. New York: Harcourt, Brace, and World, 1961. A classic in the philosophy of science, featuring clear discussions of reductionism vs.

holism, teleological vs. nonteleological explanations, etc.

Nagel, Ernest and James R. Newman. Godel's Proof. New York: New York University Press, 1958. Paperback. An enjoyable and exciting presentation, which was, in many ways, the inspiration for my own book.

Index

XV

* Nievergelt, Jurg, J. C. Farrar, and E. M. Reingold. Computer Approaches to Mathe,nat teal Problems. Englesyood Clif-f-s, N. J.: Prentice-Hall, 1974. An unusual collection of different types of problems which can be and have been attacked on computers-for instance, the "3n + I problem" (mentioned in my Rria with Diverse Variations) and other problems of number theory.

Pattee, Howard H., ed. Hierarchy Theory. New York: George Braziller, 1973. Paperback.

Subtitled "The Challenge of Complex Systems". Contains a good article by Herbert Simon covering some of the same ideas as does my Chapter on "Levels of Description".

Peter, R6zsa. Recursive Functions. New York: Academic Press, 1967. A thorough discussion of primitive recursive functions, general recursive functions, partial recursive functions, the diagonal method, and many other fairly technical topics.

Quine, Willard Van Ornman. The Ways of Paradox, and Other Essays. New York: Random House, 1966. A collection of Quine's thoughts on many topics. The first essay deals with carious sorts of paradoxes, and their resolutions. In it, he introduces the operation I call "quining" in my book.

lishiRanganathan, S. R. Ramanujan, The Man and the Mathematician. London: Asia Pubng House, 1967. An occult-oriented biography of the Indian genius by an admirer.

An odd but charming book.

Reichardt. Jasia. Cybernetics, Arts, and Ideas. Boston: New York Graphic Society, 197 1. A weird collection of ideas about computers and art, music, literature. Some of it is definitely off the deep end-hut some of it is not. Examples of the latter are the articles

"A Chance for Art" by J. R. Pierce, and "Computerized Haiku" by Margaret Masterman.Renyi, Alfred. Dialogues on Mathematics. San Francisco: Holden-Day, 1967. Paper hack. Three simple but stimulating dialogues involving classic characters in history, trying to get at the nature of mathematics. For the general public.

** Rips Paul. Zen Flesh, Zen Bones. New York: Doubleday, Anchor Books. Paperback.

This book imparts very well the flavor of Zen-its antirational, antilanguage, antireduc iionistic, basically holistic orientation.Rogers, Hartley. Theory of Recursive Functions and Effective Computability. New York:McGraw-Hill, 1967. A highly technical treatise, but a good one to learn from. Containsdiscussions of many intriguing problems in set theory and recursive function theory.

Rokeach, Milton. The Three Christs of' Ypsilanti. New York: Vintage Books, 1964.paperback. A study of schizophrenia and the strange breeds of "consistency"

which arise in the afflicted. A fascinating conflict between three men in a mental institution, all of whom imagined they were God, and how they dealt with being brought face to face for many months.

Rose, Steven. The Conscious Brain, updated ed. New York: Vintage Books, 1976.

Paperback. An excellent book-probably the best introduction to the study of the brain.

Contains full discussions of the physical nature of the brain, as well as philosophical discussions on the nature_ of mind, reductionism vs. holism, free will vs. determinism, etc. from a broad, intelligent, and humanistic viewpoint. Only his ideas on Al are way off.

Rosenblueth, Arturo. Mind and Brain: A Philosophy of Science. Cambridge, Mass.:M.I.T. Press, 1970. Paperback. A well written book by a brain researcher who deals with most of the deep problems concerning mind and brain.

Index

XVI

* Sagan, Carl, ed. Communication with Extraterrestrial Intelligence. Cambridge, Mass.: M.I.T. Press, 1973. Paperback. Transcripts of a truly far-out conference, where a stellar group of scientists and others battle it out on this speculative issue.

Salmon, Wesley, ed. Zeno's Paradoxes. New York: Bobbs-Merrill, 1970. Paperback. A collection of articles on Zeno's ancient paradoxes, scrutinized under the light of modern set theory, quantum mechanics, and so on. Curious and thought-provoking, occasionally humorous.

Sanger. F., et al. "Nucleotide sequence of bacteriophage 16X174 DNA", Nature 265