Alan Turing: The Enigma (120 page)

(
4.34
) AMT’s letters to Newman are in
KCC.
They are undated but can mostly be placed by passing references to events.

(
4.35
) This essay, ‘The Reform of Mathematical Notation and Phraseology’, remained unpublished. The typescript is in
KCC
with other unpublished work on type theory. Excerpts are included in a historical paper by R.O. Gandy, ‘The Simple Theory of Types’, in
Logic Colloquium 1976
, eds. R.O. Gandy and J.M.E. Hyland (1977).

(
4.36
) AMT’s joint paper with M.H.A. Newman was ‘A Formal Theorem in Church’s Theory of Types’, in
J. Symbolic Logic 7
(1942).

(
4.37
) AMT’s paper appeared in the same 1942 volume of
the Journal of Symbolic Logic.
The two ‘forthcoming’ papers, ‘Some Theorems about Church’s System’ and ‘The Theory of Virtual Types’, never appeared. But in 1947 (see page 355 and note 6.34) he submitted a further paper on type theory which represented a revision of work done at this period.

(
4.38
) Hinsley I, page 338.

(
4.39
) Beesly, as note 4.11, page 164. I have inserted ‘September’ for Beesly’s ‘November’ to make it consistent with the Hinsley account.

(
4.40
) Letter quoted from Hinsley II, page 655.

(
4.41
) Hinsley II, page 657.

(
4.42
) Quoting from B. Randell,
The Colossus
, an account written from the engineering side. First published as a University of Newcastle-upon-Tyne report in 1976 this is now available in the Metropolis volume (see note 4.21).

(
4.43
) Peter Hilton was speaking informally during a conference session of
Reminiscences of Logicians,
published as a section of
Algebra and Logic,
Springer Mathematical Notes 450, ed. J. Crossley, 1975.

(
4.44
) As note 4.21.

(
4.45
) Hinsley II follows earlier writers in calling the German enciphering machine a
Geheimschreiber.
But my understanding is that there was more than one type of machine covered by this generic term, and that the photograph of a Siemens machine in B. Johnson,
The Secret War
(as note 4.10) is not actually of the one that was deciphered as Fish.

(
4.46
) As note 4.43.

(
4.47
) Stories
taken from
EST.
With mind-boggling
sang froid
she added: ‘The idea of “Prof.” being nearly arrested caused much amusement in his department.’

(4.48) As note 4.43.

(
4.49
) Hinsley II, page 56.

(
4.50
) I am grateful to the State Department for supplying copies of documents relating to AMT’s entry to the US in 1942. They are of a purely routine administrative nature. They account for all the references to AMT in the general index to State Department files held in the National Archives, Washington. In contrast, there are no corresponding British documents. There is a reference in the index to Foreign Office correspondence for 1942 to ‘
Turing
: sea travel facilities to Washington: finances.’ But the relevant file has been ‘weeded’: destroyed.

(
4.51
) FO/371/32346.

(
4.52
) As note 4.2.

(
4.53
) I owe this reference to Dr G. DiVita. It was on 14 February 1941. Of course the report gave no indication of the scale and modernity of operations, but it is curious to see any mention whatever of ‘Nazi codes’ being broken, when comprehensive secrecy on the subject lasted for a quarter of a century after Nazi Germany’s demise.

(
4.54
) For AMT’s pre-war voyages I was able to draw upon the Board of Trade passenger lists. But none exist for the wartime period, so the evidence here is indirect. The State Department information (see note 4.50) shows that he was admitted at New York on 13 November 1942. Information from the Naval Historical Center, Department of the Navy, Washington D.C. shows that this was the day that the
Queen Elizabeth
arrived.

The fast passenger liners converted to troop transporters being the normal means of ferrying high-level personnel, I have assumed this to settle the question. But it is confused by the statement of Mrs Turing that his passage west was very overcrowded, and that he was the only civilian on board apart from a couple of children. Here, surely, she was mistaken. It was the
eastbound
passages which were desperately crowded. The
Queen Elizabeth
carried a mere 557 passengers west, most of them civilians, to return in March with 10,261 troops. See also note BP 11, for evidence regarding AMT’s eastbound voyage.

Bridge Passage

(
BP 1
) This is the most substantial anecdote from the wartime period in
EST,
and a rare example of where Mrs Turing’s deference to officials took second place to an authentic Alan Turing tone of voice. Apart from some early childhood details, this is also almost the first place in
EST
where Mrs Turing’s personal recollection emerges. My guess is that it was the hint of AMT making an important mission to America that made her take more notice of him.

(
BP 2
) The index to Foreign Office correspondence for 1943 contains on page 428 a reference to complaints (themselves ‘weeded’) about insufficient accreditation. This might have included AMT’s – but in any case adds a few decibans to an otherwise unlikely-sounding story.

(
BP 3
) Beesly, as note 4.11, pages 152, 161.

(
BP 4
) The date of arrival, like subsequent dates
and details of AMT’s period in New York, derives from contemporary Bell Laboratories personnel records made available to me. But with AMT’s visit making such an impression on his mother, there are a few odd details of reminiscence in
EST,
based presumably on his cryptic replies to her interrogation. There was ‘some hold-up about his job, which involved a useless period of idling in New York’ – very likely the two weeks or so before 19 January, and due to ‘clearance’ arrangements, just the thing to annoy him. Mrs Turing’s own assertion about the purpose of his visit to America was that ‘he probably saw something of the progress of computing machinery in the States.’ But probably AMT said Oh, seeing some of their machines, Mother’, and the word ‘computing’ was Mrs Turing’s guesswork. She also wrote ‘He seems to have taken the opportunity to visit Princeton’ – he could certainly easily have stopped off on one of his several journeys between New York and Washington. Her oddest comment was in reference to the mix-up upon his arrival: ‘Even on Ellis Island he would have found something of interest, perhaps more than he found at Washington.’ While this again reflected the way that everyone in secret work had to spin out the trivial and play down the serious, there is a hint here that while AMT could hardly say, ‘Well, Mother, I was handing over to the Americans all the work we’ve been doing for the last three years,’ he allowed something of this to come through.

(
BP 5
)
National Service in War and Peace (1925–1975)
, the second volume of
A History of Engineering and Science in the Bell System
, Bell Telephone Laboratories, 1978. I have taken my account of the Vocoder and the X-system directly from this source. The X-system was ‘one of the starting points of the digital transmission age that followed’, despite being until 1975 ‘an unmentionable system’.

(
BP 6
) PRO file CAB 79/25. The Memorandum referred to has not been released. I am indebted to David Kahn for this reference.

(
BP 7
) Minute dated 27 April 1943, in CAB 79/27.

(
BP 8
) C.E. Shannon, ‘Communication in the Presence of Noise’,
Proc. I.R.E.
(1948) is annotated: Original manuscript received by the Institute, July 23 1940.’ His paper ‘Communication Theory of Secrecy Systems’,
Bell System Technical Journal,
1949, a very rare example of cryptology treated from a post-1930 standpoint in the open literature, was originally ‘A Mathematical Theory of Cryptography’, a Bell confidential report dated 1 September 1945.

(
BP 9
) C.E. Shannon, ‘A Symbolic Analysis of Relay and Switching Circuits’,
Trans. Amer. I.E.E. 57
(1938). According to the Bell
History
, it was as a result of this that ‘the design of relay circuits changed rapidly from being a somewhat esoteric art to being a science, and it became possible to teach it as an engineering discipline.’

(
BP 10
) W.S. McCulloch and W. Pitts, ‘A Logical Calculus of the Ideas Immanent in Nervous Activity’,
Bull. Math. Biophys.
5, (1943). Their paper contained no reference to
Computable Numbers
, but in a discussion after a lecture of von Neumann (the same as in note 6.57), McCulloch mentioned
that it was AMT’s paper that had inspired their ideas. See von Neumann’s
Collected Works
(Pergamon, 1963), volume V, page 319.

(
BP 11
) The evidence regarding AMT’s eastbound voyage is less clear than for that of November 1942. According to
EST
‘he returned in a destroyer or similar naval vessel and experienced a good tossing on the Atlantic.’ But I think that she was mistaken here; it is hard to believe that the ‘top cryptanalyst’ would have been entrusted to a destroyer when a fast independent troop transporter was available. Instead, I think her recollection of him being the only civilian on board a crowded ship (see note 4.54) must in fact refer to
this
voyage. Then it fits (apart from the ‘couple of children’) with the information (from the Naval Historical Center, Washington) about the
Empress of Scotland.
This sailing, furthermore, was the only independent eastbound sailing in the rest of March. The week’s delay may be accounted for by the fact that this was when the convoy battle was at its height. Since Mrs Turing was certainly fallible – an example being in her annotations to
KCC
, which incorrectly stated Jack Crawford’s death to have occurred before AMT’s visit in 1938 – I have based the narrative on this not quite conclusive evidence.

(
BP 12
) I am grateful to Richard Plant for pointing out this reference in H. Heiber,
Reichsführer!
(Deutsche Verlags-Anstalt, Stuttgart, 1968).

(
BP 13
) E.M. Forster,
Post-Munich
, 1939, reprinted in
Two Cheers for Democracy
(Edward Arnold & Co., 1951).

Running Up

(
5.1
) Volume I of
Allied Communications Intelligence and the Battles of the Atlantic
, report SRH 009 declassified by the National Security Agency, available at the National Archives, Washington.

(
5.2
) Kapitän H. Bonatz, head of the
B. Dienst
, quoted in M. Middlebrook,
Convoy
(Allen Lane, 1976).

(
5.3
) PRO file FO 850/171 contains a memorandum of May 1945, from the Cypher Policy Board to the Foreign Office, with instructions for use of the Typex. It explains that ‘When encyphering on the Typex machine, the encyphered version of a letter can never be the letter itself. This sometimes makes it possible to assign with absolute accuracy even a small number of words known or estimated to be in a message to the actual letters of the cypher version …’, and gives procedures for burying addresses and other stereotyped beginnings and endings amidst nonsense, inserting extra letters between and within words, and so forth. These were just the procedures which, if correctly applied, would render Enigma transmissions immune to decipherment. One cannot tell whether the existence of such a memorandum means that the lesson had, or had not, been learnt by British operators within the six years of war.

(
5.4
) The year between March 1943 and March 1944 is the least well documented of AMT’s life. Certainly there is clear evidence that both before and after this period he was engaged as a cryptographic consultant, and it is reasonable to suppose that this was also true during this year of catching-up. There are surely some interesting facts yet to emerge concerning his interaction with
this phase of the war, although my impression is that there was nothing engaging him with the intensity that characterised the earlier period. The other dark year of his life was, of course, his last. There might in fact be some connection between them, since if he continued to do top level work in examining Anglo-American communication systems in preparation for D-Day, he would have had access to new American machine systems and much else still important in years after the Second World War. And who would have known how much he knew? As one apparently given access to American establishments on Churchill’s personal authority, he was quite outside the usual service systems.

(
5.5
) Frank Clare,
The Cloven Pine
(Seeker & Warburg, 1943).

(
5.6
) B. Randell,
The Colossus
, as note 4.42.

(
5.7
) The Explanatory Caption attached to the photographs of the Colossus in PRO file FO 850/234 claims a direct link with Babbage and
Computable Numbers: