Editing Alan Turing (section)

==Career and research==
When Turing returned to Cambridge, he attended lectures given in 1939 by [[Ludwig Wittgenstein]] about the [[foundations of mathematics]].<ref>{{Harvnb|Hodges|1983|p=152}}</ref> The lectures have been reconstructed verbatim, including interjections from Turing and other students, from students' notes.<ref>{{Cite book |editor-first=Cora |editor-last=Diamond |editor-link=Cora Diamond |title=Wittgenstein's Lectures on the Foundations of Mathematics |publisher=University of Chicago Press |year=1976}}</ref> Turing and Wittgenstein argued and disagreed, with Turing defending [[Philosophy of mathematics#Formalism|formalism]] and Wittgenstein propounding his view that mathematics does not discover any absolute truths, but rather invents them.<ref>{{Harvnb|Hodges|1983|pp=153–154}}</ref>

===Cryptanalysis===
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."<ref>{{Cite AV media | last = Briggs | first = Asa | author-link = Asa Briggs | title = Britain's Greatest Codebreaker | type = TV broadcast | publisher = [[Channel 4|UK Channel 4]] | date = 21 November 2011}}</ref>

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|cryptanalysis of the Enigma cipher machine]] used by [[Nazi Germany]], together with [[Dilly Knox]], a senior GC&CS codebreaker.<ref>{{Cite book | author-link = Jack Copeland | last = Copeland | first = Jack | chapter = Colossus and the Dawning of the Computer Age | page = 352 | title = Action This Day | publisher = Bantam | date = 2001 | isbn = 978-0-593-04910-5 | editor1-first = Michael | editor1-last = Smith | editor2-first = Ralph | editor2-last = Erskine }}</ref> 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 rotor details|Enigma machine's rotors]] and their method of decrypting [[Enigma machine]]'s messages, Turing and Knox developed a broader solution.<ref>{{Harvnb|Copeland|2004a|p=217}}</ref> The Polish method relied on an insecure [[Cryptanalysis#Indicator|indicator]] procedure that the Germans were likely to change, which they in fact did in May 1940. Turing's approach was more general, using [[Cryptanalysis of the Enigma#Crib-based decryption|crib-based decryption]] for which he produced the functional specification of the [[bombe]] (an improvement on the Polish [[Bomba (cryptography)|Bomba]]).<ref>{{cite news |last=Clark |first=Liat |url=https://www.wired.co.uk/news/archive/2012-06/18/turing-contributions?page=all |title=Turing's achievements: codebreaking, AI and the birth of computer science (Wired UK) |magazine=Wired |date=18 June 2012 |access-date=31 October 2013 |archive-url=https://web.archive.org/web/20131102122933/http://www.wired.co.uk/news/archive/2012-06/18/turing-contributions?page=all |archive-date=2 November 2013 |url-status=live }}</ref>

[[File:Turing flat.jpg|thumb|right|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.<ref name=Copeland2006p378>Copeland, 2006 p.&nbsp;378.</ref> Like all others who came to Bletchley, he was required to sign the [[Official Secrets Act 1939|Official Secrets Act]], in which he agreed not to disclose anything about his work at Bletchley, with severe legal penalties for violating the Act.<ref name="Collins">{{cite web |last=Collins |first=Jeremy |title=Alan Turing and the Hidden Heroes of Bletchley Park: A Conversation with Sir John Dermot Turing |date=24 June 2020 |location=New Orleans |publisher=The National WWII Museum |url=https://www.nationalww2museum.org/war/articles/alan-turing-betchley-park |access-date=24 August 2021 |archive-date=2 December 2021 |archive-url=https://web.archive.org/web/20211202101721/https://www.nationalww2museum.org/war/articles/alan-turing-betchley-park |url-status=live }}</ref>

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 [[Her Majesty's Government Communications Centre|Hanslope Park]] that was codenamed ''Delilah''.<ref>{{Cite web |title=How Alan Turing Cracked The Enigma Code |url=https://www.iwm.org.uk/history/how-alan-turing-cracked-the-enigma-code |access-date=12 July 2023 |website=Imperial War Museums |language=en |archive-date=24 January 2022 |archive-url=https://web.archive.org/web/20220124140731/https://www.iwm.org.uk/history/how-alan-turing-cracked-the-enigma-code |url-status=live }}</ref><ref>{{Cite journal |last1=Turing |first1=Alan M. |last2=Bayley |first2=D. |date=2012 |title=Report on Speech Secrecy System DELILAH, a Technical Description Compiled by A. M. Turing and Lieutenant D. Bayley REME, 1945–1946 |url=http://www.tandfonline.com/doi/abs/10.1080/01611194.2012.713803 |journal=Cryptologia |language=en |volume=36 |issue=4 |pages=295–340 |doi=10.1080/01611194.2012.713803 |s2cid=205488183 |issn=0161-1194 |access-date=26 August 2024 |archive-date=12 July 2023 |archive-url=https://web.archive.org/web/20230712092022/https://www.tandfonline.com/doi/abs/10.1080/01611194.2012.713803 |url-status=live }}</ref>

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''<ref>{{cite web | last = Turing | first = Alan | year = c. 1941 | title = The Applications of Probability to Cryptography | id = The National Archives (United Kingdom): HW 25/37 | url = http://discovery.nationalarchives.gov.uk/details/r/C11510465 | access-date = 25 March 2015 | archive-url = https://web.archive.org/web/20150407234050/http://discovery.nationalarchives.gov.uk/details/r/C11510465 | archive-date = 7 April 2015 | url-status = live }}</ref> and ''Paper on Statistics of Repetitions'',<ref>{{cite web | last = Turing | first = Alan | year = c. 1941 | title = Paper on Statistics of Repetitions | id = The National Archives (United Kingdom): HW 25/38 | url = http://discovery.nationalarchives.gov.uk/details/r/C11510466 | access-date = 25 March 2015 | archive-url = https://web.archive.org/web/20150408013845/http://discovery.nationalarchives.gov.uk/details/r/C11510466 | archive-date = 8 April 2015 | url-status = live }}</ref> which were of such value to GC&CS and its successor [[GCHQ]] that they were not released to the [[The National Archives (United Kingdom)|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:<ref name=bbcrichard>{{cite news |last=Vallance |first=Chris |title=Alan Turing papers on code breaking released by GCHQ |url=https://www.bbc.co.uk/news/technology-17771962 |access-date=20 April 2012 |work=BBC News |date=19 April 2012 |archive-url=https://web.archive.org/web/20121004192554/http://www.bbc.co.uk/news/technology-17771962 |archive-date=4 October 2012 |url-status=live }}</ref>

{{blockquote|text=[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".<ref>{{Harvnb|Hodges|1983|p=208}}</ref><ref>{{cite book |title=The Prof's Book: Turing's Treatise on the Enigma |first=Alan M. |last=Turing |year=1940 |url=https://archive.org/details/hw-25-3/ |url-access=registration |quote=In late 1940 Alan Turing wrote a report describing the methods he and his colleagues at Bletchley Park had used to break into the German Enigma cipher systems. At Bletchley it was known as 'the Prof's Book.' A copy of this handbook was at last released from secrecy by the American National Security Agency in April 1996, under the title ''Turing's Treatise on the Enigma''. Subsequently, a much better original copy was released by the (British) National Archives, box HW 25/3. This also revealed a title which had been lost in the American copy: ''Mathematical theory of ENIGMA machine''. (Though, oddly, the report does not actually have any mathematical theory.)}}</ref> According to historian [[Ronald Lewin]], [[I.J. Good|Jack Good]], a cryptanalyst who worked with Turing, said of his colleague:

{{blockquote|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.<ref>{{Harvnb|Lewin|1978|p=57}}</ref>}}

[[Peter Hilton]] recounted his experience working with Turing in [[Hut 8]] in his "Reminiscences of Bletchley Park" from ''A Century of Mathematics in America:''<ref>{{Cite web|url=http://www.ams.org/publicoutreach/math-history/hmath1-hilton22.pdf|title=A Century of Mathematics in America, Part 1, Reminiscences of Bletchley Park|last=Hilton|first=Peter|archive-url=https://web.archive.org/web/20190829112241/http://www.ams.org/publicoutreach/math-history/hmath1-hilton22.pdf|archive-date=29 August 2019|url-status=live}}</ref>

{{blockquote| 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.|sign=|source=}}

Hilton echoed similar thoughts in the Nova [[PBS]] documentary ''Decoding Nazi Secrets''.<ref>{{Cite web|url=https://www.pbs.org/wgbh/nova/transcripts/2615decoding.html|title=NOVA {{!}} Transcripts {{!}} Decoding Nazi Secrets {{!}} PBS|last=Hilton|first=Peter|website=[[PBS]]|archive-url=https://web.archive.org/web/20190829112240/https://www.pbs.org/wgbh/nova/transcripts/2615decoding.html|archive-date=29 August 2019|url-status=live}}</ref>

While working at Bletchley, Turing, who was a talented [[Long-distance running|long-distance runner]], occasionally ran the {{convert|40|mi}} to London when he was needed for meetings,<ref>{{Cite book | last = Brown | first = Anthony Cave | author-link = Anthony Cave Brown | title = Bodyguard of Lies: The Extraordinary True Story Behind D-Day | page = 19 | publisher=The Lyons Press | year = 1975 | isbn = 978-1-59921-383-5 | url = https://archive.org/details/bodyguardoflies00brow | url-access = registration}}</ref> and he was capable of world-class marathon standards.<ref>{{cite news|url=https://www.theguardian.com/commentisfree/2010/mar/10/alan-turing-2012-olympics|title=An Olympic honour for Alan Turing|author=Graham-Cumming, John|newspaper=The Guardian|date=10 March 2010|location=London|access-date=10 December 2016|archive-url=https://web.archive.org/web/20161201171628/https://www.theguardian.com/commentisfree/2010/mar/10/alan-turing-2012-olympics|archive-date=1 December 2016|url-status=live}}</ref><ref>{{cite web | first=Pat | last=Butcher | url=http://www.globerunner.org/index.php/09/in-praise-of-great-men/ | title=In Praise of Great Men | publisher=Globe Runner | date=14 September 2009 | access-date=23 June 2012 | archive-url=https://web.archive.org/web/20130818145759/http://www.globerunner.org/index.php/09/in-praise-of-great-men/ | archive-date=18 August 2013 | url-status=live }}</ref> Turing tried out for the [[Great Britain at the 1948 Summer Olympics|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 [[Tom Richards (athlete)|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.<ref>{{cite web | last1 = Hodges | first1 = Andrew | author-link = Andrew Hodges | title = Alan Turing: a short biography | url = http://www.turing.org.uk/bio/part6.html | publisher = Alan Turing: The Enigma | access-date = 12 June 2014 | archive-url = https://web.archive.org/web/20130914091359/http://www.turing.org.uk/bio/part6.html | archive-date = 14 September 2013 | url-status = live }}</ref><ref>{{cite news | last1 = Graham-Cumming | first1 = John | author-link = John Graham-Cumming | title = Alan Turing: a short biography | url = https://www.theguardian.com/commentisfree/2010/mar/10/alan-turing-2012-olympics | newspaper = The Guardian | date = 10 March 2010 | access-date = 12 June 2014 | archive-url = https://web.archive.org/web/20141108165218/http://www.theguardian.com/commentisfree/2010/mar/10/alan-turing-2012-olympics | archive-date = 8 November 2014 | url-status = live }}</ref><ref>{{cite web | last1 = Butcher | first1 = Pat | title = Turing as a runner | url = http://www-groups.dcs.st-and.ac.uk/~history/Extras/Turing_running.html | publisher = The MacTutor History of Mathematics archive | date = December 1999 | access-date = 12 June 2014 | archive-url = https://web.archive.org/web/20141113020916/http://www-groups.dcs.st-and.ac.uk/~history/Extras/Turing_running.html | archive-date = 13 November 2014 | url-status = live }}</ref> When asked why he ran so hard in training he replied:

{{blockquote|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.<ref>{{cite web |url=https://kottke.org/18/04/alan-turing-was-an-excellent-runner |first=Jason |last=Kottke |title=Turing was an excellent runner |website=kottke.org |date=17 April 2018 |access-date=26 August 2024 |archive-date=9 June 2021 |archive-url=https://web.archive.org/web/20210609192748/https://kottke.org/18/04/alan-turing-was-an-excellent-runner |url-status=live }}</ref>}}

Due to the problems of [[counterfactual history]], it is hard to estimate the precise effect Ultra intelligence had on the war.<ref>See for example {{cite book|last=Richelson|first=Jeffery T.|title=A Century of Spies: Intelligence in the Twentieth Century|date=1997|publisher=Oxford University Press|location=New York|page=296|author-link=Jeffrey T. Richelson}} and {{cite book|last=Hartcup|first=Guy|title=The Effect of Science on the Second World War|date=2000|publisher=Macmillan Press|location=Basingstoke, Hampshire|pages=96–99|author-link=Guy Hartcup}}</ref> However, official war historian [[Harry Hinsley]] estimated that this work shortened the war in Europe by more than two years and saved over 14&nbsp;million lives.<ref name="Hinsley 1996">{{citation | last = Hinsley | first = Harry | author-link = Harry Hinsley | title = The Influence of ULTRA in the Second World War | orig-date = 1993 | year = 1996 | url = http://www.cix.co.uk/~klockstone/hinsley.htm | access-date = 26 August 2024 | archive-date = 15 October 2022 | archive-url = https://web.archive.org/web/20221015210957/https://www.cix.co.uk/~klockstone/hinsley.htm | url-status = live }} Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University</ref>

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.<ref name="Collins"/> Thus, even though Turing was appointed an [[Order of the British Empire|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.<ref>{{cite news | title = Alan Turing: Colleagues share their memories | url = https://www.bbc.co.uk/news/technology-18541715 | date = 23 June 2012 | work = BBC News | access-date = 21 June 2018 | archive-url = https://web.archive.org/web/20180707105436/https://www.bbc.co.uk/news/technology-18541715 | archive-date = 7 July 2018 | url-status = live }}</ref><ref name="thegazette.co.uk">{{cite web|url=https://www.thegazette.co.uk/all-notices/content/114|title=This month in history: Alan Turing and the Enigma code|website=thegazette.co.uk|access-date=6 February 2019|archive-url=https://web.archive.org/web/20190626211800/https://www.thegazette.co.uk/all-notices/content/114|archive-date=26 June 2019|url-status=live}}</ref>

===Bombe===
Within weeks of arriving at Bletchley Park,<ref name="Copeland2006p378" /> Turing had specified an electromechanical machine called the [[bombe]], which could break Enigma more effectively than the Polish ''[[bomba (cryptography)|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.<ref>{{Cite book |last= Welchman |first= Gordon |author-link= Gordon Welchman |orig-year= 1982 |year= 1997 |title= The Hut Six story: Breaking the Enigma codes |page= 81 |location= Cleobury Mortimer, England |publisher= M&M Baldwin |isbn= 978-0-947712-34-1 }}</ref>

[[File:Bombe-rebuild.jpg|thumbnail|right|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 (cryptanalysis)|crib]]'': a fragment of probable [[plaintext]]. For each possible setting of the rotors (which had on the order of 10<sup>19</sup> states, or 10<sup>22</sup> states for the four-rotor U-boat variant),<ref>Jack Good in "The Men Who Cracked Enigma", 2003: with his caveat: "if my memory is correct".</ref> the bombe performed a chain of logical deductions based on the crib, implemented [[Electromechanics|electromechanically]].<ref>{{cite web |url=https://www.tnmoc.org/bombe |title=The Turing-Welchman Bombe |website=The National Museum of Computing |access-date=18 March 2021 |archive-date=24 January 2022 |archive-url=https://web.archive.org/web/20220124200142/https://www.tnmoc.org/bombe |url-status=live }}</ref>

The bombe detected when a contradiction had occurred and ruled out that setting, moving on to the next. Most of the possible settings would cause contradictions and be discarded, leaving only a few to be investigated in detail. A contradiction would occur when an enciphered letter would be turned back into the same plaintext letter, which was impossible with the Enigma. The first bombe was installed on 18 March 1940.<ref>{{Harvnb|Oakley|2006|p=40/03B}}</ref>

==== Action This Day ====
{{main|Action This Day (memo)}}

By late 1941, Turing and his fellow cryptanalysts [[Gordon Welchman]], [[Conel Hugh O'Donel Alexander|Hugh Alexander]] and [[Stuart Milner-Barry]] were frustrated. Building on the [[Biuro Szyfrów#Gift to allies|work of the Poles]], they had set up a good working system for decrypting Enigma signals, but their limited staff and bombes meant they could not translate all the signals. In the summer, they had considerable success, and shipping losses had fallen to under 100,000 tons a month; however, they badly needed more resources to keep abreast of German adjustments. They had tried to get more people and fund more bombes through the proper channels, but had failed.<ref name=":0" />

On 28 October they wrote directly to [[Winston Churchill]] explaining their difficulties, with Turing as the first named. They emphasised how small their need was compared with the vast expenditure of men and money by the forces and compared with the level of assistance they could offer to the forces.<ref name=":0">{{Harvnb|Hodges|1983|p=218}}</ref> As [[Andrew Hodges]], biographer of Turing, later wrote, "This letter had an electric effect."<ref name="Hodges 1983 221">{{Harvnb|Hodges|1983|p=221}}</ref> Churchill wrote a memo to [[Hastings Ismay, 1st Baron Ismay|General Ismay]], which read: "ACTION THIS DAY. Make sure they have all they want on extreme priority and report to me that this has been done." On 18 November, the chief of the secret service reported that every possible measure was being taken.<ref name="Hodges 1983 221"/> The cryptographers at Bletchley Park did not know of the Prime Minister's response, but as Milner-Barry recalled, "All that we did notice was that almost from that day the rough ways began miraculously to be made smooth."<ref>Copeland, ''The Essential Turing'', [http://www.maths.ed.ac.uk/~aar/turingletter.pdf pp. 336–337] {{Webarchive|url=https://web.archive.org/web/20150218142127/http://www.maths.ed.ac.uk/~aar/turingletter.pdf |date=18 February 2015 }}.</ref> More than two hundred bombes were in operation by the end of the war.<ref name=codebreaker>{{cite web | last1 = Copeland | first1 = Jack | last2 = Proudfoot | first2 = Diane | author-link = Jack Copeland | title = Alan Turing, Codebreaker and Computer Pioneer | url = http://www.alanturing.net/turing_archive/pages/Reference%20Articles/codebreaker.html | publisher = alanturing.net | date = May 2004 | access-date = 27 July 2007 | archive-url = https://web.archive.org/web/20070709065520/http://www.alanturing.net/turing_archive/pages/Reference%20Articles/codebreaker.html | archive-date = 9 July 2007 | url-status = live }}</ref>

===Hut 8 and the naval Enigma===
[[File:Turing-statue-Bletchley 14.jpg|thumb|upright|Statue of Turing holding an Enigma machine by [[Stephen Kettle]] at Bletchley Park, commissioned by [[Sidney Frank]], built from half a million pieces of Welsh slate<ref>{{cite web |title=Bletchley Park Unveils Statue Commemorating Alan Turing |url=http://www.bletchleypark.org.uk/news/docview.rhtm/454075 |access-date=30 June 2007 |archive-url=https://web.archive.org/web/20070630083823/http://www.bletchleypark.org.uk/news/docview.rhtm/454075 |archive-date=30 June 2007 |url-status=live }}</ref>]]

Turing decided to tackle the particularly difficult problem of cracking the [[Cryptanalysis of the Enigma#German Naval Enigma|German naval use of Enigma]] "because no one else was doing anything about it and I could have it to myself".<ref name=MahonP14>{{Harvnb|Mahon|1945|p=14}}</ref> In December 1939, Turing solved the essential part of the naval [[Enigma machine#Indicator|indicator]] system, which was more complex than the indicator systems used by the other services.<ref name=MahonP14 /><ref>{{Harvnb|Leavitt|2007|pp=184–186}}</ref>

That same night, he also conceived of the idea of ''[[Banburismus]]'', a sequential statistical technique (what [[Abraham Wald]] later called [[sequential analysis]]) to assist in breaking the naval Enigma, "though I was not sure that it would work in practice, and was not, in fact, sure until some days had actually broken".<ref name=MahonP14 /> For this, he invented a measure of weight of evidence that he called the ''[[Ban (unit)|ban]]''. ''Banburismus'' could rule out certain sequences of the Enigma rotors, substantially reducing the time needed to test settings on the bombes.<ref>{{Cite journal|last=Gladwin|first=Lee|date=Fall 1997|title=Alan Turing, Enigma, and the Breaking of German Machine Ciphers in World War II|url=https://www.archives.gov/files/publications/prologue/1997/fall/turing.pdf|journal=Prologue Magazine|volume=Fall 1997|pages=202–217|via=National Archives|access-date=13 April 2019|archive-url=https://web.archive.org/web/20190626211657/https://www.archives.gov/files/publications/prologue/1997/fall/turing.pdf|archive-date=26 June 2019|url-status=live}}</ref> Later this sequential process of accumulating sufficient weight of evidence using decibans (one tenth of a ban) was used in [[cryptanalysis of the Lorenz cipher]].<ref>{{Citation | last1 = Good | first1 = Jack | author-link = I. J. Good | last2 = Michie | first2 = Donald | author2-link = Donald Michie | last3 = Timms | first3 = Geoffrey | title = General Report on Tunny: With Emphasis on Statistical Methods | year = 1945 | id = UK Public Record Office HW 25/4 and HW 25/5 | url = http://www.alanturing.net/turing_archive/archive/t/t15/TR15-018.html | at = Part 3 Organisation: 38 Wheel-breaking from Key, Page 293 | access-date = 13 April 2019 | archive-url = https://web.archive.org/web/20190421091539/http://www.alanturing.net/turing_archive/archive/t/t15/TR15-018.html | archive-date = 21 April 2019 | url-status = live }}</ref>

Turing travelled to the United States in November 1942 and worked with US Navy cryptanalysts on the naval Enigma and bombe construction in Washington.<ref>{{Harvnb|Hodges|1983|pp=242–245}}</ref><ref>{{Cite web |title=Alan Turing's Report from Washington, 1942 |url=https://www.turing.org.uk/sources/washington.html |access-date=12 July 2023 |website=www.turing.org.uk |archive-date=12 July 2023 |archive-url=https://web.archive.org/web/20230712083844/https://www.turing.org.uk/sources/washington.html |url-status=live }}</ref> He also visited their [[United States Naval Computing Machine Laboratory|Computing Machine Laboratory]] in [[Dayton, Ohio]].<ref>{{Cite web |title=Alan Turing's Dayton Report, 1942 |url=https://www.turing.org.uk/sources/dayton123.html |access-date=12 July 2023 |website=www.turing.org.uk}}</ref>

Turing's reaction to the American bombe design was far from enthusiastic:

{{blockquote|text=The American Bombe programme was to produce 336 Bombes, one for each wheel order. I used to smile inwardly at the conception of Bombe hut routine implied by this programme, but thought that no particular purpose would be served by pointing out that we would not really use them in that way.

Their test (of commutators) can hardly be considered conclusive as they were not testing for the bounce with electronic stop finding devices. Nobody seems to be told about rods or offiziers or banburismus unless they are really going to do something about it.<ref>{{Cite journal |last=Turing |first=Alan M. |year=2001 |journal=Cryptologia |volume=25 |issue=1 |pages=1–10 |doi=10.1080/0161-110191889734 |title=Visit to National Cash Register Corporation of Dayton, Ohio |s2cid=14207094 }}</ref>|source=}}

During this trip, he also assisted at [[Bell Labs]] with the development of [[secure speech]] devices.<ref>{{Harvnb|Hodges|1983|pp=245–253}}</ref> He returned to Bletchley Park in March 1943. During his absence, [[Colonel Hugh O'Donel Alexander|Hugh Alexander]] had officially assumed the position of head of Hut 8, although Alexander had been ''de facto'' head for some time (Turing having little interest in the day-to-day running of the section). Turing became a general consultant for cryptanalysis at Bletchley Park.<ref>{{Cite web|url=https://www.marshallfoundation.org/newsroom/marshall-legacy-series/codebreaking/|title=Marshall Legacy Series: Codebreaking – Events|website=marshallfoundation.org|access-date=7 April 2019|archive-url=https://web.archive.org/web/20190407030638/https://www.marshallfoundation.org/newsroom/marshall-legacy-series/codebreaking/|archive-date=7 April 2019|url-status=live}}</ref>

Alexander wrote of Turing's contribution:

{{blockquote|There should be no question in anyone's mind that Turing's work was the biggest factor in Hut 8's success. In the early days, he was the only cryptographer who thought the problem worth tackling and not only was he primarily responsible for the main theoretical work within the Hut, but he also shared with Welchman and Keen the chief credit for the invention of the bombe. It is always difficult to say that anyone is 'absolutely indispensable', but if anyone was indispensable to Hut 8, it was Turing. The pioneer's work always tends to be forgotten when experience and routine later make everything seem easy and many of us in Hut 8 felt that the magnitude of Turing's contribution was never fully realised by the outside world.<ref>{{Harvnb|Alexander|circa 1945|p=42}}</ref>}}

===Turingery===
In July 1942, Turing devised a technique termed ''[[Turingery]]'' (or jokingly ''Turingismus<ref>{{Harvnb|Copeland|2006|p=380}}</ref>'') for use against the [[Lorenz cipher]] messages produced by the Germans' new ''Geheimschreiber'' (secret writer) machine. This was a [[teleprinter]] [[Rotor machine|rotor cipher attachment]] codenamed ''Tunny'' at Bletchley Park. Turingery was a method of ''wheel-breaking'', i.e., a procedure for working out the cam settings of Tunny's wheels.<ref>{{Harvnb|Copeland|2006|p=381}}</ref> He also introduced the Tunny team to [[Tommy Flowers]] who, under the guidance of [[Max Newman]], went on to build the [[Colossus computer]], the world's first programmable digital electronic computer, which replaced a simpler prior machine (the [[Heath Robinson (codebreaking machine)|Heath Robinson]]), and whose superior speed allowed the statistical decryption techniques to be applied usefully to the messages.<ref>{{Harvnb|Copeland|2006|p=72}}</ref> Some have mistakenly said that Turing was a key figure in the design of the Colossus computer. Turingery and the statistical approach of Banburismus undoubtedly fed into the thinking about [[cryptanalysis of the Lorenz cipher]],<ref>{{Harvnb|Gannon|2007|p=230}}</ref><ref>{{Harvnb|Hilton|2006|pp=197–199}}</ref> but he was not directly involved in the Colossus development.<ref>{{Harvnb|Copeland|2006|pp=382, 383}}</ref>

===Delilah===
Following his work at [[Bell Labs]] in the US,<ref>{{Harvnb|Hodges|1983|pp=245–250}}</ref> Turing pursued the idea of electronic enciphering of speech in the telephone system. In the latter part of the war, he moved to work for the Secret Service's Radio Security Service (later [[Her Majesty's Government Communications Centre|HMGCC]]) at [[Hanslope Park]].<ref>{{cite journal| last = Harper| first = John| author-link = John Harper (computer engineer)| title = Delilah Voice Secrecy System| journal = Resurrection: The Journal of the Computer Conservation Society| issue = 101| pages = 8–9| publisher = The Computer Conservation Society| date = Spring 2023| url = https://www.computerconservationsociety.org/resurrection/res101.htm#d| access-date = 28 June 2023}}</ref><ref>{{cite journal| last = Harper| first = John| author-link = John Harper (computer engineer)| title = Delilah Voice Secrecy System [part 2]: The Design, Development and Commissioning of Delilah in 1943 – 1945| journal = Resurrection: The Journal of the Computer Conservation Society| issue = 102| pages = 16–19| publisher = The Computer Conservation Society| date = Summer 2023| url = https://www.computerconservationsociety.org/resurrection/res102.htm#c| access-date = 28 June 2023| archive-date = 3 July 2023| archive-url = https://web.archive.org/web/20230703233634/https://www.computerconservationsociety.org/resurrection/res102.htm#c| url-status = live}}</ref> At the park, he further developed his knowledge of electronics with the assistance of [[Royal Electrical and Mechanical Engineers|REME]] officer Donald Bayley. Together they undertook the design and construction of a portable [[secure voice]] communications machine codenamed ''[[Delilah (voice encryption)|Delilah]]''.<ref>{{Harvnb|Hodges|1983|p=273}}</ref> The machine was intended for different applications, but it lacked the capability for use with long-distance radio transmissions. In any case, Delilah was completed too late to be used during the war. Though the system worked fully, with Turing demonstrating it to officials by encrypting and decrypting a recording of a [[Winston Churchill]] speech, Delilah was not adopted for use.<ref>{{Harvnb|Hodges|1983|p=346}}</ref> Turing also consulted with Bell Labs on the development of [[SIGSALY]], a secure voice system that was used in the later years of the war.

===Early computers and the Turing test===
[[File:Alan Turing 78 High Street Hampton blue plaque.jpg|thumb|Plaque, 78 High Street, [[Hampton, London|Hampton]]]]
Between 1945 and 1947, Turing lived in [[Hampton, London|Hampton]], London,<ref>{{openplaque|1619}}</ref> while he worked on the design of the [[ACE (computer)|ACE]] (Automatic Computing Engine) at the [[National Physical Laboratory (United Kingdom)|National Physical Laboratory (NPL)]]. He presented a paper on 19 February 1946, which was the first detailed design of a [[stored-program computer]].<ref>{{Harvnb|Copeland|2006|p=108}}</ref> [[John von Neumann|Von Neumann]]'s incomplete ''[[First Draft of a Report on the EDVAC]]'' had predated Turing's paper, but it was much less detailed and, according to [[John R. Womersley]], Superintendent of the NPL Mathematics Division, it "contains a number of ideas which are Dr. Turing's own".<ref>{{cite news | last = Randell | first = Brian | author-link = Brian Randell | title = A History of Computing in the Twentieth Century: Colossus | year = 1980 | url = http://www.cs.ncl.ac.uk/research/pubs/books/papers/133.pdf | access-date = 27 January 2012 | archive-url = https://web.archive.org/web/20120127144927/http://www.cs.ncl.ac.uk/research/pubs/books/papers/133.pdf | archive-date = 27 January 2012 | url-status = live }} citing {{Cite journal | last = Womersley | first = J.R. | author-link = John R. Womersley | title = 'ACE' Machine Project | journal=Executive Committee, National Physical Laboratory, Teddington, Middlesex | date = 13 February 1946 }}</ref>

Although ACE was a feasible design, the effect of the [[Official Secrets Act 1939|Official Secrets Act]] surrounding the wartime work at Bletchley Park made it impossible for Turing to explain the basis of his analysis of how a computer installation involving human operators would work.<ref>{{cite book |title=Alan Turing: The Enigma |publisher=Princeton University Press |author-link=Andrew Hodges |last=Hodges |first=Andrew |page=[https://books.google.com/books?id=4muYDwAAQBAJ&q=%22Twenty%20years%20ahead%20of%20his%20time%22 416] |year=2014 |isbn=978-0-691-16472-4}}</ref> This led to delays in starting the project and he became disillusioned. In late 1947 he returned to Cambridge for a sabbatical year during which he produced a seminal work on ''Intelligent Machinery'' that was not published in his lifetime.<ref>See {{harvnb|Copeland|2004b|pp=410–432}}</ref> While he was at Cambridge, the [[Pilot ACE]] was being built in his absence. It executed its first program on 10 May 1950, and a number of later computers around the world owe much to it, including the [[English Electric DEUCE]] and the American [[Bendix G-15]]. The full version of Turing's ACE was not built until after his death.<ref>{{cite web|url=http://www.npl.co.uk/about/history/notable-individuals/turing/|title=Turing at NPL|access-date=3 July 2015|archive-url=https://web.archive.org/web/20150705082340/http://www.npl.co.uk/about/history/notable-individuals/turing/|archive-date=5 July 2015|url-status=live}}</ref>

According to the memoirs of the German computer pioneer [[Heinz Billing]] from the [[Max Planck Institute for Physics]], published by Genscher, Düsseldorf, there was a meeting between Turing and [[Konrad Zuse]].<ref>{{cite web|url=http://www.mathcomp.leeds.ac.uk/turing2012/Images/Turing_Zuse.pdf|title=Did Alan Turing interrogate Konrad Zuse in Göttingen in 1947?|author=Bruderer, Herbert|access-date=7 February 2013|archive-url=https://web.archive.org/web/20130521211106/http://www.mathcomp.leeds.ac.uk/turing2012/Images/Turing_Zuse.pdf|archive-date=21 May 2013|url-status=live}}</ref> It took place in [[Göttingen]] in 1947. The interrogation had the form of a colloquium. Participants were Womersley, Turing, Porter from England and a few German researchers like Zuse, Walther, and Billing (for more details see Herbert Bruderer, ''Konrad Zuse und die Schweiz'').

[[File:Alan Turing Blue Plaque, University of Manchester.jpg|thumb|right|A [[blue plaque]] commmemorating Alan Turing's work at the [[University of Manchester]] where he was a [[Reader (academic rank)|Reader]] from 1948 to 1954]]

In 1948, Turing was appointed [[Reader (academic rank)|reader]] in the [[School of Mathematics, University of Manchester|Mathematics Department]] at the [[University of Manchester]]. He lived at "Copper Folly", 43 Adlington Road, in [[Wilmslow]].<ref>{{Cite web|url=https://www.manchestereveningnews.co.uk/news/greater-manchester-news/alan-turing-enigma-machine-home-20918089|title=Alan Turing's home could be yours - for £1.1m|first=Charlotte|last=Dobson|date=28 June 2021|website=Manchester Evening News}}</ref> A year later, he became deputy director of the Computing Machine Laboratory, where he worked on software for one of the earliest [[Von Neumann architecture|stored-program]] computers—the [[Manchester Mark 1]]. Turing wrote the first version of the Programmer's Manual for this machine, and was recruited by Ferranti as a consultant in the development of their commercialised machine, the Ferranti Mark 1. He continued to be paid consultancy fees by Ferranti until his death.<ref>{{Cite book|url=https://www.manturing.net/|title=Alan Turing's Manchester|last=Swinton|first=Jonathan|publisher=Infang Publishing|year=2019|isbn=978-0-9931789-2-4|location=Manchester|access-date=18 March 2019|archive-url=https://web.archive.org/web/20190217172318/https://www.manturing.net/|archive-date=17 February 2019|url-status=live}}</ref> During this time, he continued to do more abstract work in mathematics,<ref name="doi10.1093/qjmam/1.1.287">{{Cite journal|last1 = Turing |first1 = A.M.|doi = 10.1093/qjmam/1.1.287 |title = Rounding-Off Errors in Matrix Processes |journal = The Quarterly Journal of Mechanics and Applied Mathematics |volume = 1| pages = 287–308 |year = 1948| issue=1 |hdl = 10338.dmlcz/103139|doi-access = free }}</ref> and in "[[Computing Machinery and Intelligence]]",<ref name=mind>{{cite q|Q772056}}</ref> Turing addressed the problem of [[artificial intelligence]], and proposed an experiment that became known as the [[Turing test]], an attempt to define a standard for a machine to be called "intelligent". The idea was that a computer could be said to "think" if a human interrogator could not tell it apart, through conversation, from a human being.<ref>{{Cite book |author-link=Stevan Harnad |last=Harnad |first=Stevan |year=2008 |chapter-url=http://eprints.soton.ac.uk/262954/ |chapter=The Annotation Game: On Turing (1950) on Computing, Machinery and Intelligence |archive-url=https://web.archive.org/web/20171018070225/https://eprints.soton.ac.uk/262954/ |archive-date=18 October 2017 |editor1-last=Epstein |editor1-first=Robert |editor2-last=Peters |editor2-first=Grace |title=Parsing the Turing Test: Philosophical and Methodological Issues in the Quest for the Thinking Computer |publisher=Springer|isbn=9781402067082 }}</ref> In the paper, Turing suggested that rather than building a program to simulate the adult mind, it would be better to produce a simpler one to simulate a child's mind and then to subject it to a course of education. A [[Turing test#Reverse Turing test and CAPTCHA|reversed]] form of the Turing test is widely used on the Internet; the [[CAPTCHA]] test is intended to determine whether the user is a human or a computer.

In 1948, Turing, working with his former undergraduate colleague, [[D.G. Champernowne]], began writing a [[chess]] program for a computer that did not yet exist. By 1950, the program was completed and dubbed the [[Turochamp]].<ref>{{cite magazine|last=Clark|first=Liat|title=Turing's achievements: codebreaking, AI and the birth of computer science|url=https://www.wired.co.uk/news/archive/2012-06/18/turing-contributions?page=all|magazine=Wired|access-date=11 November 2013|archive-url=https://web.archive.org/web/20131102122933/http://www.wired.co.uk/news/archive/2012-06/18/turing-contributions?page=all|archive-date=2 November 2013|url-status=live}}</ref> In 1952, he tried to implement it on a [[Ferranti Mark 1]], but lacking enough power, the computer was unable to execute the program. Instead, Turing "ran" the program by flipping through the pages of the algorithm and carrying out its instructions on a chessboard, taking about half an hour per move. The game was recorded.<ref>{{Cite web |url=http://www.chessgames.com/perl/chessgame?gid=1356927 |title=Alan Turing vs Alick Glennie (1952) "Turing Test" |archive-url=https://web.archive.org/web/20060219033248/http://www.chessgames.com/perl/chessgame?gid=1356927 |archive-date=19 February 2006 |website=Chessgames.com}}</ref> According to [[Garry Kasparov]], Turing's program "played a recognizable game of chess".<ref>{{Cite news |last=Kasparov |first=Garry |title=Smart machines will free us all |newspaper=The Wall Street Journal |date=15–16 April 2017 |page=c3}}</ref> The program lost to Turing's colleague [[Alick Glennie]], although it is said that it won a game against Champernowne's wife, Isabel.<ref>{{mactutor|id=Champernowne|title=David Gawen Champernowne}}</ref>

His Turing test was a significant, characteristically provocative, and lasting contribution to the debate regarding artificial intelligence, which continues after more than half a century.<ref>{{Cite journal | last1 = Pinar Saygin | first1 = A. | last2 = Cicekli | first2 = I. | last3 = Akman | first3 = V. | journal = Minds and Machines | volume = 10 | issue = 4 | pages = 463–518 | year = 2000 |title=Turing Test: 50 Years Later| doi = 10.1023/A:1011288000451 | hdl = 11693/24987 | s2cid = 990084 | hdl-access = free }}</ref>

===Pattern formation and mathematical biology===
When Turing was 39 years old in 1951, he turned to [[Mathematical and theoretical biology|mathematical biology]], finally publishing his masterpiece "[[The Chemical Basis of Morphogenesis]]" in January 1952. He was interested in [[morphogenesis]], the development of patterns and shapes in biological organisms. He suggested that a system of chemicals reacting with each other and diffusing across space, termed a [[reaction–diffusion system]], could account for "the main phenomena of morphogenesis".<ref name=chemical>{{cite Q|Q769913 }}</ref> He used systems of [[partial differential equations]] to model catalytic chemical reactions. For example, if a catalyst A is required for a certain chemical reaction to take place, and if the reaction produced more of the catalyst A, then we say that the reaction is [[autocatalytic]], and there is positive feedback that can be modelled by nonlinear differential equations. Turing discovered that patterns could be created if the chemical reaction not only produced catalyst A, but also produced an inhibitor B that slowed down the production of A. If A and B then diffused through the container at different rates, then you could have some regions where A dominated and some where B did. To calculate the extent of this, Turing would have needed a powerful computer, but these were not so freely available in 1951, so he had to use linear approximations to solve the equations by hand. These calculations gave the right qualitative results, and produced, for example, a uniform mixture that oddly enough had regularly spaced fixed red spots. The Russian biochemist [[Boris Pavlovich Belousov|Boris Belousov]] had performed experiments with similar results, but could not get his papers published because of the contemporary prejudice that any such thing violated the [[second law of thermodynamics]]. Belousov was not aware of Turing's paper in the ''[[Philosophical Transactions of the Royal Society]]''.<ref>{{Cite book |first=John |last=Gribbin |title=Deep Simplicity |page=126 |publisher=Random House |year=2004}}</ref>

Although published before the structure and role of [[DNA]] was understood, Turing's work on morphogenesis remains relevant today and is considered a seminal piece of work in mathematical biology.<ref>{{cite web|url=http://www.swintons.net/deodands/archives/000087.html |title=Turing's Last, Lost work |access-date=28 November 2011 |url-status=dead |archive-url=https://web.archive.org/web/20030823032620/http://www.swintons.net/deodands/archives/000087.html |archive-date=23 August 2003 }}</ref> One of the early applications of Turing's paper was the work by James Murray explaining spots and stripes on the fur of cats, large and small.<ref>{{cite journal | last=Murray | first=James D. | title=How the Leopard Gets Its Spots | journal=Scientific American  | volume=258 | issue=3 | date=March 1988 | jstor=24989019 | pages=80–87 | doi=10.1038/scientificamerican0388-80 | bibcode=1988SciAm.258c..80M }}</ref><ref>{{Cite book |first=James D. |last=Murray |title=Mathematical Biology I |year=2007 |chapter=Chapter 6 |publisher=Springer Verlag}}</ref><ref>{{Cite book |first=John |last=Gribbin |title=Deep Simplicity |page=134 |publisher=Random House |year=2004}}</ref> Further research in the area suggests that Turing's work can partially explain the growth of "feathers, hair follicles, the branching pattern of lungs, and even the left-right asymmetry that puts the heart on the left side of the chest".<ref>{{cite journal|doi=10.1126/science.338.6113.1406|pmid=23239707|title=Turing Pattern Fingered for Digit Formation|journal=Science|volume=338|issue=6113|pages=1406|year=2012|last1=Vogel|first1=G.|bibcode=2012Sci...338.1406V}}</ref> In 2012, Sheth, et al. found that in mice, removal of [[Hox genes]] causes an increase in the number of digits without an increase in the overall size of the limb, suggesting that Hox genes control digit formation by tuning the wavelength of a Turing-type mechanism.<ref>{{Cite journal |last1 = Sheth |first1 = R. |last2 = Marcon |first2 = L. |last3 = Bastida |first3 = M.F. |last4 = Junco |first4 = M. |last5 = Quintana |first5 = L. |last6 = Dahn |first6 = R. |last7 = Kmita |first7 = M. |last8 = Sharpe |first8 = J. |last9 = Ros |first9 = M.A. |doi = 10.1126/science.1226804 |title = Hox Genes Regulate Digit Patterning by Controlling the Wavelength of a Turing-Type Mechanism |journal = Science |volume = 338 |issue = 6113 |pages = 1476–1480 |year = 2012 |pmid = 23239739 |pmc = 4486416 |bibcode = 2012Sci...338.1476S }}</ref> Later papers were not available until ''Collected Works of A.&nbsp;M.&nbsp;Turing'' was published in 1992.<ref>{{cite web|title=The Alan Turing Bibliography|url=http://www.turing.org.uk/sources/biblio3.html|page=morphogenesis|publisher=turing.org.uk|access-date=27 July 2015|author=Andrew Hodges|archive-url=https://web.archive.org/web/20150905180420/http://www.turing.org.uk/sources/biblio3.html|archive-date=5 September 2015|url-status=live}}</ref>

A study conducted in 2023 confirmed Turing's mathematical model hypothesis. Presented by the [[American Physical Society]], the experiment involved growing [[chia seed]]s in even layers within trays, later adjusting the available moisture. Researchers experimentally tweaked the factors which appear in the Turing equations, and, as a result, patterns resembling those seen in natural environments emerged. This is believed to be the first time that experiments with living vegetation have verified Turing's mathematical insight.<ref>{{cite news|url=https://www.sciencenews.org/article/seeds-alan-turing-patterns-nature-math|author=James R. Riordon|date=26 March 2023|title=Chia seedlings verify Alan Turing's ideas about patterns in nature|work=Science News|access-date=26 August 2024|archive-date=2 July 2024|archive-url=https://web.archive.org/web/20240702160511/https://www.sciencenews.org/article/seeds-alan-turing-patterns-nature-math|url-status=live}}</ref><ref>{{cite news|url=https://meetings.aps.org/Meeting/MAR23/Session/F46.3|author=Brendan D'Aquino|date=7 March 2023|title=Abstract: F46.00003 : Studying Turing patterns in vegetation|work=American Physical Society|access-date=26 August 2024|archive-date=2 July 2024|archive-url=https://web.archive.org/web/20240702162242/https://meetings.aps.org/Meeting/MAR23/Session/F46.3|url-status=live}}</ref>