更改

【最终版】战争结束时，所有在布莱切利公园工作过的人都收到了一份备忘录，提醒他们《官方保密法》规定的沉默准则不会随着战争的结束而结束，而是会无限期地继续下去。因此，尽管图灵在1946年被英王乔治六世任命为大英帝国军官(OBE)，但他的工作多年来一直是秘密。

【最终版】战争结束时，所有在布莱切利公园工作过的人都收到了一份备忘录，提醒他们《官方保密法》规定的沉默准则不会随着战争的结束而结束，而是会无限期地继续下去。因此，尽管图灵在1946年被英王乔治六世任命为大英帝国军官(OBE)，但他的工作多年来一直是秘密。

=== Bombe炸弹 ===

=== Bombe解码器 ===

{{Main|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>{{Citation |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>

{{Main|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>{{Citation |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>

在抵达 Bletchley Park 的几周内，图灵就指定了一种叫做 bombe 的机电设备，这种设备能够比波兰炸弹机(波兰)更有效地破解英格玛密码机，而波兰密码机正是源于此。通过数学家戈登 · 威尔奇曼提出的改进，炸弹成为主要的工具之一，也是主要的自动化工具，用于攻击密码信息。

在抵达 Bletchley Park 的几周内，图灵就指定了一种叫做解码器的机电设备，这种设备能够比波兰炸弹机(波兰)更有效地破解英格玛密码机，而波兰密码机正是源于此。通过数学家戈登 · 威尔奇曼提出的改进，解码器成为主要的工具之一，也是主要的自动化工具，用于攻击密码信息。

【最终版】在到达布莱切利公园的几周内，图灵指定了一种叫做bombe的机电机器，它比波兰的bomba kryptologiczna更能破解谜机。数学家戈登·韦尔奇曼(Gordon Welchman)提出了一种增强技术，炸弹机成为攻击谜机加密信息的主要工具之一，也是主要的自动化工具。[[File:Bombe-rebuild.jpg|thumbnail|right|A working replica of a [[bombe]] now at [[The National Museum of Computing]] on Bletchley Park|链接=Special:FilePath/Bombe-rebuild.jpg]]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 10¹⁹ states, or 10²² 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> Jack Good in "The Men Who Cracked Enigma", 2003: with his caveat: "if my memory is correct". 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}}</ref>

【最终版】在到达布莱切利公园的几周内，图灵指定了一种叫做解码器的机电机器，它比波兰的bomba kryptologiczna更能破解谜机。数学家戈登·韦尔奇曼(Gordon Welchman)提出了一种增强技术，解码器成为攻击谜机加密信息的主要工具之一，也是主要的自动化工具。[[File:Bombe-rebuild.jpg|thumbnail|right|A working replica of a [[bombe]] now at [[The National Museum of Computing]] on Bletchley Park|链接=Special:FilePath/Bombe-rebuild.jpg]]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 10¹⁹ states, or 10²² 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> Jack Good in "The Men Who Cracked Enigma", 2003: with his caveat: "if my memory is correct". 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}}</ref>

该 bombe 搜索可能正确的设置使用一个英格玛消息(即，转子顺序，转子设置和插件板设置)使用一个合适的抄袭: 一个可能的明文片段。对于每个可能的转子设置(大约有1019个状态，或者四旋翼 u 型潜艇的1022个状态) ，杰克 · 古德在2003年的《破解谜团的人》中写道: “如果我的记忆是正确的”。炸弹根据婴儿床执行一系列逻辑推理，用电子机械方式实现。

该 bombe 搜索可能正确的设置使用一个英格玛消息(即，转子顺序，转子设置和插件板设置)使用一个合适的抄袭: 一个可能的明文片段。对于每个可能的转子设置(大约有1019个状态，或者四旋翼 u 型潜艇的1022个状态) ，杰克 · 古德在2003年的《破解谜团的人》中写道: “如果我的记忆是正确的”。炸弹根据婴儿床执行一系列逻辑推理，用电子机械方式实现。

【最终版】炸弹机使用一段可能的明文片段来搜索Enigma信息可能的正确设置(即转子顺序、转子设置和配线板设置)。对于每一种可能的旋翼设置(大约有1019个州，或者四旋翼u型潜艇的1022个州)，杰克·古德在2003年的《破解谜机的人》中警告说:“如果我的记忆是正确的”。炸弹在婴儿床的基础上进行了一系列的逻辑推理，这是用电机械实现的。

【最终版】解码器使用一段可能的明文片段来搜索Enigma信息可能的正确设置(即转子顺序、转子设置和配线板设置)。对于每一种可能的旋翼设置(大约有1019个状态，或者四旋翼u型潜艇的1022个状态)，杰克·古德在2003年的《破解谜机的人》中警告说:“如果我的记忆是正确的”。解码器在原有的基础上进行了一系列的逻辑推理，这是用电机械实现的。

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>

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>

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">{{Harvnb|Hodges|1983|p=218}}</ref>

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">{{Harvnb|Hodges|1983|p=218}}</ref>

到1941年底，图灵和他的密码分析师同事戈登 · 威尔奇曼、休 · 亚历山大和斯图尔特 · 米尔纳-巴里都感到沮丧。在波兰人工作的基础上，他们建立了一个很好的解密英格玛信号的工作系统，但是他们有限的人员和炸弹意味着他们无法翻译所有的信号。在夏天，他们取得了相当大的成功，运输损失已经降到每月不到10万吨; 然而，他们急需更多的资源来跟上德国的调整。他们试图通过适当的渠道获得更多的人和资金更多的炸弹，但失败了。

到1941年底，图灵和他的密码分析师同事戈登 · 威尔奇曼、休 · 亚历山大和斯图尔特 · 米尔纳-巴里都感到沮丧。在波兰人工作的基础上，他们建立了一个很好的解密英格玛信号的工作系统，但是他们有限的人员和炸弹意味着他们无法翻译所有的信号。在夏天，他们取得了相当大的成功，信息传输损失已经降到每月不到10万的量值; 然而，他们急需更多的资源来跟上德国的调整。他们试图通过适当的渠道获得更多的人和资金更多的炸弹，但失败了。

【最终版】1941年末，图灵和他的密码分析师同事戈登·韦尔奇曼、休·亚历山大和斯图尔特·米尔纳-巴里感到很沮丧。在波兰人工作的基础上，他们建立了一个很好的破译Enigma信号的工作系统，但他们有限的人手和炸弹意味着他们无法翻译所有的信号。在夏季，他们取得了相当大的成功，航运损失下降到每月10万吨以下;然而，他们急需更多的资源来跟上德国的调整步伐。他们试图通过适当的渠道招募更多的人，资助更多的炸弹，但失败了。

【最终版】1941年末，图灵和他的密码分析师同事戈登·韦尔奇曼、休·亚历山大和斯图尔特·米尔纳-巴里感到很沮丧。在波兰人工作的基础上，他们建立了一个很好的破译Enigma信号的工作系统，但他们有限的人手和解码器意味着他们无法翻译所有的信号。在夏季，他们取得了相当大的成功，信息传输损失已经降到每月不到10万的量值;然而，他们急需更多的资源来跟上德国的调整步伐。他们试图通过适当的渠道招募更多的人，资助更多的炸弹，但失败了。

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" /> 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>

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" /> 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>

10月28日，他们直接写信给温斯顿·丘吉尔解释他们的困难，首先提到的是图灵。她们强调，与军队花费的大量人力和财力相比，她们的需求是多么微不足道，与她们能够提供给军队的援助水平相比，她们的需求又是多么微不足道。正如图灵的传记作者安德鲁 · 霍奇斯后来写道: “这封信产生了电子效应。”丘吉尔给伊斯梅将军写了一份备忘录，上面写着: “今日行动。确保他们得到了他们想要的一切，并给我报告说已经完成了这项工作。”11月18日，特勤处处长报告说，正在采取一切可能的措施。Bletchley Park 的密码专家们并不知道首相的反应，但正如米尔纳-巴里回忆的那样，“我们所注意到的是，几乎从那天起，崎岖的道路奇迹般地变得平坦起来。“ Copeland，The Essential Turing，pp。336–337 .到战争结束时，已有两百多个炸弹投入使用。

10月28日，他们直接写信给温斯顿·丘吉尔解释他们的困难，首先提到的是图灵。她们强调，与军队花费的大量人力和财力相比，她们的需求是多么微不足道，与她们能够提供给军队的援助水平相比，她们的需求又是多么微不足道。正如图灵的传记作者安德鲁 · 霍奇斯后来写道: “这封信产生了电子效应。”丘吉尔给伊斯梅将军写了一份备忘录，上面写着: “今日行动。确保他们得到了他们想要的一切，并给我报告说已经完成了这项工作。”11月18日，特勤处处长报告说，正在采取一切可能的措施。Bletchley Park 的密码专家们并不知道首相的反应，但正如米尔纳-巴里回忆的那样，“我们所注意到的是，几乎从那天起，崎岖的道路奇迹般地变得平坦起来。“ Copeland，The Essential Turing，pp。336–337 .到战争结束时，已有两百多个解码器投入使用。

【最终版】10月28日，他们直接写信给温斯顿·丘吉尔，解释他们的困难，图灵是第一个。他们强调，与军队的巨大人力和资金支出相比，他们的需求是多么小，与他们能够提供给军队的援助水平相比。正如图灵的传记作者安德鲁·霍奇斯(Andrew Hodges)后来写道:“这封信有一种令人震惊的效果。”丘吉尔给伊斯梅将军写了一份备忘录，上面写道:“今天就行动起来。确保他们能优先得到他们想要的一切，并向我报告，这件事已经完成了。”11月18日，特勤局局长报告说，正在采取一切可能的措施。布莱切利公园的密码学家并不知道首相的反应，但据米尔纳-巴里回忆，“我们所注意到的是，几乎从那天起，崎岖的道路奇迹般地变得平坦了。”到战争结束时，有两百多架炸弹投入使用。[[File:Turing-statue-Bletchley 14.jpg|thumb|right|upright|Statue of Turing 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>|链接=Special:FilePath/Turing-statue-Bletchley_14.jpg]]

【最终版】10月28日，他们直接写信给温斯顿·丘吉尔，解释他们的困难，图灵是第一个。他们强调，与军队的巨大人力和资金支出相比，他们的需求是多么小，与他们能够提供给军队的援助水平相比。正如图灵的传记作者安德鲁·霍奇斯(Andrew Hodges)后来写道:“这封信有一种令人震惊的效果。”丘吉尔给伊斯梅将军写了一份备忘录，上面写道:“今天就行动起来。确保他们能优先得到他们想要的一切，并向我报告，这件事已经完成了。”11月18日，特勤局局长报告说，正在采取一切可能的措施。布莱切利公园的密码学家并不知道首相的反应，但据米尔纳-巴里回忆，“我们所注意到的是，几乎从那天起，崎岖的道路奇迹般地变得平坦了。”到战争结束时，有两百多个解码器投入使用。[[File:Turing-statue-Bletchley 14.jpg|thumb|right|upright|Statue of Turing 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>|链接=Special:FilePath/Turing-statue-Bletchley_14.jpg]]

===Hut 8 and the naval Enigma8号营房和海军谜机===

===Hut 8 and the naval Enigma8号营房和海军谜机===

Turing decided to tackle the particularly difficult problem of [[Cryptanalysis of the Enigma#German Naval Enigma|German naval 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>

Turing decided to tackle the particularly difficult problem of [[Cryptanalysis of the Enigma#German Naval Enigma|German naval 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>

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>{{cite journal | first=Alan M. | last=Turing | author-link=Alan Turing | title=The Chemical Basis of Morphogenesis | journal=Philosophical Transactions of the Royal Society of London B | date=14 August 1952 | doi=10.1098/rstb.1952.0012 | volume=237 | number=641 | pages=37–72 | bibcode=1952RSPTB.237...37T | s2cid=120437796 }}</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>John Gribbin, ''Deep Simplicity'', p. 126, Random House, 2004</ref>John Gribbin, Deep Simplicity, p. 126, Random House, 2004

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>{{cite journal | first=Alan M. | last=Turing | author-link=Alan Turing | title=The Chemical Basis of Morphogenesis | journal=Philosophical Transactions of the Royal Society of London B | date=14 August 1952 | doi=10.1098/rstb.1952.0012 | volume=237 | number=641 | pages=37–72 | bibcode=1952RSPTB.237...37T | s2cid=120437796 }}</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>John Gribbin, ''Deep Simplicity'', p. 126, Random House, 2004</ref>John Gribbin, Deep Simplicity, p. 126, Random House, 2004

1951年，39岁的图灵转向数学生物学，最终于1952年1月出版了他的杰作《形态发生的化学基础》。他对形态发生很感兴趣，即生物有机体中模式和形状的发展。他认为，一个化学物质相互反应并在空间扩散的系统，称为反应扩散系统，可以解释“形态发生的主要现象”。他用偏微分方程系统来模拟催化化学反应。例如，如果一个特定的化学反应需要一个催化剂 a，并且如果该反应产生了更多的催化剂 a，那么我们说该反应是自催化的，并且有正反馈，可以用非线性微分方程来模拟。图灵发现，如果化学反应不仅产生了催化剂 a，而且还产生了抑制剂 b，从而减缓了 a 的生成，那么这些图案就可以被创造出来。如果 a 和 b 以不同的速率在容器中扩散，那么可能会有 a 占优势的区域和 b 占优势的区域。为了计算这种程度，图灵需要一台功能强大的计算机，但是在1951年，这些计算机还没有那么容易获得，所以他不得不用线性近似法手工求解方程。这些计算给出了正确的定性结果，并产生了一种均匀的混合物，例如，奇怪的是，这种混合物有规则地分布着固定的红点。俄罗斯生物化学家 Boris Belousov 也进行过类似的实验，但由于当时的偏见，他的论文无法发表，因为任何这样的事情都违反了热力学第二定律。贝洛索夫并不知道图灵在《皇家学会哲学汇刊》上发表的论文。126，Random House，2004

1951年，39岁的图灵转向数学生物学，最终于1952年1月出版了他的杰作《形态发生的化学基础》。他对形态发生很感兴趣，即生物有机体中模式和形状的发展。他认为，一个化学物质相互反应并在空间扩散的系统，称为反应扩散系统，可以解释“形态发生的主要现象”。他用偏微分方程系统来模拟催化化学反应。例如，如果一个特定的化学反应需要一个催化剂 a，并且如果该反应产生了更多的催化剂 a，那么我们说该反应是自催化的，并且有正反馈，可以用非线性微分方程来模拟。图灵发现，如果化学反应不仅产生了催化剂 a，而且还产生了抑制剂 b，从而减缓了 a 的生成，那么这些图案就可以被创造出来。如果 a 和 b 以不同的速率在容器中扩散，那么可能会有 a 占优势的区域和 b 占优势的区域。为了计算这种程度，图灵需要一台功能强大的计算机，但是在1951年，这些计算机还没有那么容易获得，所以他不得不用线性近似法手工求解方程。这些计算给出了正确的定性结果，并产生了一种均匀的混合物，奇怪的是它有规律地间隔着固定的红点。俄罗斯生物化学家 Boris Belousov 也进行过类似的实验，但由于当时的偏见，他的论文无法发表，因为任何这样的事情都违反了热力学第二定律。贝洛索夫并不知道图灵在《皇家学会哲学汇刊》上发表的论文。126，Random House，2004

【最终版】1951年，图灵39岁的时候，他转向数学生物学，最终在1952年1月出版了他的杰作《形态发生的化学基础》。他对形态发生感兴趣，也就是生物有机体中模式和形状的发展。他认为，一个化学物质相互作用并在空间中扩散的系统，被称为反应-扩散系统，可以解释“形态发生的主要现象”。他用偏微分方程组来模拟催化化学反应。例如，如果某一化学反应的发生需要催化剂a，如果反应产生了更多的催化剂a，那么我们就说这个反应是自催化的，有一个正反馈可以用非线性微分方程来模拟。图灵发现模式可以创建如果不仅产生了催化剂的化学反应,而且还产生一种抑制剂B，减速A。如果A和B的生产以不同的速率扩散到容器中,然后你可以有一些地区主导A和B。为了计算这个范围，图灵需要一台强大的计算机，但在1951年，这台计算机还没有普及，所以他不得不使用线性近似来手工求解方程。这些计算给出了正确的定性结果，并产生了，例如，一种均匀的混合物，奇怪的是，它有规律地间隔着固定的红点。俄罗斯生物化学家鲍里斯·别洛乌索夫(Boris Belousov)也做过类似的实验，但他的论文未能发表，因为当时人们认为这样的实验违反了热力学第二定律。别洛乌索夫并不知道图灵在《皇家学会哲学学报》上发表的论文。约翰·格里宾，《深层的简单》，第126页，兰登书屋，2004年。

【最终版】1951年，图灵39岁的时候，他转向数学生物学，最终在1952年1月出版了他的杰作《形态发生的化学基础》。他对形态发生感兴趣，也就是生物有机体中模式和形状的发展。他认为，一个化学物质相互作用并在空间中扩散的系统，被称为反应-扩散系统，可以解释“形态发生的主要现象”。他用偏微分方程组来模拟催化化学反应。例如，如果某一化学反应的发生需要催化剂A，如果反应产生了更多的催化剂A，那么我们就说这个反应是自催化的，有一个正反馈可以用非线性微分方程来模拟。图灵发现在特定情况下扩散系统模式将会被刻画出来，如果化学反应不仅仅产生了催化剂A，而且同时还产生了抑制剂B，这里的抑制剂B会减缓A的产生。如果A和B的生产以不同的速率扩散到容器中,然后你可以有一些地区主导A和B。为了计算这个范围，图灵需要一台强大的计算机，但在1951年，这台计算机还没有普及，所以他不得不使用线性近似来手工求解方程。这些计算给出了正确的定性结果，并产生了，例如，一种均匀的混合物，奇怪的是，它有规律地间隔着固定的红点。俄罗斯生物化学家鲍里斯·别洛乌索夫(Boris Belousov)也做过类似的实验，但他的论文未能发表，因为当时人们认为这样的实验违反了热力学第二定律。别洛乌索夫并不知道图灵在《皇家学会哲学学报》上发表的论文。约翰·格里宾，《深层的简单》，第126页，兰登书屋，2004年。

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>James Murray, ''How the leopard gets its spots'', Scientific American, vol 258, number 3, p.&nbsp;80, March 1988</ref><ref>James Murray, ''Mathematical Biology I'', 2007, Chapter 6, Springer Verlag</ref><ref>John Gibbin, Deep Simplicity, p.&nbsp;134, Random House, 2004</ref> James Murray, How the leopard gets its spots, Scientific American, vol 258, number 3, p. 80, March 1988James Murray, Mathematical Biology I, 2007, Chapter 6, Springer VerlagJohn Gibbin, Deep Simplicity, p. 134, Random House, 2004 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>

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>James Murray, ''How the leopard gets its spots'', Scientific American, vol 258, number 3, p.&nbsp;80, March 1988</ref><ref>James Murray, ''Mathematical Biology I'', 2007, Chapter 6, Springer Verlag</ref><ref>John Gibbin, Deep Simplicity, p.&nbsp;134, Random House, 2004</ref> James Murray, How the leopard gets its spots, Scientific American, vol 258, number 3, p. 80, March 1988James Murray, Mathematical Biology I, 2007, Chapter 6, Springer VerlagJohn Gibbin, Deep Simplicity, p. 134, Random House, 2004 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>

个人生活1941年，图灵向 Hut 8的同事琼 · 克拉克求婚，她是一位数学家和密码分析家，但他们的婚约是短暂的。在向他的未婚妻承认自己是同性恋后，图灵决定不再继续这段婚姻。据报道，他的未婚妻对此并不担心。

个人生活1941年，图灵向 Hut 8的同事琼 · 克拉克求婚，她是一位数学家和密码分析家，但他们的婚约是短暂的。在向他的未婚妻承认自己是同性恋后，图灵决定不再继续这段婚姻。据报道，他的未婚妻对此并不担心。

===Conviction for indecency因猥亵而被定罪===

===Conviction for indecency因猥亵而被定罪===

In January 1952, Turing was 39 when he started a relationship with Arnold Murray, a 19-year-old unemployed man. Just before Christmas, Turing was walking along Manchester's [[Wilmslow Road|Oxford Road]] when he met Murray just outside the [[Dancehouse|Regal Cinema]] and invited him to lunch. On 23 January, Turing's house was burgled. Murray told Turing that he and the burglar were acquainted, and Turing reported the crime to the police. During the investigation, he acknowledged a sexual relationship with Murray. Homosexual acts were criminal offences in the United Kingdom at that time,<ref>{{Harvnb|Hodges|1983|p=458}}</ref> and both men were charged with "[[gross indecency]]" under [[Criminal Law Amendment Act 1885#Section 11|Section 11]] of the [[Criminal Law Amendment Act 1885]].<ref name="LeavittP268">{{Harvnb|Leavitt|2007|p=268}}</ref> Initial [[committal procedure|committal proceedings]] for the trial were held on 27 February during which Turing's solicitor "reserved his defence", i.e., did not argue or provide evidence against the allegations.

In January 1952, Turing was 39 when he started a relationship with Arnold Murray, a 19-year-old unemployed man. Just before Christmas, Turing was walking along Manchester's [[Wilmslow Road|Oxford Road]] when he met Murray just outside the [[Dancehouse|Regal Cinema]] and invited him to lunch. On 23 January, Turing's house was burgled. Murray told Turing that he and the burglar were acquainted, and Turing reported the crime to the police. During the investigation, he acknowledged a sexual relationship with Murray. Homosexual acts were criminal offences in the United Kingdom at that time,<ref>{{Harvnb|Hodges|1983|p=458}}</ref> and both men were charged with "[[gross indecency]]" under [[Criminal Law Amendment Act 1885#Section 11|Section 11]] of the [[Criminal Law Amendment Act 1885]].<ref name="LeavittP268">{{Harvnb|Leavitt|2007|p=268}}</ref> Initial [[committal procedure|committal proceedings]] for the trial were held on 27 February during which Turing's solicitor "reserved his defence", i.e., did not argue or provide evidence against the allegations.

有人认为，可能是图灵对算命的信仰导致了他的沮丧情绪。年轻时，图灵曾被算命师告知他将成为一个天才。1954年5月中旬，在他去世前不久，图灵在与格林鲍姆一家一起去海上圣安内斯的一日游中再次决定咨询算命师。根据格林鲍姆夫妇的女儿芭芭拉的说法: 但那是一个阳光明媚的日子，艾伦心情愉快，我们就去了... ... 然后他觉得去黑潭的快乐海滩是个好主意。我们找到了一个算命师的帐篷，艾伦说他想进去，所以我们就在附近等他回来... ... 这张阳光明媚的面孔已经缩成了一张苍白、颤抖、惊恐的脸。发生了一些事情。我们不知道算命先生是怎么说的，但是他显然非常不开心。我想那可能是我们听说他自杀之前最后一次见到他。

有人认为，可能是图灵对算命的信仰导致了他的沮丧情绪。年轻时，图灵曾被算命师告知他将成为一个天才。1954年5月中旬，在他去世前不久，图灵在与格林鲍姆一家一起去海上圣安内斯的一日游中再次决定咨询算命师。根据格林鲍姆夫妇的女儿芭芭拉的说法: 但那是一个阳光明媚的日子，艾伦心情愉快，我们就去了... ... 然后他觉得去黑潭的快乐海滩是个好主意。我们找到了一个算命师的帐篷，艾伦说他想进去，所以我们就在附近等他回来... ... 这张阳光明媚的面孔已经缩成了一张苍白、颤抖、惊恐的脸。发生了一些事情。我们不知道算命先生是怎么说的，但是他显然非常不开心。我想那可能是我们听说他自杀之前最后一次见到他。

【最终版】有人认为，图灵对算命的信仰可能是他情绪低落的原因。图灵年轻时，一个算命先生说他会是个天才。1954年5月中旬，就在图灵去世前不久，他和格林鲍姆一家去海边的圣安妮一日游时，又决定请教算命先生。据格林鲍姆的女儿芭芭拉说:但那天阳光明媚，艾伦心情也很好，我们就出发了……然后他觉得去布莱克浦的快乐海滩是个好主意。我们找到了一个算命人的帐篷，艾伦说他想进去，所以我们在附近等他回来……这张阳光、愉快的脸已萎缩成一张苍白、颤抖、惊恐的脸。发生了什么事。我们不知道算命先生说了什么，但他显然非常不高兴。我想那可能是我们最后一次见他在我们听说他自杀之前。

【最终版】有人认为，图灵对算命的信仰可能是他情绪低落的原因。图灵年轻时，一个算命先生说他会是个天才。1954年5月中旬，就在图灵去世前不久，他和格林鲍姆一家去海边的圣安妮一日游时，又决定请教算命先生。据格林鲍姆的女儿芭芭拉说:但那天阳光明媚，艾伦心情也很好，我们就出发了……然后他觉得去布莱克浦的快乐海滩是个好主意。我们找到了一个算命人的帐篷，艾伦说他想进去，所以我们在附近等他回来……这张阳光、开朗的脸已萎缩成一张苍白、颤抖、惊恐的脸。发生了什么事。我们不知道算命先生说了什么，但他显然非常不高兴。我想那可能是我们最后一次见他在我们听说他自杀之前。

===Government apology and pardon政府道歉和赦免===

===Government apology and pardon政府道歉和赦免===

In August 2009, British programmer John Graham-Cumming started a petition urging the British government to apologise for Turing's prosecution as a homosexual. The petition received more than 30,000 signatures.The petition was only open to UK citizens. The Prime Minister, Gordon Brown, acknowledged the petition, releasing a statement on 10 September 2009 apologising and describing the treatment of Turing as "appalling":Thousands of people have come together to demand justice for Alan Turing and recognition of the appalling way he was treated. While Turing was dealt with under the law of the time and we can't put the clock back, his treatment was of course utterly unfair and I am pleased to have the chance to say how deeply sorry I and we all are for what happened to him&amp;nbsp;... So on behalf of the British government, and all those who live freely thanks to Alan's work I am very proud to say: we're sorry, you deserved so much better.

In August 2009, British programmer John Graham-Cumming started a petition urging the British government to apologise for Turing's prosecution as a homosexual. The petition received more than 30,000 signatures.The petition was only open to UK citizens. The Prime Minister, Gordon Brown, acknowledged the petition, releasing a statement on 10 September 2009 apologising and describing the treatment of Turing as "appalling":Thousands of people have come together to demand justice for Alan Turing and recognition of the appalling way he was treated. While Turing was dealt with under the law of the time and we can't put the clock back, his treatment was of course utterly unfair and I am pleased to have the chance to say how deeply sorry I and we all are for what happened to him&amp;nbsp;... So on behalf of the British government, and all those who live freely thanks to Alan's work I am very proud to say: we're sorry, you deserved so much better.