Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  Despite all these amazing virtues, Christopher Morcom was human. He had nearly got into trouble when he was dropping stones down train funnels from the railway bridge and struck a railwayman instead. Another exploit involved sending gas-filled balloons over the field to the Sherborne Girls’ School. Nor was their time in the laboratories too solemn. Another boy, a tough athlete called Mermagen, joined them for physics, and the three of them had to work through the practical experiments in a little annex while Gervis taught his class. These classes were enlivened by Gervis’s sausage-lamps, painted bulbs which he used as electrical resistances. ‘Take another sausage-lamp, boy!’ was his catchphrase, and the three of them worked out a comic sketch around the things, which Christopher was thinking of setting to music.

  In the summer term of 1929 they were doing only the dull revision work for the Higher School Certificate, but even this was coloured by romance since ‘As always it was my great ambition to do as well as Chris. I was always as well supplied with ideas as he, but have not the same thoroughness in carrying them out.’ Alan had never before taken any notice of naggings to take care over details and style, since he had worked for himself, by himself. But now perhaps he recognised that what was good enough for Christopher Morcom was good enough for him, and that he should train himself to communicate in the way that the system required. He had not yet acquired the necessary skill. Andrews observed that he was ‘at last trying to improve his style in written work,’ but Eperson, writing that his work for the Higher Certificate showed ‘distinct promise’, re-emphasised the need to ‘put a neat and tidy solution on paper.’ The examiner for the mathematics of the Higher Certificate24 commented that:

  A.M. Turing showed an unusual aptitude for noticing the less obvious points to be discussed or avoided in certain questions and for discovering methods which would at once shorten or illumine the solutions. But he appeared to lack the patience necessary for careful computation of algebraic verification, and his handwriting was so bad that he lost marks frequently – sometimes because his work was definitely illegible, and sometimes because his misreading his own writing led him into mistakes. His mathematical ability was not of a standard to compensate entirely for the cumulative effects of these faults.

  Alan obtained 1033 marks in the mathematics papers, compared with Christopher’s 1436.

  The Morcoms were a wealthy, vigorous scientific and artistic family, with a base in a Midlands engineering firm. They had developed a Jacobean dwelling near Bromsgrove in Worcestershire into a large country house, the Clock House, where they lived in some style. Christopher’s grandfather had been an entrepreneur in stationary steam engines, and the Birmingham company of Belliss and Morcom, of which his father, Colonel Reginald Morcom, had recently become chairman, now also built steam turbines and air compressors. Christopher’s mother was the daughter of Sir Joseph Swan, who starting from a very ordinary background had become in 1879 the inventor, independently of Edison, of the electric light. Colonel Morcom retained an active interest in scientific research, while Mrs Morcom matched his energy in her own pursuits. At the Clock House she ran a goat farm; she bought and renovated cottages in the neighbouring village of Catshill; she was out every day on some project or county duty. She had studied in London at the Slade School of Art, and in 1928 returned there, taking a flat and a studio near Victoria, and producing sculpture of force and style. It was typical of her flair and zest that when back at the Slade she still pretended to be ‘Miss Swan’, but then invited other art students back to the Clock House, involving herself in absurd disguises when she doubled as Mrs Morcom.

  Rupert Morcom, the elder son, had entered Sherborne in 1920, and had won a scholarship in science to Trinity College, Cambridge; he was now engaged in research at the Technische Hochshule in Zurich. Like Alan he was an avid experimenter, but one with the advantage that his parents had been able to construct a laboratory for him at home. His younger brother, who also had the use of the laboratory, now told Alan of all this, exciting great envy.

  In particular, Christopher told Alan about an experiment that Rupert had taken up before going to Cambridge in 1925. It concerned a chemical effect which Andrews often used to draw the interest of the younger boys. By chance it involved Alan’s old favourite, iodine. Solutions of iodates and sulphites, when mixed, would result in the precipitation of free iodine, but in a rather striking way. Alan later explained: ‘It is a beautiful experiment. Two solutions are mixed in a beaker and after waiting for some very definite period of time, the whole suddenly becomes a deep blue. I have known it take a time, 30 secs., and then turn blue in 1/10 of a sec. or less.’ Rupert had been investigating not the easy problem of working out the recombination of ions, but that of explaining this time delay. It required a knowledge of physical chemistry, and an understanding of differential equations, both beyond the school syllabus. Alan wrote:

  Chris and I wanted to find a relation between the time and the concentrations of the solutions and thereby verify Rupert’s theories. Chris had already done some experiments upon it. We were looking forward very much to the experiment. The results unfortunately did not agree with theory and I made more experiments during the following holidays and invented a new theory. I sent the results to him and so we started to write to one another in the holidays.

  He did more than write to Christopher – he invited him to Guildford. Ross, as housemaster, would have been horrified by this audacious step.25 Christopher replied26 (after some delay) on 19 August:

  … Before getting on to experiments I must thank you very much for your invitation to come and stay with you, but I am afraid I shall not be able to come as we are going away somewhere, probably abroad for about three weeks, just at that time … I am sorry not to be able to come; it is very kind of you to ask me.

  As for the iodates, new ventures at the Clock House had rendered them definitely passé. There were experiments to measure air resistance, liquid friction, another problem in physical chemistry with Rupert (‘I enclose the integral which you might like to try’), plans for a twenty foot long reflecting telescope, and

  … So far all I have done is to make an adding machine for pounds and ounces. It works surprisingly well. I think I have given up Maths for these holidays, having just read a very good book on Physics in general including relativity.

  Alan laboriously copied the ingenious experiment on air resistance that Christopher had devised and wrote back with more ideas about chemistry and a mechanics problem, only for Christopher to pour cold water on both in a letter of 3 September:

  I haven’t studied your conical pendulum carefully but I can’t so far understand you’re [sic] method. Incidentally I believe you’re equations of motion have a mistake in them. …

  I am now helping my brother analyse American plasticine for an artist. … The procedure is to boil with organic solvents. … I made a quite good plasticine and very nearly like the stuff we want, by mixing this iron soap with flowers of sulphur … and adding a little mutton fat. Hope you are having good holidays; see you on 21st, Yrs, C.C. Morcom.

  But chemistry had now given way to astronomy, to which Christopher had introduced Alan earlier in the year. Alan had been given Eddington’s Internal Constitution of the Stars by his mother for his seventeenth birthday, and had also acquired a 11/2-inch telescope. Christopher had a four-inch telescope (‘He never tired of talking about his wonderful telescope if he thought one was interested’) and had been given a star atlas for his eighteenth birthday. Besides astronomy, Alan was also reading deep into The Nature of the Physical World, for in his letter27 of 20 November 1929 there was a paraphrase of part of its account:

  Schrödinger’s quantum theory requires 3 dimensions for every electron he considers. Of course he does not believe that there are really about 1070 dimensions, but that this theory will explain the behaviour of an electron. He thinks of 6 dimensions, or 9, or whatever it may be without forming any mental picture. If you like you can say that for every new electron you in
troduce these new variables analogous to the coordinates of space.

  This came from Eddington’s description of that other change in fundamental physical concepts, one much more mysterious than relativity. The quantum theory had done away with the billiard-ball corpuscles and the ethereal waves of the nineteenth century, and replaced both by entities which had characteristics both of particles and of waves; lumpy but nebulous.

  Eddington had a lot to say, for the 1920s had been a decade of rapid advance in theoretical physics, following up the spate of discoveries at the turn of the century. In 1929 Schrödinger’s formulation of the quantum theory of matter was only three years old. The two boys also read books by Sir James Jeans, the other Cambridge astronomer, and here too there were entirely new developments. It had only just been established that some nebulae were clouds of gas and stars on the margins of the Milky Way, and that others were completely separate galaxies. The mental picture of the universe had expanded a millionfold. Alan and Christopher discussed these ideas and ‘usually didn’t agree’, wrote Alan, ‘which made things much more interesting.’ Alan kept ‘some pieces of paper with Chris’ ideas in pencil and mine in ink scrawled all over them. We even used to do this during French.’

  The date 28/9/29 appeared on them, and so did the official work:

  Monsieur … recevez monsieur mes salutations empressés*

  Cher monsieur … Veuillez agréer I’expression des mes sentiments distingués

  Cher ami … Je vous serre cordialement la main .. . mes affectueux souvenirs .. . votre affectioné

  but also there were generalised noughts and crosses, a reaction involving iodine and phosphorus, and a diagram which suggested doubting Euclid’s axiom that for every line there would be exactly one parallel line passing through a given point.

  Alan kept these pages, as souvenirs affectueux, although he could never express his sentiments distingués. As for serrer cordialement la main, or more – that was probably pretty firmly repressed in his mind, although soon he would write: ‘There were times when I felt his personality particularly strongly. At present I am thinking of an evening when he was waiting outside the labs, and when I came too, he grasped me with his big hand and took me out to see the stars.’

  Alan’s father was delighted, if amazed, when the reports began to change their tone. His interest in mathematics was confined to the calculation of income tax, but he was proud of Alan, and so was John, who admired him for taking on the system and getting away with it. There had been a method in his madness all along. Unlike his wife, Mr Turing never claimed to have the faintest idea of what his son was doing, and this was the theme of a punning couplet that Alan once read out from his father’s letter in his study:

  I don’t know what the ‘ell ‘e meant

  But that is what ‘e said ‘e meant !

  Alan seemed quite happy with this bluff and trusting ignorance. Mrs Turing, however, took the more accusing line of ‘I told you so,’ and made a good deal of the idea that her choice of school had been the right one. She had certainly paid a certain amount of attention to Alan, and it had not all been in the direction of moral improvement, for she liked to feel that she understood his love of science.

  Alan was now in a position to think of winning a scholarship to university, a scholarship representing not only merit but a reasonable income, almost enough to live on as an undergraduate. An exhibition, awarded to second-class candidates, would mean significantly less. Christopher, now eighteen, was expected to win a Trinity College scholarship like his brother. It was ambitious of Alan to attempt the same at seventeen. In mathematics and science, Trinity held the highest reputation among the colleges of the university which was itself, after Göttingen in Germany, the scientific centre of the world.

  The public schools were good at putting candidates through the daunting procedure for entrance scholarships to the ancient universities, and Sherborne also gave Alan a £30 per annum subsidy. But there was no automatic red carpet laid down. The scholarship examinations were distinguished by questions of an open-ended, imaginative kind, without a published syllabus. They gave a taste of future life. To Alan this was an excitement in itself, but there was more than this to stimulate his ambition. There was Christopher, who would so shortly be leaving Sherborne; there was some muddle over when this would be, but it would probably be at Easter 1930. To fail in the scholarship would be to lose Christopher for more than a year. Perhaps it was this uncertainty that provoked gloomy forebodings in November, when Alan had recurring thoughts that something would happen before Easter to prevent Christopher from going to Cambridge.

  The Cambridge examinations opened up the prospect of a whole week in Christopher’s company, unconstrained by the house system – ‘I was looking forward as much to spending a week with Chris as to seeing Cambridge.’ On Friday 6 December, Christopher’s study-mate Victor Brookes was to be driving from London to Cambridge, and had offered to take Alan as well as Christopher. They went on the train together to London, where they stopped off to see Mrs Morcom. She took them to her studio, allowed them to play at chipping marble from a bust that she was working on, and then gave them lunch at her flat. Christopher used to tease Alan a good deal, and had a particular running joke about ‘deadly stuff, the joke being to pretend that certain harmless substances were really poisonous. He joked about the vanadium in the special Morcom vanadium-steel cutlery being ‘absolutely deadly’.

  In Cambridge they could live the lives of young gentlemen for a week, with rooms of their own and no lights-out. There was dinner in the Hall of Trinity College, in evening dress, with the portrait of Newton looking down. It was an opportunity to meet and compare themselves with candidates from other schools. Alan made one new acquaintance, Maurice Pryce, with whom he established an easy rapport through almost identical interests in mathematics and physics. Pryce was taking the examination for the second time. A year before he had sat under Newton’s portrait and had said to himself that now nothing else would suffice. And although Christopher was rather blasé about everything, that was what it was like for them all: nothing could be quite the same again.

  It was, wrote Alan, ‘a very good meal’, and then they

  went to play Bridge with some other Sherburnians in Trinity Hall. We were … to be back at our Colleges by 10 o’clock but at 4 minutes to 10 Chris wanted to play another hand. I wouldn’t let him, and as it was, we were only back just in time. The next day, Saturday, we played cards again ‘Rummy’ this time. After ten o’clock Chris and I went on playing other games. I remember very clearly Chris’ broad smile when we decided we didn’t want to go to bed just yet. We played till 12–15. A few days later we tried to get into the Observatory. We had been invited by an astronomer friend of Chris’ to go there if it was fine. Our idea of what was fine did not quite agree with his.

  Christopher ‘loved all games and was always finding out new ones (of the more trivial kind).’ He used to ‘try to make people believe things that were credible but just not true,’ and at Cambridge persuaded Alan to advance his watch by twenty minutes. ‘He was immensely pleased when I found out.’ They also went to the cinema together, joined by Norman Heatley, who had been Christopher’s friend at a preparatory school, and was now a Cambridge undergraduate. Christopher told him how Alan had a notation of his own for the calculus, and had to translate everything into standard formulae when he did examinations. This aspect of Alan’s independence also worried Eperson, who found that ‘on paper his solutions were often unorthodox, and required the writer’s elucidation.’ He doubted whether the Cambridge examiners would perceive the mind that struggled behind the hand.

  On the way back from the cinema, Alan hung back and walked with Heatley, to test how much Christopher wanted his company. He was rewarded:

  Evidently I looked rather lonely as Chris beckoned to me (mostly I think with his eyes) to walk beside him. Chris knew I think so well how I liked him, but hated me shewing it.

  Alan was conscious that he wa
s a boy in another house, and that everything was open to comment. (‘We never went on bicycle rides together. I think perhaps Chris was rather ragged about me at the house.’) But this pleased him ‘ever so much’.

  After what Alan said had been the happiest week of his life, the boys went back to school on 13 December for the last few days of term. At the house supper, they sang about Alan:

  The maths brain lies often awake in his bed

  Doing logs to ten places and trig in his head

  The results were published on 18 December in The Times, just after term ended. It was a Great Crash. Christopher had won a Trinity scholarship, and Alan had not. Writing in congratulation, Alan had a letter in return with a particularly friendly tone:

  20/12/29

  Dear Turing,

  Thank you very much for your letter. I was as sorry you did not get a schol as I was pleased that I did. What Mr Gow says means that you would have certainly got an Exhibition if you had put it down …

  … Have had two of the clearest nights I have known. I have never seen Jupiter better and I could see 5 or 6 belts and even some detail on one of the large central belts. Last night I saw no. 1 satellite come out from eclipse. It appeared quite suddenly (during a few seconds) at some distance from Jupiter and looked very attractive. It is the first time I have seen one. I also saw Andromeda Neb. very clearly but did not stay out long. Saw spectrum of Sirius, Pollux and Betelgeux and also bright line spectrum of Orion nebula. Am at moment making a spectrograph. Will write again later. Happy Christmas etc. Yrs ever C.C.M.