Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game

by Andrew Hodges

  The amplitude of the waves is largely controlled by the concentration V of ‘poison’.

  In his Natural Wonders way, he called the chemical whose function was to inhibit growth, the ‘poison’ – a macabre touch, given that in his own body it had recently been the other way round. He continued:

  If the quantity R is small it means that the poison diffuses very fast. This reduces its power of control, for if the U values are large in a patch and large quantities are produced, the effect of the poison will mainly be to diffuse out of the patch and prevent the increase of U in the neighbourhood…. If R is allowed to be too large it can happen that the ‘side-band suppression’ effect even prevents the formation of a hexagonal lattice….

  Such observations reflected an insight gained from many trials even with this one model which was, as it happened, an ‘Outline of Development of the Daisy’. He had quite literally been ‘watching the daisies grow’ – not only by ‘examining 15 plants’, rather as he had done with Joan Clarke in 1941, but on his universal machine. But this was only one particular branch of his investigations: there was another headed FIRCONES, with an associated computer routine OUTERFIR; and another headed KJELL theory, which concerned another form of his basic equations, and which was associated with routines called KJELLPLUS, IBSEN and other Nordic names. All of this went rather beyond the material that he was writing up for publication, so there was no lack of prospects.

  He was working with Robin on the theory of types, and they planned to write a joint paper. He also wrote a popular article on the ‘word problem’, which appeared in the Penguin Science News in early 1954.* The Russian mathematician P. S. Novikov had announced42 that the ‘word problem’ for groups was indeed unsolvable by any definite method; Alan’s article explained this and tied it in with some questions in topology, showing that the problem of deciding whether some knot was the same as some other knot was essentially a ‘word problem’ of this kind. It was up to date, and looked forward to the complete proof of the Russian result becoming available. He was interested in solving problems up to the end: a last letter of May 1954 to Robin discussed certain ideas of Robin’s for ‘getting round the Gödel argument’ but ended with: ‘Looked at the rainbow problem again. Can do it rather successfully for sound, but total failure for electricity. Love, Alan.’ When out walking together in Charnwood Forest, near Leicester, they had seen an unusual double rainbow, a phenomenon that Alan insisted on analysing. There had to be a reason for it.

  If he was looking for something new, it was in theoretical physics, which likewise he had put on one side since the 1930s. Before the war he had spoken to Alister Watson of his interest in the ‘spinors’ that appeared in Dirac’s theory of the electron, and in his last year he did some work43 on the algebraic foundations of the spinor calculus. He defined what he called ‘founts’, after printers’ founts of type.* He was also interested in the idea Dirac had suggested in 1937,44 according to which the constant of gravitation would change with the age of the universe. Once at lunchtime he said to Tony Brooker, ‘Do you think that a palaeontologist could tell from the footprint of an extinct animal, whether its weight was what it was supposed to be?’ And always distrustful of the official line in quantum mechanics, he revived his interest in the foundations of the subject. He found a paradox within the standard interpretation, as von Neumann had set it out, because he noticed that if a quantum system were ‘observed’ frequently enough, its evolution could be made indefinitely slow, and in the limit of continuous observation would freeze to a stop. Thus the standard account depended upon an implicit assumption that this mysterious moment of ‘observation’ occurred only at discrete intervals.

  He had some further heretical ideas which he explained to Robin:45 ‘Quantum Mechanists always seem to require infinitely many dimensions; I don’t think I can cope with so many – I’m going to have about a hundred or so – that ought to be enough, don’t you think?’ And he had the germ of another idea: ‘Description must be non-linear, prediction must be linear.’ A shift of interest on his part into fundamental physics would have been well-timed; the development of relativity theory was to begin a great revival in 1955, after years in wartime doldrums. The interpretation of quantum mechanics, little developed since von Neumann’s work in 1932, was also a subject crying out for new ideas, and was one well suited to his particular kind of mind.

  It was not true, as Mrs Turing liked to think, that he was on the verge of making an ‘epoch-making discovery’ when he died; on the other hand, there was no clear pattern of decline or failure in his intellectual life that might in itself explain its abrupt end. It was rather a fluid, transitional period such as had occurred before in his development, and this time accompanied by a wider range of interests, and a more open attitude to intellectual and emotional life.

  Nor, as others saw it, was this last year in any way eventful; quite the reverse. One strange incident alone stood out, and might have pointed to the existence of matters on his mind that few could possibly appreciate. It was in mid-May 1954, when Alan went with the Greenbaum family for a Sunday visit to Blackpool. It was a very fine day, and they walked cheerfully along the Golden Mile of seaside amusements, until they came across the Gypsy Queen, the fortune-teller. Alan went in, to consult her. Had not a gypsy foretold his genius, in 1922? The Greenbaums waited outside, and found themselves waiting for half an hour. When he came out, he was as white as a sheet, and would not speak another word as they went back to Manchester on the bus. They did not hear from him again, until he called on the Saturday two days before his death when, as it happened, they were out. They heard of his death before returning the call.

  What was his fortune? Audentes Fortuna Juvat was the Turing family motto, but his uncle Arthur had died in the Great Game, ambushed in an ill-protected British position in 1899. As for Alan, in the great Looking Glass game of life, it was less clear what happened. But there was certainly a part of his mind which Robin and Nick and Franz Greenbaum did not know, and which did not belong to himself, but to those who moved the pieces: White and Red. The board was ready for an end game different from that of Lewis Carroll’s, in which Alice captured the Red Queen, and awoke from nightmare. In real life, the Red Queen had escaped to feasting and fun in Moscow. The White Queen would be saved, and Alan Turing sacrificed.

  When Alan met Don Bayley in October 1952, he had told him something – though without going into detail – that no other of his friends knew. He had been helping Hugh Alexander with cryptanalytical work. He also said that he could no longer do such work, because there was no room for homosexuals in that field. He accepted it as a fact. As a psychological blow, this was probably but a minor one compared with the others of 1952. It might have been more of a blow to GCHQ which – so Alan told Tony Brooker – had at one point offered him the colossal salary of £5000 to have him back for a year. For no more than during the war could government have operated as a monolithic entity, and the cryptological establishment, with its strong Cambridge connections, might well have been reluctant to lose its star consultant. A different view, however, would prevail in the ‘Security Service’, or MI5, whose role in 1952 had been extended by the Home Secretary, Sir David Maxwell-Fyfe. And the rapidly developing concept of ‘security’ was enjoying ever greater sway during these last two years of Alan Turing’s life.46 Although the least political person, he could not isolate himself from the state’s changing demands. Indeed, he was at the heart of the problem.

  Mechanical methods, clinical management, security – alike they were developments towards explicitness and rationalisation, and alike they were movements in which the American authorities were a step ahead. In 1950 a Senate subcommittee47 had enquired into

  the extent of the employment of homosexuals and other sex perverts in Government; to consider reasons why [sic] their employment by the Government is undesirable; and to examine into the efficacy of the methods used in dealing with the problem.

  The inquiry, the first of its kind
, had several findings. One was that homosexuals were generally unsuitable because

  it is generally believed that those who engage in overt acts of perversion lack the emotional stability of normal persons. In addition there is an abundance of evidence to sustain the conclusion that indulgence in acts of sex perversion weakens the moral fiber of an individual to a degree that he is not suitable for a position of responsibility.

  In this phase of the enquiry, the committee had drawn upon the knowledge of eminent psychiatrists. For their second main finding, however, they leant upon other authorities:

  The conclusion of the subcommittee that a homosexual or other sex pervert is a security risk is not based upon mere conjecture. That conclusion is predicated upon a careful review of the opinions of those best qualified to consider matters of security in Government, namely, the Intelligence agencies of the Government.

  Through its experience of the Second World War, the American government had come to place great faith in Intelligence. Following up the lead given by William Stephenson, it now had its own organisation for foreign spying and manipulation, the Central Intelligence Agency. Much had changed since 1945, when America seemed set to revert to an isolated role guarding hemispheric interests. British foreign policy since the war had always worked towards the retention of an American interest in Europe, although the planners of 1945 could hardly have imagined the form that this would take, now embodied in the North Atlantic Treaty and kindred agreements. Rapidly shedding the pre-war innocence of worldly affairs, America now enjoyed through the CIA its opportunity to behave like every other nation state, only more so, and in particular to emulate the British secret service. One difference, however, was that this organisation was not concealed from its legislators in the British manner, and so quite openly:

  Testimony … was taken from representatives of the Federal Bureau of Investigation, the Central Intelligence Agency, and the intelligence services of the Army, Navy and Air Force. All of these agencies are in complete agreement that sex perverts in Government constitute security risks.

  The lack of emotional stability which is found in most sex perverts and the weakness of their moral fiber, makes them susceptible to the blandishments of the foreign espionage agent … Furthermore, most perverts tend to congregate at the same restaurants, night clubs and bars…. It is an accepted fact among intelligence agencies that espionage organizations the world over consider sex perverts who are in possession of or have access to confidential material to be prime targets where pressure can be exerted. In virtually every case despite protestations by the perverts that they would never succumb to blackmail, invariably they express considerable concern over the fact that their condition might become known to their friends, associates, or the public at large.

  The FBI witnessed that ‘orders have been issued by high Russian intelligence officials to their agents to secure details of the private lives of Government officials …’ and the conclusion was clear. There was, indeed, a solid core of incontestable reality in the argument. The social stigma rendered gay men peculiarly liable to blackmail, and Soviet espionage could be expected to use this fact just like any other. It was a political fact of life. It meant that, in a curious way, Alan Turing’s life had become part of the Red King’s dream.

  The special position of homosexuals did not come as something new to the world. But now the reaction of government to this and to other aspects of individual behaviour had to take on a new explicitness. This was a transitional period, when procedures appropriate to the 1930s and to the emergency of the Second World War were rapidly being superseded by those of superpowers equipped with arsenals of atomic bombs. Now large scientific establishments had to be maintained indefinitely, against the possibility of a war that might be lost in hours. Now the whole world was supposed to be a battlefield, the Kremlin being held responsible for every development in world affairs that did not accord with American interests. Now the logical war, as well as the physical war, was fully recognised; but during an official peace the flow of information into and out of a country could not be controlled as directly as in wartime. Instead, in one way or another, the problem was that of how to control the flow into and out of people’s heads.

  Ideally, the state apparatus would all be in the form of machines, but until that could be achieved, it would have to be embodied in the brains of human beings – brains in which the information could not be erased, in which it might be combined with unknown data and instructions, and which when off duty could transport it into unknown places. The problem facing the state was compounded by the fact that science had not yet made it possible to read the thoughts of a person who did not choose to reveal them. People remained dangerously unpredictable. Yet some of that unpredictability was necessary, if the state was to elicit invention and initiative. It was a similar difficulty, that of rewarding ‘independence of character’ within a system of ‘mere routine’, that had troubled Nowell Smith.

  Brilliant but unsound, the scientists had won the wizard war and become the priests and magicians of the modern world. Yet if wars could be won by magic machines, incomprehensible to military men and administrators, then they could also so be lost. Success and danger were opposite sides of the same coin. Once disdained, then treated with a patronising awe, the scientists of the 1930s had bailed out the Allied governments. Making themselves indispensable, they had won an enhanced position – but at the cost of innocence. The political meaning of science had changed, and the climate of the 1950s was one in which contradictions ignored in the 1930s were being forced to the surface.

  The discovery that Fuchs had been passing atomic secrets to Russia had brought some of these to light. No one claimed that he had acted out of malice, desire for monetary gain, negligence or pique. At least for a time he had been a true convert and had believed he was doing the right thing. The war correspondent Alan Moorehead drew the moral in his 1952 book The Traitors48:

  Perhaps Fuchs was telling the truth when he claimed after his arrest that his loyalties were now fixed in England, and his public cursing of Russian Marxism was sincere. But he was basically a man who would always refer to his own conscience first and society afterwards. There is no place for such men in an ordered community. They belong where Fuchs now is, sewing mailbags, in Stafford Gaol.

  It was a hard saying, for it meant that Keynes and Russell, Forster and Shaw, Orwell and G. H. Hardy all alike belonged in prison. Like Einstein, they had permitted themselves to doubt the axioms, and even if they agreed to obey the rules, it had been their own choice so to do. That very detachment, that sense of making a choice, was precisely what the ordered community would have to deny. Yet English liberal writers had themselves admitted this logical conclusion, even though their culture, different in this respect from that of Germany, largely depended upon the blind eye being turned to such contradictions. Keynes, for instance, had referred to the ‘consequences of being found out’ as having to be accepted. Ideals of ‘freedom and consistency of mind’, as Fred Clayton had expressed them, simply had no place when matters of real importance to the world were concerned. The brief episode of ‘creative anarchy’ might have disguised the truth, but by 1950 the political facts of life were clear again.

  Science, with its claims to identify an objective reality independent of laws and customs and loyalties; science with its movement towards abstract thought; science for which the world was a single country – science might suggest the danger of detachment from the axioms of society. But so, both more directly and dramatically, did any form of sex which departed from the socially approved forms. Homosexuals in particular had chosen to set themselves above the clear and unmistakable judgment of society, and posed the problem of the guilty without guilt, lawbreakers with moral assurance. Did there not lie an embryonic Fuchs in each? There lay a great difference, in that Fuchs had been doing what he had explicitly promised not to do – and Fuchs had arrogated the right to power, the right to change history, rather than the right to control imm
ediate relationships. But with most gay men playing an imitation game, they could not help sharing in dishonesty and deception; and nor could anyone know for certain where personal relationships might lead.

  These were not new questions, although in the era of threatened atomic warfare they took on a new urgency. Never far below the surface, indeed, lay the highly traditional equation between sodomy, heresy and treachery. It was an equation which, even if overstated by Senator McCarthy, contained its grain of truth. Christian doctrine no longer mattered to the state, but belief in its social and political institutions certainly did. The family system, depending upon sex as a commodity for men to earn and women to surrender, remained a central doctrine of that faith, and the very idea of homosexuality undermined it. In the post-war re-establishment of male employment and female domesticity, that threat became more conscious. To those who perceived marriage and child-raising as duties rather than as choices, homosexuals appeared as the secret, seductive protagonists of a heresy, portrayed in religious terms of ‘converts’ and ‘proselytising’ and assumed, together with Soviet-inspired communists, to be plotting a conversion of the world – a mirror-image Christianity, in which the forbidden would be made compulsory.

  The East Coast liberal, or in Britain, the public school educated intellectual, was particularly open to the suspicion of the less privileged, who had no means of knowing what had transpired in what Alan called ‘the church of Princeton and the hall of King’s’. Meanwhile the axioms of politics held that, granted the existence of an enemy, real or imaginary, any dissension or falling out of line could be regarded as weakening the state, and hence a form of treachery. And it was commonly suggested that a man who could do that thing, the worst thing in the world, was capable of anything. He had lost all mental control. He might love the enemy. For all these reasons there was life in the ancient myth, or mythette, of the homosexual traitor.*