Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two faculties, which we may call intuition and ingenuity. (We are leaving out of account that most important faculty which distinguishes topics of interest from others; in fact, we are regarding the function of the mathematician as simply to determine the truth or falsity of propositions.) The activity of the intuition consists in making spontaneous judgments which are not the result of conscious trains of reasoning. …
and he claimed that his ideas on ‘ordinal logics’ represented one way of formalising this distinction. But it was not established that ‘intuition’ had anything to do with the incompleteness of finitely defined formal systems. After all, no one knew of this incompleteness until 1931, while intuition was a good deal older. It was the same ambiguity as in Computable Numbers, which mechanised mind, yet pointed out something beyond mechanisation. Did this have a significance for human minds? His views were not clear at this stage.
As for the future, his intention was to return to King’s, provided that, as expected, they renewed his Fellowship which was, in March 1938, at the end of its first three years. On the other hand, his father wrote advising him (not very patriotically, perhaps) to find an appointment in the United States. For some reason King’s College was slow in notifying him that the extension of his fellowship had been made. Alan wrote to Philip Hall on 30 March:
I am writing a thesis for a Ph.D, which is proving rather intractable, and I am always rewriting parts of it. …
I am rather worried about the fact that I have heard nothing about re-election to my Fellowship. The most plausible explanation is simply that there has been no re-election, but [I] prefer to think there is some other reason. If you would make some cautious enquiries and send me a postcard I should be very grateful.
I hope Hitler will not have invaded England before I come back.
After the union with Austria on 13 March everyone was beginning to take Germany seriously. Meanwhile, Alan did dutifully go to Eisenhart and ask him ‘about possible jobs over here; mostly for Daddy’s information, as I think it is unlikely I shall take one unless you are actually at war before July. He didn’t know of one at present, but said he would bear it all in mind.’ But then a job materialised. Von Neumann himself offered a research assistant-ship at the IAS.
This might have meant a certain priority being given to von Neumann’s research areas – at that time in the mathematics associated with quantum mechanics and other areas of theoretical physics, and not including logic or the theory of numbers. On the other hand, a position with von Neumann would be the ideal start to the American academic career, which, presumably, Alan’s father thought wise. Competition was intense, and the market, already in depression, was flooded by European exiles. The stamp of approval from von Neumann would carry great weight.
In professional terms, this was a big decision. But all Alan wrote of the opportunity to Philip Hall on 26 April was: ‘Eventually a possibility of a job here turned up’, and to Mrs Turing on 17 May ‘I had an offer of a job here as von Neumann’s assistant at $1500 a year but decided not to take it.’ For he had cabled King’s to check that the fellowship had been renewed, and since it had, the decision was clear.
Despite himself, he had made his name in the Emerald City. It was not entirely necessary to have a reputation in order to be listened to. By this time, von Neumann was aware of Computable Numbers, even if he had not been a year earlier. For when he travelled with Ulam to Europe in this summer of 1938, he proposed26 a game of ‘writing down on a piece of paper as big a number as we could, defining it by a method which indeed has something to do with some schemata of Turing’s.’* But whatever the attractions, remunerations and compliments, the real issue was much simpler. He wanted to go home to King’s.
The thesis, which in October he had hoped to finish by Christmas, was delayed. ‘Church made a number of suggestions which resulted in the thesis being expanded to an appalling length.’ A clumsy typist himself, he engaged a professional, who in turn made a mess of it. It was eventually submitted on 17 May. There was an oral examination on 31 May, conducted by Church, Lefschetz and H.F. Bohnenblust. ‘The candidate passed an excellent examination, not only in the special field of mathematical logic, but also in other fields.’ There was a quick test in scientific French and German as well. It was vaguely absurd, to be examined in this way while at the same time he was refereeing the PhD thesis of a Cambridge candidate. This, as it happened, he had to reject. (To Philip Hall on 26 April: ‘I hope my remarks don’t encourage the man to go and rewrite the thing. The difficulty with these people is to find out a really good way of being blunt. However I think I’ve given him something to keep him quiet a long time if he really is going to rewrite it.’) The PhD was granted on 21 June. He made little use of the title, which had no application at Cambridge, and which elsewhere was liable to prompt people to retail their ailments.
His departure from the land of Oz was rather different from that in the fable. The Wizard was not a phoney, and had asked him to stay. While Dorothy had disposed of the Wicked Witch of the West, in his case it was the other way round. Though Princeton was fairly secluded from the orthodox, Teutonic side of America, it shared in a kind of conformity that made him ill at ease. And his problems remained unresolved. He was inwardly confident – but as in the Murder in the Cathedral which he saw performed in March (Very much impressed’) he was living and partly living.
In one way, however, he resembled Dorothy. For all the time, there was something that he could do, and which was just waiting for the opportunity to emerge. On 18 July Alan disembarked at Southampton from the Normandie, with the electric multiplier mounted on its breadboard and wrapped up securely with brown paper. ‘Will be seeing you in the middle of July’, he had written to Philip Hall, ‘I also expect to find the back lawn crisscrossed with 8 ft. trenches.’ It had not come to that, but there were more discreet preparations, in which he could take part himself.
Alan was right in thinking that H M Government was concerned with codes and ciphers.* It maintained a department to do the technical work. In 1938 its structure was still a legacy of the Great War, a continuation of the organisation discreetly known as Room 40 that the Admiralty had set up.
After the initial break of a captured German code book, passed to the Admiralty by Russia in 1914, a great variety of wireless and cable signals had been deciphered by a mostly civilian staff, recruited from universities and schools. The arrangement had the peculiar feature that the director, Admiral Hall, enjoyed control over diplomatic messages (for instance the famous Zimmermann telegram). Hall was no stranger to the exercise of power.27 It was he who showed Casement’s diary to the press, and there were more important instances of his28 ‘acting on intelligence independently of other departments in matters of policy that lay beyond the concerns of the Admiralty.’ The organisation survived the armistice, but in 1922 the Foreign Office succeeded in detaching it from the Admiralty. By then it had been renamed as the ‘Government Code and Cypher School’, and was supposed to study29 ‘the methods of cypher communication used by foreign powers’ and to ‘advise on the security of British codes and cyphers.’ It now came technically under the control of the head of the secret service,† himself nominally responsible to the Foreign Secretary.
The director of GC and CS, Commander Alastair Denniston, was allowed by the Treasury to employ thirty civilian Assistants,30 as the high-level staff were called, and about fifty clerks and typists. For technical civil service reasons, there were fifteen Senior and fifteen Junior Assistants. The Senior Assistants had all served in Room 40, except perhaps Feterlain, an exile from Russia who became head of the Russian section. There was Oliver Strachey, who was brother of Lytton Strachey and husband of Ray Strachey, the well-known feminist, and there was Dillwyn Knox, the classical scholar and Fellow of Kings until the Great War. Strachey and Knox had both been members of the Keynesian circle at its Edwardian peak. The Junior Assi
stants had been recruited as the department expanded a little in the 1920s; the most recently appointed of them, A.M. Kendrick, had joined in 1932.
The work of GC and CS had played an important part in the politics of the 1920s. Russian intercepts leaked to the press helped to bring down the Labour government in 1924. But in protecting the British Empire from a revived Germany, the Code and Cypher School was less vigorous. There was a good deal of sucess in reading the communications of Italy and Japan, but the official history31 was to describe it as ‘unfortunate’ that ‘despite the growing effort applied at GC and CS to military work after 1936, so little attention was devoted to the German problem.’
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 phil
osopher 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 Alan’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.
Alan Turing: The Enigma The Centenary Edition Page 25