McCorduck, Pamela. Machines Who Think. San Francisco: W. H. Freeman, 1979.
Mettrie, Julien Offray de la. Man a Machine. La Salle, Illinois: Open Court, 1912.
Metzinger, Thomas. Being No One: The Self-Model Theory of Subjectivity. Cambridge, Mass.: MIT Press, 2003.
Miller, Fred D. and Nicholas D. Smith. Thought Probes: Philosophy through Science Fiction. Englewood Cliffs: Prentice-Hall, 1981.
Minsky, Marvin. The Society of Mind. New York: Simon & Schuster, 1986.
— — — . The Emotion Machine. New York: Simon & Schuster, 2006.
Monod, Jacques. Chance and Necessity. New York: Vintage Press, 1972.
Moravec, Hans. Robot: Mere Machine to Transcendent Mind. New York: Oxford University Press, 1999.
Morden, Michael. “Free will, self-causation, and strange loops”. Australasian Journal of Philosophy 68 (1990), pp. 59–73.
Nagel, Ernest and James R. Newman. Gödel’s Proof. New York: New York University Press, 1958. (Revised edition, edited by Douglas R. Hofstadter, 2001.)
Neumann, John von. Theory of Self-Reproducing Automata (edited and completed by Arthur W. Burks). Urbana: University of Illinois Press, 1966.
Niven, Ivan and Herbert S. Zuckerman. An Introduction to the Theory of Numbers. New York: John Wiley & Sons, 1960.
Nørretranders, Tor. The User Illusion. New York: Viking, 1998.
Nozick, Robert. Philosophical Explanations. Cambridge, Mass.: Harvard University Press, 1981.
Pais, Abraham. Inward Bound: Of Matter and Forces in the Physical World. New York: Oxford University Press, 1986.
— — — . Niels Bohr’s Times. New York: Oxford University Press, 1991.
Parfit, Derek. Reasons and Persons. New York: Oxford University Press, 1984.
Pattee, Howard H. Hierarchy Theory: The Challenge of Complex Systems. New York: Braziller, 1973.
Peitgen, H.-O. and P. H. Richter. The Beauty of Fractals. New York: Springer, 1986.
Penfield, Wilder and Lamar Roberts. Speech and Brain-Mechanisms. Princeton: Princeton University Press, 1959.
Penrose, Roger. The Emperor’s New Mind. New York: Oxford University Press, 1989.
Perry, John (ed.). Personal Identity. Berkeley: University of California Press, 1975.
Péter, Rózsa. Recursive Functions. New York: Academic Press, 1967.
Pfeiffer, John. The Human Brain. New York: Harper Bros., 1961.
Poundstone, William. The Recursive Universe. New York: William Morrow, 1984.
Pullman, Bernard. The Atom in the History of Human Thought. New York: Oxford University Press, 1998.
Pushkin, Alexander S. Eugene Onegin: A Novel in Verse (translated by James Falen). New York: Oxford University Press, 1995.
— — — . Eugene Onegin: A Novel Versification (translated by Douglas Hofstadter). New York: Basic Books, 1999.
Quine, Willard Van Orman. The Ways of Paradox, and Other Essays. Cambridge, Mass.: Harvard University Press, 1976.
Ringle, Martin. Philosophical Perspectives in Artificial Intelligence. Atlantic Highlands: Humanities Press, 1979.
Rucker, Rudy. Infinity and the Mind. Boston: Birkhäuser, 1982.
Sander, Emmanuel. L’analogie, du Naïf au Créatif: Analogie et Catégorisation. Paris: Éditions L’Harmattan, 2000.
Schank, Roger C. Dynamic Memory. New York: Cambridge University Press, 1982.
Schweitzer, Albert. Aus Meiner Kindheit und Jugendzeit. Munich: C. H. Beck, 1924.
Searle, John. “The Myth of the Computer” (review of The Mind’s I ). The New York Review of Books, April 29, 1982, pp. 3–6.
Shanker, S. G. (ed.). Gödel’s Theorem in Focus. New York: Routledge, 1988.
Simon, Herbert A. The Sciences of the Artificial. Cambridge, Mass.: MIT Press, 1969.
Singer, Peter and Jim Mason. The Way We Eat: Why Our Food Choices Matter. Emmaus, Pennsylvania: Rodale Press, 2006.
Skinner, B. F. About Behaviorism. New York: Random House, 1974.
Smullyan, Raymond M. Theory of Formal Systems. Princeton: Princeton Univ. Press, 1961.
— — — . The Tao Is Silent. New York: Harper & Row, 1977.
— — — . What Is the Name of This Book? Englewood Cliffs, New Jersey: Prentice-Hall, 1978.
— — — . This Book Needs No Title. Englewood Cliffs, New Jersey: Prentice-Hall, 1980.
— — — . 5000 B.C. and Other Philosophical Fantasies. New York: St. Martin’s Press, 1983.
— — — . Gödel’s Incompleteness Theorems. New York: Oxford University Press, 1992.
Sperry, Roger. “Mind, Brain, and Humanist Values”, in John R. Platt (ed.), New Views on the Nature of Man. Chicago: University of Chicago Press, 1965.
Steiner, George. After Babel. New York: Oxford University Press, 1975.
Stewart, Ian. Galois Theory (second edition). New York: Chapman and Hall, 1989.
Suppes, Patrick C. Introduction to Logic. New York: Van Nostrand, 1957.
Thigpen, Corbett H. and Hervey M. Cleckley. The Three Faces of Eve. New York: McGraw-Hill, 1957.
Treisman, Anne. “Features and Objects: The Fourteenth Bartlett Memorial Lecture”. Cognitive Psychology 12, no. 12 (1980), pp. 97–136.
Ulam, Stanislaw. Adventures of a Mathematician. New York: Scribner’s, 1976.
Unger, Peter. “Why There Are No People”. Midwest Studies in Philosophy, 4 (1979).
— — — . “I Do Not Exist”. In G. F. MacDonald (ed.), Perception and Identity. Ithaca: Cornell University Press, 1979.
Wadhead, Rosalyn. The Posh Shop Picketeers. Tananarive: Wowser & Genius, 1931.
Webb, Judson. Mechanism, Mentalism, and Metamathematics. Boston: D. Reidel, 1980.
Weinberg, Steven. Dreams of a Final Theory. New York: Pantheon, 1992.
— — — . Facing Up. Cambridge, Mass.: Harvard University Press, 2001.
Wells, David G. The Penguin Dictionary of Curious and Interesting Numbers. New York: Viking Penguin, 1986.
— — — . Prime Numbers. New York: John Wiley & Sons, 2005.
Wheelis, Allen. The Quest for Identity. New York: W. W. Norton, 1958.
Whitehead, Alfred North and Bertrand Russell. Principia Mathematica, Volumes I–III. London: Cambridge University Press, 1910–1913.
Wilder, Raymond L. Introduction to the Foundations of Mathematics. New York: John Wiley & Sons, 1952.
Wolf, Robert S. A Tour through Mathematical Logic. Washington, D.C.: The Mathematical Association of America, 2005.
Wooldridge, Dean. Mechanical Man: The Physical Basis of Intelligent Life. New York: McGraw-Hill, 1968.
Wynne, Clive D. L. Do Animals Think? Princeton: Princeton University Press, 2004.
Yourgrau, Palle. A World Without Time: The Forgotten Legacy of Gödel and Einstein. New York: Basic Books, 2005.
PERMISSIONS AND ACKNOWLEDGMENTS
GRATEFUL acknowledgement is hereby made to the following individuals, publishers, and companies for permission to use material that they have provided or to quote from sources for which they hold the rights. Every effort has been made to locate the copyright owners of material reproduced in this book. Omissions that are brought to our attention will be corrected in subsequent editions.
Thanks to William Frucht for the cover photograph of video feedback and for all the photographs in the color insert in Chapter 4.
Thanks to Daniel Hofstadter and Monica Hofstadter for photographs of various loopy structures, used as interludes between chapters.
Thanks to Kellie and Richard Gutman for two photographs in Chapter 4.
Thanks to Jeannel King for her poem “Ode to a Box of Envelopes” in Chapter 7.
Thanks to Silvia Sabatini for the photograph of the lap loop in Anterselva di Mezzo, facing Chapter 8.
Thanks to Peter Rimbey for the photograph of Carol and Douglas Hofstadter facing Chapter 16.
Thanks to David Oleson for his parquet deformation “I at the Center” in Chapter 17.
“Three Kangaroos” logo, designed by David Lance Goines © R
avenswood Winery. Reprinted with permission by Joel Peterson, Ravenswood Winery.
“Three Ravens” logo, designed by David Lance Goines © Ravenswood Winery. Reprinted with permission by Joel Peterson, Ravenswood Winery.
“Peanuts” cartoon, dated 08/14/1960: © United Feature Syndicate, Inc. Reprinted with permission by United Media.
M. C. Escher, Drawing Hands © 2006 M. C. Escher Company, Holland. All rights reserved. www.mcescher.com. Reprinted with permission.
Whitehead, Alfred North and Bertrand Russell, Principia Mathematica (second edition), Volume I (1927), page 629, reprinted in 1973 © Cambridge University Press.
“Nancy” cartoon: “Sluggo dreaming”: © United Feature Syndicate, Inc. Reprinted with permission by United Media.
Morton Salt “Umbrella Girl” © Morton International, Inc. Reprinted with permission of Morton International, Inc.
Excerpt from Karen Horney, Our Inner Conflicts, © 1945 by W. W. Norton & Co., Inc. Reprinted with permission by W. W. Norton & Company.
Excerpts from Daniel Dennett, Consciousness Explained © 1991 by Daniel C. Dennett. Reprinted with permission by Hachette Book Group USA.
Excerpt from Carson McCullers, The Heart Is a Lonely Hunter. Copyright © 1940, renewed 1967, by Carson McCullers. Reprinted by permission of Houghton Mifflin Company. All rights reserved.
Excerpts from Derek Parfit, Reasons and Persons © 1984 Oxford University Press. Reprinted with permission of Oxford University Press.
Excerpts from Albert Schweitzer, Aus meiner Kindheit und Jugendzeit. © C. H. Beck, Munich, 1924. Personal translation for use in this book only, by Douglas Hofstadter. Reprinted with permission.
INDEX
A
abbreviations piled on abbreviations
aboutness, double, of Gödel’s formula
absorbing someone else’s essence
“abstraction ceiling” in author’s mind
abstractions: as causes; centrality of: formidable tower of, in human minds
abstractly swirling patterns
accidents in mathematics: absence of; possibility of
accretion: of self-model; of soul
Ackermann’s function
active symbols, see symbols
affinity of souls, see chemistry (interpersonal)
afterglow of a soul
Aimable, the village baker
“alacrity, celerity, assiduity”, etc.
Alfbert, the; dream of
Alf and Bertie’s Posh Shop
algorithmic information theory
Ali, Muhammad
Alienware machine, emulated by Macintosh
Alighieri, Dante
alignment: of PM theorems and code numbers; of truths and PM theorems; of two souls in married couple dedicated to common goals
allegoric license
“Alle Menschen Müssen Sterben” (Bach)
Alzheimer’s disease
ambiguity of operations inside computers
américain, pronunciation of the word in movie
amino acids
amplification of input in audio feedback; saturation of
analogies: central role of, in this book; as fabric of human thought; having force proportional to precision and visibility; index entries for; jumping out automatically; made by bees; as mediating reference; research on; retrieved automatically by new events; rivalry between two similar ones; seen as simmball patterns in the careenium; self-referential; as source of meaning; tossed off effortlessly; trivial-seeming examples; by W. V. O. Quine
analogies, serious examples of: between Alfbert and Whitehead/Russell; between audio and video feedback; between Aurélie and Pomponnette; between the author’s mind and others’ minds; between the author’s view of “I” and quantum mechanics; between beer cans and neurons; between brain and oil refinery; between brains and countries; between brains and PM as substrates for strange loops; between brain structures and genes or atoms; between butterfly swarms and souls; between careenium and brain; between careenium and pinball machine; between cars and dogs; between Chantal looking at movie and Russell looking at Gödel’s formula; between children with muddy boots; between cookies on same plate; between couples; between crystal and orchard; between death and eclipse; between decision-making and political elections; between dedicated machines and music boxes; between dog looking at pixels and Russell looking at Gödel’s formula; between domino chainium and traffic jam; between donning piece of clothing and identifying with someone else; between Doug and Carol; between edibility and provability; between electron clouds and human souls; between entwined video loops and entwined souls; between epiphenomena in brain and in mineral; between formula containing own Gödel number and elephant in matchbox; between gems in Caspian Sea and powers in Fibonacci sequence; between genes and novels; between Gödel’s construction and black-belt judo maneuver; between Gödel number k and Morton Salt can; between Gödel’s strange loop and video feedback; between grapplings with death and beautiful sailboat; between growing soul and accreting planetoid; between Guru and Göru; between heart and brain; between heart-shaped bread and heart on collar; between human soul and train; between “I” and dollar bill; between “I” and either “i” or “Twe”; between “I” and “Epi”; between “I” and video-feedback galaxy; between Imp and KG; between K. Gödel’s article on Principia Mathematica and G. Külot’s review of Prince Hyppia: Math Dramatica; between Klüdgerot and Kurt Gödel; between Leafpilishness and Consciousness; between learning to be someone else and learning a foreign language; between leg-tingles and ants (and ginger ale); between life and hedge maze; between listener not relating to Bartók and magnetic field not penetrating superconductor; between mosquito and flush toilet; between mosquito and heat-seeking missile; between mosquito and red spot; between naïve careenium and young Doug; between Newtonian physics and naïve view of self; between oneself and others; between pairsons and persons; between Parfit and Einstein; between picket lines in play and outside theater; between pieces of cake; between pixel patterns and events; between PM and sinking boat; between prim numbers and prime numbers; between Principia Mathematica and invaded fortress; between quoted phrases and Gödel numbers; between recursion and plant growth; between recursive sequences of numbers and PM theorems; between robot vehicle and an ant; between Rosalyn Wadhead and Russell and Whitehead; between salt box and picture of salt box; between salt-box picture and Gödel’s self-referential trick; between saucy numbers and unpennable lines in plays; between self-reference and self-replication; between self-symbol and video feedback; between Sluggo dreaming of himself and self-quoting sentence; between “soap digest rack” spelled out in Sanskrit and Gödel’s formula spelled out in PM notation; between souledness and tallness; between Sperry’s and Gödel’s balancing acts; between strange loops and selves; between symbols in brain and books in library; between uninteresting number and Berry’s number; between universal machines and chameleonic integers; between universal machines and people; between unpennable lines and unprovable strings; between unscalability of KJ and unprovability of KG; between video feedback and iteration in complex plane; between windmill and thoughtmill; between Xerxes’ breath and Yolanda’s breath; between Y. Ted Enrustle and Whitehead and Russell
Andromeda galaxy
animacy, found in inanimate substrate
animals: killing of; self-awareness of
another soul, living inside oneself
ant: crossing property lines; rescued; Schweitzer’s personal
Antarctica, reality of
Anterselva di Mezzo
anthropomorphic language, temptation of
ants’ disrespect for property lines
“ants in my leg”
“Anything you can docan do meta”
arbitrarily extensible repertoires of categoriessee also concepts, symbols
arbitrarily subtle properties of whole numbers; see also universality
arbitrary mapping between stimuli and sensations
Archimedes
arithmetization of PM formulas
Arnheim, Rudi and Mary
Around the World in Eighty Days
arrangement as cause
artificial “I”, still far off
artificial intelligence; see also robots
“ashes to ashes, dust to dust”
atomes crochus, avoir des (“having hooked atoms”), as French for interpersonal chemistry
atoms as abstract entities
audio feedback; pitch of; vanilla loop in
Aurélie, straying wife
Aus meiner Kindheit und Jugendzeit (Schweitzer)
Austen, Jane
Austranius
authority, arguments by
Avogadro’s number
awareness: of dance of symbols; levels of, compared; see also consciousness, perception
axioms: analogous to seeds in recursion; as top lines of PM proofs
B
b (Berry’s number)
Babbage, Charles
baby: impoverished perceptual system of; lack of self at birth or conception
Bach, Johann Sebastian; cantata by; organ music by; tricentennial birthday party for
“bachelor”, elusiveness of concept
bad-breath analogy
bandwidth of communication as determinant of degree of interpenetration
banishment of toy guns from household
barber paradox
barberry jelly
“bare” strange loop of selfhood
barking, reverberant
Bartók, Béla; violin concerto # 2
baseball and football sensations swapped
Baskerville, John
basketball: skill in, as part of self-symbol; unpredictability of, when tossed
Beardsley, Dick
beauty, as bedrock cause for humans
“because” coinciding with “although”
Bechet, Sidney
beer cans and ping-pong balls as substrate for thinking
bees, swarm of, opposing caged-bird metaphor
Beethoven, Ludwig van
behaviors, attempted and evaluated
being: in two places at the same time; at two times in the same place
I Am a Strange Loop Page 53
