Alan Turing: The Enigma (47 page)

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 people, 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 a
³⁰
‘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 that
³¹

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.

Jack Good, like Alan, had the Bletchley mind, not being simply ‘a mathematician’, but a person who enjoyed exploring the connections between logical skills and the physical world. Chess interested him too, and unlike Alan he was a Cambridgeshire county player. He had already in 1938 published a light-hearted article on mechanised chess-playing in the first issue of
Eureka
, the house magazine of the Cambridge mathematics students. Besides playing chess, Alan taught Jack Good the game of Go, and before long found himself being beaten at that as well.

Over meal-times on night shift they would talk about the problem of mechanising chess. They latched on to a basic idea, which they agreed to be obvious. It was that a chess player might often see wonderful moves that could be made if only the opponent would do such-and-such, but in serious play, White would assume that Black would always exploit the situation to maximum advantage. White’s strategy therefore would be to make the move
least advantageous
to Black – the move making Black’s best move the least successful of all the possible best moves – the minimum maximum, in fact.