One underlying reason for this was economic. Denniston had to plead for an increase in staff to match the military activity in the Mediterranean. In the autumn of 1935, the Treasury allowed an increase of thirteen clerks, although only on a temporary basis of six months at a time. It was a typical communication32 from Denniston to the Treasury in January 1937 that read:
The situation in Spain … remains so uncertain that there is an actual increase in traffic to be handled since the height of the Ethiopian crisis, the figures for cables handled during the last three months of 1934, 1935 and 1936 being
1934 10,638
1935 12,696
1936 13,990
During the past month the existing staff has only been able to cope with the increase in traffic by working overtime.
During 1937, the Treasury agreed to an increase in the permanent staff. But this measure did not meet a situation in which:33
The volume of German wireless transmissions … was increasing; it was steadily becoming less difficult to intercept them at British stations; yet even in 1939, for lack of sets and operators, by no means all German Service communications were being intercepted. Nor was all intercepted traffic being studied. Until 1937-38 no addition was made to the civilian staff as opposed to the service personnel at GC and CS; and because of the continuing shortage of German intercepts, the eight graduates then recruited were largely absorbed by the same growing burden of Japanese and Italian work that had led to expansion of the Service sections.
It was not simply a question of numbers and budgets, however. This elderly department was failing to rise to the mechanical challenge of the late 1930s. The years after the First World War had been ‘the golden age of modern diplomatic codebreaking’.34 But now the German communications presented GC and CS with a problem beyond their powers – the Enigma machine:35
By 1937 it was established that, unlike their Japanese and Italian counterparts, the German Army, the German Navy and probably the Air Force, together with other state organisations like the railways and the SS used, for all except their tactical communications, different versions of the same cypher system – the Enigma machine which had been put on the market in the 1920s but which the Germans had rendered more secure by progressive modifications. In 1937 GC and CS broke into the less modified and less secure model of this machine that was being used by the Germans, the Italians and the Spanish nationalist forces. But apart from this the Enigma still resisted attack, and it seemed likely that it would continue to do so.
The Enigma machine was the central problem that confronted British Intelligence in 1938. But they believed it was unsolvable. Within the existing system, perhaps it was. In particular, this department of classicists, a sort of secret shadow of King’s down in Broadway Buildings, did not include a mathematician.
No addition was made to permanent staff in 1938 to meet this striking deficiency. But36 ‘plans were made to take on some 60 more cryptanalysts in the event of war.’ And this was where Alan Turing came into the story, for he was one of the recruits. He might possibly have been in touch with the government since 1936. Or he might have stepped off the Normandie with the intention of demonstrating his multiplier. But more likely he was suggested to Denniston through one of the elder dons who had worked in Room 40 in the First World War. One of these was Professor Adcock, a Fellow of King’s since 1911. Had Alan ever spoken of codes and ciphers on the King’s High Table, his enthusiasm could quickly have been communicated to GC and CS. One way or another, he was a natural recruit. On his return in the summer of 1938, he was taken on to a course at the GC and CS headquarters.
Alan and his friends could see that war was likely, despite all the hopes of 1933, and found it important to see that they were used in some sensible way, rather than in leading cannon-fodder over the top. It was hard to separate this feeling from that of wanting to avoid injury, and the government’s policy for reserving intellectual talent came as some relief, releasing them from guilt. In this way, Alan Turing made his fateful decision, and chose to begin his long association with the British government. For all his suspicion of ‘HM Government’, it must have been exciting to be allowed to see the back of the shop. But it meant that he had for the first time surrendered a part of his mind, with a promise to keep the government’s secrets.
Though stern and demanding, the government that he joined, like the White Queen who took Alice on her journey, was in a muddled state, struggling with safety pins and string. The failure to make a serious effort at the Enigma was but one aspect of an incoherent strategy, which all the world could see in September 1938. Until that month, British people could still convince themselves that there were logical ‘solutions’ to German ‘grievances’ within the existing framework. After that month, moral debates about fairness and self-determination finally ceased to cloak the essential reality of power. The Cambridge population re-assembled for what was to be ‘the year under the terror’ in the words of Frank Lucas, a King’s don. The White Queen had squealed before the prick of the needle actually came. London children had been evacuated to Newnham College, and the male undergraduates had felt themselves on the brink of enlistment. Nothing was clear, but that something dreadful was in the offing. Radical agitation emphasised the devastating power expected of the modern air raid, while the government seemed to have nothing in mind but the building of bombers to execute a counter-attack.
The old world might be nearing its end, but there was a little escape into fantasy on offer from the new. Snow White and the Seven Dwarfs arrived at Cambridge in October, and Alan played exactly the part expected by Cambridge of King’s dons by going to see it with David Champernowne. He was very taken with the scene where the Wicked Witch dangled an apple on a string into a boiling brew of poison, muttering
Dip the apple in the brew
Let the Sleeping Death seep through
He liked to chant the prophetic couplet over and over again.
Alan also invited Shaun Wylie over from Oxford as guest at the college feast. Shaun Wylie and David Champernowne had been fellow scholars at Winchester. Alan had mentioned the multiplying cipher idea to Champ, but he told Shaun about the summer course, saying that he had put his name forward to the authorities as a possible recruit. The Princeton treasure hunts therefore had a serious consequence. He also said that he had been studying probability theory, and would like to experiment with tossing coins, but would feel silly if someone came in, although in King’s he need hardly have worried about appearing eccentric. They also played war games. David Champernowne had ‘Denis Wheatley’s exciting new war game – Invasion’, for which they invented new rules to make it a better game. Maurice Pryce, then in his second year as a university lecturer, had a conversation with Alan about the new idea of uranium fission, and Maurice found an equation for the conditions required for a chain reaction to start.*
Presumably Alan had again applied for a lectureship, but if so he had again been disappointed. However, he had offered to the faculty a course for the spring term on Foundations of Mathematics. (Newman was not giving one this year.) This they accepted,37 awarding the rather nominal £10 fee, as was the custom for mathematically respectable, but not officially commissioned Part III lectures. He was also asked to assess the claims of Friedrich Waismann, the philosopher from the Vienna Circle, exiled in Britain and expelled for misbehaviour from Wittgenstein’s retinue, who wanted to lecture on Foundations of Arithmetic. So Alan had carved out a small niche for himself.
On 13 November 1938, Neville Chamberlain attended the Armistice Day service in the University Church, and a bishop gratifyingly referred to the ‘courage, insight and perseverance of the Prime Minister in his interviews with Herr Hitler that saved the peace of Europe six weeks ago.’ But some Cambridge opinion was more in touch with reality. In King’s, Professor Clapham chaired a committee for the reception of Jewish refugees allowed in by the government after the November wave of violence in Germany. These were events with a particular meaning for Ala
n’s friend Fred Clayton, who between 1935 and 1937 had spent time studying first in Vienna and then in Dresden, with experiences very different from the jolly hockey-sticks of Princeton.
They meant two very difficult and hurtful things. On the one hand, he was highly conscious of the implications of the Nazi regime. On the other, there were two boys, one the younger son of a Jewish widow living in the same house in Vienna, one at the school where he had taught in Dresden. The November 1938 events had put the Vienna family in great peril, and he received appeals for help from Frau S——. He tried to help her get her sons to England, and this was achieved just before Christmas by the Quakers’ Relief Action. They found themselves in a refugee camp on the coast at Harwich, and wrote to Fred, who soon made a visit. In the dank, freezing, slave-market atmosphere some other young refugees rendered some German and English songs, and the passage from Schiller’s Don Karlos about Elizabeth receiving those fleeing from the Netherlands. Fred was already very fond of Karl, an affection which fatherless Karl returned, and went away to help find someone to foster him.
On hearing this story, Alan’s reaction was wholehearted. One wet Sunday in February 1939 he cycled with Fred to the camp at Harwich. He had conceived the idea of sponsoring a boy who wanted to go to school and university. Most of the boys were only too glad to be free of school for good. Of the very few exceptions, one was Robert Augenfeld – ‘Bob’ from the moment of his arrival in England – who had decided when he was ten that he wanted to be a chemist. He came from a Viennese family of considerable distinction and his father, who had been an aide-de-camp in the First World War, had instructed him to insist he should continue with his education. He had no means of support in England, and Alan agreed to sponsor him. It was impractical, for Alan’s fellowship stipend would run to nothing of the kind, although he had probably saved some of Procter’s money. His father wrote asking ‘Is it wise, people will misunderstand?’ which annoyed Alan, although David Champernowne thought his father had a good point.
But the immediate practical problems were soon solved. Rossall, a public school on the Lancashire coast, had offered to take in a number of refugee boys without fee. Fred’s protégé Karl was going to take a place there, and this was arranged for Bob as well. Bob had to travel up north to be interviewed, where Rossall accepted him with the proviso that he should first improve his English at a preparatory school. On the way he had been looked after by the Friends in Manchester, and they in turn approached a rich, Methodist, mill-owning family to take him in. (Karl was fostered in just the same way.) This settled his future, and although Alan was ultimately responsible for him, and Bob always felt a great debt, he did not have to pay for more than some presents and school kit to help the boy get started. His recklessness had been justified, although it certainly helped that Bob was mentally as tough as Alan, having survived the loss of everything he knew, and being determined to fight for his own future education.
Meanwhile Alan was becoming more closely involved with the problems of GC and CS. At Christmas there was another training session at the headquarters in Broadway. Alan went down and stayed at a hotel in St James’s Square with Patrick Wilkinson, the slightly senior classics don at King’s, who had also been drawn in. Thereafter, every two or three weeks, he would make visits to help with the work. He found himself attached to Dillwyn Knox, the Senior Assistant, and to young Peter Twinn, a physics postgraduate from Oxford, who had joined as a new permanent Junior when a vacancy was advertised in February. Alan would be allowed to take back to King’s some of the work they were doing on the Enigma. He said he ‘sported his oak’ when he studied it, as well he might. It was wise of Denniston not to wait until hostilities opened before letting his reserve force see the problems. But they were getting nowhere. A general knowledge of the Enigma machine was not enough upon which to base an attack.
It would have amazed Mrs Turing, if she had known that her younger son was being entrusted with state secrets. Alan had by this time developed a skilful technique for dealing with his family, and his mother in particular. They all thought of him as devoid of common sense, and he in turn would rise to the role of absent-minded professor. ‘Brilliant but unsound’, that was Alan to his mother, who undertook to keep him in touch with all those important matters of appearance and manners, such as buying a new suit every year (which he never wore), Christmas presents, aunts’ birthdays, and getting his hair cut. She was particularly quick to note and comment on anything that smacked of lower-middle-class manners. Alan tolerated this at home, using his persona as the boy genius to advantage. He avoided confrontation – in the case of religious observance by singing Christmas hymns while he worked over Easter and vice versa, or by referring in conversation to ‘Our Lord’ with a perfectly straight face. He was not exactly telling lies, but successfully avoiding hurt by deception. This was not something he would do for anyone else, but for him, as for most people, the family was the last bastion of deceit.
There was, however, another side to the relationship: Mrs Turing did sense that he had done something incomprehensibly important, and was most impressed by the interest aroused in his work abroad. Once a letter came from Japan! For some reason she was particularly struck by the fact that Scholz was going to mention Alan’s work in the 1939 revision of the German Encyklopädie der mathematischen Wissenschaften.38 It needed such official-sounding reverberations for her to feel that anything had happened. Alan in turn was not above using his mother as a secretary; she sent out some of the reprints of Computable Numbers while he was in America. He also made an effort to explain mathematical logic and complex numbers to her – but with a complete lack of success.
It was in the spring of 1939 that he gave his first Cambridge lecture course. He started with fourteen Part III students, but ‘no doubt the attendance will drop off as the term advances,’ he wrote home. He must have kept at least one, for he had to set questions on his course for the examination in June. One of these asked for a proof of the result of Computable Numbers. It must have been very pleasing to be able to set as an examination problem in 1939, the question that Newman had posed as unanswered only four years before.
But at the same time, Alan joined Wittgenstein’s class on Foundations of Mathematics. Although this had the same title as Alan’s course, it was altogether different. The Turing course was one on the chess game of mathematical logic; extracting the neatest and tightest set of axioms from which to begin, making them flower according to the exact system of rules into the structures of mathematics, and discovering the technical limitations of that procedure. But Wittgenstein’s course was on the philosophy of mathematics; what mathematics really was.
Wittgenstein’s classes were unlike any others; for one thing, the members had to pledge themselves to attend every session. Alan broke the rules and received a verbal rap on the knuckles as a result: he missed the seventh class, very possibly because of his journey to the Clock House where, on 13 February, an entire side chapel of the parish church was dedicated to Christopher, on the ninth anniversary of his death. This particular course extended over thirty-one hours, twice a week for two terms. There were about fifteen in the class, Alister Watson among them, and each had to go first for a private interview with Wittgenstein in his austere Trinity room. These interviews were renowned for their long and impressive silences, for Wittgenstein despised the making of polite conversation to a far more thoroughgoing degree than did Alan. At Princeton, Alan had told Venable Martin of how Wittgenstein was ‘a very peculiar man’, for after they had talked about some logic, Wittgenstein had said that he would have to go into a nearby room to think over what had been said.
Sharing a brusque, outdoor, spartan, tie-less appearance (though Alan remained faithful to his sports jacket, in contrast to the leather jacket worn by the philosopher), they were rather alike in this intensity and seriousness. Neither one could be defined by official positions (Wittgenstein, then fifty, had just been appointed Professor of Philosophy in succession to G. E. Moore
), for they were unique individuals, creating their own mental worlds. They were both interested only in fundamental questions, although they went in different directions. But Wittgenstein was much the more dramatic figure. Born into the Austrian equivalent of the Carnegies, he had given away a family fortune, spent years in village school-teaching, and lived alone for a year in a Norwegian hut. And even if Alan was a son of Empire, the Turing household had precious little in common with the Palais Wittgenstein.
Wittgenstein39 wanted to ask about the relationship of mathematics to ‘words of ordinary everyday language’. What, for instance, did the chess-like ‘proofs’ of pure mathematics have to do with ‘proof’ as in ‘The proof of Lewy’s guilt is that he was at the scene of his crime with a pistol in his hand’? As Wittgenstein kept saying, the connection was never clear. Principia Mathematica only pushed the problem to another place: it still required people to agree on what it meant to have ‘a proof’; it required people to agree what counting and recognising and symbols meant. When Hardy said that 317 was a prime because it was so, what did this mean? Did it only mean that people would always agree if they did their sums right? How did they know what were the ‘right’ rules? Wittgenstein’s technique was to ask questions which brought words like proof, infinite, number, rule, into sentences about real life, and to show that they might make nonsense. As the only working mathematician in the class, Alan tended to be treated as responsible for everything that mathematicians ever said or did, and he rather nobly did his best to defend the abstract constructions of pure mathematics against Wittgenstein’s attack.
In particular, there was an extended argument between them about the whole structure of mathematical logic. Wittgenstein wanted to argue that the business of creating a watertight, automatic logical system had nothing to do with what was ordinarily meant by truth. He fastened upon the feature of any completely logical system, that a single contradiction, and a self-contradiction in particular, would allow the proof of any proposition:
Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game Page 26
