TURING (ALAN)

Autograph mathematical calculations setting out and solving a problem in n-dimensional geometry, 2 pages, [Bletchley Park, 1941 or 1942]

Footnotes

TURING & EQUILATERAL TRIANGLES: RECREATIONAL MATHEMATICS AT BLETCHLEY PARK.

These pages of closely written calculations by Alan Turing (1912-1954) were found amongst the papers of Rolf Noskwith (1919-2017), a cryptographer who worked closely with Turing in Hut 8 at Bletchley Park (see lot...). Together they worked on German Naval Enigma Codes from June 1941 until Turing left for America in the Autumn of 1942 to assist the US Navy's codebreakers. According to Professor Jack Copeland, who has kindly deciphered Turing's 'elegant' mathematics, as he puts it, these calculations '...form an excellent example of the recreational mathematics that went on at Bletchley Park. Turing's extensive recreational mathematical work while at Bletchley included, for example, his correspondence with Max Newman (published in The Essential Turing), his 1942 paper with Newman in The Journal of Symbolic Logic, and his seminal work on computerized chess, mechanized learning, and other aspects of what he called 'machine intelligence'...'. The importance of such 'recreational mathematics' was therefore not to be underestimated. Noskwith, in his own account of life at Bletchley, remembers '...We all recognised his genius; perhaps for this reason he was known as 'Prof'. We regarded him as eccentric but I can not remember any specific eccentricities. By the time of my arrival in Hut 8 the basic principles of the work were well established so that there was less scope for his genius... and [he] left altogether in late 1942. While he was with us he was always approachable and ready to help with technical problems. It may have been my fault that I did not find it easy to communicate with him...' (Noskwith, R., 'Hut 8 from the Inside', in ed. Erskine, R., Smith, M., The Bletchley Park Code-Breakers, London, 2011, chapter 12, p.192). Turing's solution is not dated but as he only worked with Noskwith for just over a year, it can be assumed that it was written between June 1941 and late 1942.

These calculations are not merely a complex mathematical exercise, they also serve to demonstrate the culture of intellectual enquiry and collaboration that pervaded amongst the recruits to Bletchley Park. Turing and his colleagues had a deep-rooted interest in problem solving and puzzles and that this should continue alongside their more serious work on codebreaking is unsurprising. Patrick Mahon, later head of Hut 8, in his History of Hut Eight 1939-1945 (alanturing.net), notes that their success lay not in the fact that the men and women working at Bletchley thought it a worthwhile job per se, but that they thought '...the problem was an interesting and amusing one...' and that '...the work of Hut 8 combined to a remarkable extent a sense of urgency and importance with the pleasure of playing an intellectual game...' (chapter XII). Their leisure time was therefore, to a certain extent, an extension of their intellectual interests and, indeed, Noskwith writes of his colleagues' reluctance to leave work at the end of a long shift, so engrossed they were in the challenges of the day. However, it must be said that there were many other activities at Bletchley to occupy their time - tiddlywinks, table-tennis, rounders, tennis, cricket, musical societies and much else. Noskwith talks of the active Dramatic Society who '...put on plays and reviews of a high standard, there was a lot of music and we played chess and bridge. Most men went about in old sports jackets and shabby corduroy trousers. Once when a visiting Admiral was taken around the site by the Director he is reported to have asked: 'What are all these velvet arsed bastards doing here?'... There really was a spirit of camaraderie among the cryptanalysts and a sense of a common purpose. I can recall no personality clashes or big outbursts of temper. I attribute this to the fascination of the work, the satisfaction of getting results, exemplary leadership and, above all, the personalities of the individuals...' (Noskwith, p.192).

As is shown by the papers in the accompanying lot, Noskwith was recruited fresh from Trinity College, Cambridge, at the age of 22 and was assigned to Hut 8 under Shaun Wylie: '...I entered a completely different new world when I learned that the German Navy enciphered its signals using a machine called Enigma... our function was to produce cribs, a crib being a guess of what a portion of a particular signal might be saying. A correct crib, tested on the bombes (...developed by Alan Turing), would lead to the solution of a day's keys...' (Noskwith, p.186). In October 1941 he was responsible for the breakthrough in finding the crib for the complex Offizier code: '...I was not expecting to be successful and went home on leave before the testing on a bombe was complete. Wylie promised to confirm a positive result by sending me a telegram containing the name of a fish. When a telegram arrived with the word 'pompano' I had to look it up in a dictionary to make sure that 'pompano' was a fish...' (Noskwith, p.188). Developments in technology meant that during the last year of the war Noskwith was one of only four cribsters required to remain in Hut 8 – Patrick Mahon, Joan Clarke (Turing's one-time fiancé), Richard Pendered and himself - working on a shift rota round the clock but 'always dependent on a big supporting cast' of secretaries and Wrens who ran the bombe machines in spartan conditions. 'All the main keys were broken regularly during this period...' Noskwith notes (p.190) and throughout the course of the war Hut 8 successfully decoded about 1,120,000 messages, with the largest number of messages registered in one day being 2,133 on 13th March 1945.

We are grateful to Distinguished Professor Jack Copeland, Director of the Turing Archive for the History of Computing (www.AlanTuring.net) for his help in preparing this catalogue entry.