54 “I remember Turing telling me”: Gandy, preface to “On Computable Numbers, with an Application to the Entscheidungsproblem,” Ibid., 10–11.
55 “We may say most aptly”: Charles Babbage and His Calculating Engine: Selected Writings by Charles Babbage and Others, ed. Philip Morrison and Emily Morrison (New York: Dover, 1961), 252.
55 Gandy, “The Confluence of Ideas in 1936,” 55.
57 “What are the possible processes”: Alan Turing, “On Computable Numbers with an Application to the Entscheidungsproblem,” Mathematical Logic, 37.
57 “as the real numbers”: Ibid., 18.
57 “it is characteristic of Turing”: Hodges, Turing: A Natural Philosopher (London: Phoenix, 1997), 8.
57 “the issue of computability”: Penrose, New Mind, 66.
58 “According to my definition”: Turing, “Computable Numbers,” 18.
58 “a man in the process”: Ibid., 19.
58 “in the machine”: Ibid.
59 “At any stage of the motion”: Ibid., 20.
59 “The description that he then gave”: Newman, “Obituary for Dr. A. M. Turing,” Times (London), June 16, 1954, 10.
60 “divided into squares”: Turing, “Computable Numbers,” 38.
61 “lies in the fact that”: Ibid., 19.
61 “The difference from our point of view”: Ibid., 37–38.
61 “are bound to be”: Ibid., 37.
62 “must use successive observations”: Ibid., 38.
62 “into ‘simple operations’”: Ibid.
64 “changes of distribution”: Ibid.
64 “immediate recognisability”: Ibid., 38–39.
64 “most mathematical papers”: Ibid., 39.
65 “simple operations”: Ibid.
65 “some of these changes necessarily”: Ibid.
65 “We may now construct”: Ibid.
72 “The first three symbols on the tape”: Ibid., 22.
76 “the convention of writing”: Ibid., 23.
77 “a finitely described procedure”: Stephen C. Kleene, “Turing’s Analysis of Computability, and Major Applications of It,” Universal Turing Machine, 17.
81 “any computable sequence”: Turing, “Computable Numbers,” 27.
81 “to each computable sequence”: Ibid., 29.
82 “We shall avoid confusion”: Ibid., 21.
83 “It is possible to invent”: Ibid., 29–30.
83 “which will write down”: Ibid., 30.
83 “complete configuration”: Ibid., 20.
86 “that if M can be constructed”: Ibid., 30.
86 “at present the machine”: Ibid.
87 “It is not altogether obvious”: Ibid.
87 “the sequences of letters”: Ibid., 30–31.
88 “would be rather more complicated”: Penrose, New Mind, 55.
89 “convinced themselves that all”: Kleene, “Turing’s Analysis of Computability,” 30.
89 Description number for U: Penrose, New Mind, 74.
90 “number which is a description number”: Turing, “Computable Numbers,” 20.
93 “although perfectly sound”: Ibid., 34.
93 “gives a certain insight into”: Ibid.
94 “we conclude that”: Ibid., 35.
96 “By a combination of these processes”: Ibid., 36.
97 “In the complete configuration”: Ibid., 48.
97 “has the interpretation”: Ibid., 47.
97 “There is a general process:” Ibid., 36.
4: God Is Slick
99 “It is difficult to-day”: Newman, “Royal Society Memoir,” 272.
99 “instruction note”: Hodges, Enigma, 108.
100 “We have a will”: Turing Archive, AMT/C/29, Jan. 31, 1934.
100 “Personally I think that”: Ibid.
101 “Then as regards”: Ibid.
102 “Only connect”: Forster, Howards End (London: Penguin Books, 1983), 188.
103 “depended, in accordance”: Keynes, Two Memoirs, 83.
104 “It should probably be remarked”: Turing, “Computable Num-bers,” Mathematical Logic, 47.
104 Gödel’s attempt to prove the existence of God: Casti and DePauli, Gödel, 71–72.
105 “I may add that my objectivistic conception”: Hao Wang, From Mathematics to Philosophy (London: Routledge and Kegan Paul, 1974), 9.
105 “that Turing machines”: Casti and DePauli, Gödel, 108.
105 “is analogous to ‘the printed book’”: Hodges, Natural Philo-sopher, 18.
106 “skeptical of Turing’s analysis”: Solomon Feferman, “Historical Introduction,” Mathematical Logic, 3–4.
107 “doing the same things”: Turing Archive, AMT/K/1/40, May 29, 1936.
107 “An offprint which you kindly sent me”: Quoted in Hodges, Enigma, 112.
107 “strong preference for working everything out”: Newman, “Royal Society Memoir,” 269.
108 “it is almost true to say”: Gandy, “Confluence of Ideas in 1936,” 78.
108 “a function for which”: Casti and DePauli, Gödel, 81.
109 “In the following formulation”: Emil Post, “Finite Combinatory Processes: Formulation 1,” in The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, ed. Martin Davis (Mineola, N.Y.: Dover, 1993), 289.
110 “like a cross between a panda”: Gian-Carlo Rota, “Fine Hall in Its Golden Age: Remembrances of Princeton in the Early Fifties,” http://libweb.princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/pmcxrota.htm, 1.
111 “that he often met Church”: Interview with Albert Tucker by William Aspray, April 13, 1984, “Mathematical Journals and Communication,” http://libweb.princeton.edu/libraries/firestone/ rbsc/finding_aids/mathoral/pmc32.htm #(PMC32)6, 5.
111 “toward the end of the tea session”: Interview with Albert Tucker by William Aspray, April 11, 1984, “Fine Hall,” http://libweb .princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/pmc30.htm - (PMC30)9, 7.
111 “If Weyl says it’s obvious”: Interview with Stephen C. Kleene and J. Barkley Rosser, by William Aspray, April 26, 1984, http://libweb.princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/ pmc23.htm, 6.
111 “began with a ten-minute ceremony”: Rota, “Fine Hall,” 2.
112 “he was completely oblivious”: Interview with Kleene and Rosser, 8.
112 “such a statement”: Rota, “Fine Hall,” 2.
112 “the remarkable feature”: Kleene, “Origins of Recursive Function Theory,” Annals of the History of Computing 3, no. 1 (Jan. 1981): 62.
112 “for rendering the identification”: Ibid., 61.
112 “possibly more convincing”: Turing, “Computability and λ-Definability,” Mathematical Logic, 59.
112 “there were not many others”: Interview with Alonzo Church by William Aspray, May 17, 1984, http://libweb.princeton.edu/ libraries/firestone/rbsc/finding_aids/mathoral/pmc05.htm, 10.
113 “If you don’t mind”: Ibid., 9.
114 “Of all the ungainly things”: S. Turing, Alan M. Turing, 51.
Berengaria: Turing Archive, AMT/K/1/41, Sept. 8, 1936.
115 “The mathematics department here”: Ibid., AMT/K/1/42, Oct. 6, 1936.
115 Optimism of Bernays: Gandy, “Confluence of Ideas in 1936,” 59.
115 “he was very standoffish”: Turing Archive, AMT/K/1/43, Oct. 14, 1936.
117 “not always understood”: A Princeton Companion, http://etc .princeton.edu/CampusWWW/Companion/veblenoswald.html.
118 “honorary member of the clique”: Interview with Shaun Wylie by Frederik Nebeker, June 21, 1985,http://ibweb.princeton.edu/ libraries/firestone/rbsc/finding_aids/mathoral/pmc45.htm, 10.
119 “talking shop”: Turing Archive, AMT/K/1/43, Oct. 14, 1936.
119 “Though prepared to find”: S. Turing, Alan M. Turing, 52.
120 “I am sending you some cuttings”: Turing Archive, AMT/K/1/46, Nov. 22, 1936.
120
“horrified at the way people”: Ibid., AMT/K/1/48, Dec. 3, 1936.
120 “I believe the government”: Ibid., AMT/K/1/51, Jan. 1, 1937.
121 “glad that the Royal Family”: Ibid., AMT/K/1/59, May 19, 1937.
121 “Church had me out to dinner”: Ibid., AMT/K/1/43, Oct. 14, 1936.
121 “Yes, I forgot about him”: Church/Aspray, 10.
122 “I have had two letters”: Turing Archive, AMT/K/1/56, Feb. 22, 1937.
122 von Neumann’s talk with Gödel: Casti and DePauli, Gödel, 50.
122 “was one of the first”: Feferman, “Turing in the Land of O(z),” Universal Turing Machine, 113.
123 “You had von Neumann”: Interview with Joseph Daly and Churchill Eisenhart by William Aspray, July 10, 1984, http://libweb.princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/ pmc07.htm, 4.
124 “Maurice is much more conscious”: Turing Archive, AMT/ K/1/57, March 29, 1937.
125 “As a matter of fact”: Alonzo Church, review of “On Computable Numbers, with an Application to the Entscheidungsproblem.” Journal of Symbolic Logic 2, no. 1 (March 1937): 43.
125 “actually easier to work with”: Aspray/Kleene/Rosser, PMC23, 10.
126 “One should have a reputation”: Turing Archive, AMT/K/1/51, Jan. 1, 1937.
127 “I went to the Eisenharts”: Ibid., AMT/K/1/56, Feb. 22, 1937.
127 “a rich man”: Ibid., AMT/K/1/59, May 19, 1937.
130 Hardy’s pessimism: Marcus Du Sautoy, The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics (New York: HarperCollins, 2003), 188.
131 “The number of protons”: Hardy, Ramanujan (Cambridge: Cambridge University Press, 1940), 17.
131 Lehman’s method: Feferman, “Turing in the Land of O(z),” 110.
132 “a generation”: Hodges, Enigma, 118.
132 “the ‘real’ mathematics”: Hardy, A Mathematician’s Apology (Cambridge: Cambridge University Press, 1967), 119–20.
132 “no one has yet discovered”: Ibid., 140.
132 “gentle and clean”: Ibid., 121.
133 “You have often asked me”: Turing Archive, AMT/K/1/43, Oct. 14, 1936.
134 “multiply the number”: Quoted in Hodges, Enigma, 138.
136 “regarded as thoroughly unsatisfactory”: Kleene, “General Recur-sive Function,” 59.
136 “only after Turing’s formulation”: Ibid., 61.
137 “giving an absolute definition”: Gödel, “Remarks before the Princeton Bicentennial Conference on Problems in Mathematics, 1946,” in Davis, Undecidable, 84.
137 “due to A. M. Turing’s”: Ibid., 71.
137 Gödel’s dissatisfaction: Feferman, “Historical Introduction,” 5–6.
138 “pure mathematics is the subject”: Casti and DePauli, Gödel, 28.
138 “distanc[ing] himself from”: Ibid., 71.
5: The Tender Peel
139 “a part of his mind”: Hodges, Enigma, 148–49.
140 Turing went to see Snow White: Ibid., 149.
141 attended another training course: Ibid., 151.
141 “Apparatus would be”: Quoted ibid., 155.
142 design of Liverpool machine: Du Sautoy, Music of the Primes, 188.
142 precision-cut gear wheels: Hodges, Enigma, 156.
143 two courses with the same name: Ibid., 152.
144 “to be an elderly man”: Norman Malcolm, Ludwig Wittgenstein: A Memoir (London: Oxford University Press, 1958), 23.
145 “were given without preparation”: Ibid., 24.
145 “He always wore”: Ibid., 24–25.
145 “were austerely furnished”: Ibid., 25.
146 “One had to be brave”: Ibid., 25–26.
146 “I might as well talk”: Ibid., 26–27.
146 “Wittgenstein applied his own”: Casti and DePauli, Gödel, 71–72.
146 “Suppose I say to Turing”: Wittgenstein’s Lectures on the Foundations of Mathematics, Cambridge 1939, ed. Cora Diamond (Chicago: University of Chicago Press, 1989), 20.
147 “Don’t treat your common sense”: Ibid., 68.
147 “tempt”: Ibid., 139.
147 “I understand but”: Ibid., 67
148 “We say of a proof that”: Ibid., 199.
148 “Professor Hardy says”: Ibid., 138–39.
149 “What is counting?”: Ibid., 115.
149 “that whenever numerals”: Ibid., 31.
149 “You might call this figure”: Ibid., 36–37.
150 “The ordinary meanings of”: Ibid., 37.
151 “One could make this comparison”: Ibid., 96–97.
152 “If a man says”: Ibid., 206–7.
152 “I may give you the rules”: Ibid., 210–11.
153 “a logical system”: Ibid., 212.
153 “practical things may go wrong”: Ibid., 216.
153 “The question is”: Ibid., 217.
154 “But how do you know that”: Ibid., 218.
155 “Before we stop”: Ibid., 219–20.
156 “out of the paradise”: Ibid., 103.
156 “Suppose I am a general and I receive”: Ibid., 201.
157 “Suppose I am a general and I give”: Ibid., 212.
157 “a sort of Victorian mock-Tudor”: Stephen Budiansky, Battle of Wits: The Complete Story of Codebreaking in World War II (New York: Touchstone, 2000), 118.
157 “even to the untrained eye”: David Russo, “Architecture and the Architect,” http://www.utdallas.edu/~dtr021000/cse4352/ architects.doc.
159 alter the orders of the keyword: Budiansky, Battle of Wits, 67.
165 “Sphinx of the Wireless”: Singh, The Code Book: The Secret History of Codes and Codebreaking (London: Fourth Estate, 1999), 138.
171 100,391,791,500 further permutations: Ibid., 136. incorporating the indicator code: Hodges, Enigma, 164.
176 “Make sure they have”: Quoted ibid., 221.
178 “For centuries”: Singh, Code Book, 149.
179 “keine Zusätze”: Turing, Excerpts from the “Enigma Paper,” Mathematical Logic, 230–31.
184 the gunner on an English ship: Budiansky, Battle of Wits, 157.
186 “the fundamental mathematical insight”: Ibid., 131.
186 “these contradictions”: Hodges, Enigma, 183–84. obsessive counting of tire revolutions: Ibid., 209.
187 “pompousness or officialdom”: Quoted ibid., 204.
187 “much more conscious”: Turing Archive, AMT/K/1/57, March 29, 1937.
189 “we might have lost”: Singh, Code Book, 176.
6: The Electronic Athlete
192 Subsequent Robinsons: Hodges, Enigma, 267n.
193 a stranger propositioned him: Ibid., 249.
196 “found the idea of”: Irvine, preface to S. Turing, Alan M. Turing, xii.
196 “seemed to think it”: Hodges, Enigma, 284.
196 “If it had ended unhappily”: Forster, Maurice, 218.
197 “had hoped for”: Ibid., 221–22.
197 “Sometimes you’re sitting”: Quoted in Hodges, Enigma, 373.
198 “the possible adaptation”: Quoted ibid., 306.
199 17,468 vacuum tubes: Mary Bellis, “Inventors of the Modern Com-puter,” http://inventors.about.com/library/weekly/aa060298.htm, 1.
199 “With the advent of”: Martin H. Welk, “The ENIAC Story,” http://ftp.arl.mil/~mike/comphist/eniac-story.html, 1.
200 “screwdriver interference”: Turing, “Intelligent Machinery,” in Mechanical Intelligence, ed. D. C. Ince (Amsterdam: North-Holland, 1992), 115.
201 “While it appeared that”: John von Neumann, “First Draft of a Report on the EDVAC,” June 30, 1945, 3.
202 “tackle whole problems”: Turing, “Proposal for Development in the Mathematics Division of an Automatic Computing Engine (ACE),” Mechanical Intelligence, 1.
202 “There will positively be no”: Ibid., 2.
203 “Possibly it might still”: Turing, “Lecture to the London Mathematical Society on 20 February 19
47,” Mechanical Intelligence, 104.
203 if not “infinite”: Ibid., 88.
203 “desirable feature”: Ibid., 89.
204 “form of memory”: Ibid., 88.
204 “really fast machine”: Ibid., 89.
204 “cuts out the sign”: Wittgenstein’s Lectures, 20.
204 “The machine interprets”: Turing, “Lecture to the London Mathematical Society,” 103.
205 “I would say that fair play”: Ibid., 104–5.
206 “To continue my plea”: Ibid., 105.
207 “the calculator itself”: Ibid., 102.
208 “That it is electronic”: Ibid., 87.
209 “Construction of range tables”: Turing, “Report on the ACE,” Mechanical Intelligence, 20–22.
209 “be made to do any job”: Turing, “Lecture to the London Mathematical Society,” 87.
209 “To perform the various logical operations”: Turing, “Report on the ACE,” 8.
209 magnetic wire: Turing, “Lecture to the London Mathematical Society,” 89.
210 “much the most hopeful”: Ibid., 84.
210 “It should be possible”: Turing, “Report on the ACE,” 20.
210 “a standard instruction”: Ibid., 17.
210 “have to be made up by”: Ibid., 25.
211 “grasp the principle”: Hodges, Enigma, 335.
211 “The most that Alan”: S. Turing, Alan M. Turing, 70.
212 “comprised men from”: Ibid., 111.
212 “about twelve years ago”: Quoted ibid., 79.
213 “evening paper”: Ibid., 80.
213 “be able quite easily”: Quoted ibid., 81.
213 “power of judgment”: Quoted ibid.
215 “I have read Wilkes’ proposal”: Quoted in Hodges, Enigma, 352.
215 “intended primarily”: Quoted ibid., 353.
215 “very opinionated”: Quoted ibid., 353.
215 “minimalist ideas”: Davis, Engines, 189.
216 “the actual size of”: Quoted in Hodges, Enigma, 408.
216 “to be very much alone”: Davis, Engines, 192.
216 “Virtually all computers”: Quoted ibid., 193.
217 “disappointed with”: S. Turing, Alan M. Turing, 86–87.
218 “was not a particularly good”: Quoted ibid., 87.
218 “to the similarities”: Ibid., 88.
219 “With this store available”: “Max Newman and the Mark I,” http://www.computer50.org/mark1/newman.html, 2.
The Man Who Knew Too Much: Alan Turing and the Invention of the Computer (Great Discoveries) Page 25
