220 “mathematical problems”: Hodges, Enigma, 341.
220 looked like a beetle: Ibid., 375.
221 use “as much of”: Quoted ibid., 375.
222 “machinery might be”: Turing, “Intelligent Machinery,” 107.
222 “an unwillingness”: Ibid., 107–8.
222 “being purely emotional”: Ibid., 108.
223 “can go on through”: Ibid.
223 “It is related that”: Ibid., 108–9.
224 “that intelligence in machinery”: Ibid., 107.
224 “the view that the credit”: Ibid., 109.
224 “form a continuous”: Ibid.
224 “intended to produce”: Ibid.
224 “discrete controlling”: Ibid., 110.
225 “A great positive reason”: Ibid. 116–17.
226 “take a man as a whole”: Ibid., 117.
226 five possible applications: Ibid.
227 “The training of the human child”: Ibid., 121.
228 “If the untrained infant’s mind”: Ibid., 125.
228 “the machine very soon”: Ibid., 123.
229 “Certainly the nerve”: Ibid., 117.
229 “is determined as much”: Ibid., 127.
7: The Imitation Game
231 “late lavatorial”: Quoted in Hodges, Enigma, 391.
231 “carpeted in”: W. G. Sebald, The Emigrants, trans. Michael Hulse (New York: New Directions, 1996), 151.
232 “to a number”: Turing, “Programmer’s Handbook (2nd Edition) for the Manchester Electronic Computer Mark II,” http://www.computer50.org/kgill/mark1/program.html, 3.
232 “saddled users”: Martin Campbell-Kelly, “Turing’s Papers on Programming,” Mathematical Logic, 244.
232 “Because zero was”: Ibid., 245.
233 “bizarre in the extreme”: Ibid.
234 Lucas’s method: Hodges, Enigma, 398.
234 “As every vehicle”: Quoted ibid., 402; from an interview with Martin Campbell-Kelly.
236 “Not until a machine”: British Medical Journal, June 25, 1949; quoted in Hodges, Enigma, 405.
237 “create concepts”: “No Mind for Mechanical Man,” Times (London), June 10, 1949, 2.
237 “This is only a foretaste”: “The Mechanical Brain,” Times (London), June 11, 1949, 4.
238 “Isn’t that just like”: S. Turing, Alan M. Turing, 91.
238 “The university was”: “The Mechanical Brain,” 4.
239 “the rather mysterious description”: “The Mechanical Brain: Successful Use of Memory-Storage,” Times (London), June 14, 1949, 5.
239 “responsible scientists”: Illtyd Trethowan, letter to the editor, Times (London), June 14, 1949, 5.
239 “There would be plenty to do”: “Intelligent Machinery: A Heretical Theory,” in S. Turing, Alan M. Turing, 133–34.
240 “those who have never loved”: “Umbrage of Parrots,” Times (London), June 16, 1949, 5.
241 “I propose to consider”: Turing, “Computing Machinery and Intelligence,” 133.
241 “is played with three people”: Ibid., 133–34.
243 “Turing’s gender-guessing”: Hodges, Natural Philosopher, 38.
243 “The new problem”: Turing, “Computing Machinery and Intelligence,” 134–35.
244 “It might be urged”: Ibid., 135.
244 “I put it to you”: Turing Archive, AMT/B/6, 6.
245 “we wish to exclude”: Turing, “Computing Machinery and Intelligence,” 135–36.
245 “Scudder, why do you think”: Forster, Maurice, 194.
246 “domestic analogy”: Turing, “Computing Machinery and Intelligence,” 138.
246 “I believe that in about fifty years’ time”: Ibid, 142.
247 “the theological objection”: Ibid., 143.
248 “In attempting to construct”: Ibid.
248 “The consequences of”: Ibid., 144.
249 “the appropriate critical question”: Ibid., 145.
250 “This argument appears”: Ibid., 146.
250 “sure that Professor Jefferson”: Ibid.
250 “to discover whether someone”: Ibid.
251 “than be forced into”: Ibid., 147.
251 “Be kind, resourceful, beautiful”: Ibid., 147–48 (with some minor punctuation changes).
252 “There are, however, special remarks”: Ibid., 148.
252 “Do you eat oysters?”: Quoted in http://www.outsmartmagazine .com/issue/i06-02/tonycurtis.php.
253 “The claim that”: Turing, “Computing Machinery and Intelli-gence,” 148.
254 “Errors of functioning”: Ibid., 149.
254 “that a machine cannot”: Ibid.
254 “a computer can do whatever”: Ibid., 150.
254 “if we adhere to”: Ibid., 151.
254 “If each man had”: Ibid., 152.
255 “I have set up”: Ibid., 153.
255 “Unfortunately the statistical evidence”: Ibid., 153.
255 “Let us play”: Ibid.
256 “Then it will be natural”: Ibid., 153–54.
256 “presuppose any feelings”: Ibid., 157.
257 “the use of punishments”: Ibid.
257 “Instead of trying”: Ibid., 156.
257 “It will not, for instance”: Ibid.
258 “the imperatives that”: Ibid., 158.
258 “the rules which get changed”: Ibid.
258 “will eventually compete”: Ibid., 160.
259 “God Save the King”: Hodges, Enigma, 447.
260 “a negligible advance”: Turing, “Some Calculations of the Riemann Zeta-Function,” Pure Mathematics, 97.
8. Pryce’s Buoy
261 “I am so glad”: S. Turing, Alan M. Turing, 103.
261 “high emotional content”: Turing Archive, AMT/B/6, 26.
262 “the intervention of”: Ibid., 23.
262 “When the work”: Ibid., 33.
262 “a computing machine”: Ibid., 20.
262 “necessary for the machine”: Ibid., 28.
262 “more interested in curbing”: Ibid., 29.
263 “until he saw it touch”: Hodges, Enigma, 452.
263 “That old slow coach”: Turing Archive, AMT/B/6, 36.
264 “not interested in the fact”: Turing Archive, AMT/B/6, 5.
264 “Turing had arrived”: Newman, “Royal Society Memoir,” 278.
265 “he shared many jokes”: S. Turing, Alan M. Turing, 92. meeting Arnold Murray: Hodges, Enigma, 450. £50 worth of his belongings: Ibid., 454.
267 “do his worst”: Ibid., 455.
267 “Mr. Hall—you reckernize”: Forster, Maurice, 193.
267 “By God, if you’d spilt”: Ibid., 196.
268 “knew all about”: Hodges, Enigma, 456.
268 “I don’t think I really”: Turing Archive, AMT/D/14a, 1952.
270 “I have a delightful story”: Turing Archive, AMT/D/14a, 1953.
271 “Alec always felt”: Turing Archive, AMT/A/13, undated.
272 “He didn’t care to wear”: Ibid.
272 “had been out of work”: Ibid.
272 “very hungry and rather cold”: Ibid.
273 “That chap who was walking round”: Ibid.
273 “He didn’t smoke”: Ibid.
274 “‘Don’t mind if I do’”: Ibid.
274 “the door opened for you”: Ibid.
275 “You will by now have heard”: Turing Archive, AMT/A/15, June 6, 1954.
276 “There is not the slightest doubt”: Turing Archive, AMT/A/16, May 1, 1955.
276 “difficult to connect”: Turing Archive, AMT/A/17, June 13, 1954.
277 “I can confirm”: Turing Archive, AMT/A/17, Aug. 18, 1954.
277 “If I may say so”: Turing Archive, AMT/A/23, Sept. 24, 1960. Messages from the Unseen World: “The Letter Written by Robin Gandy to Max Newman in June 1954,” Mathematical Logic, 267.
279 “a new quantum mechanics”: Ibid., 266.
279 “No ma
thematician should ever”: Hardy, Apology, 70.
279 “involved an apple”: Hodges, Enigma, 129.
Further Reading
For any reader interested in learning more about Alan Turing, there is nowhere better to begin than with Andrew Hodges’ Alan Turing: The Enigma (Walker, 2000). This fine biography is at once shrewd, sensitive, and exhaustive—the sort of book that makes other books possible.
The most important of Turing’s papers—including “Computable Numbers” and “Mechanical Intelligence”—have been collected in The Essential Turing: The Ideas That Gave Birth to the Computer Age, edited by B. Jack Copeland and published by Oxford University Press on the occasion of what would have been the mathematician’s ninetieth birthday. Turing’s complete writings can be found in the four-volume Collected Works of A. M. Turing, published by North-Holland. Of particular interest are the volumes entitled Mathematical Logic (2001) and Mechanical Intelligence (1992). Turing’s letters, as well as letters to him and the drafts of some of his papers, are stored in the archives at King’s College, Cambridge. (I am indebted to Dr. Rosamund Moad for making these documents available to me.) A number of these can be consulted online at http://www.turing archive.org.
Surprisingly few books take on Turing as their exclusive subject. Concise introductions to Turing’s ideas can be found in Hodges’ Turing: A Natural Philosopher (Phoenix, 1997) and Jon Agar’s Turing and the Universal Machine (Icon, 2001). Alan Turing: Life and Legacy of a Great Thinker, edited by Christof Teuscher (Springer-Verlag, 2004), brings together essays (and a play) on Turing by, among others, Hodges, Martin Davis, Daniel Dennett, and Douglas Hofstadter.
Many of the other primary texts to which I refer have been collected in three useful omnibus volumes: The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, edited by Martin Davis (Dover, 1993); From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, edited by Jean van Heijenoort (Harvard University Press, 1967); and The Universal Turing Machine: A Half-Century Survey, edited by Rolf Herkin (Springer-Verlag, 1995). In addition, the interviews with Princeton mathematicians cited in chapter 4 can be consulted online at http://infoshare1.princeton.edu/libraries/firestone/rbsc/ finding_aids/mathoral/math.html. Finally, many documents from the period during which Turing worked at Manchester can be viewed at http://www. computer50.org.
For those interested in learning about the prehistory of computers, Martin Davis’s Engines of Logic: Mathematicians and the Origins of the Computer (Norton, 2000) provides a lucid and thorough introduction. I would also like to recommend David Berlinski’s The Advent of the Algorithm: The Three-Hundred Year Journey from an Idea to the Computer (Harvest, 2001). Good overviews of Gödel’s work include Gödel’s Proof, by Ernest Nagel and James R. Newman (New York University Press, 2001): Gödel: A Life of Logic, by John L. Casti and Werner DePauli (Basic Books, 2000), and Rebecca Goldstein’s Incompleteness: The Proof and Paradox of Kurt Gödel (Norton/Atlas, 2005). A diverting riff on Georg Cantor’s work on infinity, including the Diagonal argument, can be found in David Foster Wallace’s Everything and More: A Compact History of ` (Norton/Atlas, 2003). Jeremy J. Gray’s The Hilbert Challenge (Oxford University Press, 2000) offers a fascinating overview of Hilbert’s “program,” while Constance Reid’s Hilbert (Springer-Verlag, 1970) is a surprisingly moving account of this great mathematician’s life and work.
The year 2003 saw the publication of three equally readable, yet utterly distinct, books on the Riemann hypothesis: John Derbyshire’s Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (Joseph Henry Press), Marcus du Sautoy’s The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics (HarperCollins), and Karl Sabbagh’s The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics (Farrar, Straus, Giroux). These were joined, in 2005, by Dan Rockmore’s witty and engaging Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers (Pantheon, 2005). This last book, cleverly, puts the prime page numbers in boldface. Of the numerous accounts in print of Turing’s work at Bletchley Park during World War II, I would particularly recommend the one in Stephen Budiansky’s Battle of Wits: The Complete Story of Codebreaking in World War II (Touchstone, 2000). A “virtual tour” of Bletchley Park can be taken at http://www.bletchleypark.org.uk.
Since Turing’s death, numerous books and essays have appeared that interrogate, challenge, and extend his arguments. Of these, the most compelling—at least for me—are Roger Penrose’s The Emperor’s New Mind: Concerning Computers, Minds and the Laws of Physics (Oxford University Press, 1999) and John Searle’s Minds, Brains, and Science (Harvard University Press, 1984), which outlines the now infamous “thought experiment” of the Chinese room.
Lastly, the Alan Turing homepage at http://www.turing.org.uk/, as maintained by Andrew Hodges, remains a touchstone for anyone interested in the life and work of this great mathematician.
I am indebted to Jesse Cohen and Prabhakar Ragde for their help in the preparation of this book; to Jim Humphreys for pointing out some errors that I have corrected for the paperback edition and all future hardcover editions; and to Martin Davis, who has been gracious and patient enough to point out several occasions in which my less then precise language might lead to confusion. With his help, I hope that I have made this new revision of the book an improvement on the original in terms of lucidity and exactitude.
Index
Page numbers in italics refer to illustrations.
Page numbers in italics refer to illustrations.
Abel, Niels Henrik, 132
Aberdeen Proving Ground, Ballistic Research Laboratories at, 200
ACE (automatic computing engine), 201–17, 219, 221, 223, 224, 227, 263, 264
Ackermann, Wilhelm, 51
Alexander, Hugh, 178, 193, 269, 277
algebra, 50
algorithms, 49–51
Alice in Wonderland (Carroll), 228
a-machines, 56, 57–60, 66–83, 99, 108–9, 112
binary notational system used in, 69–72
circular vs. circle-free, 81–82, 83, 89–90, 91
coding system of, 79–80
configuration of, 58–59
sample sequences of, 71–77, 82
as Turing machine, 59, 241
universal machine as test of, 83–98
American Journal of Mathematics, 113
American Mathematical Society, 106
analog machines, 135, 142
anti-Semitism, 30n, 126n
Anti-War Council, 20
Apostles, 19, 103, 217
apple, poisoned, 140–41, 279–80
Apple Computers, 280
Apted, Michael, 158n
Arabic (denary), notation, 67, 69–70
“Architecture and the Architect” (Russo), 157–58
arithmetic, fundamental theorem of, 43
Army, U.S., 200
ars magna, 49
artificial intelligence, see machine intelligence
Aspray, William, 112, 113, 114, 121, 123
Association for Computing Machinery, 214n
Atkins, James, 20n, 279
atomic bomb, 133, 200
Austen, Jane, 195
automatic computing engine, see ACE
axioms, 33, 35, 44
Babbage, Charles, 55–56, 59, 162, 201–2, 254
Baby (Manchester computer), 231–35, 235, 236–39, 255, 259–60
Back to Methuselah (Shaw), 19
Banburismus, 191
Basic Law of Arithmetic, The (Die Grundgesetze der Arithmetik) (Frege), 31, 32
Bates, Audrey, 233
Battle of Wits (Budiansky), 163n
Bayley, Donald, 194, 195, 196, 197, 217
BBC Third Programme, 261–63
bell curve, 24
Bell Laboratories, 192, 193
Bernays, Paul, 115
Bessel functions, 78
Beuttell, Alfred, 15
; Beuttell, Victor, 15
Bieberbach, Ludwig, 37
binary system, 29n, 69–72, 134, 208
biological growth, mathematical model of, 263–64
Birkhoff, George David, 126
bits, 232
Bletchley Park:
architecture of, 157–58
cryptanalysis work at, 6, 158, 171, 176–86, 181, 188–90, 191–92, 208, 210–11, 232, 259
Hanslope Park vs., 194
secrecy on work at, 6, 177, 188–89, 212
social life at, 176
as tourist site, 189–90
women workers at, 177–78
Bloomsbury movement, 19, 21
body:
mechanistic view of, 10, 225–26, 229, 236
spirit vs., 101–2
bombes, 175, 180–83, 181, 186, 188, 189, 193–94, 198
Boole, George, 29–30, 138
Boolean algebra, 29n, 71, 134
Bosanquet, R. G., 143
brain function, machine imitation of, 193, 203, 218, 224–26, 237, 263–64
Braithwaite, Richard B., 122, 261, 262
Brewster, Edwin Tenney, 10–11
Brouwer, L. E. J., 37, 110, 148
Budiansky, Stephen, 157, 163m, 172, 182, 186
Burgess, Guy, 269
Buridan, Jean, 26
Burrell, Bobby, 118
Butler, Samuel, 20, 239
Byron, George Gordon, Lord, 55, 254
calculus ratiocinator, 29, 52
Cambridge University:
Mathematical Laboratory of, 214, 220–21
Trinity College, 16, 21, 143, 145
see also King’s College
Campbell-Kelly, Martin, 232–33
Cantor, Georg, 39, 40, 91, 156, 279
Captain Ridley’s Shooting Party, 158, 171
cardinal numbers, 30–31
Carpenter, Edward, 195–96, 197
Carroll, Lewis, 228
Casti, John L., 108n, 146
cathode-ray tubes, 209–10, 219, 231–32, 237
central limit theorem, 24
Champernowne, David, 54, 140
characteristica universalis, 49
chess, 218
computer programs of, 209, 229–30
child development, teaching systems and, 203, 227–29, 256–58
Chopin, Frédéric, 124
Church, Alonzo, 115, 147, 152, 218
The Man Who Knew Too Much: Alan Turing and the Invention of the Computer (Great Discoveries) Page 26