Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  Running suited him, for it was a self-sufficient exercise, without equipment or social connotations. It was not that he had sprinting speed, nor indeed much grace, for he was rather flat-footed, but he developed great staying power by forcing himself on. It was not important to Sherborne, where what mattered was that (to Peter Hogg’s surprise) he became a ‘useful forward’ in the house team. But it was noticed with admiration by Knoop, and it was certainly important to Alan himself: He was not the first intellectual to impose this kind of physical training upon himself, and to derive lasting satisfaction from proving his stamina in running, walking, cycling, climbing, and enduring the elements. It was part of his ‘back to nature’ yearnings. But necessarily there were other elements involved; he perceived tiring himself out by running as an alternative to masturbation. It would probably be hard to overestimate the importance to his life of the conflicts surrounding his sexuality from this time onwards – both in controlling the demands of his body, and in a growing consciousness of emotional identity.

  In December it was the same arrival at Waterloo, on the way to Cambridge, but no trip to Mrs Morcom’s studio. Instead his mother and John (now an articled clerk in the City) were there to meet him, and Alan said he would go and see Howard Hughes’ aerial film Hell’s Angels. At Cambridge he failed again to win a Trinity scholarship. But his greater confidence was not entirely misplaced, for he was elected to a scholarship at the college of his second choice, King’s. He was placed eighth in order of the Major Scholars, with £80 per annum.*

  Everyone congratulated him. But he had set himself to do something, something that Christopher had been ‘called away from’. For a person with a mathematical mind, an ability to deal with very abstract relations and symbols as though with tangible everyday objects, a King’s scholarship was a demonstration like sight-reading a sonata or repairing a car – clever and satisfying, but no more. Many had won better scholarships, and at an earlier age. More to the point than the word ‘brilliant’ which now came to schoolmasters’ lips was the couplet that Peter Hogg sang at the house supper:

  Our Mathematician comes next in our lines

  With his mind deep in Einstein – and study light fines.

  For he had thought deeply about Einstein and had broken the rules to do so.

  Alan hibernated for two more terms – it was the usual thing. There was not much in the way of temporary employment in the conditions of 1931. By now he had settled upon mathematics rather than science as his future course at Cambridge. In February 1931 he acquired G.H. Hardy’s Pure Mathematics, the classic work with which university mathematics began. He took the Higher Certificate for a third time, this time with mathematics as major subject, and at last gained a distinction. He also entered again for the Morcom prize and won it. This time it came with a Prize Record Book, which Alan wrote ‘was most fascinatingly done and bears such a spirit of Chris in the clear bright illumination.’ The Morcoms had commissioned it in a contemporary neo-mediaeval style, which stood out sharply from the fusty Sherborne background.

  In the Easter holiday, on 25 March, he went on a walking and hitchhiking trip with Peter Hogg (a keen ornithologist) and an older boy, George Maclure. On their way from Guildford to Norfolk they spent one night in a working men’s hostel, which suited Alan, indifferent to anything more fancy (though it shocked his mother). One day, rather typically, he walked on by himself while the other two accepted a lift. He also spent five days on the OTC course at Knightsbridge barracks, qualifying in drill and tactics. This rather amazed John, who detected an unwonted enthusiasm in Alan for dressing up as a soldier. Perhaps he found this rare contact with men from outside the upper-middle-class cocoon to be strangely exciting.

  David Harris became his fag, and found him well-meaning but absent-minded as a master. One of Boughey’s revolutionary innovations was that prefects were allowed to have prefects from other houses to tea on Sunday afternoons, and occasionally Harris had to cook baked beans on toast when Alan availed himself of the concession. Alan had reached the summit of privilege. He continued with perspective drawing, stimulated by Victor’s interest and considerable artistic talent. They had many discussions on perspective and geometry. Alan entered a line drawing of the Abbey for a school art competition in July, and gave it to Peter Hogg. (Victor won a prize for his water-colour painting.) And then Valete, A. M. Turing, School Prefect, Sergeant in the OTC, Member of Duffers! Alan collected a number of prizes and a £50 per annum Cambridge subsidy from the Sherborne endowments. He was also awarded a King Edward VI gold medal for mathematics. At the Commemoration, he received the faint praise which was to be his only mention while at school in the Sherborne magazine8, marking out his proper place in the scheme of things. The scholarship winners were:

  G.C. Laws, who had been extraordinarily helpful to him (the Headmaster), a real mainstay to the tone of the place and a perpetually genial and cheerful and thoroughly best type of Shirburnian. (Applause.) The other open scholarship, mathematics, was gained by A.M. Turing who, in his sphere, was one of the most distinguished boys they had had recently.

  O’Hanlon described this as ‘a very successful close’ to ‘an interesting career, with varied experiences’, expressing gratitude for Alan’s ‘essentially loyal help’.

  Mrs Morcom had invited Alan and Mrs Turing to stay again in the summer. A letter from Alan of 14 August, answering some more of Mrs Morcom’s questions, and enclosing all of Christopher’s letters, said that his mother should have written to make the arrangements. But, for some reason, no visit was made. Instead, for the first two weeks of September, Alan went with O’Hanlon to Sark. Peter Hogg, Arthur Harris, and two old friends of O’Hanlon made up the party. They stayed at an eighteenth-century farmhouse, and spent the days on the rocky shores of the island, where Alan bathed naked. Arthur Harris was sketching in water colours, when Alan came up behind him, pointing to a heap of horse manure that lay on the road ahead. ‘I hope you’re going to put that in,’ he said.

  Few new students crossed the threshold of King’s College without some trepidation induced by its grandeur. Yet the translation to Cambridge was by no means a plunge into an entirely new environment, for in many ways the university resembled a very large public school – without its violence, but inheriting many of its attitudes. Anyone familiar with the subtle relationship of loyalties to house and school would find nothing perplexing in the system of college and university. The 11 pm curfew, the obligation to wear a gown after sunset, the prohibition on unchaperoned visits by the other sex, were lightly borne by the great majority of those in statu pupillari. They felt newly free, to drink and smoke and spend the day as they chose.

  Cambridge was positively feudal in its arrangements. The majority of the undergraduates came from public schools, and the minority who came from a lower-middle-class background, having won scholarships from grammar schools, had to adapt to the peculiar relationship between ‘gentlemen’ and ‘servants’. As for ladies, they were supposed to be content with their two colleges.

  As with public schools, there was a great deal about the ancient universities which had less to do with learning than with social status, with courses in geography and estate management for those of a less academic turn of mind. But the jolly raggings, debaggings and destruction of earnest students’ rooms had ended with the Twenties. With the depression, the Thirties had begun, stringent and serious. And nothing could interfere with that precious freedom – a room of one’s own. Cambridge rooms had double doors, and the convention was that the occupant who ‘sported his oak’ by locking the outer door was not at home. At last Alan could work, or think, or just be miserable – for he was far from happy – however and whenever he chose. His room could be as muddled and as untidy as he liked, so long as he made his peace with the college servants. He might be disturbed by Mrs Turing, who would scold him for the dangerous way he cooked breakfast on the gas ring. But these interruptions were very occasional, and after this first year, Alan saw his parents only on
fleeting visits to Guildford. He had gained his independence, and was at last left alone.

  But there were also the university lectures, which on the whole were of a high standard; the Cambridge tradition was to cover the entire mathematics course with lectures which were in effect definitive textbooks, by lecturers who were themselves world authorities. One of these was G.H. Hardy, the most distinguished British mathematician of his time, who returned in 1931 from Oxford to take up the Sadleirian Chair at Cambridge.

  Alan was now at the centre of scientific life, where there were people such as Hardy and Eddington who at school had been only names. Besides himself, there were eighty-five students who thus embarked upon the mathematics degree course, or ‘Tripos’ as Cambridge had it, in 1931. But these fell into two distinct groups: those who would offer Schedule A, and those who would sit for Schedule B as well. The former was the standard honours degree, taken like all Cambridge degrees in two Parts, Part I after one year, and Part II two years later. The Schedule B candidates would do the same, but in the final year they would also offer for examination an additional number – up to five or six – of more advanced courses. It was a cumbersome system, which was changed the following year, the Schedule B becoming ‘Part III’. But for Alan Turing’s year it meant neglecting study for Part I, which was something of a historical relic, hard questions on school mathematics, and instead beginning immediately on the Part II courses, leaving the third year free to study for the advanced Schedule B papers.

  The scholars and exhibitioners would be expected to offer Schedule B, and Alan par excellence was among them, one of those who could feel themselves entering another country, in which social rank, money, and politics were insignificant, and in which the greatest figures, Gauss and Newton, had both been born farm boys. David Hilbert, the towering mathematical intellect of the previous thirty years, had put it thus:9 ‘Mathematics knows no races … for mathematics, the whole cultural world is a single country,’ by which he meant no idle platitude, for he spoke as the leader of the German delegation at the 1928 international congress. The Germans had been excluded in 1924 and many refused to attend in 1928.

  Alan responded with joy to the absolute quality of mathematics, its apparent independence of human affairs, which G.H. Hardy expressed another way:10

  317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.

  Hardy was himself a ‘pure’ mathematician, meaning that he worked in those branches of the subject independent not only of human life, but of the physical world itself. The prime numbers, in particular, had this immaterial character. The emphasis of pure mathematics also lay upon absolutely logical deduction.

  On the other hand, Cambridge also laid emphasis on what it called ‘applied’ mathematics. This did not mean the application of mathematics to industry, economics, or the useful arts, there being in English universities no tradition of combining high academic status with practical benefits. It referred instead to the interface of mathematics and physics, generally physics of the most fundamental and theoretical kind. Newton had developed the calculus and the theory of gravitation together, and in the 1920s there had been a similar fertile period, when it was discovered that the quantum theory demanded techniques which were miraculously to be found in some of the newer developments of pure mathematics. In this area the work of Eddington, and of others such as P.A.M. Dirac, placed Cambridge second only to Göttingen, where much of the new theory of quantum mechanics had been forged.

  Alan was no foreigner to an interest in the physical world. But at this point, what he needed most was a grip on rigour, on intellectual toughness, on something that was absolutely right. While the Cambridge Tripos – half ‘pure’ and half ‘applied’ – kept him in touch with science, it was to pure mathematics that he turned as to a friend, to stand against the disappointments of the world.

  Alan did not have many other friends – particularly in this first year, in which he still mentally belonged to Sherborne. The King’s scholars mostly formed a self-consciously élite group, but he was one of the exceptions. He was a shy boy of nineteen, who had had an education more to do with learning silly poems by rote, or writing formal letters, than with ideas or self-expression. His first friend, and link with the others of the group, was David Champernowne, one of the other two mathematical scholars. He came from the mathematical sixth form of Winchester College, where he had been a scholar, and was more confident socially then Alan. But the two shared a similar ‘sense of humour’, being alike unimpressed by institutions or traditions. They also shared a hesitancy in speech, although David Champernowne’s was more slight than Alan’s. It was and remained a rather detached, public school kind of friendship, but important to Alan was that ‘Champ’ was not shocked by unconventionality. Alan told him about Christopher, showing him a diary that he had kept of his feelings since the death.

  They would go to college tutorials together. To begin with, it was a case of Alan catching up, for David Champernowne had been much better taught, and Alan’s work was still poorly expressed and muddled. Indeed, his friend ‘Champ’ had the distinction of publishing a paper11 while still an undergraduate, which was more than Alan did. The two supervisors of mathematics at King’s were A.E. Ingham, serious but with a wry humour, the embodiment of mathematical rigour, and Philip Hall, only recently elected a Fellow, under whose shyness lay a particular friendly disposition. Philip Hall liked taking Alan, and found him full of ideas, talking excitedly in his own strange way, in which his voice went up and down in pitch rather than in stress. By January 1932 Alan was able to write in an impressively off-hand way:

  I pleased one of my lecturers rather the other day by producing a theorem, which he found had previously only been proved by one Sierpinski, using a rather difficult method. My proof is quite simple so Sierpinski* is scored off.

  But it was not all work, because Alan joined the college Boat Club. This was unusual for a scholar, for the university was stuck with the polarising effect of the public schools, and students were supposed to be either ‘athletes’, or ‘aesthetes’. Alan fitted into neither category. There was also the other problem of mental and physical balance, for he fell in love again, this time with Kenneth Harrison, who was another King’s scholar of his year, studying the Natural Sciences Tripos. Alan talked to him a good deal about Christopher, and it became clear that Kenneth, who also had fair hair and blue eyes, and who also was a scientist, had become a sort of reincarnation of his first great flame. One difference, however, was that Alan did speak up for his own feelings, as he would never have dared with Christopher. They did not meet with reciprocation, but Kenneth admired the straightforwardness of his approach, and did not let it stop them from talking about science.

  At the end of January 1932, Mrs Morcom sent back to Alan all the letters between him and Christopher which he had surrendered to her in 1931. She had copied them out – quite literally – in facsimile. It was the second anniversary of his death. Mrs Morcom sent a card asking him to dinner on 19 February at Cambridge, and he in turn made the arrangements for her stay. It was not the most convenient weekend, he being engaged with the Lent boat races and obliged to be abstemious at dinner. But Alan found time to show her round: Mrs Morcom noted that his rooms were Very untidy’, and they went on to see where Alan and Christopher had stayed in Trinity for the scholarship examination, and where Mrs Morcom imagined Christopher would have sat in Trinity chapel.

  In the first week of April, Alan went to stay at the Clock House again, this time with his father. Alan slept in Christopher’s sleeping bag. They all went together to see the window of St Christopher, now installed in Catshill parish church, and Alan said that he could not have imagined anything more beautiful of its kind. Christopher’s face had been incorporated into the window – not as the sturdy St Christopher fording the stream, but as the secret Christ. On Sunday he went to communion there, and at
the house they held an evening gramophone concert. Mr Turing read and played billiards with Colonel Morcom, while Alan played parlour games with Mrs Morcom. Alan went out one day for a long walk with his father, and they had another day at Stratford-upon-Avon. On the last evening, Alan asked Mrs Morcom to come and say goodnight to him, as he lay in Christopher’s place in bed.

  The Clock House still held the spirit of Christopher Morcom. But how could this be? Could the atoms of Alan’s brain be excited by a non-material ‘spirit’, like a wireless set resonating to a signal from the unseen world? It was probably on this visit12 that Alan wrote out for Mrs Morcom the following explanation:

  NATURE OF SPIRIT

  It used to be supposed in Science that if everything was known about the Universe at any particular moment then we can predict what it will be through all the future. This idea was really due to the great success of astronomical prediction. More modern science however has come to the conclusion that when we are dealing with atoms and electrons we are quite unable to know the exact state of them; our instruments being made of atoms and electrons themselves. The conception then of being able to know the exact state of the universe then really must break down on the small scale. This means then that the theory which held that as eclipses etc. are predestined so were all our actions breaks down too. We have a will which is able to determine the action of the atoms probably in a small portion of the brain, or possibly all over it. The rest of the body acts so as to amplify this. There is now the question which must be answered as to how the action of the other atoms of the universe are regulated. Probably by the same law and simply by the remote effects of spirit but since they have no amplifying apparatus they seem to be regulated by pure chance. The apparent non-predestination of physics is almost a combination of chances.