User:سائغ/E2

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Career and research[edit]

When Turing returned to Cambridge, he attended lectures given in 1939 by Ludwig Wittgenstein about the foundations of mathematics.[1] The lectures have been reconstructed verbatim, including interjections from Turing and other students, from students' notes.[2] Turing and Wittgenstein argued and disagreed, with Turing defending formalism and Wittgenstein propounding his view that mathematics does not discover any absolute truths, but rather invents them.[3]

Cryptanalysis[edit]

During the Second World War, Turing was a leading participant in the breaking of German ciphers at Bletchley Park. The historian and wartime codebreaker Asa Briggs has said, "You needed exceptional talent, you needed genius at Bletchley and Turing's was that genius."[4]

From September 1938, Turing worked part-time with the Government Code and Cypher School (GC&CS), the British codebreaking organisation. He concentrated on cryptanalysis of the Enigma cipher machine used by Nazi Germany, together with Dilly Knox, a senior GC&CS codebreaker.[5] Soon after the July 1939 meeting near Warsaw at which the Polish Cipher Bureau gave the British and French details of the wiring of Enigma machine's rotors and their method of decrypting Enigma machine's messages, Turing and Knox developed a broader solution.[6] The Polish method relied on an insecure indicator procedure that the Germans were likely to change, which they in fact did in May 1940. Turing's approach was more general, using crib-based decryption for which he produced the functional specification of the bombe (an improvement on the Polish Bomba).[7]

Two cottages in the stable yard at Bletchley Park. Turing worked here in 1939 and 1940, before moving to Hut 8.

On 4 September 1939, the day after the UK declared war on Germany, Turing reported to Bletchley Park, the wartime station of GC&CS.[8] Like all others who came to Bletchley, he was required to sign the Official Secrets Act, in which he agreed not to disclose anything about his work at Bletchley, with severe legal penalties for violating the Act.[9]

Specifying the bombe was the first of five major cryptanalytical advances that Turing made during the war. The others were: deducing the indicator procedure used by the German navy; developing a statistical procedure dubbed Banburismus for making much more efficient use of the bombes; developing a procedure dubbed Turingery for working out the cam settings of the wheels of the Lorenz SZ 40/42 (Tunny) cipher machine and, towards the end of the war, the development of a portable secure voice scrambler at Hanslope Park that was codenamed Delilah.

By using statistical techniques to optimise the trial of different possibilities in the code breaking process, Turing made an innovative contribution to the subject. He wrote two papers discussing mathematical approaches, titled The Applications of Probability to Cryptography[10] and Paper on Statistics of Repetitions,[11] which were of such value to GC&CS and its successor GCHQ that they were not released to the UK National Archives until April 2012, shortly before the centenary of his birth. A GCHQ mathematician, "who identified himself only as Richard," said at the time that the fact that the contents had been restricted under the Official Secrets Act for some 70 years demonstrated their importance, and their relevance to post-war cryptanalysis:[12]

  • [He] said the fact that the contents had been restricted "shows what a tremendous importance it has in the foundations of our subject". ... The papers detailed using "mathematical analysis to try and determine which are the more likely settings so that they can be tried as quickly as possible." ... Richard said that GCHQ had now "squeezed the juice" out of the two papers and was "happy for them to be released into the public domain".

Turing had a reputation for eccentricity at Bletchley Park. He was known to his colleagues as "Prof" and his treatise on Enigma was known as the "Prof's Book".[13] According to historian Ronald Lewin, Jack Good, a cryptanalyst who worked with Turing, said of his colleague:

  • In the first week of June each year he would get a bad attack of hay fever, and he would cycle to the office wearing a service gas mask to keep the pollen off. His bicycle had a fault: the chain would come off at regular intervals. Instead of having it mended he would count the number of times the pedals went round and would get off the bicycle in time to adjust the chain by hand. Another of his eccentricities is that he chained his mug to the radiator pipes to prevent it being stolen.[14]}}

Peter Hilton recounted his experience working with Turing in Hut 8 in his "Reminiscences of Bletchley Park" from A Century of Mathematics in America:[15]

  • It is a rare experience to meet an authentic genius. Those of us privileged to inhabit the world of scholarship are familiar with the intellectual stimulation furnished by talented colleagues. We can admire the ideas they share with us and are usually able to understand their source; we may even often believe that we ourselves could have created such concepts and originated such thoughts. However, the experience of sharing the intellectual life of a genius is entirely different; one realizes that one is in the presence of an intelligence, a sensibility of such profundity and originality that one is filled with wonder and excitement.

Alan Turing was such a genius, and those, like myself, who had the astonishing and unexpected opportunity, created by the strange exigencies of the Second World War, to be able to count Turing as colleague and friend will never forget that experience, nor can we ever lose its immense benefit to us.

Hilton echoed similar thoughts in the Nova PBS documentary Decoding Nazi Secrets.[16]

While working at Bletchley, Turing, who was a talented long-distance runner, occasionally ran the 40 miles (64 km) to London when he was needed for meetings,[17] and he was capable of world-class marathon standards.[18][19] Turing tried out for the 1948 British Olympic team, but he was hampered by an injury. His tryout time for the marathon was only 11 minutes slower than British silver medallist Thomas Richards' Olympic race time of 2 hours 35 minutes. He was Walton Athletic Club's best runner, a fact discovered when he passed the group while running alone.[20][21][22] When asked why he ran so hard in training he replied:

  • I have such a stressful job that the only way I can get it out of my mind is by running hard; it’s the only way I can get some release.[23]

Due to the problems of counterfactual history, it is hard to estimate the precise effect Ultra intelligence had on the war.[24] However, official war historian Harry Hinsley estimated that this work shortened the war in Europe by more than two years and saved over 14 million lives.[25]

At the end of the war, a memo was sent to all those who had worked at Bletchley Park, reminding them that the code of silence dictated by the Official Secrets Act did not end with the war but would continue indefinitely.[9] Thus, even though Turing was appointed an Officer of the Order of the British Empire (OBE) in 1946 by King George VI for his wartime services, his work remained secret for many years.[26][27]

Bombe[edit]

Main article: Bombe

Within weeks of arriving at Bletchley Park,[8] Turing had specified an electromechanical machine called the bombe, which could break Enigma more effectively than the Polish bomba kryptologiczna, from which its name was derived. The bombe, with an enhancement suggested by mathematician Gordon Welchman, became one of the primary tools, and the major automated one, used to attack Enigma-enciphered messages.[28]

A working replica of a bombe now at The National Museum of Computing on Bletchley Park

The bombe searched for possible correct settings used for an Enigma message (i.e., rotor order, rotor settings and plugboard settings) using a suitable crib: a fragment of probable plaintext. For each possible setting of the rotors (which had on the order of 1019 states, or 1022 states for the four-rotor U-boat variant),[29] the bombe performed a chain of logical deductions based on the crib, implemented electromechanically.[30]

  1. ^ Hodges 1983, p. 152
  2. ^ Cora Diamond (ed.), Wittgenstein's Lectures on the Foundations of Mathematics, University of Chicago Press, 1976
  3. ^ Hodges 1983, pp. 153–154
  4. ^ Briggs, Asa (21 November 2011). Britain's Greatest Codebreaker (TV broadcast). UK Channel 4.
  5. ^ Copeland, Jack (2001). "Colossus and the Dawning of the Computer Age". In Smith, Michael; Erskine, Ralph (eds.). Action This Day. Bantam. p. 352. ISBN 978-0-593-04910-5.
  6. ^ Copeland 2004a, p. 217
  7. ^ Clark, Liat (18 June 2012). "Turing's achievements: codebreaking, AI and the birth of computer science (Wired UK)". Wired. Archived from the original on 2 November 2013. Retrieved 31 October 2013.
  8. ^ a b Copeland, 2006 p. 378.
  9. ^ a b Collins, Jeremy (24 June 2020). "Alan Turing and the Hidden Heroes of Bletchley Park: A Conversation with Sir John Dermot Turing". nationalww2museum.org. New Orleans: The National WWII Museum. Retrieved 24 August 2021.
  10. ^ Turing, Alan (c. 1941). "The Applications of Probability to Cryptography". The National Archives (United Kingdom): HW 25/37. Archived from the original on 7 April 2015. Retrieved 25 March 2015.
  11. ^ Turing, Alan (c. 1941). "Paper on Statistics of Repetitions". The National Archives (United Kingdom): HW 25/38. Archived from the original on 8 April 2015. Retrieved 25 March 2015.
  12. ^ Vallance, Chris (19 April 2012). "Alan Turing papers on code breaking released by GCHQ". BBC News. Archived from the original on 4 October 2012. Retrieved 20 April 2012.
  13. ^ Hodges 1983, p. 208
  14. ^ Lewin 1978, p. 57
  15. ^ Hilton, Peter. "A Century of Mathematics in America, Part 1, Reminiscences of Bletchley Park" (PDF). Archived (PDF) from the original on 29 August 2019.
  16. ^ Hilton, Peter. "NOVA | Transcripts | Decoding Nazi Secrets | PBS". PBS. Archived from the original on 29 August 2019.
  17. ^ Brown, Anthony Cave (1975). Bodyguard of Lies: The Extraordinary True Story Behind D-Day. The Lyons Press. ISBN 978-1-59921-383-5.
  18. ^ Graham-Cumming, John (10 March 2010). "An Olympic honour for Alan Turing". The Guardian. London. Archived from the original on 1 December 2016. Retrieved 10 December 2016.
  19. ^ Butcher, Pat (14 September 2009). "In Praise of Great Men". Globe Runner. Archived from the original on 18 August 2013. Retrieved 23 June 2012.
  20. ^ Hodges, Andrew. "Alan Turing: a short biography". Alan Turing: The Enigma. Archived from the original on 14 September 2013. Retrieved 12 June 2014.
  21. ^ Graham-Cumming, John (10 March 2010). "Alan Turing: a short biography". The Guardian. Archived from the original on 8 November 2014. Retrieved 12 June 2014.
  22. ^ Butcher, Pat (December 1999). "Turing as a runner". The MacTutor History of Mathematics archive. Archived from the original on 13 November 2014. Retrieved 12 June 2014.
  23. ^ Kottke, Jason. "Turing was an excellent runner". kottke.org.
  24. ^ See for example Richelson, Jeffery T. (1997). A Century of Spies: Intelligence in the Twentieth Century. New York: Oxford University Press. p. 296. and Hartcup, Guy (2000). The Effect of Science on the Second World War. Basingstoke, Hampshire: Macmillan Press. pp. 96–99.
  25. ^ Hinsley, Harry (1996) [1993], The Influence of ULTRA in the Second World War Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University
  26. ^ "Alan Turing: Colleagues share their memories". BBC News. 23 June 2012. Archived from the original on 7 July 2018. Retrieved 21 June 2018.
  27. ^ "This month in history: Alan Turing and the Enigma code". thegazette.co.uk. Archived from the original on 26 June 2019. Retrieved 6 February 2019.
  28. ^ Welchman, Gordon (1997) [1982], The Hut Six story: Breaking the Enigma codes, Cleobury Mortimer, England: M&M Baldwin, p. 81, ISBN 978-0-947712-34-1
  29. ^ Jack Good in "The Men Who Cracked Enigma", 2003: with his caveat: "if my memory is correct".
  30. ^ "The Turing-Welchman Bombe". The National Museum of Computing. Retrieved 18 March 2021.
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