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图灵决定解决德国海军谜团这个特别困难的问题，“因为没有其他人对此做任何事，而我可以独享它”。1939年12月，图灵解决了海军指示器系统的关键部分，它比其他军种使用的指示器系统更复杂。

图灵决定解决德国海军谜团这个特别困难的问题，“因为没有其他人对此做任何事，而我可以独享它”。1939年12月，图灵解决了海军指示器系统的关键部分，它比其他军种使用的指示器系统更复杂。

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>

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>

同一天晚上，他还提出了 Banburismus 的想法，这是一种序列统计技术(亚伯拉罕 · 沃尔德后来称之为序列分析) ，以帮助破解海军的谜团，“尽管我不确定它在实践中是否有效，事实上，直到有些日子真正破解之前，我也不确定。”为此，他发明了一种衡量证据重量的方法，他称之为禁令。班布里斯马斯可以排除恩尼格玛转子的某些序列，大大缩短了测试炸弹设置所需的时间。后来，这种使用十分之一密码(decibans)积累足够重量证据的顺序过程被用于对洛伦兹密码的密码分析。

同一天晚上，他还提出了 Banburismus 的想法，这是一种序列统计技术(亚伯拉罕 · 沃尔德后来称之为序列分析) ，以帮助破解海军的谜团，“尽管我不确定它在实践中是否有效，事实上，直到有些日子真正破解之前，我也不确定。”为此，他发明了一种衡量证据重量的方法，他称之为禁令。班布里斯马斯可以排除恩尼格玛转子的某些序列，大大缩短了测试炸弹设置所需的时间。后来，这种使用十分之一密码(decibans)积累足够重量证据的顺序过程被用于对洛伦兹密码的密码分析。

Turing travelled to the United States in November 1942<ref>{{Harvnb|Hodges|1983|pp=242–245}}</ref> and worked with US Navy cryptanalysts on the naval Enigma and bombe construction in Washington; he also visited their [[United States Naval Computing Machine Laboratory|Computing Machine Laboratory]] in [[Dayton, Ohio]].

Turing travelled to the United States in November 1942<ref>{{Harvnb|Hodges|1983|pp=242–245}}</ref> and worked with US Navy cryptanalysts on the naval Enigma and bombe construction in Washington; he also visited their [[United States Naval Computing Machine Laboratory|Computing Machine Laboratory]] in [[Dayton, Ohio]].

图灵于1942年11月前往美国，与美国海军密码分析师一起在华盛顿进行海军恩尼格玛密码机和炸弹建造; 他还参观了位于俄亥俄州代顿的计算机实验室。

图灵于1942年11月前往美国，与美国海军密码分析师一起在华盛顿进行海军恩尼格玛密码机和炸弹建造; 他还参观了位于俄亥俄州代顿的计算机实验室。

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.

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.|source=}}他们的测试(换向器)很难被认为是决定性的，因为他们没有测试弹跳与电子停止寻找设备。似乎没有人被告知棒、官员或班布里斯马斯，除非他们真的要做些什么。开始

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.|source=}}他们的测试(换向器)很难被认为是决定性的，因为他们没有测试弹跳与电子停止寻找设备。似乎没有人被告知棒、官员或班布里斯马斯，除非他们真的要做些什么。开始

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>

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>

在这次旅行中，他还在贝尔实验室协助开发安全语音设备。他于1943年3月返回 Bletchley Park。在他缺席期间，休 · 亚历山大正式担任了 Hut 8的负责人，尽管亚历山大实际上已经领导了一段时间(图灵对该部分的日常运行没有什么兴趣)。图灵成为了 Bletchley Park 密码分析的总顾问。

在这次旅行中，他还在贝尔实验室协助开发安全语音设备。他于1943年3月返回 Bletchley Park。在他缺席期间，休 · 亚历山大正式担任了 Hut 8的负责人，尽管亚历山大实际上已经领导了一段时间(图灵对该部分的日常运行没有什么兴趣)。图灵成为了 Bletchley Park 密码分析的总顾问。

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>}}亚历山大这样评价图灵的贡献:

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>}}亚历山大这样评价图灵的贡献:

===Turingery===

===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>

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>

1942年7月，图灵发明了一种称为 Turingery (或开玩笑地称为 Turingismus)的技术，用来对付德国人的新型秘密作家机器产生的洛伦兹密码信息。这是一台电传打字机转子密码附件，代号为 Tunny，位于 Bletchley Park。车轮修理是车轮折断的一种方法，也就是计算出图尼车轮凸轮设置的一种程序。他还把 Tunny 团队介绍给了 Tommy Flowers，后者在 Max Newman 的指导下，建造了世界上第一台可编程数字电子计算机——巨像计算机，它取代了之前更简单的机器(Heath Robinson) ，其出色的速度使得统计解密技术能够有效地应用于信息。有些人错误地认为图灵是巨像计算机设计中的关键人物。图灵厄立特和班布里斯马斯的统计方法无疑为洛伦兹密码的密码分析思想提供了思路，但他并没有直接参与巨像的发展。

1942年7月，图灵发明了一种称为 Turingery (或开玩笑地称为 Turingismus)的技术，用来对付德国人的新型秘密作家机器产生的洛伦兹密码信息。这是一台电传打字机转子密码附件，代号为 Tunny，位于 Bletchley Park。车轮修理是车轮折断的一种方法，也就是计算出图尼车轮凸轮设置的一种程序。他还把 Tunny 团队介绍给了 Tommy Flowers，后者在 Max Newman 的指导下，建造了世界上第一台可编程数字电子计算机——巨像计算机，它取代了之前更简单的机器(Heath Robinson) ，其出色的速度使得统计解密技术能够有效地应用于信息。有些人错误地认为图灵是巨像计算机设计中的关键人物。图灵厄立特和班布里斯马斯的统计方法无疑为洛伦兹密码的密码分析思想提供了思路，但他并没有直接参与巨像的发展。

===Delilah===

===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]]. At the park, he further developed his knowledge of electronics with the assistance of engineer 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.

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]]. At the park, he further developed his knowledge of electronics with the assistance of engineer 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.

继美国贝尔实验室的工作之后，图灵在电话系统中追求电子加密语音的想法。在战争后期，他转而为特勤局的无线电安全服务(后来的 hmgc)在 Hanslope Park 工作。在公园里，他在工程师唐纳德 · 贝利的帮助下进一步发展了他的电子学知识。他们一起设计和建造了一个代号为 Delilah 的便携式安全语音通信机器。这种机器是为不同的应用而设计的，但是它缺乏用于长距离无线电传输的能力。无论如何，黛利拉完成得太晚了，不能在战争期间使用。虽然这个系统运行良好，图灵通过加密和解密一段温斯顿·丘吉尔的演讲录音向官员们展示了它，Delilah 并没有被采用。图灵还咨询了贝尔实验室关于 SIGSALY 的开发，这是一个安全的语音系统，在战争后期使用。

继美国贝尔实验室的工作之后，图灵在电话系统中追求电子加密语音的想法。在战争后期，他转而为特勤局的无线电安全服务(后来的 hmgc)在 Hanslope Park 工作。在公园里，他在工程师唐纳德 · 贝利的帮助下进一步发展了他的电子学知识。他们一起设计和建造了一个代号为 Delilah 的便携式安全语音通信机器。这种机器是为不同的应用而设计的，但是它缺乏用于长距离无线电传输的能力。无论如何，黛利拉完成得太晚了，不能在战争期间使用。虽然这个系统运行良好，图灵通过加密和解密一段温斯顿·丘吉尔的演讲录音向官员们展示了它，Delilah 并没有被采用。图灵还咨询了贝尔实验室关于 SIGSALY 的开发，这是一个安全的语音系统，在战争后期使用。

===Early computers and the Turing test===

===Early computers and the Turing test===

[[File:Alan Turing 78 High Street Hampton blue plaque.jpg|thumb|Plaque, 78 High Street, [[Hampton, London|Hampton]]|链接=Special:FilePath/Alan_Turing_78_High_Street_Hampton_blue_plaque.jpg]]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, UK|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 web | 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>citing

[[File:Alan Turing 78 High Street Hampton blue plaque.jpg|thumb|Plaque, 78 High Street, [[Hampton, London|Hampton]]|链接=Special:FilePath/Alan_Turing_78_High_Street_Hampton_blue_plaque.jpg]]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, UK|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 web | 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>citing

早期的计算机和图灵测试1945年至1947年，图灵生活在汉普顿，在国家物理实验室(NPL)从事自动计算引擎(ACE)的设计工作。他在1946年2月19日发表了一篇论文，这是第一个详细设计的储存程式计算机。的不完整的 EDVAC报告书的第一份草案在图灵论文之前就已经发表了，但是它没有那么详细，而且，根据 NPL 数学部门的负责人 John r. Womersley 的说法，它“包含了许多图灵博士自己的想法”。引用

早期的计算机和图灵测试1945年至1947年，图灵生活在汉普顿，在国家物理实验室(NPL)从事自动计算引擎(ACE)的设计工作。他在1946年2月19日发表了一篇论文，这是第一个详细设计的储存程式计算机。的不完整的 EDVAC报告书的第一份草案在图灵论文之前就已经发表了，但是它没有那么详细，而且，根据 NPL 数学部门的负责人 John r. Womersley 的说法，它“包含了许多图灵博士自己的想法”。引用

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://www.google.com/books/edition/Alan_Turing_The_Enigma/4muYDwAAQBAJ?hl=en&gbpv=1&bsq=%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>

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://www.google.com/books/edition/Alan_Turing_The_Enigma/4muYDwAAQBAJ?hl=en&gbpv=1&bsq=%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>

尽管 ACE 是一个可行的设计，但围绕 Bletchley Park 战时工作的《官方机密法》(Official Secrets Act)的影响，使得图灵无法解释他对涉及人工操作员的计算机安装如何工作的分析基础。这导致了项目开始的延迟，他开始感到幻灭。1947年末，他回到剑桥休假一年，在此期间，他完成了一部关于智能机械的开创性著作，但这部著作在他有生之年并未出版。当他在剑桥的时候，飞行员 ACE 正在他不在的时候建造。它在1950年5月10日执行了它的第一个程序，后来世界各地的许多计算机都归功于它，包括英国电动 DEUCE 和美国本迪克斯 G-15。图灵 ACE 的完整版直到他死后才被制造出来。

尽管 ACE 是一个可行的设计，但围绕 Bletchley Park 战时工作的《官方机密法》(Official Secrets Act)的影响，使得图灵无法解释他对涉及人工操作员的计算机安装如何工作的分析基础。这导致了项目开始的延迟，他开始感到幻灭。1947年末，他回到剑桥休假一年，在此期间，他完成了一部关于智能机械的开创性著作，但这部著作在他有生之年并未出版。当他在剑桥的时候，飞行员 ACE 正在他不在的时候建造。它在1950年5月10日执行了它的第一个程序，后来世界各地的许多计算机都归功于它，包括英国电动 DEUCE 和美国本迪克斯 G-15。图灵 ACE 的完整版直到他死后才被制造出来。

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'').

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'').

根据杜塞尔多夫的根舍出版社出版的德国计算机先驱亨氏马克斯·普朗克物理学研究所的回忆录，图灵和康拉德 · 祖泽之间有过一次会面。故事发生在1947年的格丁根。这种审问采取了座谈会的形式。参与者分别是来自英国的沃姆斯利、图灵、波特和一些德国研究人员，比如 Zuse、 Walther 和 Billing (更多细节参见 Herbert Bruderer、 Konrad Zuse 和 die Schweiz)。

根据杜塞尔多夫的根舍出版社出版的德国计算机先驱亨氏马克斯·普朗克物理学研究所的回忆录，图灵和康拉德 · 祖泽之间有过一次会面。故事发生在1947年的格丁根。这种审问采取了座谈会的形式。参与者分别是来自英国的沃姆斯利、图灵、波特和一些德国研究人员，比如 Zuse、 Walther 和 Billing (更多细节参见 Herbert Bruderer、 Konrad Zuse 和 die Schweiz)。

In 1948, Turing was appointed [[Reader (academic rank)|reader]] in the [[School of Mathematics, University of Manchester|Mathematics Department]] at the [[Victoria University of Manchester]]. 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|hdl = 10338.dmlcz/103139}}</ref> and in "[[Computing Machinery and Intelligence]]" (''[[Mind (journal)|Mind]]'', October 1950), 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>[[Stevan Harnad|Harnad, Stevan]] (2008) [http://eprints.soton.ac.uk/262954/ The Annotation Game: On Turing (1950) on Computing, Machinery and Intelligence] {{Webarchive|url=https://web.archive.org/web/20171018070225/https://eprints.soton.ac.uk/262954/ |date=18 October 2017 }}. In: Epstein, Robert & Peters, Grace (Eds.) ''Parsing the Turing Test: Philosophical and Methodological Issues in the Quest for the Thinking Computer''. Springer</ref> Harnad, Stevan (2008) The Annotation Game: On Turing (1950) on Computing, Machinery and Intelligence . In: Epstein, Robert & Peters, Grace (Eds.) Parsing the Turing Test: Philosophical and Methodological Issues in the Quest for the Thinking Computer. Springer 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 was appointed [[Reader (academic rank)|reader]] in the [[School of Mathematics, University of Manchester|Mathematics Department]] at the [[Victoria University of Manchester]]. 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|hdl = 10338.dmlcz/103139}}</ref> and in "[[Computing Machinery and Intelligence]]" (''[[Mind (journal)|Mind]]'', October 1950), 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>[[Stevan Harnad|Harnad, Stevan]] (2008) [http://eprints.soton.ac.uk/262954/ The Annotation Game: On Turing (1950) on Computing, Machinery and Intelligence] {{Webarchive|url=https://web.archive.org/web/20171018070225/https://eprints.soton.ac.uk/262954/ |date=18 October 2017 }}. In: Epstein, Robert & Peters, Grace (Eds.) ''Parsing the Turing Test: Philosophical and Methodological Issues in the Quest for the Thinking Computer''. Springer</ref> Harnad, Stevan (2008) The Annotation Game: On Turing (1950) on Computing, Machinery and Intelligence . In: Epstein, Robert & Peters, Grace (Eds.) Parsing the Turing Test: Philosophical and Methodological Issues in the Quest for the Thinking Computer. Springer 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.

1948年，图灵被任命为曼彻斯特维多利亚大学数学系的讲师。一年后，他成为计算机机器实验室的副主任，在那里，他为最早的存储程序计算机之一——曼彻斯特 Mark 1——开发软件。图灵为这台机器写了第一版程序员手册，并被费兰蒂聘为他们商业化机器费兰蒂马克1的开发顾问。他继续支付费朗蒂咨询费，直到他去世。在此期间，他继续从事更多抽象的数学工作，在《计算机器与智能》(1950年10月，心智)一书中，图灵提出了人工智能的问题，并提出了一个后来被称为图灵测试的实验，试图为机器定义一个被称为“智能”的标准。当时的想法是，如果人类审讯者无法通过对话将电脑与人类区分开来，那么电脑就可以说是在“思考”。哈纳德，斯蒂文(2008)的注释游戏: 关于图灵(1950)的计算，机械和智能。年: 爱普斯坦，罗伯特 & 彼得斯，格雷斯(编)解析图灵测试: 思维计算机探索中的哲学与方法论问题。斯普林格在论文中，图灵提出，与其编写一个程序来模拟成人的思维，不如编写一个更简单的程序来模拟儿童的思维，然后对其进行一系列的教育。图灵测试的反向形式在互联网上被广泛使用; CAPTCHA 测试的目的是确定用户是人还是计算机。

1948年，图灵被任命为曼彻斯特维多利亚大学数学系的讲师。一年后，他成为计算机机器实验室的副主任，在那里，他为最早的存储程序计算机之一——曼彻斯特 Mark 1——开发软件。图灵为这台机器写了第一版程序员手册，并被费兰蒂聘为他们商业化机器费兰蒂马克1的开发顾问。他继续支付费朗蒂咨询费，直到他去世。在此期间，他继续从事更多抽象的数学工作，在《计算机器与智能》(1950年10月，心智)一书中，图灵提出了人工智能的问题，并提出了一个后来被称为图灵测试的实验，试图为机器定义一个被称为“智能”的标准。当时的想法是，如果人类审讯者无法通过对话将电脑与人类区分开来，那么电脑就可以说是在“思考”。哈纳德，斯蒂文(2008)的注释游戏: 关于图灵(1950)的计算，机械和智能。年: 爱普斯坦，罗伯特 & 彼得斯，格雷斯(编)解析图灵测试: 思维计算机探索中的哲学与方法论问题。斯普林格在论文中，图灵提出，与其编写一个程序来模拟成人的思维，不如编写一个更简单的程序来模拟儿童的思维，然后对其进行一系列的教育。图灵测试的反向形式在互联网上被广泛使用; CAPTCHA 测试的目的是确定用户是人还是计算机。

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>[http://www.chessgames.com/perl/chessgame?gid=1356927 Alan Turing vs Alick Glennie (1952) "Turing Test"] {{Webarchive|url=https://web.archive.org/web/20060219033248/http://www.chessgames.com/perl/chessgame?gid=1356927 |date=19 February 2006 }} Chessgames.com</ref> Alan Turing vs Alick Glennie (1952) "Turing Test"  Chessgames.com According to [[Garry Kasparov]], Turing's program "played a recognizable game of chess."<ref>Kasparov, Garry, Smart machines will free us all, ''The Wall Street Journal'', 15–16 April 2017, p. c3</ref> Kasparov, Garry, Smart machines will free us all, The Wall Street Journal, 15–16 April 2017, p. c3  The program lost to Turing's colleague [[Alick Glennie]], although it is said that it won a game against Champernowne's wife, Isabel.<ref>{{cite web|last1=O'Connor|first1=J.J.|last2=Robertson|first2=E.F.|title=David Gawen Champernowne|url=http://www-history.mcs.st-and.ac.uk/Biographies/Champernowne.html|work=MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland|access-date=22 May 2018|archive-url=https://web.archive.org/web/20171019123016/http://www-history.mcs.st-and.ac.uk/Biographies/Champernowne.html|archive-date=19 October 2017|url-status=live}}</ref>

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>[http://www.chessgames.com/perl/chessgame?gid=1356927 Alan Turing vs Alick Glennie (1952) "Turing Test"] {{Webarchive|url=https://web.archive.org/web/20060219033248/http://www.chessgames.com/perl/chessgame?gid=1356927 |date=19 February 2006 }} Chessgames.com</ref> Alan Turing vs Alick Glennie (1952) "Turing Test"  Chessgames.com According to [[Garry Kasparov]], Turing's program "played a recognizable game of chess."<ref>Kasparov, Garry, Smart machines will free us all, ''The Wall Street Journal'', 15–16 April 2017, p. c3</ref> Kasparov, Garry, Smart machines will free us all, The Wall Street Journal, 15–16 April 2017, p. c3  The program lost to Turing's colleague [[Alick Glennie]], although it is said that it won a game against Champernowne's wife, Isabel.<ref>{{cite web|last1=O'Connor|first1=J.J.|last2=Robertson|first2=E.F.|title=David Gawen Champernowne|url=http://www-history.mcs.st-and.ac.uk/Biographies/Champernowne.html|work=MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland|access-date=22 May 2018|archive-url=https://web.archive.org/web/20171019123016/http://www-history.mcs.st-and.ac.uk/Biographies/Champernowne.html|archive-date=19 October 2017|url-status=live}}</ref>

1948年，图灵与他以前的本科生同事 d.g。Champernowne，开始为一台还不存在的计算机编写国际象棋程序。到了1950年，这个项目完成了，并被称为图罗尚。在1952年，他试图实现它在一个费朗蒂马克1，但由于缺乏足够的权力，计算机无法执行该程序。取而代之的是，图灵通过快速浏览算法页面并在棋盘上执行指令来“运行”程序，每次运行大约需要半个小时。比赛被记录了下来。Alan Turing vs Alick Glennie (1952)“ Turing Test”chessgames. com 根据 Garry Kasparov 的说法，图灵的程序“玩的是一种公认的国际象棋游戏。“卡斯帕罗夫，加里，智能机器将解放我们所有人，《华尔街日报》 ，2017年4月15日至16日，第 c3页。虽然据说它在一场比赛中击败了尚伯努尼的妻子伊莎贝尔，但这个程序输给了图灵的同事阿利克 · 格伦尼。

1948年，图灵与他以前的本科生同事 d.g。Champernowne，开始为一台还不存在的计算机编写国际象棋程序。到了1950年，这个项目完成了，并被称为图罗尚。在1952年，他试图实现它在一个费朗蒂马克1，但由于缺乏足够的权力，计算机无法执行该程序。取而代之的是，图灵通过快速浏览算法页面并在棋盘上执行指令来“运行”程序，每次运行大约需要半个小时。比赛被记录了下来。Alan Turing vs Alick Glennie (1952)“ Turing Test”chessgames. com 根据 Garry Kasparov 的说法，图灵的程序“玩的是一种公认的国际象棋游戏。“卡斯帕罗夫，加里，智能机器将解放我们所有人，《华尔街日报》 ，2017年4月15日至16日，第 c3页。虽然据说它在一场比赛中击败了尚伯努尼的妻子伊莎贝尔，但这个程序输给了图灵的同事阿利克 · 格伦尼。

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>

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>

他的图灵测试是对人工智能争论的一个重要的、有特点的、持久的贡献，这场争论持续了半个多世纪。

他的图灵测试是对人工智能争论的一个重要的、有特点的、持久的贡献，这场争论持续了半个多世纪。

===Pattern formation and mathematical biology===

===Pattern formation and mathematical biology===

===<nowiki>= = 模式形成和数学生物学 =</nowiki>===

===模式形成和数学生物学 ===

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，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

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>