* X-ray measurements give only the amplitudes of the different frequency components in the diffracted X-rays, and not the phases. The analysis depends upon guessing the phases, the criterion of a correct guess being that when the amplitudes and phases are put together, they lead to a picture of the crystal which is in accord with physical reality, with the right number of atoms and a positive electron density. This is exactly the same idea as guessing a key, given a piece of cipher-text: the criterion of a correct guess being that it give a sensible message.
The analogy with cryptanalysis is even closer in that the crystallographer attacks the problem, at first sight too enormous for contemplation, by making a hypothesis about the structure of the crystal. Thus Watson and Crick pursued the DNA analysis, as did Pauling, by making good guesses about the helix structure, and thus getting closer and closer to the solution. This is essentially the same idea as the ‘Probable Word’ method, which also effects a drastic reduction in the number of possible keys – so that with the Enigma, for instance, they were left only with a small number of Bombe ‘stops’ to try out for sensible German plain-text.
It is not surprising that Alan Turing could see how to quantify the idea of information required for a guess to be possible: this was very close to the quantification of ‘weight of evidence’ which constituted his major conceptual advance at Bletchley.
* Shannon was sceptical about this programme of work, and Shannon had a good point. By 1977 computer calculations would show that among the first seven million zeroes of the zeta function, there is not one that lies off the special line. This was a case where a brute force attack could yield only a negative result.
* If the operations are represented by letters, then such a sequence is represented by a ‘word’ – hence the name of the problem. For a finite group, there would of course exist such a definite method, namely the crude one of working through all the possibilities. The problem arises for infinite groups.
† A ‘semi-group’ is the abstract version of a set of operations which meets half of the conditions required for a ‘group’: the operations cannot necessarily be reversed.
‡ A ‘cancellation semi-group’ is a semi-group with a property which makes it closer to being a group: if AC = BC then it must be that A = B.
* Polanyi rejected this argument, saying that a machine was a machine, a human mind was a human mind, and no amount of evidence could change this a priori fact.
* This oscillation between the two concepts of computability found its way into his Programmers’ Handbook: on the first page the programmer was greeted by the assertion that ‘There is also a part of the machine called the control which corresponds to the [human] computer himself. If his possible behaviour were very accurately represented this would have to be a formidably complicated circuit. However we really only require him to be able to obey the written instructions and these can be made so explicit that the control can be quite simple.’
* Thus a contemporary review article44 stated ‘The importance of the principle of patterned ‘field’ activities in the determination of embryonic systems has been generally recognised. … Yet their nature and mode of operation are still among the greatest puzzles of modern biology.’
* More strictly, all but the Manchester and Toronto machines were of a slightly modified design, the Mark I*.
* Meanwhile D.G. Prinz, who worked for Ferranti, quite independently programmed the Manchester computer to solve two-move chess problems. But this would have been of minimal interest to Alan; given that a solution exists it is simply a matter of patience to run through every possibility until it is found. Unless it gave an idea of how the brain did it, or some feel of ‘pitting one’s wits’ against the machine, the problem of doing the programming, however ingenious, would have had little appeal for him. As in 1941, he was not interested in chess in itself, but as a model for thought.
* In this game three piles of matches are laid out, and two players take turns to remove as many matches as they please from any one pile. The player who removes the last match is the winner.
* Until his death in 1975, Christopher Strachey was to be a central innovative figure in British computing, and his draughts-playing program seminal in the study of ‘machine intelligence’.
* Alan was introduced to Angus Wilson at Cambridge by Robin Gandy. Although Angus Wilson had worked at Bletchley, he had not met Alan there.
† Was this plain-text or cipher-text? This is a good example of where the meaning of a word depends upon its social embodiment. At least since the 1930s it had been in general use among homosexual men as a code word with a plain meaning – in America. Thus D.W. Cory’s pioneer work The Homosexual in America, which appeared in 1951, explained: ‘Needed for years was an ordinary, everyday, matter-of-fact word, that could express the concept of homosexuality without glorification or condemnation. It must have no odium of the effeminate stereotype about it. Such a word has long been in existence, and in recent years has grown in popularity. The word is gay.’ Alan Turing would usually use ‘homosexual’ or, among his friends, the word ‘queer’. But he could have known the American usage, and would entirely have approved of D.W. Cory’s rationale of it. For this reason the word will be used from here onwards; any anachronistic or transatlantic effect thus introduced will reflect quite properly the difficulty that Alan Turing had in communicating his attitudes in the Britain of the early 1950s. As with the ‘computer’ he was ahead of his time.
* The BBC had made a more seasonal contribution to the public understanding of computers by broadcasting the Manchester machine’s rendering of ‘Jingle Bells’ and ‘Good King Wenceslas’.
8
On the Beach
In paths untrodden,
In the growth by margins of pond-waters,
Escaped from the life that exhibits itself,
From all the standards hitherto publish’d, from the
pleasures, profits, conformities,
Which too long I was offering to feed my soul,
Clear to me now standards not yet publish’d, clear to
me that my soul,
That the soul of the man I speak for rejoices in comrades,
Here by myself away from the clank of the world,
Tallying and talk’d to here by tongues aromatic,
No longer abash’d, (for in this secluded spot I can
respond as I would not dare elsewhere,)
Strong upon me the life that does not exhibit itself,
yet contains all the rest,
Resolv’d to sing no songs to-day but those of manly attachment,
Projecting them along that substantial life,
Bequeathing hence types of athletic love,
Afternoon this delicious Ninth-month in my forty-first year,
I proceed for all who are or have been young men,
To tell the secret of my nights and days,
To celebrate the need of comrades.
It had not taken the police long to detect Alan Turing’s crime. It was almost inevitable once he had made the original report of the burglary, for the police had been able to identify Harry’s fingerprints. He was already in custody on another charge in Manchester, and before long made a statement which referred to Arnold telling him of having ‘business’ at Alan’s home. The further information Alan had volunteered on the Sunday merely gave the police their opportunity to act with confidence.
Alan took them upstairs to where he was working with his desk calculator. The detectives, Mr Wills and Mr Rimmer, found themselves in an unfamiliar environment, the room littered with pieces of paper covered with mathematical symbols. They told Alan that they ‘knew all about it’, leaving him unclear whether they were talking about the burglary or of something else. He later told Robin that he had to admire their interrogation technique. They asked him to repeat the description he had given them on the Sunday morning, and Alan said,1 ‘He’s about twenty-five years of age, five foot ten inches, with black hair.’ Imitation wa
s not Alan Turing’s strong point – perhaps an intelligent machine would have done better. This feeble attempt sank like a stone. Mr Wills said, ‘We have reason to believe your description is false. Why are you lying?’
This was the moment for ‘I don’t know what came over me’, or the other phrases employed by more politically-minded persons, but once the detectives had shown their hand, Alan blurted out everything that they wanted to hear, in particular admitting that he had concealed the identity of the informant because he ‘had an affair with him’. Mr Wills asked ‘Would you care to tell us what kind of an affair you have had with him?’, and this policemanlike question elicited from Alan a memorable phrase, detailing in semi-official language three of the activities that had taken place. ‘A very honourable man’, the detectives thought him as they cautioned him in the usual way, and they were the more impressed when he volunteered a statement of five handwritten pages. Relieved of the usual necessity to translate human life into police language, they were most appreciative of what was ‘a lovely statement’, written in ‘a flowing style, almost like prose’, although ‘beyond them in some of its phraseology’. They were particularly struck by his absence of shame. ‘He was a real convert. … he really believed he was doing the right thing.’
Alan had commented to the detectives that he thought a Royal Commission was sitting ‘to legalise it’. There he was wrong. And almost certainly he underestimated the seriousness of what in his statement became ‘the offence’. Harry had been justified in assuming that Alan was fair game for robbery. As a sex criminal, he had forfeited the protection of the law. Alan’s statement illustrated the difficulty he faced in grasping this fundamental fact. It was mostly concerned with the undecidable problem of Arnold’s veracity, and details of ‘the offence’, though freely and even defiantly supplied, appeared as incidental to what he perceived as the story. It might be called unrealistic of him to expect a relationship rooted in such inequality to develop as an ‘affair’ between free individuals; he took no account of the fact that words and actions could mean different things to people in different social circumstances. Yet if this showed a lack of realism, a liberal intellectual dream world, it was an unreality also consciously sought and appreciated by Arnold, who had found himself challenged and moved by being treated as a friend of the élite. And the greater unreality lay in Alan’s attitude to the law, which was not interested in his mental dilemmas, but was very much concerned with his bodily activities. He found it almost too absurd for belief; but the fact remained that it was this, ‘the offence’, that the police were investigating with persistent, conscientious, thoroughness.
The detectives did not, however, extend their questioning to his whole past life. In this respect they only took his fingerprints and photograph, to be checked against Scotland Yard records for previous offences. As supporting evidence of the crimes they also took what correspondence he had relating to Arnold. Afterwards, Alan was aware that if he had said Harry was lying, the police might have been unable to make any case against him. As it was, they were able to complete their duties with ease. On Saturday morning Mr Wills arrested Arnold in the Manchester printing shop (a job he immediately lost), took him to Wilmslow police station and showed him Alan’s statement. Mr Wills was soon able to write out a statement for Arnold to sign, spelling out ‘offences’ in copious detail. This in turn Alan agreed on Monday 11 February to be ‘materially correct’. The police had solved a crime which attracted up to two years of imprisonment.
The crime was, in fact, that of ‘Gross Indecency contrary to Section 11 of the Criminal Law Amendment Act 1885’. It was defined purely in terms of parts of the male body, and applied absolutely, irrespective of such factors as age, financial advantage, and whether the activity was in a public or a private place. Alan’s statement left no room for doubt that he was guilty, and he was wrong in imagining that what he had done might soon be ‘legalised’. He was right, however, in thinking that changes were taking place in the official perception of homosexuality. Above all, the silence was being broken.*
Indeed the turn of the 1940s had seen a renewal in Britain of the process which had led to that 1885 Act, to the trials of Oscar Wilde, and to the books of Havelock Ellis and Edward Carpenter in the 1890s. The point about the law was that it had replaced the vague theological ‘crime against nature’, or the ‘crime not to be mentioned among Christians’, by a definite rule. When Oscar Wilde spoke of ‘the love that dares not speak its name’, he identified a crucial aspect of what was happening – the speaking up, the ‘flaunting’, the explicitness.
In the next fifty years, incursions into British public consciousness by such books as The Loom of Youth and The Cloven Pine had been exceedingly circumspect and allusive in nature. But in the 1940s a new wave of explicitness swept across the Atlantic to break upon the more austere and tight-lipped culture of the island race. Since 1938, for instance, the zoologist Alfred Kinsey had been documenting the unofficial reality of human sex, and in 1948 he revealed a breach of the ‘fixed moral codes’ so massive that, like the evidence confronting Dönitz, its implications were too profound to be entertained.
While for a time such revelations could, in Britain, be dismissed as American extravagance and vulgarity, the ‘head in the sand’ attitude was already doomed. In many ways what was happening was a delayed effect of the war – or rather, like so many wartime developments, the expression of ideas which had begun in the ‘mechanization, rationalization, modernization’ of the late 1930s. While in military affairs the old regime had been forced to adopt modern methods for the sake of survival in 1942, the parallel developments in social policy took longer to filter through. The opening of a public debate about male homosexuality in Britain in 1952 was the conflict of the small back room, in another sphere.
In 1952, as in 1942, the times were out of joint. The rulers of Great Britain were still apt to regard the behaviour of its population as that of a public school. In 1952 the pocket money and the tuck shop were under better management than before, and there was less open complaining from the Modern side. But the return of the old Headmaster in October 1951 had suggested invidious comparisons with former triumphs. In 1951 Britain had lost control over Iran and Egypt, countries so successfully held against German encroachment not ten years before. As during the crisis of imperialism in the 1890s, military loss of control could be identified with sexual loss of control. In the traditional view, homosexuality was an act, or practice, into which any man might be led – and such lapses into ‘slackness’ were to be prevented not only in the armed forces, but in the national life which raised and moulded them.
Such a view, however, could already be identified with that of an older generation, and one which had been pushed aside since 1940. For nearly a hundred years there had existed a quite different kind of official description, which concentrated not upon the act, but the state of mind. Considerable efforts had been made to elucidate a ‘homosexual type’, or a ‘homosexual personality’, rather as the nineteenth century psychologists had also devoted energy to defining criminal, or mentally deficient, or other ‘degenerate types’. The word ‘homosexual’ was itself a nineteenth century medical neologism. Freud was often credited with making this mode of description available to people. Indeed, Alan and Robin would sometimes puzzle over the question of how people had been able to think about sexual desire before Freud’s day.
In his 1950 Mind article, Alan had referred to the ‘skin of an onion’ analogy as helpful:
In considering the functions of the mind or the brain we find certain operations which we can explain in purely mechanical terms. This we say does not correspond to the real mind: it is a sort of skin which we must strip off if we are to find the real mind. But then in what remains we find a further skin to be stripped off, and so on. Proceeding in this way do we ever come to the ‘real’ mind, or do we eventually come to the skin which has nothing in it?
His own view, of course, was that the mind was like an onion,
and not like an apple, there being no central, irreducible, undetermined core. In a different way, nineteenth and twentieth century science had been peeling the onion of the mind, and had dented the concept of responsibility with ‘mental illness’, shell-shock, neurosis, breakdowns and so forth. Where was the line to be drawn? The conservative fear was that every kind of behaviour would be excused by appeal to some irresistible, uncontrollable force majeure. Like Polanyi and Jefferson, they sought a non plus ultra to the pretensions of mental determinism, a barrier against the flood of threats to traditional values unleashed by the Second World War. They found one in homosexuality: the new men’s talk of ‘conditions’ and ‘complexes’ was not to be allowed to excuse a deadly social evil, corrupting and weakening everything in its path.
At the same time, yet a third kind of description was gradually coming into focus, that of homosexual men as socially defined. From this point of view, the emphasis was to be placed not upon thoughts and feelings, nor on sexual acts, but on the particular patterns of acquaintanceship, money, and occupations associated with homosexuality. The sociologist ‘Gordon Westwood’, whose book Society and the Homosexual opened the British debate in 1952, described male homosexuality in all of these ways, one after the other. Reaching a wider audience, the Sunday Pictorial’s series of reports2on ‘Evil Men’ also broke what it called ‘the conspiracy of silence on the subject’ the same year, and likewise treated it from a modern psychological and social perspective, rather than in terms of the law. ‘Most people’, the newspaper explained, ‘know there are such things – “Pansies” – mincing effeminate, young men who call themselves queers.’ But these obvious ‘freaks and rarities’, it continued, represented but the tip of the iceberg. The problem was far greater than most people realised, and the time had come to tackle it.
Alan Turing: The Enigma The Centenary Edition Page 72