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

by David Leavitt

  Such episodes punctuate his life. During the Second World War, he enrolled in the infantry section of the home guard so that he could learn to shoot. Asked on a form, “Do you understand that by enrolling in the Home Guard you place yourself liable to military law?” he answered no, since he could conceive of no advantage to be gained in answering yes. He underwent the training and became a first-class marksman, his friend Peter Hilton later recalled, but as the war drew to a close, he lost interest in the home guard and stopped attending parades, at which point he was summoned before the authorities to explain his absences. Naturally the officer interviewing him reminded him that as a soldier it was his duty to attend parades, to which Turing replied, “But I am not a soldier.” And he was not. Because he had answered no to the question on the form, he was in fact not subject to military law, and hence under no obligation to attend parades. As Andrew Hodges observes, this “Looking Glass ploy of taking instructions literally” led to a similar ruckus when Turing’s identity card was found unsigned; he argued “that he had been told not to write anything on it.”

  Of course, from the standpoint of mathematical logic, in each of these instances Turing was behaving with utmost correctness. Mathematical logic is distinct from ordinary human discourse in that its statements both mean what they say and say what they mean, which is why a sentence like “Don’t worry about picking me up, I’ll just walk home through the sleet on my bad leg” is unlikely to find its way into a logic textbook. Star Trek’s Mr. Spock was notoriously insensitive to implication, double entendre, and passive aggression, and there was more than a touch of Mr. Spock in Turing, who often got into trouble because of his inability to “read between the lines.”

  All told, he did not do badly at Sherborne. He was a passable athlete, and though on one occasion he had to contend with a master who shouted, “This room smells of mathematics! Go out and fetch a disinfectant spray!” his teachers and his fellow students as a rule appreciated his talents and encouraged him in them. (The teachers, however, complained routinely that his work was untidy.) He even made a few friends, among them Victor Beuttell, whose father, Alfred Beuttell, had in 1901 invented something called the “Linolite electric strip reflector lamp.” In 1927 Beuttell was at work on a new invention, the “K-ray Lighting System,” which was intended to provide uniform illumination for pictures or posters. When he asked Turing to help him find a formula for determining what should be the proper curvature of the glass used, the boy not only came up with one immediately but pointed out that the thickness of the glass would also affect the illumination—something no one else had noticed. Beuttell gratefully made the necessary changes, and the lighting system was soon put into production.

  A few years later, at Cambridge, Turing would give his friend Fred Clayton “the impression that public schools could be relied upon for sexual experiences.” How much experience he actually had at Sherborne remains unclear, despite an ambiguous reference, in Mrs. Turing’s memoir, to his having kept a “private locked diary” that another boy “out of mischief or from some other motive” stole and forced open. The unnamed perpetrator “irreparably damaged the book, in which was probably entered mathematical research. This piece of wantonness has deprived us of valuable records from which his early development might have been traced.” Mrs. Turing concludes by recalling that the loss “very much distressed Alan” but does not consider what “other motive” might have been at play.

  Turing’s closest friend at Sherborne was Christopher Morcom, a boy, like him, prodigiously gifted in the sciences, whom he met in 1928. Their relationship blossomed along the classic trajectory of nineteenth-century “romantic friendship,” marked by flurries of rhapsodic emotion—Turing wrote that he “worshipped the ground [Morcom] trod on”—but with a dose of mathematics thrown in; that is to say, when they were together, the boys were more likely to talk about relativity and the value of p—which Turing, in his spare time, had calculated to thirty-six decimal points—than about poetry. Despite their seemingly dry subject matter, these conversations hummed, at least for Turing, with poetic intensity. Ironically, a few decades earlier an American doctor had recommended the study of mathematics as a cure for homosexuality.

  Christopher Morcom was probably not homosexual. Had the relationship progressed beyond Sherborne School to Cambridge, where Morcom had won the place at Trinity College that Turing coveted, it might well have come to the same end that met so many of his friendships, with the physical advance gently but firmly repulsed. But then in 1930, before he was even able to begin Trinity, Christopher Morcom died of tuberculosis. The loss devastated Turing. “I feel that I shall meet Morcom again somewhere and that there will be some work for us to do together,” he wrote to his mother, “as there was for us to do here. . . . It never seems to have occurred to me to make other friends besides Morcom, he made everyone else seem so ordinary.” Mrs. Turing herself might have been saying more than she realized when in a note to Morcom’s mother, who had let Alan have some of Christopher’s things, she wrote that her son was “treasuring with the tenderness of a woman the pencils and the beautiful star map and other souvenirs you gave him.”

  Not surprisingly, the loss of this beau ideal had the effect of fixing in Turing’s imagination an ideal of romantic love before that ideal could have time either to sour or to transmute itself into an adult relationship. In E. M. Forster’s novel Maurice (1914), the eponymous hero’s love for Clive Durham first resolves into a sustained and presumably sustainable partnership (but, significantly, one that excludes sex, at Clive’s insistence) and then dissolves into rancor when Clive decides to marry. Turing, by contrast, was never given the chance to follow his attraction to Chris Morcom through to whatever its inevitable outcome might have been. Perhaps as a result, he spent much of the rest of his short life seeking to replicate this great and unfulfilled love.

  In the fall of 1931 Turing matriculated at King’s College, Cambridge, where he was given rooms in Bodley’s Court. At first glance King’s might seem an ideal place for a young homosexual mathematician to have landed. The college was ornately beautiful, rich (thanks in part to the stewardship of the economist John Maynard Keynes), and renowned for an attitude of liberal tolerance. It had a very “gay” reputation. Forster, as infamous for his homosexuality as he was famous for his novels, lived within spitting distance of Turing’s rooms. Had he been less shy, Turing might have made Forster’s acquaintance and perhaps been invited to one of the evening gatherings in which the author, now getting on in years, read aloud from the manuscript of Maurice, which he had decided not to publish until after his death.* From Cambridge’s flourishing aesthetic and philosophical circles, however, Maurice himself, in Forster’s novel, feels shut out, and Turing in many ways bore a closer resemblance to Maurice than to his creator. Though he lacked Maurice’s blokishness, not to mention his instinct for practical life, he was, like Maurice, bourgeois and unfinished.* Also like Maurice, he felt no shame or doubt about his own homosexuality, and was even linked with another undergraduate for whom he had “longings” by some crossword puzzle clues in a King’s magazine. In the novel, it is Clive, Maurice’s first love and a self-proclaimed aesthete, who ends up backing away from his own homosexuality and marrying. Maurice, the more outwardly conventional of the pair, remains firm in his identity, as Turing would.

  The climate for homosexual men and women in England in the 1930s was far from tolerant. “England has always been disinclined to accept human nature,” Mr. Lasker-Jones, the hypnotist whom he consults in order to go straight, tells Maurice—an assertion evidenced by the Labouchere amendment of 1885, which criminalized unspecified “acts of gross indecency” between adult men in public or private and which would remain law until 1967. Under the terms of the amendment, Oscar Wilde had been arrested, tried, and sent to Reading Gaol. More recently, the withdrawal from circulation of Radclyffe Hall’s lesbian novel The Well of Loneliness (1928) had provoked Forster to collect signatures in support of the book, whic
h he privately loathed. (James Douglas of the Sunday Express had written of The Well of Loneliness, “I would rather give a healthy boy or a healthy girl a phial of prussic acid than this novel. Poison kills the body, but moral poison kills the soul.”) Even within the protective walls of King’s, to be as open about one’s homosexuality as Turing was either insane or revolutionary. Or perhaps it was simply logical—further evidence of his literal-mindedness, his obliviousness to the vagaries of “the world.” Turing neither glorified nor pathologized his own homosexuality. He simply accepted it and assumed (wrongly) that others would as well.

  Despite this openness, or perhaps because of it, his experience of King’s was remote from the ones described by its more luminary graduates in the many memoirs and novels they would afterward write. The college was famous for its links to Bloomsbury, to the world of the arts and theater. Although Turing went to see a production of George Bernard Shaw’s play Back to Methuselah, however, he wasn’t the sort of undergraduate likely to be invited to tea parties at which Shaw might be a guest. He was too shy to lend intellectual cachet, too awkward and ill-dressed to qualify as a beauty. Timidity probably kept him from approaching the dazzling sophisticates with whom he ate his meals, some of whom belonged to the famous university conversation society known as the Apostles. (Its members included Forster, Bertrand Russell, John Maynard Keynes, Lytton Strachey, Ludwig Wittgenstein, and Leonard Woolf.) Turing was not asked to join. Nor was he asked to join either the play-reading Ten Club or the Massinger Society, the members of which talked philosophy late into the night. Forster’s Cambridge novel, The Longest Journey (1907), opens with a similar gathering: Ansell, Rickie, and their friends sit before a fire, arguing over whether a hypothetical cow remains in a field after her observer leaves (a variation on the old “if a tree falls in a forest” game). Their dialogue is at once flirtatious, idealistic, and rambunctiously boyish. Then Rickie says, “I think I want to talk,” and tells the story of his youth. Turing, even if he had been invited to one of these meetings, would probably have been too shy to make such a claim on other people’s time.

  The problem was not that entrée into such circles was by definition closed to mathematicians: the number theorist G. H. Hardy (also homosexual) and “Bertie” Russell traveled in much the same milieu as Forster and Keynes. Both, however, possessed a worldliness and savoir faire that Turing could not hope to match. Instead, he stood on the sidelines, and watched, and read. Among other things, he read Samuel Butler’s Erewhon (1871), with its warning against machines taking over the world from mankind. By nature a nonconformist, he flouted Cambridge’s traditional division between aesthetes and athletes, and took up rowing. (He was in the college trial eights in 1931, 1933, and 1934.) He also took up the violin (after a fashion). He read The New Statesman and came under the influence of the King’s economist Arthur Pigou, who, along with Keynes, advocated more equal distribution of wealth. He joined the Anti-War Council, the purpose of which was to organize chemicals and munitions workers to strike if war was declared, and gave a talk on “Mathematics and Logic” before the Moral Science Club. True, he did not travel with the Lytton Stracheys of his day, choosing instead to forge friendships (one of them sexual) with boys who, like him, were interested in the sciences, even if, unlike him, they knew how to tie their ties properly.* And yet he was as much a citizen of King’s as Risley, the Wilde-like pundit (modeled on Strachey) who so dazzles and intimidates Maurice. “At Trinity he would have been a lonelier figure,” Hodges writes. Nor did Trinity welcome questioning as King’s did. If Turing got as far as he did in mathematics, it was because, in Hodges’ words, he was willing to “doubt the axioms,” and that willingness was an essential part of the King’s legacy.

  To the extent that King’s preached a philosophy, it was a creed of moral autonomy that had its origins in the philosophical writings of G. E. Moore (1873–1958) and, in particular, his Principia Ethica (1903). Moore’s refutation of absolute idealism and advocacy of “goodness” as a simple, self-defining quality that should serve as the basis for daily conduct provided an ethical underpinning for the philosophy of the burgeoning Bloomsbury movement and put the crowd at King’s at a significant remove from the English intellectual mainstream. As John Maynard Keynes would later recall, while he and his fellows accepted “Moore’s religion, so to speak,” they discarded his “morals.” They were thus able to transform Moore’s somewhat quaint utopianism into a credo of sexual and aesthetic liberation, according to which “nothing mattered except states of mind, our own and other people’s of course, but chiefly our own. These states of mind were not associated with action or achievement or with consequences. They consisted in timeless, passionate states of contemplation and communion, largely unattached to ‘before’ and ‘after.’” Keynes is notably careful to elide gender specification when he adds, “The appropriate subjects of passionate contemplation and communion were a beloved person, beauty and truth, and one’s prime objects in life were love, the creation and enjoyment of aesthetic experience and the pursuit of knowledge. Of these love came a long way first.”

  Nor did such a philosophy exclude mathematics. Russell’s influence is obvious in Keynes’s assertion

  I have called this faith a religion, and some sort of relation of neo-platonism it surely was. But we should have been very angry at the time with such a suggestion. We regarded all this as entirely rational and scientific in character. Like any other branch of science, it was nothing more than the application of logic and rational analysis to the material presented as sense-data. Our apprehension of good was exactly the same as our apprehension of green, and we purported to handle it with the same logical and analytical technique which was appropriate to the latter*. . . . Russell’s Principles of Mathematics came out in the same year as Principia Ethica; and the former, in spirit, furnished a method for handling the material provided by the latter.

  Keynes then gives an example that is as extraordinary for its appropriation of the language of mathematical logic as for its evasion (once again) of gender:

  If A was in love with B and believed that B reciprocated his feelings, whereas in fact B did not, but was in love with C, the state of affairs was certainly not so good as it would have been if A had been right, but was it worse or better than it would have become if A discovered his mistake? If A was in love with B under a misapprehension as to B’s qualities, was this better or worse than A’s not being in love at all? If A was in love with B because A’s spectacles were not strong enough to see B’s complexion, did this altogether, or partly, destroy the value of A’s state of mind?

  Clearly this world, with its spectacled A’s and good (or bad) complexioned B’s, was one in which a homosexual mathematician should have thrived. Cambridge in general (and King’s in particular) provided an ideal environment for intellectual and erotic experimentation, encouraging dissent while protecting the incipient dissident from the sort of violent counterreaction that his ideas and behavior might have provoked in a more public forum. None of this, in other words, was real—and as a testing ground, it allowed these young men to flex the muscles with which they would eventually challenge British complacency. “We entirely repudiated a personal liability on us to obey general rules,” Keynes writes. “. . . This was a very important part of our faith, violently and aggressively held, and for the outer world it was our most obvious and dangerous characteristic.” Such a philosophy jibed well with Forster’s famous ethic of personal relations, which he voiced most controversially when he asserted that, given the choice between betraying his friend or his country, he hoped he would have the courage to betray his country. His was “the fearless uninfluential Cambridge that sought for reality and cared for truth,” as he wrote in an introduction to The Longest Journey, yet it was also the Cambridge that took for granted its own elite removal from the ordinary world, and if Turing, as Hodges shows, was a less than ideal citizen of this Cambridge, it was at least in part because Sherborne’s “dowdy, Spartan amateurism,
” as well as “its anti-intellectualism,” had contributed to make him a man who “did not think of himself as placed in a superior category by virtue of his brains.” One suspects that Turing would have appreciated the much more even-keeled portrait of the university that the novelist Forrest Reid provided in his 1940 memoir Private Road, in which he wrote plainly, “Cambridge, I cannot deny, disappointed me.”

  Indeed, it is in his mathematical research, more than in the record of his life, that one sees most vividly the fruits of Turing’s tenure at King’s. His initial work was in pure mathematics, including group theory. (A 1935 publication has the daunting title “Equivalence of Left and Right Almost Periodicity.”) Early on, as at Sherborne, he was proving what had already been proven: “I pleased one of my lecturers rather the other day by producing a theorem,” he wrote to his mother in January 1932, “which he had found had previously only been proved by one Sierpinski, using a rather difficult method. My proof is quite simple so Sierpinski is scored off.” (The theorem was probably one from 1904, concerning lattice points.) A course on the methodology of science, given in 1933 by the astrophysicist Arthur Eddington (1882–1944), took him in the same direction, leading him to undertake—and find—a proof for why measurements, when plotted on a graph, tend to form the famous “bell curve” of statistics. Alas, Turing soon discovered that his result—the “central limit theorem”—had also already been proven, in 1922. His failure to check before starting off reflected, once again, both his solitariness and his tendency to be reckless. Nonetheless, he was encouraged to include the result in his dissertation, “On the Gaussian Error Function,” the bulk of which he had finished by the end of 1934, and on March 16, 1935, on the basis of this dissertation, he was elected a fellow of King’s College. Because he was still only twenty-two, a bit of doggerel circulated in Sherborne circles: