Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  * His estate amounted to £4603 5s 4d. But a larger sum, £6742 4s 11d, was payable by Manchester University – it was the amount due as a death grant under the terms of the superannuation policy to which he had subscribed. The verdict of suicide did not affect the payment, which, as John Turing ensured, went entirely to Mrs Turing.

  * Almost certainly the volume of plates from the German zoologist Ernst Haeckel’s report on the Radiolaria, part of the immense series published by the British government in the 1880s with the scientific results of the voyage of the HMS Challenger from 1873 to 1876.

  * It was entitled Solvable and Unsolvable Problems, and first gave an example of a ‘solvable’ problem. This was a solitaire game (actually the ‘fifteen puzzle’) in which, as he described, there were only a finite number of possibilities to consider (namely 16! = 20,922,789,888,000). Hence, in principle, the game could be ‘solved’ simply by listing all the possible positions. This helped to illustrate the nature of an absolutely ‘unsolvable’ problem, such as he went on to describe, but the large number also demonstrated the gap between theoretical and practical ‘solvability’. As it happened, of course, the Bombe had indeed exploited the finiteness of the Enigma by just such a brute force method, but in general the knowledge that a number is ‘only’ finite is not of practical significance. One cannot play chess, nor deduce all the wirings of an Enigma machine, by knowing that the possibilities are finite. The ‘fifteen puzzle’, indeed, poses a tough problem to the computer programmer. Turing machines, when embodied in the physical world, are severely limited by considerations other than those of logic.

  * 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.

  * Ministry of Supply

  * 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 or 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’ from 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 resu
me,

  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 diffficulty; 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.

  Yet there was one point his mother grasped that better informed people could be too sophisticated to see, namely that in 1945 he had set out to build a computer. She stuck to this at a time when everything surrounding the subject was still suffused in embarrassment. And more generally, she displayed an amazing tenacity and nerve in tackling the male institutions from which she was excluded, and in refusing to be daunted by the polite evasiveness that she met. For of course there were two areas that were out of bounds – what he had done in the war and his homosexuality. A number of people felt they could not contribute anything whatever with honesty unless the unmentionable were mentioned – and of course it was not mentioned, no more than in any of the other written pieces. With the war she got a little further, being allowed to say that ‘he was one of a team whose joint work was an important factor in our winning the war’ – a hint which was as strong as anything that appeared in the next ten years.† Tiptoeing among the minefields – and perhaps anyone but her would have found it impossible to continue – she did, ultimately, stand up for him as few others would.

  What was sad was not that she failed to do what was manifestly beyond her powers; it was that although she had her own insights and stories they did not, in fact, add up to an understanding or even a formul
ation of the particular enigma that Alan had posed for her. At the end she closed with a comparison of what she had written with the Lives of the Saints – Alan would have derided this attempt to get him through the eye of the needle, and yet had she pursued with any seriousness the subtle conflict of the ‘pure’ and the ‘applied’ she could quite legitimately have expressed it in religious language and found something quite special to say. But here she offered nothing: for examination marks, government service, and the building of machines appeared alike as undifferentiated Good Things. The absence of any question mark around the place of science was perhaps one reason why her book, pitiful by the standards that would be expected of a literary or political biography, attracted the gentle praise of critics. It was a holiday for a world trying to forget Dr Strangelove. At last, it seemed, here was a scientist untouched by the traumas of the 1940s and 1950s! There was a half-truth in this notion, there being something of the 1880s in Alan Turing as well as in his mother; but again it was hardly the whole story.

  During the 1960s, and into the 1970s, Newman and Sara Turing were the sources upon which various encyclopedia entries, potted biographies and popular articles drew. But by the turn of the decade there were small sprouts of a different kind of comment pushing their way through the Stoney ground. One factor was simply the expansion and greater sophistication of what had become ‘computer science’, slightly modifying the status of computers as altogether infra dig. for a mathematician. It was in 1969 that Donald Michie published the NPL report Intelligent Machinery, he himself being concerned to set a lead in British developments. He commented in this period on how the prevailing attitude was that ideas about machine intelligence were a diversion from serious work; but the 1970s ushered in a greater appreciation of the computer as a universal machine, concerned with any and every form of logical manipulation, and not necessarily at work on arithmetical calculations. This general development encouraged a clearer understanding of what Alan Turing had envisaged from the beginning.*