The Man Who Knew Too Much: Alan Turing and the Invention of the Computer (Great Discoveries)

by David Leavitt

  And here the story breaks off. We never learn what happens to Ron and Alec. They are left forever on the brink of possibility—perhaps of possible happiness—untouched by the shadow that had swooped down and destroyed the life of their creator.

  3.

  Mrs. Clayton, his housekeeper, found Alan Turing’s dead body in his bed on the morning of June 8, 1954. Nearby was an apple out of which several bites had been taken.

  “You will by now have heard of the death of Mr. Alan,” she wrote to his mother.

  It was such an awful shock. I just didn’t know what to do. So I flew across to Mrs. Gibson’s and she rang Police and they wouldn’t let me touch or do a thing. & I just couldn’t remember your address I had been away for the week end and went up tonight as usual to get his meal. Saw his bedroom light on the lounge curtains not drawn back, milk on step and paper in door. So I thought he’d gone out early & forgot to put his light off. So I went & knocked at his bedroom door. Got no answer so walked in. saw him in bed he must have died during the night. The police have been up here again to night for me to make a statement.

  She then added,

  Mr. And Mrs. Gibson saw Mr. Alan out walking Mon. evening he was perfectly all right then. The week end before he’d had W [sic] Gandy over for the week end & they seemed to have had a really good time. Then Mr. & Mrs. Webb came to dinner Tues. & Mrs. Webb had afternoon tea with him Wed: the day she removed.

  To Mrs. Clayton, the possibility that Turing had committed suicide seemed inconceivable enough to warrant her offering evidence against it (though not so inconceivable that she felt no need to bring it up). Nonetheless, the result of the inquest, held on June 10, was that Turing had killed himself. It seemed that the apple had been dipped in a cyanide solution.

  In the years following his death, many of Turing’s friends entered into a sort of conspiracy with his mother to propagate the myth that his death was the result not of suicide but of a scientific experiment gone awry. In cooking up this theory, they pointed to the stock of chemicals (including potassium cyanide) that he kept at his house, as well as his array of scientific equipment. For example, Dr. Greenbaum, the psychoanalyst, wrote to Mrs. Turing,

  There is not the slightest doubt to me that Alan died by an accident. You describe Alans fashion of experimenting so vividly that I can see him pottering about. He was like a child while experimenting not always taking in the observed [illegible] but also testing it with his fingers. . . . [W]hen he died he was never as far away from suicide as there.

  Likewise his neighbor, Mrs. Webb, told Mrs. Turing that she found it

  difficult to connect the verdict of the coroner with Alan’s behaviour before we left Park Villa on June 3rd. He invited us to dinner on June 1rst and we spent a most delightful evening with him then. I saw him several times during the next two days and on the day we moved he invited me in for a cup of tea. He made toast and we had it on the kitchen table. It was such a jolly party, Mrs. Clayton joining us for a cup of tea when she came in. Alan was full of plans for coming to visit us at Styal on his way home from the university in the afternoons, and I cannot believe that he had any idea then of what he was going to do. It must have come upon him quite suddenly.

  Hugh Alexander, still in the thick of cryptanalysis, wrote to Mrs. Turing,

  I can confirm what you say about his being in good spirits lately; I had a letter from him about a month before he died saying that he was having treatment, that he felt it was doing him good and that he was in better spirits than he had been [censored].* Because of this I was particularly shocked when I read what had happened and I am very glad to learn that it might well have been an accident.

  As late as 1960 Mrs. Turing was still collecting evidence to support her version of events. This last letter came from Turing’s former colleague W. T. Jones, now a professor of philosophy at Pomona College in California:

  If I may say so, I think that all of the evidence—both positive and negative—tends to support your views about the circumstances of his death. By “negative” I mean, that I do not think Alan was at all the sort of person who would take his own life. By “positive,” I mean that he was the sort of person who would be careless about (rather, inattentive to) dangerous aspects of the experiments he was conducting.

  Interestingly, none of Turing’s friends ever seems to have considered, at least in writing, a third possibility (one, admittedly, for which there is no evidence, at present anyway): namely, that the suicide was staged; that the man in the white suit had become—like the hero of Alfred Hitchcock’s 1934 film—a man who knew too much.

  If he did kill himself, he seems to have thought that he was going somewhere. Remember that in the untitled story, Alec Pryce is an authority on interplanetary travel. In March 1954, a few months before his death, Turing sent Robin Gandy a series of four cryptic postcards. The first was lost. The other three consisted of a list of numbered aphorisms bearing the collective title Messages from the Unseen World:

  III. The Universe is the interior of the light cone of the creation

  IV. Science is a differential Equation. Religion is a Boundary Condition. (sgd) Arthur Stanley*

  V. Hyperboloids of wondrous Light

  Rolling for aye through Space and Time

  Harbour those Waves which somehow might

  Play out God’s wondrous pantomime

  VI. Particles are founts

  VII. Charge = e/π ang of character of a 2π rotation

  VIII. The Exclusion Principle is laid down purely for the benefit of the electrons themselves, who might be corrupted (and become dragons or demons) if allowed to associate too freely

  Other mathematicians as great as Turing had ended their lives in madness: Cantor had; also Gödel. Perhaps Turing, too, was becoming delusional near the end, imagining himself rolling through space in a “hyperboloid of wondrous light” known as Pryce’s buoy. Or perhaps, as Gandy thought, this was all part of “a new quantum mechanics . . . not intended to be taken very seriously (almost in the ‘for amusement only’ class), although no doubt he hoped something might turn up in it which could be taken seriously.” Or perhaps the new quantum mechanics involved apples, light cones, and spaceships. In A Mathematician’s Apology, Hardy had written, “No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man’s game.” Yet Turing, according to Gandy, had not lost his powers; indeed, in the months before his death, he had come up with an upper bound for the Skewes number that was lower than the one that Skewes himself had established. This would have been a significant achievement, had he chosen to publish it. But he did not. He said he didn’t want to embarrass Skewes.

  The idea of suicide, if it came upon him at all, must have come upon him suddenly. The method, on the other hand, seems to have been in the back of his mind for years. For instance, from Princeton, his friend James Atkins told Andrew Hodges, Turing had once written a letter proposing a suicide method that “involved an apple and electric wiring.” He often told his friends that he ate an apple every night before going to bed. And of course, in Cambridge, for weeks after the premiere of Snow White and the Seven Dwarfs, he would chant as he walked down the corridors of King’s,

  Dip the apple in the brew,

  Let the sleeping death seep through. . . .

  Today the apple continues to fascinate. Much is made of its metaphorical implications. (Apple of death, apple of knowledge—but too much knowledge?) A rumor circulates on the Internet that the apple that is the logo of Apple Computers is meant as a nod to Turing. The company denies any connection; on the contrary, it insists, its apple alludes to Newton. But then why has a bite been taken out?

  Perhaps what chills us is that in taking his own life, Turing actually chose to camp it up a bit—to invest his departure from a world that had treated him shabbily with some of the gothic, eerie, colorful brilliance of a Disney film. And yet in all the pages I have read about Turing—and there are scores of them—no one
has yet mentioned what seems to me the most obvious message. In the fairy tale the apple into which Snow White bites doesn’t kill her; it puts her to sleep until the Prince wakes her up with a kiss.

  * * *

  *As Newman explained, “Turing had arrived at differential equations of the form for n different morphogens in continuous tissue; where fi is the reaction function given the rate of growth of Xi, and is the rate of diffusion of Xi. He also considered the corresponding equations for a set of discrete cells.”

  *Presumably Alexander’s letter was censored because of his continuing work for the government in cryptanalysis.

  *Arthur Stanley Eddington (1882–1944), mathematical physicist with whom Turing studied at Cambridge.

  Notes

  1: The Man in the White Suit

  4 “hounded out of the world”: E. M. Forster, Maurice (London: Penguin Books, 2000), 32.

  5 “Turing believes machines think”: Turing Archive, King’s College, Cambridge, AMT/D/14a.

  8 “Alan certainly had less”: Lyn Irvine, preface to Sara Turing, Alan M. Turing (Cambridge: W. Heffer, 1959), x.

  8 “He never looked right in his clothes”: Ibid., xi.

  2: Watching the Daisies Grow

  9 “Alan was interested in figures”: S. Turing, Alan M. Turing, 11.

  9 “quockling”: Ibid., 13.

  9 “quite unable to predict”: Turing Archive, AMT/K/1/49, Dec. 1936.

  10 “a mixture in which the chief ingredient”: S. Turing, Alan M. Turing, 15.

  10 “First you must see that the lite”: Ibid., 17.

  10 “Turing’s fond of the football field”: Ibid., 19.

  11 “a quite false impression”: Ibid., 11.

  11 “down to something”: Ibid., 21.

  12 a “world in miniature”: E. M. Forster, The Longest Journey (London: Penguin Books, n.d.), 157.

  12 “not very good”: S. Turing, Alan M. Turing, 27.

  12 “was a cause of satisfaction”: Ibid., 27.

  13 “No doubt he is very aggravating”: Ibid., 29.

  13 “What is the locus of so and so?”: Ibid., 14.

  14 “Looking Glass ploy”: Andrew Hodges, Alan Turing: The Enigma (New York: Walker, 2000), 232.

  15 “This room smells of mathematics”: Quoted ibid., 29.

  15 “Linolite electric strip reflector lamp”: Ibid., 56.

  15 “the impression that public schools”: Ibid., 77.

  15 “private locked diary”: S. Turing, Alan M. Turing, 35.

  16 “worshipped the ground”: Quoted in Hodges, Enigma, 35. mathematics as a cure for homosexuality: Graham Robb, Strangers: Homosexual Love in the Nineteenth Century (New York: W. W. Norton, 2003), 69.

  16 “I feel that I shall meet Morcom”: Turing Archive, AMT/K/1/20, Feb. 16, 1930.

  16 “treasuring with the tenderness”: Quoted in Hodges, Enigma, 50.

  18 “longings”: Ibid., 76.

  18 “bourgeois, unfinished and stupid”: Forster, Maurice, 69.

  18 “England has always been disinclined”: Ibid., 185.

  18 “I would rather give a healthy boy”: James Douglas, in Sunday Express, Aug. 19, 1928; also quoted in Hodges, Enigma, 77. saw Back to Methuselah: Hodges, Enigma, 74. not asked to join Cambridge societies: Ibid., 75.

  19 “I think I want to talk”: Forster, Longest Journey 21.

  20 His closest friendships: Ibid., 74–76.

  21 “At Trinity he would have been”: Hodges, Enigma, 7.

  21 “doubt the axioms”: Ibid., 79.

  21 “Moore’s religion, so to speak”: John Maynard Keynes, Two Memoirs (London: Rupert Hart-Davis, 1949), 82. I first learned of this fascinating book from Hodges’ biography, which quotes from it.

  21 “nothing mattered except states of mind”: Ibid., 83.

  22 “I have called this faith a religion”: Ibid., 86.

  22 “would seem, on Russell’s theory”: G. H. Hardy, “Mathematical Proof,” Mind, n.s., 38, 149 (Jan. 1929): 23.

  22 “If A was in love with B”: Keynes, Two Memoirs, 86–87.

  23 “We entirely repudiated”: Ibid., 97–98.

  23 “the fearless uninfluential Cambridge”: Forster, introd. to Longest Journey, lxviii.

  24 “dowdy, Spartan amateurism”: Hodges, Enigma, 69.

  24 “Cambridge, I cannot deny”: Forrest Reid, Private Road (London: Faber and Faber, 1940), 58.

  24 “I pleased one of my lecturers”: Turing Archive, AMT/K/1/23, Jan. 31, 1932.

  25 elected a fellow: J. L. Britton, “Remarks on Turing’s Dissertation,” Pure Mathematics: The Collected Works of A. M. Turing, ed. J. L. Britton (Amsterdam: North-Holland, 1992), xix.

  25 “Turing / Must have been alluring”: Quoted in Hodges, Enigma, 94.

  26 “I will not be able to pull”: John L. Casti and Werner DePauli, Gödel: A Life of Logic (Cambridge: Basic Books, 2000), 117.

  28 “The discovery that all mathematics”: Bertrand Russell, “The Study of Mathematics,” in Contemplation and Action, 1902–14, ed. Richard A. Rempel, Andrew Brink, and Margaret Moran (London: George Allen and Unwin, 1985), 90.

  28 Leibniz’s dream: Martin Davis, Engines of Logic: Mathematicians and the Origins of the Computer (New York: W. W. Norton, 2000), 16.

  29 “If controversies were to arise”: Russell, “Mathematics and the Metaphysicians,” in Logicism and the Philosophy of Language: Selections from Frege and Russell, ed. Arthur Sullivan (Peterborough: Broadview Press, 2003), 224.

  29 “every process will represent”: George Boole, The Mathematical Analysis of Logic: Being an Essay towards a Calculus of Deductive Reasoning (Cambridge: Macmillan, Barclay, & Macmillan, 1847), 6.

  30 “that arithmetic is a branch of logic”: Gottlob Frege, Grundgesetze der Arithmetik (Hildesheim: Georg Olms, 1962), translation quoted by Richard G. Heck Jr., in “Julius Caesar and Basic Law V,” http://emerson.fas.harvard.edu/heck/pdf/JuliusCaesarandHP.pdf

  30 “a virulent racist”: Davis, Engines, 42.

  30 “a formal language”: Frege, Begriffsschrift, in Jean van Heijenoort, From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 (Cambridge: Harvard University Press, 1967), 1.

  31 “particular number is not identical”: Russell, Introduction to Mathematical Philosophy (London: George Allen and Unwin, 1919), 12.

  31 “There is just one point”: Russell, letter to Frege, in van Heijenoort, Frege to Gödel, 124–25.

  33 “Your discovery of the contradiction” Frege, letter to Russell, in van Heijenoort, Frege to Gödel, pp. 127–28.

  33 “a masterpiece discussed”: Casti and DePauli, Gödel, 43.

  34 “the extreme Russellian doctrine”: Hardy, “Mathematical Proof,” 9.

  34 “that mathematics has at its disposal”: David Hilbert, “On the Infinite,” in van Heijenoort, Frege to Gödel, 376.

  34 “substantial sciences”: Hardy, “Mathematical Proof,” 6.

  35 “I had better state at once”: Ibid., 11–12.

  35 “the chessmen, the bat”: Ibid.,14–15.

  35 “cardinal in Hilbert’s logic”: Ibid., 15.

  36 “because it characterizes”: Ernest Nagel and James R. Newman, Gödel’s Proof (New York: New York University Press, 2001), 28.

  36 “conviction of the solvability”: Jeremy J. Gray, The Hilbert Challenge (Oxford: Oxford University Press, 2000), 248.

  36 “there is no such thing as”: Constance Reid, Hilbert (New York: Springer-Verlag, 1970), 196.

  36 “Wir müssen wissen”: Gray, Hilbert Challenge, 168.

  37 “We are convinced that”: Reid, Hilbert, 188.

  37 “Let us consider that”: Ibid.

  38 “at Berlin University”: “Nazi Kultur: The New Heroic Gospel,” Times (London), Nov. 10, 1933; also quoted in Hodges, Enigma, 86.

  38 “I am primarily interested”: Hardy, “Mathematical Proof,” 6.

  40 “Let us admit that”: Hilbert, “On the Infinite,” 375.

  40 “a completely satisfactory way”: Ibid.,
375–76.

  40 “The worst that can happen”: Hardy, “Mathematical Proof,” 5. Gödel’s first public announcement: Robin Gandy, “The Confluence of Ideas in 1936,” in The Universal Turing Machine: A Half-Century Survey, ed. Rolf Herken, 2nd ed. (Vienna: Springer-Verlag, 1995), 63.

  45 “In the highly ingenious work of Gödel”: Reid, Hilbert, 198.

  46 “that proof theory could still”: Ibid., 199.

  46 “How can one expect”: Kurt Gödel, “Russell’s Mathematical Logic,” in Collected Works, vol. 2, ed. Solomon Feferman et al. (Oxford: Oxford University Press, 1990), 140–41.

  48 “this did not necessarily mean”: Simon Singh, Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem (New York: Walker, 1997), 141.

  3. The Universal Machine

  49 “between two different versions”: Egon Börger, Erich Grädel, and Yuri Gurevich, The Classical Decision Problem (Berlin: Springer-Verlag, 1997), 4.

  50 Kitab-al-jabr: Roger Penrose, The Emperor’s New Mind (Oxford: Oxford University Press, 1989), 40–41.

  50 Definition of an algorithm: Ibid., 41–42.

  51 “the main problem”: Börger et al., Decision Problem, 3n.

  51 “From the considerations”: D. Hilbert and W. Ackermann, Principles of Mathematical Logic, ed. Robert E. Luce (New York: Chelsea, 1950), 112.

  51 “There is of course no such theorem”: Hardy, “Mathematical Proof,” 16.

  52 “although at present”: Börger et al., Decision Problem, 5.

  52 “a decision procedure might”: Letter to the author.

  53 “The Hilbert decision-programme”: Max Newman, “Royal Society Memoir,” in Mathematical Logic, ed. R. O. Gandy and C. E. M. Yates (Amsterdam: Elsevier, 2001), 272.