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

by Andrew Hodges

  Alan also saw that Einstein avoided philosophical discussions of what space and time ‘really were’, and instead concentrated on something that could in principle be done. Einstein placed great emphasis on ‘rods’ and ‘clocks’ as part of an operational approach to physics, in which ‘distance’, for instance, only had meaning in terms of some well-defined measuring operation, not as an absolute ideal. Alan wrote:

  It is meaningless to ask whether the two p[oin]ts are always the same distance apart, as you stipulate that that distance is your unit and your ideas have to go by that definition…. These ways of measuring are really conventions. You modify your laws to suit your method of measurement.

  No respecter of persons, he preferred a piece of working of his own to that supplied by Einstein ‘because in this way I think it should seem less “magicky”.’ He reached the very end of the book, and gave a masterly derivation of the law* which in General Relativity would supplant Newton’s axiom, that a body subject to no external force would move in a straight line with constant speed:

  He has now got to find the general law of motion for bodies. It will have, of course, to satisfy the general Principle of Relativity. He does not actually give the law, which I think is a pity, so I will. It is: ‘The separation between any two events in the history of a particle shall be a maximum or minimum when measured along its world line.’

  To prove it, he brings in the Principle of Equivalence, which says that: ‘Any natural gravitational field is equivalent to some artificial one.’ Suppose then that we substitute an artificial field for the natural one. Now as the field is artificial there is some system at that p[oin]t which is Galileian, and as it is Galileian the particle will be moving uniformly relative to it, i.e. it has a straight world line relatively to it. Straight lines in Euclidean space have always a maximum or minimum length between two p[oin]ts. Therefore the world line satisfies the conditions given above for one system, therefore it satisfies it for all.

  As Alan explained, Einstein had not stated this law of motion in his popular account. Alan might just possibly have guessed it for himself. On the other hand, he could very well have found it in another work which was published in 1928, and which he was reading by 1929 – The Nature of the Physical World by Sir Arthur Eddington. Professor of Astronomy at Cambridge, Eddington had worked on the physics of the stars and the development of the mathematical theory of relativity. This influential book, however, was one of his popular works, in which he set out to convey the great change in the scientific world-picture that had taken place since 1900. Its rather impressionistic account of relativity did state the law of motion, although without proof, and might have supplied its form to Alan. Certainly, in one way or another, Alan had done more than study a book, for he had put several ideas together for himself.

  This study arose out of his own initiative, and Eperson did not know about it. He was thinking quite independently of his environment, which offered him little but nagging and scolding. He had had to look to his totally bewildered mother for a little encouragement. But then something new happened to put him into contact with the world.

  There was a boy in another house – Ross’s house, in fact – whose name was Morcom. As yet he was nothing but ‘Morcom’ to Alan, although later23 he became ‘Christopher’. Alan had first noticed Christopher Morcom early in 1927, and had been very struck by him, partly because he was surprisingly small for his form. (He was a year older than Alan and a year ahead in the school, but fair-haired and slight.) It was also, however, because he ‘wanted to look again at his face, as he felt so attracted.’ Later in 1927 Christopher had been away from school and then had returned looking, Alan noticed, very thin in the face. He shared with Alan a passion for science, but he was a very different person. The institutions that were for Alan such stumbling-blocks had been for Christopher Morcom the instruments of almost effortless advance, the source of scholarships, prizes and praise. He again returned late to school this term, but when he arrived Alan was waiting for him.

  His utter loneliness was pierced at last. It was difficult to make friends with an older boy from another house. Nor was Alan good at conversation. But he found an entrée in mathematics. ‘During the term Chris and I began setting one another our pet problems and discussing our pet methods.’ It would be impossible to separate the different aspects of thought and feeling. This was first love, which Alan would himself come to regard as the first of many for others of his own sex. It had that sense of surrender (‘worshipped the ground he trod on’), and a heightened awareness, as of brilliant colour bursting upon a black and white world. (‘He made everyone else seem so ordinary.’) At the same time, it was most important that Christopher Morcom was someone who took scientific ideas seriously. And gradually, though always with considerable reserve, he took Alan seriously. (‘My most vivid recollections of Chris are almost entirely of the kind things he said to me sometimes.’) So these elements were all present, and had the effect of giving Alan reason to communicate.

  Before and after Eperson’s classes Alan might talk to Christopher about relativity, or might show him other pieces of work. He had, for example, calculated π to thirty-six decimal places at about this time, perhaps making use of his own series for the inverse tangent function, and being much annoyed to find an error in the last decimal place. After a time, Alan found another opportunity to see Christopher. By accident he discovered that during a certain period on Wednesday afternoons set for private study, Chris went to the library and not to his house. (Ross did not allow boys to work unsupervised, fearing the sexual potential in unregulated associations.) ‘I so enjoyed Chris’ company there,’ wrote Alan, ‘that ever since I always used to go to the library instead of my study.’

  Yet another chance arose through the gramophone society which the progressive Eperson had started. Christopher, a fine piano player, was a keen member. Alan had little interest in music, but sometimes on Sunday afternoons he would go to Eperson’s lodgings with Blamey (who also had a gramophone and records in their shared study). There he could sit and steal glances at Christopher while the 78’s played out their disjointed versions of the great symphonies. This was, incidentally, part of Blamey’s noble effort to show Alan that there were other things in life besides mathematics. He also showed Alan how to make a crystal wireless receiver out of basic materials, having noticed that Alan had little pocket money for such things. Alan insisted on winding the coils for the variometer and was delighted to find that his clumsy hands had made something that actually worked, even if he could never aspire to rival Christopher’s dexterity.

  At Christmas, Eperson reported:

  This term has been spent, and the next two terms will have to be spent, in filling in the many gaps in his knowledge and organising it. He thinks very rapidly and is apt to be ‘brilliant’ but unsound in some of his work. He is seldom defeated by a problem, but his methods are often crude, cumbersome and untidy. But thoroughness and polish will no doubt come in time.

  He would have found the Higher Certificate dull stuff, compared with the job of organising Einstein. But he cared more about his own failure to fit in with what was expected, now that Christopher had done ‘hopelessly better’ in the test at the end of term. In the new year of 1929 there was another shuffle, and Alan joined the sixth form proper, so that he did all his classes with Christopher. He made a point of sitting next to him in every class right from the start. Christopher, Alan wrote,

  made some of the remarks I was afraid of (I know better now) about the coincidence but seemed to welcome me in a passive way. It was not long before we began doing experiments together in Chemistry and we were continually changing our ideas on all sorts of subjects.

  Unfortunately Christopher was away from classes with a cold for most of January and February, and Alan could work with him only for five weeks of the spring term.

  Chris’ work was always better than mine because I think he was very thorough. He was certainly very clever but he never neglected
details, and for instance very seldom made arithmetical slips. He had a great power in practical work of finding out just what was the best way of doing anything. To give an example of his skill, he could estimate when a minute had passed to within half a second. He could sometimes see Venus in the day-time. Of course he was born with very good eyes, but still I think it is typical of him. His skill extended to all sorts of more everyday things, such as driving, fives and billiards.

  One cannot help admiring such powers and I certainly wanted to be able to do that kind of thing myself. Chris always had a delightful pride in his performances and I think it was this that excited one’s competitive instinct to do something which might fascinate him and which he might admire. This pride extended to a pride in his possessions. He used to demonstrate the virtues of his ‘Research’ fountain pen in a way which made my mouth water and then admitted he was trying to make me jealous.

  Slightly inconsistently, Alan also wrote:

  Chris always seemed to me very modest. He would never for instance tell Mr Andrews that his ideas weren’t sound although the opportunity occurred again and again. More particularly he very much disliked to offend anyone in any way and often used to apologise (e.g. to masters) in cases where the average boy would not dream of doing so.

  The average boy, as all school stories and magazines admitted, held the masters in contempt – especially in ‘Stinks’. It was the most obvious contradiction of the system. But Christopher rose above it all:

  A thing about Chris which I think is very unusual, is that he had a very definite code of morals. One day he was talking about an essay in an exam and how it had led to the subject of ‘right and wrong’. ‘I have some very definite ideas of “right and wrong”,’ he said. Somehow I never seemed to doubt that anything that Chris would do would be right, and I think there was a lot more in that than blind admiration.

  Take dirty talk for instance. The idea of Chris having to do with such a thing seemed simply ludicrous, and of course I do not know anything at all about Chris at the house, but I should think in this respect he would prevent dirty talk by making people not want to do it rather than making them avoid shocking him. This of course tells you nothing but the way his personality impressed me. I remember an occasion when I made a remark to him on purpose, that would decidedly not pass in a drawing room, but which would not be thought anything of at school, just to see how he would take it. He made me feel sorry for saying it, without him in any way seeming silly or priggish.

  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 Hochschule 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:

&n
bsp; … 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 l 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 1½-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: