Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  Yours sincerely, A.M. Turing

  A few days later, the Ferranti Mark I computer was delivered at the Manchester department, which by now had a newly built Computing Laboratory to house it. Alan wrote to Mike Woodger back at the NPL:

  Our new machine is to start arriving on Monday [12 February 1951]. I am hoping as one of the first jobs to do something about ‘chemical embryology’. In particular I think one can account for the appearance of Fibonacci numbers in connection with fir-cones.

  It had been twenty-one years, and the computer had come of age. It was as though all that he had done, and all that the world had done to him, had been to provide him with an electronic universal machine, with which to think about the secret of life.

  Much of the computer installation that he had imagined for the ACE had now come into being; people were soon to come to it with their problems; the ‘masters’ would program it and the ‘servants’ service it. They did indeed build up a library of programs. (In fact, it was just about Alan’s last contribution to the Manchester computing system that he laid down a way of writing and filing a formal description of the programs intended for common use.) He had a room of his own in the new computer building, and was, at least in theory, the chief ‘master’. The engineers moved on to design a second, faster machine (in which he took no interest whatever), and it was up to him to take charge of the use of the first one.

  There was plenty that could be done in the way of seminars and publications and demonstrations, for this was the world’s first commercially available electronic computer, beating by a few months the UNIVAC made by Eckert and Mauchly’s firm. It also enjoyed the firm support of the British government, whose National Research Development Corporation, chaired by the administrator Lord Halsbury, managed the investment, sales and patent protection after 1949. In fact they went on to sell eight copies of the Mark I, the first to the University of Toronto, for the design of the St Lawrence Seaway, then others* more discreetly to the Atomic Weapons Research Establishment and to GCHQ. With Alan fulfilling a consultant role for GCHQ, it may be reasonably supposed that he played a part in suggesting how they should use the universal machine he had promised to Travis six years or so before. But this was not where his heart lay now. As electronic computers began to impinge upon the world economy, Alan Turing continued to back away, and remained engrossed in the otherwise forgotten ‘fundamental research’.

  A big inaugural conference was planned for July, but this work was done entirely by the engineers and Ferranti Ltd. It was not that Alan got in the way; he simply avoided participation. No one could have guessed that officially he was paid to ‘direct’ the laboratory. In the spring of 1951 he found a way to off-load his remaining responsibilities when R.A. Brooker, a young man from the Cambridge EDSAC team, called in to have a look at the new machine on his way back from a climbing weekend in west Wales. For reasons of his own he liked the idea of moving to the North, and asked Alan if he had a job to offer. Alan said he did, and in fact Tony Brooker joined later in the year.

  Alan’s detachment was annoying to the engineers, who felt that their achievement was hardly getting the recognition it deserved within the mathematical and scientific world. In many ways the Computing Laboratory remained as secret as Hut 8, just as computation remained the lowest form of mathematical life. Recognition did, however, come to Alan Turing. In the 1951 elections, which took place on 15 March, he became a Fellow of the Royal Society. The citation referred to his work on computable numbers which had, of course, been done fifteen years earlier. Alan was rather amused by this and wrote to Don Bayley (who had sent his congratulations) that they could not really have made him an FRS when he was twenty-four. The sponsors were Max Newman and Bertrand Russell. Newman had lost all interest in computers and was only grateful that Alan had regenerated his pulse with the morphogenetic theory.

  Jefferson, himself a Fellow since 1947, also sent a letter of congratulation,52 saying ‘I am so glad; and I sincerely trust that all your valves are glowing with satisfaction, and signalling messages that seem to you to mean pleasure and pride! (but don’t be deceived!).’ He managed to confuse the logical and the physical levels of description even within one sentence. Alan would refer to Jefferson as an ‘old bumbler’ because he never grasped the machine model of the mind, but Jefferson certainly found an apt description of Alan,53 as ‘a sort of scientific Shelley’. Apart from the more obvious similarities, Shelley also lived in a mess,54 ‘chaos on chaos heaped of chemical apparatus, books, electrical machines, unfinished manuscripts, and furniture worn into holes by acids,’ and Shelley’s voice too was ‘excruciating; it was intolerably shrill, harsh and discordant.’ Alike they were at the centre of life; alike at the margins of respectable society. But Shelley stormed out, while Alan continued to push his way through the treacly banality of middle-class Britain, his Shelley-like qualities muted by the grin-and-bear-it English sense of humour, and filtered through the prosaic conventions of institutional science.

  Mrs Turing was very proud of the Fellowship, a title which raised Alan to the eminence of George Johnstone Stoney, and laid on a party at Guildford where her friends could meet him – hardly the function to appeal to Alan, who once walked wordlessly out of a sherry party to which his brother had invited him, after a bare ten minutes. His mother found it hard to overcome her amazement that important personages could speak well of her Alan, but in this respect she was making progress, and had come a long way since the 1920s. Although Alan complained to his friends of her patronising fussiness and religiosity, there remained the fact that she was one of the few people who took an interest in his doings. Mostly this came out in her efforts to improve Alan’s domestic life, with instructions on the right and wrong ways to perform each little routine. (‘Mother says …’, Alan would explain to Robin, with a half-amused, half-exasparated twinkle.)

  Nor was their contact very frequent; Alan would visit Guildford about twice a year, annoying both mother and brother by announcing his imminent arrival with a telegram or postcard and no more. His mother made the journey to Wilmslow once in the summer each year. Besides the postcards there might be a few telephone calls; Alan finding for instance that they both liked the stories on Children’s Hour and telling her when a good one was coming. But Mrs Turing did like to have the feeling of involvement in Alan’s work, and felt happier with the biology than with the computers. Although she really had no clue as to what he was doing at Manchester, she would help with the wild flowers and the big maps. With her nineteenth-century optimism she construed it in terms of usefulness to humanity, bringing him closer to the Pasteur of whom she had long ago dreamed. Perhaps, she speculated, it might lead to a cure for cancer! It was not a foolish connection to draw, but it was not his motive. Nor was there any way of knowing where his Faustian dabblings might lead this time; they were just as relevant to the state-controlled embryology of Brave New World. Even if his practical methods had something in common with the naive natural history of the past century, and even if it meant a return to childhood fascinations, his work lay firmly within the great modernisation of biology, in which the technical advances of the 1930s were being followed by the application of the quantitative analysis so triumphant in physics and chemistry. The problem of life could no longer be allowed to lag behind; they had to know how its machinery worked.

  Appreciation in the Computing Laboratory was on a more down-to-earth level. There history began in 1951, and no one connected with the computer knew about Computable Numbers. At the NPL there had been strong connections with Cambridge mathematics and with the Royal Society; the new masters of the Mark I were quite a different crew, and had no sense of his past. Nor did Alan try to explain. An applied mathematics research student, N.E. Hoskin, had just become involved in using the new computer, and when he said over coffee ‘I never thought of you as an FRS,’ Alan just laughed – with that wince-inducing, mechanised laugh.

  He did look young for an FRS, although at thirty-eight he was by no mea
ns the youngest to be elected. Hardy had been elected at thirty-three, and the self-taught Indian mathematician Ramanujan at thirty. Maurice Pryce was also elected in 1951, so in this respect Alan had caught up a year on the mathematical physicist, whom he did not meet again after the war. Writing to Philip Hall at King’s, who also had congratulated him, he said it was Very gratifying to be about to join the Olympians’. After a mathematical description of his ‘waves on cows’ and ‘waves on leopards’, he added ‘I am delighted to hear Maurice Pryce is also in the list. I met him first when up for scholarship exam in 1929, but knew him best in Princeton. He was quite my chief flame at one time.’ In what was more of a mathematician’s joke he wrote, ‘I hope I am not described as “distinguished for work on unsolvable problems”.’

  In his retirement from the organisation of the laboratory, it barely impinged on Alan that the new computer was used to perform calculations for the British atomic bomb. A young scientist, A.E. Glennie, spent time at Manchester on this work. He would sometimes chat with Alan about mathematical methods, though it went no further than talk in general terms. Once, however, Alick Glennie found himself collared by Alan, when he wanted a ‘mediocre player’ on whom to try out his current chess playing program. They went back to Alan’s room for three hours in the afternoon Alan had all the rules written out on bits of paper, and found himself very torn between executing the moves that his algorithm demanded, and doing what was obviously a better move. There were long silences while he totted up the scores and chose the best minimax ploy, hoots and growls when he could see it missing chances. It was ironic that, despite all the developments of the past ten years, he was little closer to actually trying out serious chess playing on a machine – the existing computers had neither speed nor space for the problem.*

  Alick Glennie sometimes thought of Alan as Caliban, with his dark moods, sometimes gleeful, sometimes sulky, appearing in the laboratory on a somewhat random basis. He could be absurdly naive, as when bursting with laughter at a punning name that Glennie made up for an output routine: RITE. To Cicely Popplewell he was a terrible boss, but on the other hand, there was no question of having to be polite or deferent to him – it was impossible. He was regarded as a local authority on mathematical methods; those who wanted a suggestion would just have to ask him straight out, and if they could keep his interest and patience, they might get a valuable hint. Alick Glennie was rather surprised by his knowledge of hydrodynamics. All the same, he was no world-standard mathematician, and it was often more amazing to the professional mathematician what he did not know, than what he did. He never approached the von Neumann status or breadth of knowledge; indeed he had read very little mathematics since 1938.

  In April 1951 he had another look at the word problem for groups, and came up with a result which J.H.C. Whitehead at Oxford found ‘sensational’ – but it was never published.55 Max Newman kept him interested in topology, and he went to seminars. But the trend of postwar pure mathematics was moving away from his interests. Mathematics was flowering through a greater and greater abstraction for its own sake, while Caliban on his island remained somewhere in between the abstract and the physical. Nor was he a keen conference-goer, loathing the academic chitchat, but he went to the British Mathematical Colloquia that Max Newman helped to get started. In spring 1951 he went with Robin to one at Bristol, which got him interested in discussing topology with the mathematician Victor Guggenheim. But these were only diversions.

  Another diversion was offered by the BBC, whose new highbrow Third Programme was offering a series of five talks on computers. One was by Alan, the others by Newman, Wilkes, Williams and Hartree. Alan’s went out on 15 May 1951 and was entitled ‘Can Digital Computers Think?’. Largely it ran over the ground of the universal machine and the imitation principle.56 There were some references to the ‘age-old controversy’ of ‘free will and determinism’, which harked back twenty years with a mention of Eddington’s views on the indeterminacy of quantum mechanics, and back ten years with some suggestions on how to incorporate a ‘free will’ element in the machine. It could be done either by ‘something like a roulette wheel or a supply of radium’ – that is, by the kind of random number generator that worked like the Rockex tape generator, off random noise – or else by machines ‘whose behaviour appears quite random to anyone who does not know the details of their construction.’ His listeners could scarcely have imagined the secrets which lay behind that bland suggestion! He ended with his justification for investigating machine intelligence:

  The whole thinking process is still rather mysterious to us, but I believe that the attempt to make a thinking machine will help us greatly in finding out how we think ourselves.

  This short talk did not include any details of how he proposed to program a machine to think, beyond the remark that it ‘should bear a close relation to that of teaching.’ This comment sparked off an immediate reaction in a listener: Christopher Strachey, the son of Ray and Oliver Strachey.

  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.