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

by Andrew Hodges

  * While some physical quantities (such as temperature) may be described by one number, in general they will require a set of numbers; anything like a direction in space, for instance, will do so. It is usual to ‘index’ this set by a letter of the alphabet. From a modern point of view the structure of the set is a reflection of the group of symmetries associated with the physical entity, and it is common to use a different type of letter (e.g. lower-case, upper-case, Greek) when different symmetry groups are implied. The word ‘fount’ made this principle explicit.

  * Of course the equation also ran the other way: a suggestion of homosexuality could discredit the political target. In particular, it was implicit in the charge of being ‘soft on communism’.

  † The flavour of the new policy in operation was conveyed by a report in the New York Times, 2 March 1954, on progress made in the previous year: ‘… the State Department, a principal target of Senator McCarthy, had separated 117 employees as “security risks”, of whom forty-three had allegations of a subversive association in their files and forty-nine had been listed as having in their files “information indicating sex perversion”. In the big super secret Central Intelligence Agency … there were forty-eight “security risk” separations, of whom thirty-one were included with information indicating perversion …’

  * Positive vetting was now applied to those ‘privy to the whole of an important section’ of ‘a vital secret process, equipment, policy, or broad strategic plan …’ a description which would cover anything significant done by GCHQ.

  * There might have been more. He was, in particular, the ‘Deputy Director’ of the laboratory where the atomic bomb calculations were in progress, and might well have been consulted at an early stage about this use of the computer. Ferranti Ltd were also engaged upon guided-missile development. Yet these were almost common knowledge, in comparison with the subject which was to remain unmentionable for another twenty years.

  * Occasionally it was noted that gay men said they actually enjoyed their ‘condition’, had no desire to change, scorned the idea of psychiatry, or simply asked to be left alone. But these remarks were interpreted by the old guard as evidence of the arrogance and anti-social attitudes that made homosexuals so dangerous – and by the modernists as unfortunate hindrances to successful treatment.

  * Lord Jowett, Lord Chancellor in the Labour Government of 1945–51, was another speaker. But his ideas had been developed more fully in a lecture53 of late 1953, where he expressed the hope that ‘treatment by hormones or glandular secretion … will help these unhappy people to eradicate their abnormal desires.’ More generally, suggestions emanating from the small back room were more robust than those of the parliamentary debate. In April 1954, the doctors’ journal The Practitioner was devoted to an analysis of the national sexual crisis. Its editorial, besides explaining that discipline must come before happiness, and that sexual vice meant ‘slow death to the race’, endorsed the suggestion made by one contributor that homosexuals should ‘strengthen their resolve’ in some ‘natural and bracing environment’ – such as a ‘camp’ on the island of St Kilda. A contributing endocrinologist also drew upon German data on ‘the problem of homosexuality’, citing ‘the use of castration in over 100 cases of sexual perversion and homosexuality reported by Sand and Okkels (1938) who noted gratifying results in all but one case’.54 For medicine as for mathematics, the world could be a single country.

  * The British newspapers were not notable for their explanations of what was going on, but a less inhibited suggestion appeared in the Sydney Sunday Telegraph of 25 October 1953:56

  The plan originated under strong United States advice to Britain to weed out homosexuals – as hopeless security risks – from important Government jobs.

  One of the Yard’s top-rankers, Commander E. A. Cole, recently spent three months in America consulting with FBI officials in putting finishing touches to the plan….

  The Special Branch began compiling a ‘Black Book’ of known perverts in influential Government jobs after the disappearance of the diplomats Donald Maclean and Guy Burgess, who were known to have pervert associates. Now comes the difficult task of sidetracking these men into less important jobs – or of putting them behind bars.

  * Ministry of Supply.

  * It would be misleading to suggest that he had made any discovery in these jottings, but the underlying thoughts were in line with the developments of the 1950s and 1960s. III. ‘Arthur Stanley’ is Eddington, and the first postcard alluded to cosmological questions. The ‘light cone’ is an important idea in relativity theory. Einstein’s ideas were based on the concept of a 7point in space-time, this meaning a precise location in space at a precise instant of time. Imagining this as an instantaneous spark, the future ‘light cone’ of such a point is traced out by the expanding sphere of light from that spark.

  By the ‘Creation’ he would mean the ‘big bang’; it had been known since the 1920s that there were models of an expanding universe that agreed with Einstein’s general theory of relativity, and in 1935 H. P. Robertson, whose lectures Alan attended at Princeton, had further developed the theory of them. Unfortunately the astronomers’ observations of the galactic recession did not seem to be consistent with the Einstein theory, and only in the mid-1950s was the discrepancy eliminated. This was one reason why in 1948

  H. Bondi, T. Gold and F. Hoyle had suggested a new theory involving ‘continual creation’ which eliminated the ‘bang’. Alan might have heard Gold speak about it at the Ratio Club in November 1951. But apparently it did not deflect him from the earlier view, soon to be established much more firmly.

  The emphasis on a description using light cones was not a trivial insight. Such an emphasis was emerging in a quite different way through the work of A. Z. Petrov in 1954, was taken up by H. Bondi and F. A. E. Pirani later in the 1950s, and entered very strongly into the ideas of Roger Penrose, who in the early 1960s formulated new ideas about space-time. In fact a ‘Penrose diagram’ of the universe would draw it as ‘the interior of the Light Cone of the Creation’.

  IV. Implicit here is the problem of physical determinism. Most physical laws, including Einstein’s, are in the form of a differential equation, relating instantaneous rates of change to one another in such a way that in principle, given the state of a physical system at one time, it can be predicted at a later time by adding up the changes over the period. In the context of cosmology this begs the question of what the ‘initial’ state of the universe was – it was a very Eddingtonian suggestion that the study of the differential equations of physics could only be half the story. Here again, the question of the nature of the initial ‘big bang’ was to be of growing significance in the renaissance of relativity theory.

  V. Again the allusion is to the problem of physical prediction – the wave functions somehow determining the events perceived as the pantomime of macroscopic life – and again the emphasis is on a description in terms of light rays. But the ‘hyperboloids’ suggest some quite novel geometric picture of his own, lost without trace.

  VI. The reference to ‘founts’ suggests that he was thinking of describing the different elementary particles in terms of their corresponding symmetry groups – again in the mainstream of developments, although the picture as it unfolded in the 1960s was far more complicated than anyone would have known in 1954.

  VII. He was certainly not the first to think that electric charge could be interpreted in terms of rotations, and his formula was too simple-minded. But 1954 saw the renewal of interest in ‘gauge theories’, which generalised this basic idea.

  VIII. Often his letters closed with a brief line of personal comment, and this was surely the case here. There was certainly nothing new or speculative in scientific terms in this ‘message’, an allusion to the well-established Pauli Exclusion Principle. Back in 1929, when he read what Eddington had to say about the electron, Alan had noted the idea that the electrons of the universe had to be considered en-masse, not singly; the Pa
uli principle described an observed restriction on the collective behaviour which roughly speaking meant that no two electrons could be in the same place. Thus in each atom, the electrons would be stacked neatly in separate shells and orbits. As indeed he might have joked in 1929, it was like the House system that kept the boys from associating too freely. For their own benefit, of course: Don’t you see, Dr Turing, we have to do this for your own protection. …

  * But there was a last parallel in that von Neumann also moved towards the problem of biological growth, although from a different point of view. His work was likewise left incomplete; he died of cancer on 8 February 1957.

  * James Atkins himself had left the teaching of mathematics for music. He became a professional singer in 1949, and had a first Glyndebourne season in 1953.

  * In April and May 1954 the parliamentary debates were in terms of the idea (as the outraged Sunday Express put it) that ‘instead of the prison cell they should have the doctor’s clinic.’ But more knowledgeable observers had recognised that talk of either punishing or treating all homosexuals was quite unrealistic, and the publicity given to the Montagu trials gave them the opportunity to point out the damage done to the repute of the judicial system by a law so irregularly and partially enforced. A more practical policy was defined by the Sunday Times in March; contrasting ‘those things which must needs be legally tolerated’ with those which ‘must be condemned and rooted out’. On 8 July, the Home Secretary backed down and appointed J. F. Wolfenden, a public-school headmaster from 1934 to 1950, to chair a committee on the laws relating to homosexuality and prostitution. Thus Alan Turing died just as a more central strand of British administration was reasserting itself.

  In fact his crime was of the kind that everyone agreed should continue to be the object of state attention; meeting people in the street (‘importuning’), and having an affair with a working-class nineteen-year-old exemplified what was to be ‘condemned and rooted out’. But the number of prosecutions peaked in 1955, and then fell back until 1967. The government failed to set up the special hospitals or camps suggested by the medical profession, and the great panic dissipated rapidly after summer 1954. The most important effect was that the silence was broken – a first BBC radio talk being allowed on 24 May. If in fact it was the case of Alan Turing that had frightened the Churchill government out of its wits, he also played a posthumous part in the defusing of the taboo.

  He also died just before the international situation relaxed a little; at the Geneva conference China agreed to the temporary partition of Vietnam. Meanwhile McCarthy’s star fell rapidly after he attacked the US Army and the CIA. Churchill went to Washington on 24 June and repaired the Anglo-American rift. British military expenditure rose to a dramatic peak in 1954 but thereafter declined until the mid-1960s. Everyone but Alan Turing had a reprieve.

  Postscript

  As I lay with my head in your lap camerado,

  The confession I made I resume, what I said to you and the open air I resume,

  I know I am restless and make others so,

  I know my words are weapons full of danger, full of death,

  For I confront peace, security, and all the settled laws, to unsettle them,

  I am more resolute because all have denied me than I could ever have been had all accepted me,

  I heed not and have never heeded either experience, cautions, majorities, nor ridicule,

  And the threat of what is call’d hell is little or nothing to me,

  And the lure of what is call’d heaven is little or nothing to me;

  Dear camerado! I confess I have urged you onward

  with me, and still urge you, without the least

  idea what is our destination,

  Or whether we shall be victorious, or utterly quell’d and defeated.

  Alan Turing’s body was cremated on 12 June 1954 at the Woking Crematorium. His mother, brother, and Lyn Newman attended the ceremony. The ashes were dispersed in the gardens at the same place as those of his father. There is no memorial.

  Author’s Note

  For a figure in world history, there is very little source material from which to reconstruct a picture of Alan Turing – few original documents, and little in the way of published commentary. Secrecy and embarrassment of various kinds are partly responsible, but there is a paucity of information even where taboo subjects are not involved. The early development of the ACE, for instance, is covered incompletely by the surviving records – and some of the most interesting exist only thanks to unofficial individual initiative. The ACE represented a major act of public enterprise, and the events of 1946–9 largely determined the shape taken in Britain by what was soon to be seen as a second industrial revolution. Had cooperation between government, industry and brain power been continued in peace as in war, the future of the British economy might have been very different. But no special effort was made to record the course of decisions made, nor has the subject subsequently attracted the interest of historians or journalists or political theorists. And what is true of the ACE as a whole is even more true of Alan Turing’s personal part.

  One must recognise, however, that Alan Turing did not conduct his life as that of a figure in world history: he tried as best he could to continue the life of an ordinary mathematician. And mathematicians (as compared with literary or political figures, entertainers or spies) do not usually expect to be heard of or written about, whatever their contribution. They do not really expect other people to know what mathematics is, and are generally happy to be left alone. When judged by mathematical standards, one could not say that for a figure of his stature there has been any particular deficiency in records or neglect in reputation.* Pathetically small by worldly standards, the corpus of biographical material is still substantial in comparison with that of others in his profession.

  Taking first the question of what was written of him after his death, over the next twenty years or so, there were of course obituaries: Max Newman in The Times, Robin Gandy in Nature, Philip Hall in the King’s College Annual Report, and various more minor tributes. Newman followed by writing the Biographical Memoir to which Alan, as a Fellow of the Royal Society, was entitled. One of the fuller and more penetrating of the series, it treated his life and work from the point of view of a pure mathematician. The Second World War thus appeared as an interruption to his work on logic and the theory of numbers. The subject of his war work had to go unmentioned but so, with ruthless consistency, was the subject of practical computers relegated to a few lines. This analysis embodied the outlook of an intellectual tradition to which Alan Turing had certainly half-belonged, but it was not the whole story.

  One person was not satisfied with this assessment, and sensed that some other kind of recognition was due. This was Mrs Turing, who in 1956 embarked upon writing a biography of her son – an extraordinary development by any standards, in which a seventy-five-year-old Guildford lady, not hitherto notable for literary or social confidence, and knowing almost nothing about science, was left to piece together some of the debris from the wreck of the modern world’s dream. Her Victorian values still unshaken, she retained a strong belief in the idea that Alan’s work had been and would be for the benefit of humanity.

  Her slim volume appeared in 1959. There was perhaps a better book in Sara Turing, one that would have been a genuine memoir which placed the death alongside the other mysteries (as they were to her) of what her son had spent his life doing: something that could have pointed tellingly to the twentieth-century separation of science from ordinary life, and to the efforts both he and she had made to overcome that separation – though not succeeding. But this was not what she did: her book was in the form of a biography and written with an apparent emotional detachment which was in itself remarkable, considering the frightful circumstances which had inspired it.

  One reason that Alan’s mother could cast herself as a detached observer was that in so many ways she was writing about a stranger. The reader was not to know, but
there was very little in her narrative of his early life – and the period up to 1931 absorbed a third of her account – which did not come from surviving letters and school reports. She was surely trying to prolong in her mind the lately increased rapport with her son, by projecting it back into a past life of which she knew little – not an inkling, for instance, of Christopher Morcom’s significance for her son’s development. The objective stance then obliged her to set out his scientific career – another impossibility. Alan had once compared the work of writing programs to imitate intelligent behaviour as like being set to write an account of ‘family life on Mars’. Mrs Turing had set herself a task of nearly equal difficulty; rather as a computer might be programmed to write sentences of grammatical form, she was able to make a jigsaw of the titles of his papers, bits cribbed from the extant obituaries, comments solicited from other people, and newspaper cuttings. Yet she had little conception of what it meant.*

  Her position of weakness was accentuated by an extraordinarily obsequious attitude to anyone of rank or office, which meant that by implication she put her son at the level of a promising sixth-former. Indeed her whole book read much like a school report. The flow of tributes bore witness to the fact that she was still having to convince herself that he had turned out satisfactorily after all, and indeed to her astonishment that there was a world in which he had actually been admired. Undercutting him again and again, Computable Numbers was good because Scholz had been impressed by it, his interest in the brain was significant because Wiener and Jefferson approved…. Alan might have seen this assessment as a fate worse than death, although it was partly the outcome of his own failure to promote himself.