Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  The real discussion61 was recorded at the BBC Manchester studio on 10 January 1952. It was left to the brain surgeon to show the flag for the cause of consciousness, with Alan trying to haul it down. Max Newman and Richard Braithwaite, the King’s philosopher of science, acted as referees.

  It was couched in the jocular-Mandarin style of the day. ‘Of course’, wrote Alan to his mother, who listened to the broadcast, ‘most of the questions put to me were more or less written in gags.’ Braithwaite began with a very appropriate Brains’ Trust point: ‘it all depends on what is to be included in thinking.’ Alan explained the imitation game as a criterion of ‘thinking’, the others duly chipping in to put the objections. ‘Would the questions have to be sums,’ asked Braithwaite, ‘or could I ask it what it had had for breakfast?’ ‘Oh yes, anything,’ said Alan, ‘and the questions don’t really have to be questions, any more than the questions in a law court are really questions. You know the sort of thing, “I put it to you that you are only pretending to be a man,” would be quite in order.’ They discussed learning and teaching, and Braithwaite said that people’s ability to learn was determined by ‘appetites, desires, drives, instincts’ and that a learning machine would have to be equipped with ‘something corresponding to a set of appetites’.

  Newman steered a course back to the safer waters of mathematics, pointing to the act of imagination that had been required to connect the ‘real numbers’ of length with the integers of counting, which involved ‘seeing analogies between things that had not been put together before. … Can we even guess at the way a machine could make such an invention from a programme composed by a man who had not the concept in his own mind?’ Alan could guess, in fact; it was just the kind of thing he was thinking about:

  I think you could make a machine spot an analogy, in fact it’s quite a good instance of how a machine could be made to do some of those things that one usually regards as essentially a human monopoly. Suppose that someone was trying to explain the double negative to me, for instance, that if a thing isn’t not-green it must be green, and couldn’t quite get it across. He might say, ‘Well, it’s like crossing the road. You cross it, and then you cross it again, and you’re back where you started.’ This remark might just clinch it. This is one of the things one would like to work with machines, and I think it would be likely to happen with them. I imagine that the way analogy works in our brains is something like this. When two or more sets of ideas have the same pattern of logical connections, the brain may very likely economise parts by using some of them twice over, to remember the logical connections both in the one case and in the other. One must suppose that some part of my brain was used twice over in this way, once for the idea of double negation, and once for crossing the road, there and back; I am really supposed to know about both these things but can’t get what it is the man is driving at, so long as he is talking about all these dreary nots and not-nots. Somehow it doesn’t get through to the right part of the brain. But as soon as he says his piece about crossing the road it gets through to the right part, but by a different route. If there is some purely mechanical explanation of how this argument by analogy goes on in the brain, one could make a digital computer do the same.

  Wittgenstein had talked about ‘explaining’ double negation in 1939.62 But Jefferson brought the discussion back to earth with the problem of appetites. ‘If we are really to get near to anything that can be truly called “thinking”, the effects of external stimuli cannot be missed out. … You see a machine has not [an] environment, and man is in constant relation to his environment, which as it were punches him whilst he punches back. … Man is essentially a chemical machine, he is much affected by hunger and fatigue … and by sexual urges.’ Alas, those appetites that interfered with thinking! It was a strong argument against the discrete state machine. But Jefferson again spoilt his case with an appeal to the complexity of the nervous system (irrelevant since a universal machine, given sufficient storage, could emulate one of any complexity). In more rhetorical vein he continued, ‘Your machines have no genes, no pedigrees. Mendelian inheritance means nothing to wireless valves,’ and so forth. Jefferson wanted to say that he would not believe a computing machine could think until he saw it touch the leg of a lady computing machine, but they cut this out of the broadcast because (as Braithwaite said) one could hardly call that thinking. Braithwaite believed it would be necessary for the computer to incorporate an ‘emotional apparatus’ in order that it could think, but that it was not their concern to ask what problems this might lead to. The hot potato was dropped, and Jefferson concluded by reassuring the British intelligentsia that it was ‘that old slow coach, man’ who would continue to produce the ideas.

  The broadcast went out on 14 January, by which time Arnold had made his second visit to Alan’s home, and events had taken a more serious turn. Alan had arranged matters so as to cast the relationship as an ‘affair’, which meant that Arnold had arrived as a dinner guest, and expected to stay the night. Arnold responded warmly to what was for him the palatial circumstances of Hollymeade, it being particularly striking, for instance, that Alan employed a housekeeper. He was with the masters now, not the servants.

  They did not have much in common to talk about, but found links, in such a way that Arnold was highly conscious of Alan’s need to communicate and reach a fresh mind. Neither thought much of the American interference with the British attempt to oust Mossadeq in Iran. Arnold had great local patriotism and disliked the USAF bases still dominating parts of Cheshire. Besides current affairs Alan also talked about astronomy, played a tune on the violin, and let Arnold have a try. After dinner, rather the better for wine, and lying on the rug, Arnold began telling Alan about his recurrent childhood dream, or nightmare rather, in which he felt himself suspended in absolutely empty space while a strange noise would start, growing ever louder, until he woke up in a sweat. Alan asked what kind of noise it was, but Arnold could not describe it. Thinking of big empty spaces, Alan imagined the old hangar on the RAF camp along the road, and made up a science fiction story (he talked a bit about H.G. Wells) in which the hangar was itself a brain, programmed in such a way that it would work normally for anyone else, but when he went in to the hangar, he would be trapped. The doors would shut. And then he would have to play against the machine, a game of chess, the best out of three. The machine would counter his moves so quickly that he would have to make conversation to distract it. So he would talk to it, first making it show anger, then pleasing it by being stupid himself, and making it feel smug.

  ‘Can you think what I feel? Can you feel what I think?’, he said with terrific emphasis at one point, as he became more excited with the story. He quite transfixed Arnold as he took a piece of chalk, and imagined how he could beat the machine, by doing arithmetic so badly and slowly and stupidly that it would commit suicide in despair.

  Arnold tried to explain his ideas too; and Alan was patient, although he could so easily have been crushing, and led him on Socratically. ‘Whatever you think, is,’ said Alan at one point, and this meant a lot to Arnold, who had his own dreams that he wanted to come true. Alan felt frustrated because he could not better communicate his ideas: ‘There’s got to be more to it than this level,’ he told Arnold, almost in anger, adding with great emphasis ‘I’ve got to teach you, take you out of all this.’

  Dear love of comrades! – in 1891 Edward Carpenter had met his George Merrill, a working man of twenty; it began just like this, and continued for thirty years. Alan made it clear that he wanted them to sleep together as lovers, and this they did. In the morning Alan got up and made the breakfast, after which they talked and smoked and prolonged the pleasure of the night. They arranged for another visit in two weeks’ time. One subject was not, however, discussed as it might have been. This was the question of money. It was as obvious that Arnold was short of it as it was clear that Alan had more than he needed. Alan was going to do the expected thing, and was perhaps surprised when Arnold decline
d the offer. The underlying difficulty was that Arnold jibbed at a direct payment, which threatened to label him as ‘a renter’. Alan, in contrast, was highly uncomfortable about conventional social manoeuvres, whether in his mother’s drawing room or in his own bedroom. He was therefore particularly shaken next day to notice the absence of some money from his wallet, which he suspected that Arnold could have taken while he was making the breakfast. He wrote to Arnold, saying that he did not after all wish to continue the acquaintance. But Arnold arrived on his doorstep a few days later, demanding to know the reason for this rejection, and denying that he had anything to do with the loss. Alan was ‘half convinced’ by his indignation. Arnold went on to mention that as it happened he was £10 in debt for a suit bought on hire purchase, and asked to borrow £3. Alan gave him the money, saying that it was a gift, and later wrote to Arnold restoring the invitation. Arnold wrote back to thank him on the 18th, but added a request for a further £7 loan. Alan’s response was to ask for the name of the firm to which the money was owed: it was not the money but the truth of the story which was the issue for him. Again, on the 21st, Arnold arrived at Hollymeade to complain of the lack of trust that Alan showed, and left with a cheque for £7. He was going to start work in a Manchester printing shop, and so could promise to pay it back from his earnings.

  Meanwhile Robin had come to stay for the weekend, which was devoted to a discussion of his essay on Eddington’s ‘Fundamental Theory’ of physics. This Alan said was ‘very much more satisfactory than anything you have done before.’ This stern praise meant a great deal to Robin, whose 1949 King’s fellowship dissertation had met with sharp criticism from Alan which had left him in tears.

  Eddington had died in 1944 leaving unfinished an attempt to develop a theory of physics from nothing but logical necessity. It was a somewhat Turingesque venture, and met with Alan’s sympathy in principle, but he had long since decided that Eddington was ‘an old muddle-head’ and wanted to see the ‘Fundamental Theory’ debunked. Robin, who never knew how important Eddington had been to Alan twenty years before, had found a number of errors in his arguments, including one which could be regarded as a confusion of logical types. It was a nice meeting of logic and physics.

  Life went its ordinary way. Alan’s aunt Sybil had died on 6 January, and left him £500. The last survivor of his father’s generation, she had accumulated the Turing fortunes. She left £5000 to Mrs Turing, who for some reason had the idea of taking out a mortgage on her house, a policy which in a typical turn of phrase Alan called ‘about as appropriate as going out charring when you need more help in the house’. He stopped the £50 per annum he had sent her since 1949.

  He had listened to the broadcast and found his voice ‘rather less trying to listen to than before’. On Wednesday 23 January, the programme was repeated. And the same day, the environment punched him back, as Jefferson put it. Alan arrived back in the evening to find that his house had been burgled. Alan was writing next day to Fred Clayton in connection with the astronomy of the ancient world. He explained the significance of the zodiac, and ended:

  I have just had my house broken into, and am still every few hours finding some fresh thing missing. Fortunately I am insured, and little has gone that is really irreplaceable. But the whole thing has had a very disturbing effect, especially as it followed shortly on a theft from me at the University. I go about expecting a brick to fall on my head or something disagreeable and unexpected anywhere.

  A rather pathetic collection of oddments was missing – a shirt, some fish-knives, a pair of trousers, some shoes and shavers and a compass – even an opened bottle of sherry. He assessed it at a total value of £50. He reported the burglary to the police, and two CID officers came to take fingerprints in the house. Yet even while he did this, he suspected that there might be some connection with Arnold. He consulted a solicitor recommended to him by his neighbour Roy Webb, and on his advice wrote to Arnold on 1 February, reviving the question of the money missing from his wallet, saying that whatever the truth of the matter it had come between them, and that it would be best if they did not see each other again. He added in a somewhat schoolmasterish tone that it was Arnold’s duty to repay the £7. He also said that if Arnold came to his house again he would not be admitted.

  But when Arnold reacted to this letter by calling at Hollymeade on the Saturday evening, 2 February, he found himself admitted after all. Again he angrily protested his innocence, and in a moment of emotion said he could go to the police and tell everything. Alan challenged him to ‘do his worst’ – but it was an empty threat, for Arnold soon admitted he could do nothing against a man in Alans distinguished position. The anger was discharged, and a different mood prevailed. Giving Arnold a drink, Alan mentioned the burglary, and to this question Arnold immediately supplied an answer. He did not know the burglary had taken place, but did know exactly who might have done it. For he had mentioned Alan to an acquaintance called Harry, a twenty-year-old unemployed youth recently discharged from National Service in the Navy, while they were talking in the Oxford Street milk bar. They had been speaking rather boastfully of their respective successes. Harry had suggested a robbery, and although Arnold had refused to join in, he knew it had been planned.

  The result was to re-establish a friendly, and indeed an erotic relationship. Arnold once again slept with Alan, although during the night Alan found himself in two minds, at one point going downstairs to put away the glass with Arnold’s fingerprints on it, in the hope that he could compare them with those left by the burglars. Next morning they went together into Wilmslow town, and Arnold waited outside the police station while Alan went in to pass on the information about the likely culprits, fabricating a story to explain how he had come by it. He had allowed the game of Presents to be taken a fair way without making a fuss; but to let it go unchecked would, in his view, be tantamount to giving in to blackmail.

  Arnold went off having offered to do his best to track down the stolen goods, and indeed he was able to write to Alan with a report a few days later. But by that time everything had changed. One change had been marked by the Manchester bells, ringing not this time for victory, but for the death of George VI. On Thursday the new Queen Elizabeth flew back from Kenya and Winston Churchill, Prime Minister again, welcomed her at the airport. And it was on that very evening, as the new Elizabethan age began, that the detectives paid a call on Alan Turing. No man is an Island, entire of itself. Now he was in the soup.

  * Newman had written2 to von Neumann on 17 June 1946 that he was ‘at present grappling with Turing’s report, which I find a good deal less readable than yours.’ He had also spent a term at Princeton in late 1946, and discussed computers with von Neumann.

  * In 1949, on a visit to the United States, Williams scandalised the employees of IBM, whose corporate motto think was everywhere in evidence, with this analysis of how he had succeeded where they had not.

  † Yet already the end of the vacuum tube was in sight. A final letter from Jack Good to ‘Prof’, dated 3 October 1948, continued their discussion of the brain, and also asked: ‘Have you heard of the transistor (or Transitor)? It is a small crystal alleged to perform “nearly all the functions of a vacuum tube”. It might easily be the biggest thing since the war. Is England going to get a look-in?’

  * This invention, later known as an ‘index register’, was of considerable importance in the future development of computer hardware design.

  * The arrangement was now that he could receive a fellowship stipend only for a quarter in which he had spent twenty-five nights in residence – a condition fulfilled during August.

  † Running in a team with Christopher Chataway.

  * The next one was out of range at p = 521, as was discovered by computer search in 1952.

  * This promise was not entirely fulfilled, since it turned out that the tracks had been too closely packed, and often were unusable.

  * The opportunities open to him were rich, and his neglect of them very s
triking. He could, for instance, have used his knowledge of the ‘recursive function’ to develop a far more powerful and interesting treatment of the ‘sub-routine’. Church’s lambda-calculus, and all the hitherto abstruse and ‘useless’ work he had done on such problems as the ‘dots and brackets’ in mathematical logic, were now relevant to the devising of practical programming languages. The knowledge of probability and statistics that he had employed in Enigma work could equally profitably have been applied to the theory of programming. Experience with searching, sorting, and the ‘trees’ involved in his chess-playing ideas, were all particularly relevant to the data-processing problems it was now possible to attack on computers. He could have done much to set standards for the new engineering discipline, if only because he could so easily rise above the technicalities of any particular installation, and could have set his weight against the often absurd and debilitating separation of university mathematics from the developing field of computer applications. But with few exceptions, one of them being an insistence on program checking procedures which reflected his more abstract, rigorous, background, he abandoned this line of development.

  * Alan Turing himself always sought to play down any such comparison, which in his view was irrelevant to the essential thesis that the brain could be regarded as a discrete state machine. Thus in the 1948 report for the NPL he had written: ‘We could produce fairly accurate electrical models to copy the behaviour of nerves, but there seems very little point in doing so. It would be rather like putting a lot of work into cars which walked on legs instead of continuing to use wheels.’

  * The Mersenne prime problem was a highly artificial, if ingenious, application of the growing Manchester computer. Only from the autumn of 1949 could it be applied to ‘regular’ problems. Besides those of Alan Turing himself, as later described, it was used for optical calculations, tracing rays through systems of lenses, and for some mathematical work in connection with guided missiles.