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

by Andrew Hodges

  Though born to a codebreaker father and mathematician mother, Christopher Strachey had not particularly stood out as a King’s mathematics student from 1935 to 1938, and after wartime radar work was teaching at Harrow School. But the idea of machine intelligence grabbed his attention rather as it had Alan’s. In 1951 a mutual friend put him in touch with Mike Woodger at the NPL, and he embarked upon writing a draughts program for the new Pilot ACE. By May he was also working with the Turing Programmers’ Handbook with an eye to using the Manchester machine. On the evening of the broadcast he wrote a long letter57 to Alan, with ambitious plans:

  … The essential thing which would have to be done first, would be to get the machine to programme itself from very simple and general input data…. It would be a great convenience to say the least if the notation chosen were intelligible as mathematics when printed by the output … once the suitable notation is decided, all that would be necessary would be to type more or less ordinary mathematics and a special routine called, say, ‘Programme’ would convert this into the necessary instructions to make the machine carry out the operations indicated. This may sound rather Utopian, but I think it, or something like it, should be possible, and I think it would open the way to making a simple learning programme. I have not thought very seriously about this for long, but as soon as I have finished the Draughts programme I intend to have a shot at it.

  He had been thinking about the learning process, not only in the classrooms of Harrow School, but by playing the logical game of Nim* with a non-mathematical friend. Most mathematicians would know from Rouse Ball’s old Mathematical Recreations that there was an infallible rule for a winning strategy, based on expressing the number of matches in each heap in binary notation. Few people were likely to spot this rule through play, but Strachey’s friend did notice a special case of it, namely that a player who could achieve the position (n,n,0) had won, for thereafter it was only necessary to copy the opponent’s moves to reduce the heaps down to (0,0,0). It was the element of abstraction achieved by a human learner that interested Strachey. He had worked out a program which could keep a record of winning positions, and so improve its play by experience, but it could only store them individually, as (1,1,0), (2,2,0) and so on. This limitation soon allowed his novice friend to beat the program. Strachey wrote:

  This shows very clearly, I think, that one of the most important features of thinking is the ability to spot new relationships when presented with unfamiliar material….

  and his Utopian ‘Programme’ was explained as one of his ‘glimmerings of an idea as to how a machine might be made to do it.’

  Alan’s interests were by now centred on biology but he was still keen to develop such speculative ideas about mechanical thinking, in a way more detailed than he had explained in Mind. A talk given at this period58 incorporated some proposals which started off like an office filing system, or indeed the ‘intelligence’ of Hut 4:

  The machine would incorporate a memory…. It would simply be a list of all the statements that had been made to it or by it, and all the moves it had made and the cards it had played in its games. These would be listed in chronological order. Besides this straightforward memory there would be a number of ‘indexes of experiences’. To explain this idea I will suggest the form which one such index might possibly take. It might be an alphabetical index of the words that had been used, … so that they could be looked up in the memory. Another such index might contain patterns of men on parts of a ‘Go’ board that had occurred.

  But then the minds of the filing clerks would begin to be taken over by the machine itself:

  At comparatively late stages of education the memory might be extended to include important parts of the configuration of the machine at each moment, or in other words it would begin to remember what its thoughts had been. This would give rise to fruitful new forms of indexing. New forms of index might be introduced on account of special features observed in the indexes already used….

  In many ways what he was doing was to work out his own theory of psychology, with the machine (mostly in imagination) as the stage on which it could be played.

  The Inaugural Conference of the Manchester computer, from 9 to 12 July 1951, to which Alan returned after a holiday abroad, was a more mundane occasion. Alan gave one of the talks59 – a dull one on the Manchester machine code, with all the gory detail of the base-32 backwards arithmetic – and he contributed to the discussions, chipping in to press for interpretative routines to be used on the Pilot ACE.

  But Wilkes was the star, with ‘micro-programming’, an elegant new system for the design of control and arithmetic hardware. By this time it was being widely said that it was the Cambridge approach, which made concession to the human user, that held the key to the future. The Cambridge group called themselves the ‘space cadets’ and the rest, the ‘primitives’, and Alan Turing had made himself an arch-primitive by insisting on being able to follow the Manchester machine’s operations digit by digit, although, on another level, he was the boldest Dan Dare of them all, embarrassing the responsible scientists with his anthropomorphic view of machines.

  The application of computers to commercial purposes received serious discussion, and M. J. Lighthill, the new Professor of Applied Mathematics at Manchester, proposed that by 1970 ‘the use of the machine shall permeate the whole undergraduate course. Finally it may be necessary to re-orient the teaching of mathematics even in schools. However, any idea that “ABC” may at last be ousted by “/E@A” is, one hopes, only visionary.’ This complaint at the base-32 notation espoused by Alan was to be vindicated; it would soon be thought absurd to expect ordinary users to adjust themselves in this way, although in 1951 this was far from clear. This conference was Alan’s last appearance as a contributor to the programming or operating of computers, and he was already passing into legend – a ghost from the past in a science without history. A shabby and eccentric survival from the Cambridge of the 1930s, here he found himself seen, and little understood, against the classless stainless steel of the dawning 1950s.

  Mike Woodger gave a talk about the relative performance of the Manchester and NPL machine instruction codes. Alan had invited him to stay at Hollymeade for the week of the conference. His guest would have been rather frightened if he had known that Alan was homosexual, but of this he remained unaware. What he did encounter, however, was the great muddle of pots and pans full of weeds and smelly mixtures, in which Alan was pursuing his desert-island hobby, seeing what chemicals he could make out of natural materials, and in particular doing some electrolytic experiments. Mike Woodger made a big hit when he admired the brick path, but did not do so well when Alan tried to explain his progress with morphogenesis.

  For it was the biological theory, rather than the imitation game, that was his favourite topic now. At last there was something else that he was seriously interested in, that he could also talk about. As soon as the new computer was installed and working, it was set up to simulate chemical waves on his idealised ring of cells, the Turing Hydra. After much working on different cases, he came up with a convincing set of hypothetical reactions which, set to work in an initially homogeneous ‘soup’, would have the effect of setting up a stationary spatial distribution of waves of chemical concentration. This could be done at different speeds, with different results: ‘fast cooking’ and ‘slow cooking’, he called it. He also tried out the gastrulation problem, showing how random disturbances on a sphere could lead to a particular axis being picked out.

  In this work he developed a unique sense of interaction with what was, in effect, a personal computer. It was like the dialogue with the Colossus, perhaps, though Roy Duffy, the new maintenance engineer, would call it ‘playing the organ’ as he watched Alan sit at the console and use the manual controls. Everyone who used the machine had to develop a good sense of how it was actually working, if only because there were always drum tracks and cathode ray tube stores out of action, requiring modifications to be made to the
programming. But Alan developed it to a fine art, writing in instructions which would make the machine’s ‘hooter’ sound at different points, when new parameters would be required. In this way he could watch the ‘cooking’ as it went along. The user also had complete control of the running and output mode of the machine, and Alan sometimes had it display the biological patterns on the cathode ray tube monitors, or print out contour maps in the way that crystallographers had by then devised.

  Usually he worked overnight – he regularly booked Tuesday and Thursday nights. It was not all work on biology. He had, in particular, a ‘bell ringing’ program. Bell ringing? Working through every possible permutation? For whom did the bell toll? Ask not…. But usually he could be expected to emerge in the morning waving around print-outs to anyone who was around – ‘giraffe spots’, ‘pineapples’ or whatever – and then go home to sleep until the afternoon. This night-work was reflected in what was perhaps the most progressive feature of his manual, in which he explained how he made the machine itself do the secretarial work of keeping track of experiments and modifications. Even in this technical piece of writing, there was a high-level scientific play with the idea of ‘rules’ and ‘descriptions’: the programmer was allowed to use the machine in its logical sense, the engineer to use it in its physical sense, and the ‘formal mode’, as he defined it, was to print out the description of the operation that was ‘complete’ in another, higher level, sense:

  There are a number of modes or styles in which the machine may be used, and each mode has its conventions, restricting the operations considered admissible. The engineers for instance will consider the removal of a valve or the connection of two points temporarily with crocodile clips to be admissible, but would frown on certain uses of a hatchet. The removal of valves and all alterations of connections are certainly not permitted to the programmers and other users, and they have additional taboos of their own. There are in fact a number of modes of operation which might be distinguished, but only the formal mode will be mentioned here. This mode has rather stringent and definite conventions. The advantage of working in the formal mode is that the output recorded by the printer gives a complete description of what was done in any computation. A scrutiny of this record, together with certain other documents should tell one all that one wishes to know. In particular this record shows all the arbitrary choices made by the man in control of the machine, so that there is no question of trying to remember what was done at certain critical points.

  But apart from such by-products of his work, in this case anticipating the introduction of a computer ‘operating system’, the other users of the machine did not now have more than the vaguest idea of what he was doing with it; after the summer of 1951 there was virtually no contact between them.

  Alan spent August 1951 at Cambridge as usual, and from there a party consisting of himself, Robin, Nick Furbank, Keith Roberts and Robin’s friend Christopher Bennett went down on the train to London for the Festival of Britain. They went to the Science Museum in South Kensington where the science and technology exhibits were housed. Grey Walter’s cybernetic tortoises were on show, though they seemed to be going round in circles, and Robin said they were suffering from General Paralysis of the Insane. However, they observed one nice and unexpected touch: the feedback-dance that the tortoises performed in front of a mirror. Then they came across the NIMROD, which Ferranti were exhibiting: a special purpose electronic machine which would play Nim with members of the public. The Ferranti people were pleased to see Alan and said, ‘Oh Dr Turing, would you like to play the machine?’ which of course he did, and knowing the rule himself, he managed to win. The machine dutifully flashed up ‘MACHINE LOSES’ in lights, but then went into a distinctly Turingesque sulk, refusing to come to a stop and flashing ‘MACHINE WINS’ instead. Alan was delighted at having elicited such human behaviour from a machine.

  The cognoscenti among them were also nudging each other about the young men who tended the exhibits, so this was not the only pleasure. After they had taken a good look at the new scientific Britain arising from the ashes, they made off to the Festival fun fair in Battersea Park. Alan was feeling a bit more flush than usual, and broke his usual rule, which he inherited from his father, by paying for a taxi rather than going on a bus. He would not go on the roller-coaster, saying it would make him sick. But they all went in the Fun House, and goggled at each other in the ultra-violet light.

  Back at Manchester, Tony Brooker arrived, and began at once to undo the worst effects of the base-32-backwards mentality, writing new and more efficient schemes for input and output which allowed decimal notation, as well as improved sub-routine linkage. Alan did not mind in the least, but stuck to his own scheme, in which he was quite happy, his imagination quite easily visualising cow-blotches or rose-petals in a jumble of the thirty-two teleprinter symbols. Meanwhile Christopher Strachey had visited Manchester to try out a long program, the longest that anyone had dared attempt, written only from the manual and a little consultation with Cicely Popplewell. It was intended to solve a problem that Alan had suggested to him, that of making the machine simulate its own behaviour, in such a way that other programs could be tested out. At the laboratory they regarded this ambitious amateur effort with friendly scorn, knowing that like everyone’s first dabblings it stood not a chance of success. But the program was duly punched out and Strachey allowed to try it. Alan showed him how to operate the machine, offering a few quick-fire instructions, and then leaving Strachey to get on with it. Usually Alan would be impatient with others’ relative slowness, but this time he met his match. Overnight, Strachey was able to make his program work, and furthermore to amaze everyone with its final rendition of God Save the King, played on the hooter. On Alan’s recommendation, Lord Halsbury immediately offered Strachey a job with the NRDC, at a salary sufficient to persuade him away from his boys at Harrow. Alan’s days as grand master of the console were over. He had handed on the torch.*

  At the beginning of November his paper on morphogenetic theory was ready. He decided to send it to the biological series of the Royal Society Proceedings, where it was received on 9 November. This meant putting in some rather elementary mathematical discussion. As he pointed out, few people were likely to be familiar with differential equations, physical chemistry and physiology. Biologists tended to be more experienced in translating what they saw into Greek than into mathematics. Mathematicians, on the other hand, usually knew nothing of the life sciences, though Lighthill was particularly encouraging about Alan’s work. It was yet another case of him producing ideas which fell into no neat compartment of thought. The Chemistry department offered a middle ground, and Alan gave a seminar there on his theory on 11 December 1951.

  Christmas was approaching, and with it the duty of choosing presents. Alan was always conscious of this, if not of other social obligations. His personal generosity could be relied upon. He had helped his favourite aunt Sybil, who had been a missionary in India, with a Braille set when she lost her sight. (He visited her at the time of the Bristol colloquium, for she lived nearby.) He had helped his childhood friend Hazel Ward to return to missionary work after the death of old Mrs Ward, atheism notwithstanding. And to the surprise of Robin, who had heard him talk about his schooldays, he had subscribed to the Sherborne Quatercentenary appeal in 1950. This Christmas, however, he felt he owed himself a present, after finishing a paper which he regarded as the equal of Computable Numbers, setting out not just a new result, but a new framework, a new world to conquer.

  Alan later wrote a short story,60 in the new, ‘frank’, rather jaundiced, socially conscious style of Angus Wilson,* itself in E. M. Forster’s tradition. It began:

  Alec Pryce was getting rather [illegible] with his Christmas shopping. His method was slightly unconventional. He would walk round the shops in London or Manchester until he saw something which took his fancy, and then think of some one of his friends … who would be pleased by it. It was a sort of allegory of his method o
f work (though he didn’t know it) which depended on waiting for inspiration.

  When applied to Christmas shopping this method led to a variety of emotions just as much as when applied to work. Long periods of semi-despair wandering the stores, and every half hour or so, but quite erratically, something would leap out from the miserable background. This morning Alec had spent a good two hours at it. He had found a wooden fruit bowl which would just suit Mrs Bewley. She would be sure to appreciate it. Alec had also bought an electric blanket for his mother, who suffered from a poor circulation. It was more than he had wanted to pay, but she certainly needed just that, and would never think of getting one for herself. One or two other minor commitments had been dealt with. But now it was time for lunch, and Alec was walking towards the university but looking for a reasonably good restaurant.

  Alec had been working rather hard until two or three weeks before. It was about interplanetary travel. Alec had always been rather keen on such crackpot problems, but although he rather liked to let himself go rather wildly to newspapermen or on the Third Programme when he got the chance, when he wrote for technically trained readers, his work was quite sound, or had been when he was younger. This last paper was real good stuff, better than he’d done since his mid twenties when he had introduced the idea which is now becoming known as ‘Pryce’s buoy’. Alec always felt a glow of pride when this phrase was used. The rather obvious double-entendre rather pleased him too. He always liked to parade his homosexuality, and in suitable company Alec could pretend that the word was spelt without the ‘u’. It was quite some time now since he had ‘had’ anyone, in fact not since he had met that soldier in Paris last summer. Now that his paper was finished he might justifiably consider that he had earned another gay* man, and he knew where he might find one who might be suitable.

  Alan succeeded, for as he walked along Oxford Street, and pretended to look at the posters outside the Regal cinema, he caught the eye of a young man.