更改

就我个人而言，我相信精神确实与物质永恒地联系在一起，但肯定不是由同一种身体联系在一起的；关于精神与身体的实际联系，我认为身体可以保持一种“精神”，而身体是活着的和清醒的，两者是紧密相连的。当身体处于睡眠状态时，我无法猜测会发生什么，但当身体死亡时，身体的“机制”失去了，保持着灵魂，灵魂迟早会找到一个新的身体，也许会立即找到。

就我个人而言，我相信精神确实与物质永恒地联系在一起，但肯定不是由同一种身体联系在一起的；关于精神与身体的实际联系，我认为身体可以保持一种“精神”，而身体是活着的和清醒的，两者是紧密相连的。当身体处于睡眠状态时，我无法猜测会发生什么，但当身体死亡时，身体的“机制”失去了，保持着灵魂，灵魂迟早会找到一个新的身体，也许会立即找到。

 

===University and work on computability===

===University and work on computability===

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>

舍伯恩毕业后，图灵于1931年至1934年在剑桥大学国王学院读本科，在那里他获得了数学一等荣誉。1935年，22岁的他凭借一篇论文被选为国王学院的研究员，在这篇论文中，他证明了中心极限定理。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。

舍伯恩毕业后，图灵于1931年至1934年在剑桥大学国王学院读本科，在那里他获得了数学一等荣誉。1935年，22岁的他凭借一篇论文被选为国王学院的研究员，在这篇论文中，他证明了中心极限定理。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>

1936年，图灵发表了他的论文《论可计算数字，以及对可判定性的应用》。它分两部分发表在《伦敦数学学会学报》上，第一部分发表在11月30日，第二部分发表在12月23日。在本文中，图灵重新阐述了库尔特 · 哥德尔1931年关于证明和计算极限的结果，用后来被称为图灵机的形式化和简单的假设设备取代了哥德尔通用的基于算术的形式语言。可判定性问题最初是由德国数学家 David Hilbert 在1928年提出的。图灵证明了他的“通用计算机器”能够执行任何可以想象的数学计算，如果它可以表示为一种算法。他首先证明图灵机的停机问题是不可判定的: 从算法上决定图灵机是否会停机是不可能的。这篇论文被称为“历史上最有影响力的数学论文”。[[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.

 

 

1936年，图灵发表了他的论文《论可计算数字，以及对可判定性的应用》。它分两部分发表在《伦敦数学学会学报》上，第一部分发表在11月30日，第二部分发表在12月23日。在本文中，图灵重新阐述了库尔特 · 哥德尔1931年关于证明和计算极限的结果，用后来被称为图灵机的形式化和简单的假设设备取代了哥德尔通用的基于算术的形式语言。可判定性问题最初是由德国数学家 David Hilbert 在1928年提出的。图灵证明了他的“通用计算机器”能够执行任何可以想象的数学计算，如果它可以表示为一种算法。他首先证明图灵机的停机问题是不可判定的: 从算法上决定图灵机是否会停机是不可能的。这篇论文被称为“历史上最有影响力的数学论文”。

 

【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。

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。