Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  No doubt he is very aggravating, and he should know by now that I don’t care to find him boiling heaven knows what witches’ brew by the aid of two guttering candles on a naked window sill. However, he has borne his afflictions very cheerfully, and undoubtedly has taken more trouble, e.g. with physical training. I am far from hopeless.

  Alan’s only regret regarding the ‘witches’ brew’ was that O’Hanlon ‘had missed seeing at their height the very fine colours produced by the ignition of the vapour produced by super-heated candle-grease.’ Alan was still fascinated by chemistry, but not interested in doing it in a way that pleased anyone else. Mathematics and science reports such as ‘… marred by inaccuracy, untidiness, and bad style … frightfully untidy both in written and experimental work …’ continued to reflect his lack of ability to communicate effectively, while admitting that he was ‘very promising’. ‘His manner of presenting work is still disgusting,’ wrote O’Hanlon, ‘and takes away much of the pleasure it should give.’ ‘He doesn’t understand what bad manners bad writing and messy figures are.’ Ross had passed him on to another form, but he was still placed nearly at the bottom in the spring of 1928. ‘His mind seems rather chaotic at present and he finds great difficulty in expressing himself. He should read more,’ wrote the master, perhaps more enlightened than Ross.

  It was in doubt whether he could take the School Certificate and go on to the sixth form. O’Hanlon and the science masters wanted him to try, and the rest opposed it. The decision had to be made by the new headmaster, who knew nothing of Alan. Boughey had proved himself a new broom, upsetting sacred traditions of the school. The head of the Classical Sixth was no longer automatically the head of school. The prefects had been alienated when he lectured the whole school on ‘dirty talk’. (They felt he was judging Sherborne by Marlborough standards.) The staff were horrified when he issued a fiat, in front of the school, that there would be no memorial to Carey in the chapel. This incident sealed his doom. The official history20 would record that

  A natural shyness could give an impression of self-esteem and indifference to school affairs that had perhaps no great foundation in fact … he had to fight against an ill health that was largely the result of war service and he found it increasingly hard to make the public appearances or even to provide the constant private accessibility which a headmaster’s position inevitably demands.

  Whether as cause or effect, he was ‘poisoned’, as Brewster would have put it, by alcohol. The school settled down to a power struggle between Ross and Boughey, and it was the fight between old and new that settled Alan’s future, for Boughey over-ruled Ross on principle and allowed him to be entered for the School Certificate.

  During the holidays, Alan’s father coached him in English. Mr Turing had a great love of literature, although he did not have a mind for abstract ideas. He could recite from memory pages from the Bible, Kipling, and humorous Edwardian novels like Three Men in a Boat. All this was wasted on Alan, whose set work was Hamlet. For a brief moment he pleased his father by saying that at least there was one line he liked. The pleasure was dissipated when Alan explained it was the last line: ‘Exeunt, bearing off the bodies....

  For the summer term of 1928, Alan was moved to yet another form, that of the Reverend W.J. Bensly, to prepare for the examinations. He saw no reason to depart from his usual pattern, and continued to be placed at the bottom by Bensly, who rashly offered to donate a billion pounds to any charity named by Alan, should he pass in Latin. O’Hanlon, more perceptively, had predicted:

  He has as good brains as any boy that’s been here. They are good enough for him to get through even in ‘useless’ subjects like Latin, French and English.

  O’Hanlon saw some of the papers that Alan submitted. They were ‘astonishingly legible and tidy’. He passed with credits in English, French, elementary mathematics, additional mathematics, physics, chemistry – and Latin. Bensly never paid up, authority having the privilege of being able to change the rules.

  The School Certificate passed, the system allowed him a small part to play, that of the ‘maths brain’. There was no mathematical sixth at Sherborne, as at some schools, notably Winchester. There was a science sixth for whom mathematics, Alan’s best subject, was regarded as subsidiary. Nor was Alan promoted to the sixth form immediately; he was held back in the fifth for the autumn of 1928, but allowed to join the sixth form for their mathematics classes. These were taught by a young master, Eperson, just a year down from Oxford and a gentle, cultured person, the kind of master who would constantly be played up by the boys. Here was the chance for the system to redeem itself at last, the spirit breaking through the letter of the law. And in a negative way, Eperson did what Alan wanted, by leaving him alone:21

  All that I can claim is that my deliberate policy of leaving him largely to his own devices and standing by to assist when necessary, allowed his natural mathematical genius to progress uninhibited …

  He found that Alan always preferred his own methods to those supplied by the text book, and indeed Alan had gone his own way all the time, making few concessions to the school system. During the machinations over the School Certificate, or even before, he had been studying the theory of relativity from Einstein’s own popular account.22 This employed only elementary mathematics, but gave full rein to ideas which went far beyond anything in the school syllabus. For if Natural Wonders had introduced him to the post-Darwinian world, Einstein took him into the twentieth century revolution of physics. Alan produced a small red Memo Book of notes, which he gave to his mother.

  ‘Einstein here throws doubt,’ Alan commented, ‘on whether Euclid’s axioms, when applied to rigid bodies, hold. … He therefore sets out to test … the Galilei-Newtonian laws or axioms.’ He had identified the crucial point, that Einstein doubted the axioms. Not for Alan the ‘obvious duties’, for nothing was obvious to him. His brother John, who by now regarded Alan with a rather patronising, but not hostile amusement, held that

  You could take a safe bet that if you ventured on some self-evident proposition, as for example that the earth was round, Alan would produce a great deal of incontrovertible evidence to prove that it was almost certainly flat, ovular, or much the same shape as a Siamese cat which had been boiled for fifteen minutes at a temperature of one thousand degrees Centigrade.

  Cartesian doubt came as an incomprehensible intrusion into Alan’s family and school environment, an intrusion that the English coped with more by laughter than by persecution. But doubt being a very difficult and rare state of mind, it had taken the whole intellectual world a very long time to ask whether the ‘Galilei-Newtonian laws or axioms’, apparently ‘self-evident’, were actually true. Only by the late nineteenth century was it recognised that they were inconsistent with the known laws of electricity and magnetism. The implications were frightening, and it had needed Einstein to take the step of saying that the assumed basis of mechanics was actually incorrect, thereby creating the Special Theory of Relativity in 1905. This then proved inconsistent with Newton’s laws of gravity, and to remove these contradictions Einstein had gone even further, casting doubt even on Euclid’s axioms of space to create the General Theory of Relativity in 1915. The point of what Einstein had done did not lie in this or that experiment. It lay, as Alan saw, in the ability to doubt, to take ideas seriously, and to follow them to a logical if upsetting conclusion. ‘Now he has got his axioms,’ wrote Alan, ‘and is able to proceed with his logic, discarding the old ideas of time, space, etc.’

  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 certa
inly 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.