Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  The last of the German supply ships had been sunk on 23 June 1941. But that day there was something else to think about. Tweedledum had turned upon the slumbering Red King. It was not only Stalin who was caught napping; the Luftwaffe Enigma evidence pointing to an imminent German invasion had been the subject of another fight between GC and CS on the one hand and the service chiefs on the other. They had not been able to believe their ears. But now the world war had begun. From now on the Atlantic lay at Germany’s back, and the Mediterranean was a sideshow. The game had changed, and the period of anarchy was over.

  In the spring of 1941 Alan developed a new friendship. It was with Joan Clarke, a fact which presented him with a very difficult decision. First they had gone out together to the cinema a few times, and spent some leave days together. Soon everything was pointing in one direction. He proposed marriage, and Joan gladly accepted.

  Many people, in 1941, would not have thought it important that marriage did not correspond with his sexual desires; the idea that marriage should include a mutual sexual satisfaction was still a modern one, which had not yet replaced the older idea of marriage as a social duty. One thing that Alan never questioned was the form of the marriage relationship, with the wife as housekeeper. But in other ways he took a modern view, and above all was honest to a fault. So he told her a few days later that they should not count on it working out, because he had ‘homosexual tendencies’.

  He had expected this to end the question, and was surprised that it did not. He underestimated her, for Joan was not the person to be frightened by a bogey word. The engagement continued. He gave her a ring, and they made a visit to Guildford for a formal introduction to the Turing family, which went well enough. On the way they also had lunch with the Clarkes – Joan’s father was a London clergyman.

  He must have had thoughts of his own when, for instance, Joan went to Communion with his mother at Guildford. He might well have soft-pedalled the fierceness of his views in a way that in the long run would not have been possible. Again, the nebulous word ‘tendency’ fell short of the honesty with which he spoke to close male friends. If in fact he had suggested that there was more to it than that, she would have been hurt and shocked. He told Joan about Bob, explaining how he remained for the time being a financial commitment, and said that it was not a sexual matter – again true, but not quite the whole truth. But they were comrades in the aristocracy of talent, even if he was her superior in the work, and he specifically told her that he was glad he could talk to her ‘as to a man’. Alan was often lost when dealing with the Hut 8 ‘girls’, not least because he was unable to cope with the ‘talking down’ which was expected. But Joan’s position as cryptanalyst gave her the status of an honorary male.

  Alan arranged the shifts so that they could work together. Joan did not wear her ring in the Hut, and only Shaun Wylie was told that there was an actual engagement, but the others could see that something was in the offing, and Alan had managed to find a few bottles of scarce sherry, putting them by for an office party when the time came to announce it. When off duty, they talked a little about the future. Alan said that he would like them to have children, but that of course there was no question of expecting her to leave such important work at such a time. Besides, the outcome of the war, in summer 1941, was far from clear, and he still tended to pessimism. There seemed no stopping the Axis forces in Russia and the south-east.

  But when Alan said that he could talk to her as to a man, it certainly did not mean that he had to be solemn. It was the other way round: he was free to be himself, and not conventionally polite. If he came up with some scheme or entertainment then they would both join in with gusto. He had learnt how to knit, and had progressed as far as making a pair of gloves, except for sewing up the ends. Joan was able to explain how to finish them off.

  The joy, or the difficulty, was that they enjoyed so easy a friendship. They were both keen on chess, and were quite well matched, even though Joan was a novice, whose interest had been drawn by attending Hugh Alexander’s course for beginners. Alan used to call their efforts ‘sleepy chess’, taking place as they did after the nine hour night shift. Joan had only a cardboard pocket set, and proper chess pieces were unobtainable in wartime conditions, so they improvised their own solution. Alan got some clay from one of the local pits, and they modelled the figures together. Alan then fired them on the hob of the coal fire in his room at the Crown Inn. The resulting set was quite usable, if somewhat liable to breaking. He also tried to make a one-valve wireless set, telling her about the one he had made at school, but this was not such a success.

  They had been to see a matinée of a Bernard Shaw play while making their London visit, and besides Shaw, Alan was currently keen on Thomas Hardy, lending Tess of the d’Urbervilles to Joan. These were, after all, with Samuel Butler, the writers who had attacked the Victorian codes. But they spent more time taking long country bicycle rides. And because she had studied botany at school, Joan was able to join in one of Alan’s enthusiasms which went back to Natural Wonders. He was particularly interested in the growth and form of plants.

  Before the war he had read the classic work Growth and Form by the biologist D’Arcy Thompson, published in 1917 but still the only mathematical discussion of biological structure. He was particularly fascinated by the appearance in nature of the Fibonacci numbers – the series beginning

  1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…

  in which each term was the sum of the previous two. They occurred in the leaf arrangement and flower patterns of many common plants, a connection between mathematics and nature which to others was a mere oddity, but to him deeply exciting.

  One day he and Joan were lying on the Bletchley Park lawn – after a game of tennis, perhaps – and looking at the daisies. They started talking about them and Joan explained how she had been taught to record and classify the arrangement of leaves on plants by following them upwards round the stem, counting the number of leaves and the number of turns made before returning to a leaf directly above the starting-point. These numbers would usually appear in the Fibonacci series. Once Alan produced a fir cone from his pocket, on which the Fibonacci numbers could be traced rather clearly, but the same idea could also be taken to apply to the florets of the daisy flower. In this case it was rather harder to see how to count off the petals, and Joan wondered whether the numbers did not then arise merely as a consequence of the method of following them. This was pretty much the view of D’Arcy Thompson, who played down the idea that the numbers had any real significance in nature. They made a series of diagrams to test this hypothesis which did not satisfy Alan, who continued to think about ‘watching the daisies grow’.

  In 1941 everyone had to knit and glue and make their own entertainments. At the Clock House, where Mrs Morcom died this year, they were eating the young goats, and at Bletchley the shipping crisis was reflected not only in the work of Hut 8, but in the miserable régime of school dinners. Apart from the diet, the siege mentality suited Alan rather well, with matters of social protocol that in the 1930s seemed so important now falling into abeyance. He always liked making things for himself, be they gloves, radio sets or probability theorems. At Cambridge he had a way of telling the time from the stars. Now the war was on his side. In a more self-sufficient England, everyone had to live in a more Turingesque way, with less waste of energy.

  This was well understood in the higher realms of Bletchley, in many ways a New Statesman readers’ establishment, distilling the more creative elements of the ancient universities and leaving behind the upper-class finishing school mentality along with the misogynistic port-passing. By this time, the establishment had sprouted clubs for amateur dramatics and so forth. Alan was as shy as ever of this sort of thing, and never became a figure in the Bletchley social world. To some extent he was a ‘character’, but without the dominating egoism of the much older Dillwyn Knox. He retained a shy boy-next-door manner which muted his detachment from convention. Among the Hut 8 p
eople, his persona was that of ‘the Prof’; for while all the new men were ‘men of the Professor type’, the word suited him particularly well. It relieved people of the difficulty with forms of address, for women especially, and was a mark of respect while still expressing the amateur quality of his manner – more the ITMA professor than an eminent authority. Joan also called him ‘Prof’ while they were at work, although off-duty Alan commented on this, not actually objecting, but making her promise that she would not ever do so when he really was a professor, or indeed had returned to academic life. There was, in fact, a streak of vulgarity in the usage, which Mrs Turing had been quick to point out to him, comparing it with the lower-middle-class habit of wives referring to husbands by title rather than by name. But it was also that he did not want to sound presumptuous of professorial status.

  Pigou was also known as ‘prof’ to everyone in King’s, and for similar reasons. In fact, they were rather alike. David Champernowne had introduced them before the war, and Pigou became perhaps the only one of the elder King’s dons (or ‘old fogies’, as Alan was liable to call them) to know him well and indeed to find a mutual admiration. Pigou enjoyed a30 ‘sure grasp of logical relations and … fanatical intellectual integrity’, and he had ‘an astonishing capacity for simplifying life and all its important issues’, he would ‘dispense altogether with pretence as a weapon’, and his ‘eye for beauty was concerned with mountains and men’ – words that would have fitted Alan almost as well.

  In Alan’s case, there was a suggestion in the nickname of his role at school, as the tolerated ‘Maths Brain’ with his star globe and pendulum, who had performed the feat of cycling from Southampton. As at school, trivial examples of ‘eccentricity’ circulated in Bletchley circles. Near the beginning of June he would suffer from hay fever, which blinded him as he cycled to work, so he would use a gas mask to keep the pollen out, regardless of how he looked. The bicycle itself was unique, since it required the counting of revolutions until a certain bent spoke touched a certain link (rather like a cipher machine), when action would have to be taken to prevent the chain coming off. Alan had been delighted at having, as it were, deciphered the fault in the mechanism, which meant that he saved himself weeks of waiting for repairs, at a time when the bicycle had again become what it was when invented – the means of freedom. It also meant that no one else could ride it. He made a more explicit defence of his tea-mug (again irreplaceable, in wartime conditions) by attaching it with a combination lock to a Hut 8 radiator pipe. But it was picked, to tease him.

  Trousers held up by string, pyjama jacket under his sports coat – the stories, whether true or not, went the rounds. And now that he was in a position of authority, the nervousness of his manner was more open to comment. There was his voice, liable to stall in mid-sentence with a tense, high-pitched ‘Ah-ah-ah-ah-ah’ while he fished, his brain almost visibly labouring away, for the right expression, meanwhile preventing interruption. The word, when it came, might be an unexpected one, a homely analogy, slang expression, pun or wild scheme or rude suggestion accompanied with his machine-like laugh; bold but not with the coarseness of one who had seen it all and been disillusioned, but with the sharpness of one seeing it through strangely fresh eyes. ‘Schoolboyish’ was the only word they had for it. Once a personnel form came round the Huts, and some joker filled in for him, ‘Turing A.M. Age 21’, but others, including Joan, said it should be ‘Age 16’.

  He cared little for appearances, least of all for his own, generally looking as though he had just got up. He disliked shaving with a razor and used an old electric shaver instead – probably because cuts could make him pass out with the sight of blood. He had a permanent five o’clock shadow, which emphasised a dark and rough complexion which needed more than the cursory attention it received. His teeth were noticeably yellow, although he did not smoke. But what people noticed most were his hands, which were strange anyway, with odd ridges on his fingernails. These were never clean or cut, and well before the war, he had made them much worse by a nervous habit of picking at the side, raising an unpleasant peeling scar.

  To some extent, his lack of concern for appearances, like his low-budget mode of life, was an intensification of what people meant by ‘donnish’, and as such was far more striking to those outside university circles, than to those long familiar with bicycling dons eking out their stipends. It departed from the ‘don’ typology in his peculiar youthfulness of manner, but Alan Turing still presented the world outside Oxford and Cambridge with a crash course in King’s College values, and the reaction to his oddness was mostly a concentrated form of the mixture of baffled respect and head-shaking suspicion with which English intellectuals were traditionally regarded. This was particularly true at Guildford, where the engagement was perceived in terms of types, he as the don shy of women, and she as the ‘country vicar’s daughter’* and bluestocking ‘female mathematician’. It was demeaning, but the repetition of superficial anecdotes about his usually quite sensible solutions to life’s small challenges served the useful purpose of deflecting attention away from the more dangerous and difficult questions about what an Alan Turing might think about the world in which he lived. English ‘eccentricity’ served as a safety valve for those who doubted the general rules of society. More sensitive people at Bletchley were aware of layers of introspection and subtlety of manner that lay beneath the occasional funny stories. But perhaps he himself welcomed the chortling over his habits, which created a line of defence for himself, without a loss of integrity. He, this unsophisticated outsider at the centre, could be left alone at the point where it mattered.

  In the summer of 1941 that much more worldly observer Malcolm Muggeridge had cause to visit Bletchley and notice that31

  Every day after luncheon when the weather was propitious the cipher-crackers played rounders on the manor-house lawn, assuming the quasi-serious manner dons affect when engaged in activities likely to be regarded as frivolous or insignificant in comparison with their weightier studies. Thus they would dispute some point about the game with the same fervour as they might the question of free-will or determinism Shaking their heads ponderously, sucking air noisily into their noses between words – ‘I thought mine was the surer stroke’, or: ‘I can assert without contradiction that my right foot was already …’

  Alan did indeed have that way of sucking in his breath before speaking, while in Hut 8 they were, when off-duty, talking about games, free will and determinism.

  He was currently reading a new book by Dorothy Sayers, The Mind of the Maker.32 It was not his usual taste in reading, this being Sayers’ attempt to interpret the Christian doctrine of divine creation through her own experience as a novelist, but he would have enjoyed the challenge of her sophisticated attitude to free will, which she saw from God’s point of view, in the light of her knowledge that fictional characters had to find their own integrity and unpredictability, and were not determined by a master plan at the outset. One image which caught Alan’s fancy was that of Laplacian determinism suggesting that ‘God, having created his Universe, has now screwed the cap on His pen, put His feet on the mantelpiece and left the work to get on with itself.’

  This was not so new, but it must have made striking reading while the Bombes ticked away, getting on with the work by themselves – and while the Wrens did their appointed tasks, without knowing what any of it was for. He was fascinated by the fact that people could be taking part in something clever, in a quite mindless way.

  Machines, and people acting like machines, had replaced a good deal of human thought, judgment, and recognition. Few knew how the system worked, and for anyone else, it was a mystic oracle, producing an unpredictable judgment. Mechanical, determinate processes were producing clever, astonishing decisions. There was a connection here with the framework of ideas that had gone into Computable Numbers. This, of course, was far from forgotten. Alan explained the Turing machine idea to Joan, and gave her an off-print of one of Church’s papers, though she
perhaps disappointed him in her response. He also gave a talk on the subject of his discovery. Meanwhile Turing machines, reading and writing, had sprung into an exceedingly practical form of life, and were producing a kind of intelligence.

  A subject closely analogous to cryptanalysis, and which could be spoken of when off-duty, was chess. Alan’s interest was not limited to chess as recreation; he was concerned to abstract a point of principle from his effort to play the game. He became very interested in the question of whether there was a ‘definite method’ for playing chess – a machine method, in fact, although this would not necessarily mean the construction of a physical machine, but only a book of rules that could be followed by a mindless player – like the ‘instruction note’ formulation of the concept of computability. In such discussions Alan would often jokingly refer to a ‘slave’ player.

  The analogy between chess and mathematics had already been employed and in each case the same problem arose, that of how to choose the right move to reach a given goal – in the case of chess, to achieve checkmate. Gödel had shown that in mathematics there was no way at all to reach some goals, and Alan had shown that there was no mechanical way to decide whether, for a given goal, there was a route or not. But the question could still be asked as to how mathematicians, chess-players or code-breakers did in practice make those ‘intelligent’ steps, and to what extent they could be simulated by machines.

  Although his solution of the Entscheidungs problem and his work on ordinal logics had focussed attention upon the limitations of mechanical processes, it was now that the underlying materialist stream of thought began to make itself more clear, less interested in what could not be done by machines, than in discovering what could. He had demolished the Hilbert programme, but he still exuded the Hilbert spirit of attack upon unsolved problems, and enjoyed a confidence that nothing was beyond rational investigation – including rational thought itself.