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After Sherborne, Turing studied as an undergraduate from 1931 to 1934 at [[King's College, Cambridge]],<ref name="whoswho" /> where he was awarded first-class honours in mathematics. In 1935, at the age of 22, he was elected a [[Fellow]] of King's College on the strength of a dissertation in which he proved the [[central limit theorem]].<ref>See Section 3 of John Aldrich, "England and Continental Probability in the Inter-War Years", Journal Electronique d'Histoire des Probabilités et de la Statistique, vol. 5/2 [http://www.jehps.net/decembre2009.html Decembre 2009] {{Webarchive|url=https://web.archive.org/web/20180421105727/http://www.jehps.net/decembre2009.html |date=21 April 2018 }} Journal Electronique d'Histoire des Probabilités et de la Statistique</ref> See Section 3 of John Aldrich, "England and Continental Probability in the Inter-War Years", Journal Electronique d'Histoire des Probabilités et de la Statistique, vol. 5/2 Decembre 2009  Journal Electronique d'Histoire des Probabilités et de la Statistique Unknown to the committee, the theorem had already been proven, in 1922, by [[Jarl Waldemar Lindeberg]].<ref>{{Harvnb|Hodges|1983|pp=88, 94}}</ref>

After Sherborne, Turing studied as an undergraduate from 1931 to 1934 at [[King's College, Cambridge]],<ref name="whoswho" /> where he was awarded first-class honours in mathematics. In 1935, at the age of 22, he was elected a [[Fellow]] of King's College on the strength of a dissertation in which he proved the [[central limit theorem]].<ref>See Section 3 of John Aldrich, "England and Continental Probability in the Inter-War Years", Journal Electronique d'Histoire des Probabilités et de la Statistique, vol. 5/2 [http://www.jehps.net/decembre2009.html Decembre 2009] {{Webarchive|url=https://web.archive.org/web/20180421105727/http://www.jehps.net/decembre2009.html |date=21 April 2018 }} Journal Electronique d'Histoire des Probabilités et de la Statistique</ref> See Section 3 of John Aldrich, "England and Continental Probability in the Inter-War Years", Journal Electronique d'Histoire des Probabilités et de la Statistique, vol. 5/2 Decembre 2009  Journal Electronique d'Histoire des Probabilités et de la Statistique Unknown to the committee, the theorem had already been proven, in 1922, by [[Jarl Waldemar Lindeberg]].<ref>{{Harvnb|Hodges|1983|pp=88, 94}}</ref>

【最终版】从舍伯恩毕业之后，图灵于1931年至1934年在剑桥大学国王学院就读本科，在那里他获得了数学方面的一等荣誉。1935年，22岁的他凭借一篇证明中心极限定理的论文，被选为国王学院的研究员。参见约翰 · 奥尔德里奇的《两次世界大战之间的英格兰和大陆概率》第3节，《电子杂志与概率与统计学组织》 ，第一卷。2009年12月5日《电子杂志》 : 委员会不知道的概率和统计数据，这个定理已经在1922年被 Jarl Waldemar Lindeberg 证明了。

 

【最终版】从舍尔伯尼毕业后，图灵从1931年到1934年就读于剑桥大学国王学院，在那里他获得了数学方面的一等荣誉。1935年，22岁的他因为一篇证明中心极限定理的论文而被选为国王学院的院士。参见约翰 · 奥尔德里奇的《两次世界大战之间的英格兰和大陆概率》第3节，《电子杂志与概率与统计学组织》 ，第一卷。2009年12月5日《电子杂志》 : 委员会不知道的概率和统计数据，这个定理已经在1922年被 Jarl Waldemar Lindeberg 证明了。

In 1936, Turing published his paper "[[On Computable Numbers, with an Application to the Entscheidungsproblem]]".<ref>{{Harvnb|Turing|1937}}</ref> It was published in the ''Proceedings of the London Mathematical Society'' journal in two parts, the first on 30 November and the second on 23 December.<ref>{{cite book |url=https://books.google.com/books?id=MlsJuSj2OkEC&pg=PA211 |page=211 |title=Computability: Turing, Gödel, Church, and Beyond |author1=B. Jack Copeland |author2=Carl J. Posy |author3=Oron Shagrir |publisher=MIT Press |year=2013|isbn=978-0-262-01899-9 }}</ref> In this paper, Turing reformulated [[Kurt Gödel]]'s 1931 results on the limits of proof and computation, replacing Gödel's universal arithmetic-based formal language with the formal and simple hypothetical devices that became known as [[Turing machine]]s. The ''[[Entscheidungsproblem]]'' (decision problem) was originally posed by German mathematician [[David Hilbert]] in 1928. Turing proved that his "universal computing machine" would be capable of performing any conceivable mathematical computation if it were representable as an [[algorithm]]. He went on to prove that there was no solution to the ''decision problem'' by first showing that the [[halting problem]] for Turing machines is [[Decision problem|undecidable]]: it is not possible to decide algorithmically whether a Turing machine will ever halt.  This paper has been called "easily the most influential math paper in history".<ref>{{cite book |page=15 |title=Mathematics and Computation |author=Avi Wigderson |publisher=Princeton University Press |year=2019|isbn=978-0-691-18913-0 }}</ref>

In 1936, Turing published his paper "[[On Computable Numbers, with an Application to the Entscheidungsproblem]]".<ref>{{Harvnb|Turing|1937}}</ref> It was published in the ''Proceedings of the London Mathematical Society'' journal in two parts, the first on 30 November and the second on 23 December.<ref>{{cite book |url=https://books.google.com/books?id=MlsJuSj2OkEC&pg=PA211 |page=211 |title=Computability: Turing, Gödel, Church, and Beyond |author1=B. Jack Copeland |author2=Carl J. Posy |author3=Oron Shagrir |publisher=MIT Press |year=2013|isbn=978-0-262-01899-9 }}</ref> In this paper, Turing reformulated [[Kurt Gödel]]'s 1931 results on the limits of proof and computation, replacing Gödel's universal arithmetic-based formal language with the formal and simple hypothetical devices that became known as [[Turing machine]]s. The ''[[Entscheidungsproblem]]'' (decision problem) was originally posed by German mathematician [[David Hilbert]] in 1928. Turing proved that his "universal computing machine" would be capable of performing any conceivable mathematical computation if it were representable as an [[algorithm]]. He went on to prove that there was no solution to the ''decision problem'' by first showing that the [[halting problem]] for Turing machines is [[Decision problem|undecidable]]: it is not possible to decide algorithmically whether a Turing machine will ever halt.  This paper has been called "easily the most influential math paper in history".<ref>{{cite book |page=15 |title=Mathematics and Computation |author=Avi Wigderson |publisher=Princeton University Press |year=2019|isbn=978-0-691-18913-0 }}</ref>

【最终版】1936年，图灵发表了他的论文《论可计算数及其在设计问题中的应用》。它分两部分发表在《伦敦数学学会学报》上，第一部分于11月30日发表，第二部分于12月23日发表。在这篇论文中，图灵重新表述了库尔特Gödel 1931年提出的关于证明和计算极限的结果，用正式的、简单的假设设备，即图灵机，取代了Gödel基于通用算法的形式语言。决策问题(Entscheidungsproblem)最初是由德国数学家大卫·希尔伯特于1928年提出的。图灵证明了他的“通用计算机”能够执行任何可以想象的数学计算，只要它可以被表示为一种算法。他接着证明了决策问题是没有解决方案的，他首先证明了图灵机的停止问题是不可决定的:从算法上决定图灵机是否会停止是不可能的。这篇论文被称为“史上最具影响力的数学论文”。[[File:20130808 Kings College Front Court Fountain Crop 03.jpg|thumb|right|[[King's College, Cambridge]], where Turing was an undergraduate in 1931 and became a Fellow in 1935. The computer room is named after him.|链接=Special:FilePath/20130808_Kings_College_Front_Court_Fountain_Crop_03.jpg]]Although [[Turing's proof]] was published shortly after [[Alonzo Church]]'s equivalent proof using his [[lambda calculus]],<ref>{{Harvnb|Church|1936}}</ref> Turing's approach is considerably more accessible and intuitive than Church's.<ref>{{cite web|last1=Grime|first1=James|title=What Did Turing Do for Us?|url=https://nrich.maths.org/8050|website=[[NRICH]]|publisher=[[University of Cambridge]]|access-date=28 February 2016|date=February 2012|archive-url=https://web.archive.org/web/20160304175703/http://nrich.maths.org/8050|archive-date=4 March 2016|url-status=live}}</ref> It also included a notion of a 'Universal Machine' (now known as a [[universal Turing machine]]), with the idea that such a machine could perform the tasks of any other computation machine (as indeed could Church's lambda calculus). According to the [[Church–Turing thesis]], Turing machines and the lambda calculus are capable of computing anything that is computable. [[John von Neumann]] acknowledged that the central concept of the modern computer was due to Turing's paper.<ref>"von Neumann&nbsp;... firmly emphasised to me, and to others I am sure, that the fundamental conception is owing to Turing—insofar as not anticipated by Babbage, Lovelace and others." Letter by [[Stanley Frankel]] to [[Brian Randell]], 1972, quoted in [[Jack Copeland]] (2004) ''The Essential Turing'', p.&nbsp;22.</ref> "von Neumann ... firmly emphasised to me, and to others I am sure, that the fundamental conception is owing to Turing—insofar as not anticipated by Babbage, Lovelace and others." Letter by Stanley Frankel to Brian Randell, 1972, quoted in Jack Copeland (2004) The Essential Turing, p. 22. To this day, Turing machines are a central object of study in theory of computation.

【最终版】1936年，图灵发表了他的论文《论可计算数及其在设计问题中的应用》。它分两部分发表在《伦敦数学学会学报》上，第一部分于11月30日发表，第二部分于12月23日发表。在这篇论文中，图灵重新表述了库尔特Gödel 1931年提出的关于证明和计算极限的结果，用正式的、简单的假设设备，即图灵机，取代了Gödel基于通用算法的形式语言。决策问题(Entscheidungsproblem)最初是由德国数学家大卫·希尔伯特于1928年提出的。图灵证明了他的“通用计算机”能够执行任何可以想象的数学计算，只要它可以被表示为一种算法。他接着证明了决策问题是没有解决方案的，他首先证明了图灵机的停止问题是不可决定的:从算法上决定图灵机是否会停止是不可能的。这篇论文被称为“史上最具影响力的数学论文”。[[File:20130808 Kings College Front Court Fountain Crop 03.jpg|thumb|right|[[King's College, Cambridge]], where Turing was an undergraduate in 1931 and became a Fellow in 1935. The computer room is named after him.|链接=Special:FilePath/20130808_Kings_College_Front_Court_Fountain_Crop_03.jpg]]Although [[Turing's proof]] was published shortly after [[Alonzo Church]]'s equivalent proof using his [[lambda calculus]],<ref>{{Harvnb|Church|1936}}</ref> Turing's approach is considerably more accessible and intuitive than Church's.<ref>{{cite web|last1=Grime|first1=James|title=What Did Turing Do for Us?|url=https://nrich.maths.org/8050|website=[[NRICH]]|publisher=[[University of Cambridge]]|access-date=28 February 2016|date=February 2012|archive-url=https://web.archive.org/web/20160304175703/http://nrich.maths.org/8050|archive-date=4 March 2016|url-status=live}}</ref> It also included a notion of a 'Universal Machine' (now known as a [[universal Turing machine]]), with the idea that such a machine could perform the tasks of any other computation machine (as indeed could Church's lambda calculus). According to the [[Church–Turing thesis]], Turing machines and the lambda calculus are capable of computing anything that is computable. [[John von Neumann]] acknowledged that the central concept of the modern computer was due to Turing's paper.<ref>"von Neumann&nbsp;... firmly emphasised to me, and to others I am sure, that the fundamental conception is owing to Turing—insofar as not anticipated by Babbage, Lovelace and others." Letter by [[Stanley Frankel]] to [[Brian Randell]], 1972, quoted in [[Jack Copeland]] (2004) ''The Essential Turing'', p.&nbsp;22.</ref> "von Neumann ... firmly emphasised to me, and to others I am sure, that the fundamental conception is owing to Turing—insofar as not anticipated by Babbage, Lovelace and others." Letter by Stanley Frankel to Brian Randell, 1972, quoted in Jack Copeland (2004) The Essential Turing, p. 22. To this day, Turing machines are a central object of study in theory of computation.

尽管图灵的证明是在阿隆索 · 丘奇用他的 λ 微积分得到等价证明后不久发表的，但是图灵的方法比丘奇的方法更容易理解和直观。它还包含了一个通用机器的概念(现在被称为通用图灵机) ，其理念是这样一个机器可以执行任何其他计算机器的任务(实际上就像 Church 的 lambda 演算一样)。根据丘奇-图灵论文，图灵机和 lambda 微积分能够计算任何可计算的东西。约翰·冯·诺伊曼承认现代计算机的核心概念应归功于图灵的论文。“冯 · 诺依曼... ... 坚定地向我和其他人强调，基本概念应归功于图灵ーー这是巴贝奇、洛夫莱斯和其他人所没有预料到的。”斯坦利 · 弗兰克尔给布莱恩 · 兰德尔的信，1972年，引自杰克 · 科普兰(2004)《本质图灵》 ，第22页。直到今天，图灵机仍然是计算理论的中心研究对象。

【最终版】尽管图灵的证明是在Alonzo Church使用他的λ微积分的等效证明之后不久发表的，但图灵的方法要比Church的方法更容易理解和直观。它还包括一个 "通用机器 "的概念（现在被称为通用图灵机），认为这样的机器可以执行任何其他计算机器的任务（就像丘奇的λ微积分那样）。根据丘奇-图灵论，图灵机和λ微积分能够计算任何可计算的东西。约翰-冯-诺伊曼承认，现代计算机的核心概念是归功于图灵的论文。"冯-诺伊曼......向我和其他人坚定地强调，基本概念是归功于图灵的--只要是巴贝奇、洛夫拉斯和其他人没有预见到的。" 斯坦利-弗兰克尔写给布赖恩-兰德尔的信，1972年，引自杰克-科普兰（2004年）《基本图灵》，第22页。时至今日，图灵机仍是计算理论中的一个核心研究对象。

 

【最终版】尽管图灵的证明是在阿朗佐·丘奇用他的lambda微积分证明之后不久发表的，但图灵的方法比丘奇的方法更容易理解，更直观。它还包含了“通用机”(现在被称为通用图灵机)的概念，这种机器可以执行任何其他计算机器的任务(Church的lambda演算也可以)。根据丘奇-图灵理论，图灵机和lambda微积分能够计算任何可计算的东西。约翰·冯·诺伊曼承认，现代计算机的核心概念源于图灵的论文。“冯·诺依曼…他坚定地向我，也向其他人强调，这个基本概念是由图灵提出的，这是巴贝奇、洛夫莱斯等人没有预料到的。”1972年斯坦利·弗兰克尔写给布莱恩·兰德尔的信，引用于杰克·科普兰(2004)《图灵的本质》第22页。直到今天，图灵机是计算理论研究的中心对象。

From September 1936 to July 1938, Turing spent most of his time studying under Church at [[Princeton University]],<ref name="bowen19" /> in the second year as a [[Jane Eliza Procter Fellowship|Jane Eliza Procter Visiting Fellow]]. In addition to his purely mathematical work, he studied cryptology and also built three of four stages of an electro-mechanical [[binary multiplier]].<ref>{{Harvnb|Hodges|1983|p=138}}</ref> In June 1938, he obtained his PhD from the [[Princeton University Department of Mathematics|Department of Mathematics]] at Princeton;<ref>{{Cite journal

From September 1936 to July 1938, Turing spent most of his time studying under Church at [[Princeton University]],<ref name="bowen19" /> in the second year as a [[Jane Eliza Procter Fellowship|Jane Eliza Procter Visiting Fellow]]. In addition to his purely mathematical work, he studied cryptology and also built three of four stages of an electro-mechanical [[binary multiplier]].<ref>{{Harvnb|Hodges|1983|p=138}}</ref> In June 1938, he obtained his PhD from the [[Princeton University Department of Mathematics|Department of Mathematics]] at Princeton;<ref>{{Cite journal

}}</ref> his dissertation, ''[[Systems of Logic Based on Ordinals]]'',<ref name="turingphd">{{cite thesis |degree=PhD |first=Alan|last=Turing |title=Systems of Logic Based on Ordinals|publisher=Princeton University |year=1938 |doi=10.1112/plms/s2-45.1.161|author-link=Alan Turing|id={{ProQuest|301792588}}|hdl=21.11116/0000-0001-91CE-3|hdl-access=free}}</ref><ref>{{cite web | last = Turing | first = A.M. | author-link = Alan Turing | title = Systems of Logic Based on Ordinals | year = 1938 | url = https://webspace.princeton.edu/users/jedwards/Turing%20Centennial%202012/Mudd%20Archive%20files/12285_AC100_Turing_1938.pdf  | access-date = 4 February 2012 | archive-url = https://web.archive.org/web/20121023103503/https://webspace.princeton.edu/users/jedwards/Turing%20Centennial%202012/Mudd%20Archive%20files/12285_AC100_Turing_1938.pdf | archive-date = 23 October 2012 | url-status = dead }}</ref> introduced the concept of [[ordinal logic]] and the notion of [[Turing reduction|relative computing]], in which Turing machines are augmented with so-called [[oracle machine|oracles]], allowing the study of problems that cannot be solved by Turing machines. John von Neumann wanted to hire him as his [[Postdoctoral researcher|postdoctoral assistant]], but he went back to the United Kingdom.<ref>''John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More'', Norman MacRae, 1999, American Mathematical Society, Chapter 8</ref>John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More, Norman MacRae, 1999, American Mathematical Society, Chapter 8

}}</ref> his dissertation, ''[[Systems of Logic Based on Ordinals]]'',<ref name="turingphd">{{cite thesis |degree=PhD |first=Alan|last=Turing |title=Systems of Logic Based on Ordinals|publisher=Princeton University |year=1938 |doi=10.1112/plms/s2-45.1.161|author-link=Alan Turing|id={{ProQuest|301792588}}|hdl=21.11116/0000-0001-91CE-3|hdl-access=free}}</ref><ref>{{cite web | last = Turing | first = A.M. | author-link = Alan Turing | title = Systems of Logic Based on Ordinals | year = 1938 | url = https://webspace.princeton.edu/users/jedwards/Turing%20Centennial%202012/Mudd%20Archive%20files/12285_AC100_Turing_1938.pdf  | access-date = 4 February 2012 | archive-url = https://web.archive.org/web/20121023103503/https://webspace.princeton.edu/users/jedwards/Turing%20Centennial%202012/Mudd%20Archive%20files/12285_AC100_Turing_1938.pdf | archive-date = 23 October 2012 | url-status = dead }}</ref> introduced the concept of [[ordinal logic]] and the notion of [[Turing reduction|relative computing]], in which Turing machines are augmented with so-called [[oracle machine|oracles]], allowing the study of problems that cannot be solved by Turing machines. John von Neumann wanted to hire him as his [[Postdoctoral researcher|postdoctoral assistant]], but he went back to the United Kingdom.<ref>''John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More'', Norman MacRae, 1999, American Mathematical Society, Chapter 8</ref>John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More, Norman MacRae, 1999, American Mathematical Society, Chapter 8

 

== Career and research职业和研究 ==

== Career and research职业和研究 ==

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>[[Cora Diamond]] (ed.), ''Wittgenstein's Lectures on the Foundations of Mathematics'', University of Chicago Press, 1976</ref> Cora Diamond (ed.), Wittgenstein's Lectures on the Foundations of Mathematics, University of Chicago Press, 1976Turing 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>

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>[[Cora Diamond]] (ed.), ''Wittgenstein's Lectures on the Foundations of Mathematics'', University of Chicago Press, 1976</ref> Cora Diamond (ed.), Wittgenstein's Lectures on the Foundations of Mathematics, University of Chicago Press, 1976Turing 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>

【最终版】当图灵回到剑桥时，他参加了路德维希-维特根斯坦在1939年举办的关于数学基础的讲座。这些讲座被逐字重建，包括图灵和其他学生的插话，来自学生的笔记。Cora Diamond (ed.), 维特根斯坦关于数学基础的演讲》，芝加哥大学出版社, 1976图灵和维特根斯坦争论不休，图灵为形式主义辩护，维特根斯坦则提出他的观点：数学并没有发现任何绝对真理，而是发明了它们。

 

【最终版】1939年，当图灵回到剑桥时，他参加了路德维希·维特根斯坦关于数学基础的讲座。这些讲座被逐字逐句地重建，包括来自图灵和其他学生的感叹词，以及学生的笔记。科拉·戴蒙德(Cora Diamond)，《维特根斯坦的数学基础讲座》，芝加哥大学出版社，1976年，图灵和维特根斯坦争论和反对，图灵为形式主义辩护，维特根斯坦提出数学并没有发现任何绝对真理，而是发明了它们。

=== Cryptanalysis密码分析 ===

=== Cryptanalysis密码分析 ===

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>

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  | editor-first1 = Michael | editor-last1 = Smith  | editor-first2 = Ralph | editor-last2 = 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) |work=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>

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  | editor-first1 = Michael | editor-last1 = Smith  | editor-first2 = Ralph | editor-last2 = 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) |work=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>

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''.

 

【最终版】从1938年9月开始，图灵在英国密码破译组织政府Code and Cypher School (GC&CS)兼职工作。他和GC&CS高级密码破解员迪利·诺克斯一起，专注于对纳粹德国使用的谜机进行密码分析。1939年7月，在华沙附近的一次会议上，波兰密码局向英国和法国提供了英格玛密码机转子连接的细节，以及他们对英格玛密码机信息进行解密的方法。此后不久，图灵和诺克斯提出了一个更广泛的解决方案。波兰的方法依赖于一个不安全的指示程序，德国人很可能会改变，他们实际上在1940年5月就改变了。图灵的方法更一般化，他使用了基于婴儿床的解密方法，为此他制作了炸弹机的功能规格(对波兰炸弹机的改进)。[[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]].|链接=Special:FilePath/Turing_flat.jpg]]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 |website=nationalww2museum.org |location=New Orleans |publisher=The National WWII Museum |url=https://www.nationalww2museum.org/war/articles/alan-turing-betchley-park |access-date=24 August 2021}}</ref>

 

【最终版】指明炸弹是图灵在战争中取得的五个主要密码分析进展中的第一个。其他有:推导德国海军使用的指示程序;开发了一种名为Banburismus的统计程序，以便更有效地使用炸弹;开发了一种名为图灵格里(Turingery)的程序，用于计算洛伦兹SZ 40/42 (Tunny)密码机车轮的凸轮设置，在战争快结束时，还在汉斯洛普公园开发了一种代号为黛丽拉的便携式安全语音扰频器。

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 [[Government Communications Headquarters|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".}}

【最终版】通过使用统计技术来优化代码破译过程中不同可能性的试验，图灵对这一课题做出了创新的贡献。他写了两篇论文讨论的数学方法,名为概率的应用密码学和纸重复统计,这是这样的价值GC&CS及其继任者GCHQ,他们没有公布给英国国家档案馆,直到2012年4月,他出生的纪念日不久前。一位GCHQ的数学家“自称为理查德(Richard)”，当时他说，这些内容受《官方保密法》(Official Secrets Act)限制了大约70年，这一事实证明了它们的重要性，以及它们与战后密码分析的相关性:

【最终版】通过使用统计技术来优化密码破译过程中不同可能性的试验，图灵对该主题做出了创新的贡献。他写了两篇讨论数学方法的论文，题目是《概率在密码学中的应用》和《关于重复统计的论文》，这两篇论文对GC&CS及其继承者GCHQ具有如此大的价值，以至于直到2012年4月，在他诞辰一百周年前不久才被公布给英国国家档案局。一位GCHQ的数学家，"他只称自己为理查德"，当时说，这些内容根据《官方保密法》被限制了约70年，这表明它们的重要性，以及它们与战后密码分析的相关性。

[他]说，内容被限制的事实“表明它对我们学科的基础有多么重要”. ...这些论文详细地使用了“数学分析来尝试和确定哪些是更可能的设置，以便能尽快尝试。”．.． 理查德表示，GCHQ现在已经“榨干了这两份论文的汁水”，并“很高兴它们被发布到公共领域”。

[他]说，内容被限制的事实 "表明它在我们学科的基础上具有多么巨大的重要性"。... 这些论文详细介绍了使用 "数学分析来尝试和确定哪些是更有可能的设置，以便能够尽快地进行尝试"。... 理查德说，GCHQ现在已经从这两篇论文中 "榨出了汁液"，并且 "很高兴将它们发布到公共领域"。

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> According to historian [[Ronald Lewin]], [[I.J. Good|Jack Good]], a cryptanalyst who worked with Turing, said of his colleague:

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> According to historian [[Ronald Lewin]], [[I.J. Good|Jack Good]], a cryptanalyst who worked with Turing, said of his colleague:

【最终版】图灵在布莱切利公园有一个怪异的声誉。他被同事称为 "教授"，他关于英格玛的论文被称为 "教授之书"。根据历史学家Ronald Lewin的说法，与图灵共事的密码学家Jack Good曾这样评价他的同事。{{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>

 

【最终版】图灵在布莱切利公园是出了名的古怪。他被同事们称为"教授"他关于谜机的论文被称为"教授之书"根据历史学家罗纳德·卢因的说法，曾与图灵共事的密码分析师杰克·古德这样评价图灵:{{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>

 

彼得·希尔顿在他的《布莱切利公园的回忆》中讲述了他和图灵在8号小屋工作的经历:{{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.  

彼得-希尔顿在《美国的数学世纪》中的 "布莱切利公园的回忆 "中讲述了他与图灵在8号小屋合作的经历。{{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>

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>

 

希尔顿在PBS纪录片《解密纳粹秘密》中表达了类似的想法。

希尔顿在PBS纪录片《解密纳粹秘密》中表达了类似的想法。

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 | publisher=The Lyons Press | year = 1975 | isbn = 978-1-59921-383-5  }}</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 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.<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:

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 | publisher=The Lyons Press | year = 1975 | isbn = 978-1-59921-383-5  }}</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 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.<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:

【最终版】在布莱切利工作时，图灵是个有天赋的长跑运动员，当需要他参加会议时，他偶尔会跑模板：转换到伦敦，他有能力达到世界级的马拉松标准。图灵曾为1948年的英国奥运队试跑，但他受到了伤病的阻碍。他试跑马拉松的时间只比英国银牌得主托马斯-理查兹的奥运比赛时间2小时35分慢了11分钟。他是沃尔顿体育俱乐部最好的跑者，当他在单独跑步时超过队伍时发现了这一事实。当被问及为什么他在训练中跑得如此辛苦时，他回答说。{{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}}</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 | origyear = 1993 | year = 1996 | url = http://www.cix.co.uk/~klockstone/hinsley.htm }} Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University</ref>Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University

 

【最终版】在布莱切利工作的时候，图灵是一名优秀的长跑运动员，他偶尔也会按照这样的模式跑:需要开会的时候，他会去伦敦，他有能力参加世界级的马拉松比赛。1948年，图灵参加了英国奥运会代表队的选拔，但他受伤了。他的马拉松选拔赛时间只比英国银牌得主托马斯·理查兹(Thomas Richards)的奥运会比赛时间2小时35分钟慢了11分钟。他是沃尔顿运动俱乐部最好的跑步者，当他在独自跑步时超过小组时发现了这个事实。当被问及他为什么在训练中如此努力时，他回答说:{{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}}</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 | origyear = 1993 | year = 1996 | url = http://www.cix.co.uk/~klockstone/hinsley.htm }} Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University</ref>Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University

 

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>

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解码器 ===

=== Bombe解码器 ===