草稿:艾倫·圖靈
![]() | 本草稿目前為「艾倫·圖靈」的草稿。 如有任何疑問,請至討論頁發起討論。 |
艾倫·圖靈 Alan Turing OBE FRS | |
---|---|
![]() 16歲的圖靈,攝於1928年前後 | |
出生 | ![]() | 1912年6月23日
逝世 | 1954年6月7日![]() | (41歲)
死因 | 氰化物中毒自殺[a] |
墓地 | 骨灰撒在沃金火葬場 |
教育程度 | 舍伯恩學校 |
母校 | |
知名於 | |
伴侶 | 瓊·克拉克 (1941年訂婚,未結) |
獎項 | 史密斯獎(1936) |
科學生涯 | |
研究領域 | 數學、邏輯學、密碼分析、計算機科學、數理生物學[1] |
機構 | |
論文 | Systems of Logic Based on Ordinals(1938) |
博士導師 | 阿隆佐·邱奇[2] |
博士生 | 羅賓·甘迪[2][3] 比阿特麗斯·沃斯利[4] |
受影響自 | 馬克斯·紐曼[5] |
簽名 | |
![]() |
艾倫·馬西森·圖靈 OBE FRS(英語:Alan Mathison Turing[b];1912年6月23日—1954年6月7日),英國數學家、電腦科學家、邏輯學家、密碼分析師、哲學家和數理生物學家[6][7]。他深刻影響理論計算機科學的發展,將算法及運算等概念形式化為普遍認為是通用計算機的圖靈機[8][9][10],因此被普遍認為是理論計算機科學及人工智能之父[11]。
圖靈出生於倫敦麥達維爾,在南英格蘭成長。憑數學學位在劍橋大學國王學院畢業後,圖靈留校擔任院士,期間證明部分純數學的對錯問題無法通過運算解答、定義了圖靈機、繼續證明圖靈機的停機問題無法決定。1938年,圖靈取得普林斯頓大學數學系哲學博士學位。第二次世界大戰期間,圖靈來到政府通信總部的密碼破譯中心布萊切利園,為Ultra情報部門工作。他率領8號營房分部,專門負責破譯德國海軍的密碼,期間設計多種技術加快密碼破解速度,包括改良波蘭在大戰前推出的電動密碼機炸彈法,找出恩尼格瑪密碼機的設定。圖靈破譯了大量從敵軍截獲的加密信息,推動同盟國在大西洋海戰等重大戰役中擊敗軸心國[12][13]。
戰後,圖靈在英國國家物理實驗室設計出自動運算引擎,屬於第一批能夠儲存程序的計算機。1948年,圖靈加入馬克斯·紐曼在曼徹斯特維多利亞大學的計算機實驗室,開發出曼徹斯特大學計算機組,同時進軍數理生物學界。他撰寫論文研究形態發生的化學基礎[1],預言了擺動式的化學反應,例如最開始於1960年代被發現的別洛烏索夫-扎博廷斯基反應。由於大部分研究成果依照《官方保密法》封存,圖靈在世時從未獲得祖國完全認可[14]。
1952年,圖靈因同性戀行為被起訴,隨後接受代替刑罰的己烯雌酚化學閹割。1954年,在離42歲還有16天的時候,圖靈氰化物中毒死亡。死因裁決宣佈他的死乃屬自殺,不過現存證據亦支持其死於意外中毒。[15][16][17]
圖靈為後世帶來深遠的影響。出於紀念,後人為他設立雕像,用他的名字命名了許多事物,包括表彰計算機科學發明的年度獎項,而在他壽辰前發布的英格蘭銀行50英鎊紙幣印有他的肖像。根據觀眾投票結果,2019年BBC電視節目《偶像:20世紀偉人巡禮》將艾倫提名為20世紀最偉大的人。
早年及教育
[編輯]家庭
[編輯]![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Alan_Turing_%285025990183%29.jpg/170px-Alan_Turing_%285025990183%29.jpg)
1912年6月23日,圖靈生於英國倫敦麥達維爾[7],父親朱利葉斯·馬西森·圖靈(Julius Mathison Turing,1873—1947)在英屬印度馬德拉斯省(今奧里薩邦)恰特拉普爾政府任公務員[18][19],祖父約翰·羅伯特·圖靈牧師(Rev. John Robert Turing)出生在荷蘭的一個蘇格蘭商業世家,家裡有位從男爵。圖靈母親埃塞爾·薩拉·圖靈[c](Ethel Sara Turing,1881—1976)是馬德拉斯鐵路首席工程師愛德華·沃勒·斯托尼(Edward Waller Stoney)之女。斯托尼一家是盎格魯愛爾蘭人,信奉新教,在蒂珀雷里郡和朗福德郡屬於紳士階級,不過埃塞爾的童年多數在克萊爾郡度過[20]。
朱利葉斯在印度公務員局的工作讓他家人來到印度,當時他的父親在孟加拉軍隊當將軍。不過朱利葉斯和埃塞爾希望孩子們能在英國長大,於是搬到了倫敦的麥達維爾[21]。原為圖靈故居的柱廊酒店[18][22]外有一塊藍色牌匾,上面記載艾倫·圖靈於1912年6月23日出生[23][24]。圖靈有一個哥哥,叫約翰,是圖靈男爵世家第12代男爵約翰·德莫特·圖靈爵士的父親[25]。
圖靈少年時代,父親仍有公務員職責在身,他與妻子在英國黑斯廷斯[26]和印度兩地奔波,將兩個兒子託付給英國陸軍的一對退伍夫婦。圖靈在黑斯廷斯期間住在海邊的聖倫納茲上迷宮山(Upper Maze Hill)的巴斯頓旅館。旅館外有一塊藍色牌匾[27],在2012年6月23日圖靈百歲誕辰紀念日揭幕[28]。
圖靈兒時天賦異稟,鑄就了他日後天才的人生[29]。1927年,父母在吉爾福德買下一棟房子,學校放假的時候,圖靈就會在那邊。房子外也有一塊藍色牌匾[30]。
教育
[編輯]圖靈6歲到9歲在海邊的聖倫納茲查爾斯路20號(20 Charles Road)聖邁克爾斯小學(St Michael's)就讀。校長非常認可圖靈的才華,說自己見過很多聰明、刻苦用功的男孩,但「圖靈完全是天才」[31]。
1922年至1926年,圖靈來到薩塞克斯郡(今東薩塞克斯郡)法蘭特村私立學校黑茲赫斯特預科學校(Hazelhurst Preparatory School)讀書[32],之後在1926年以13歲之齡轉學到多塞特郡商業重鎮謝爾本寄宿私立學校謝爾本學校[33],借住韋斯科特之家(Westcott House)。圖靈上學第一天恰逢1926年英國大罷工,但他毅然決定上學,獨自踩着自行車,從南安普頓騎了60英里(97公里)的路程,去謝爾本上學,中途在一家客棧過夜[34]。
圖靈天生喜歡數學和科學,但謝爾本的學校更看重古典學的教學,所以那裡的老師看不起他。校長曾寫信給他的父母:「我希望他將來不會落到兩頭不到岸的境地。如果他要留在公立學校,就必須要用『知識淵博』的模樣。如果他只想成為『科學專家』,那他待在公立學校就是浪費時間[35]。」儘管如此,圖靈還是在自己喜歡的研究領域大放異彩:1927年,沒接觸初級的微積分學知識的他,已經可以解決高級的難題。1928年,16歲的圖靈接觸到阿爾伯特·愛因斯坦的著作,不僅掌握到書中的內容,而且還從意義含糊的文字中,推測到愛因斯坦對牛頓運動定律有所質疑[36]。
克里斯托弗·莫科姆
[編輯]圖靈在謝爾本結識到同窗好友克里斯托弗·科蘭·莫科姆(Christopher Collan Morcom,1911年7月13日—1930年2月13日)[37],他是圖靈的「初戀」。兩人的浪漫關係鼓勵圖靈過好之後的人生,但最終因莫科姆於1930年2月去世而告終。幾年前,莫科姆飲用受污染的牛奶,患上牛結核病,最終因該病併發症病逝[38][39][40]。
圖靈陷入莫大的悲傷,需要更加努力研究和莫科姆一起提出的科學和數學課題,才能分散注意力。圖靈在寫給莫科姆母親的信中說:
我敢肯定,這麼聰明、有魅力、不自負的伴侶,我在別的地方不可能找到。我對自己研究及天文學(他帶我進去的)的興趣,可以和他分享。他對我的感覺,我認為也有點是這樣的......我必須將更多的精力投入到自己的研究中,就好像他還在世一樣,因為這是他希望我去做的事情[41]。
莫科姆死後,圖靈和他母親一直保持聯繫。到了莫科姆忌日,圖靈一般會寫信給對方,對方則給他寄禮物[42]。莫科姆第三個忌日的前一天(1933年2月13日),圖靈寫信給他母親:
希望您收到這封信的時候,能想起克里斯。我也會想起他。之所以給您寫這封信,是想告訴您,明天我和您一樣會想起克里斯。我敢相信,如果他還在,一定會很開心。您深情的艾倫[43]。
部分人推測莫科姆的死讓圖靈不信教,成為唯物主義者[44]。顯然,到了這個時候,他仍然認為精神獨立於肉體,肉體死亡,精神永存。後來他在寫給莫科姆母親的信中說:
在我看來,精神確實永遠跟物質聯繫在一起,但肯定不會和肉體那樣的物質串連......至於精神和肉體間的實際關聯,我認為肉體可以保存『精神』,但肉體是活着的、醒着的,兩者緊密聯繫。肉體沉睡的時候,我猜不出肉體會發生什麼。但肉體消亡的時候,肉體的『機制』,保存中的『精神』消失了,精神遲早或者馬上去找一副新的肉體[45][46]。
大學生涯與可計算性的研究工作
[編輯]離開謝爾本,圖靈於1931年到1934年在劍橋大學國王學院讀本科[7],取得數學系一等榮譽。1935年,22歲的圖靈憑藉證明中心極限定理的畢業論文,成為國王學院院士[47]。不過委員會不知道該定理早在1922年就被賈爾·瓦爾德馬·林德伯格證明[48]。
1936年,圖靈發表論文《論可計算數與其在可判定性中的應用》[49]。文章於11月30日和12月23日分兩篇在《倫敦數學學會會刊》(Proceedings of the London Mathematical Society)發表[50]。在該論之前,庫爾特·哥德爾已於1931年發表了證明與計算的極限相關的結果,後來被稱作哥德爾不完備定理,而圖靈則修改哥德爾文章中的部分設定,將哥德爾的泛算術基礎的形式語言修改成一個簡單而形式的理想裝置,也就是眾所周知的圖靈機。1928年,德國數學家大衛·希爾伯特首次提出問題的可判定性這一概念,並且,圖靈證明他的「泛計算裝置」有能力執行所有可以用演算法表示出來的數學計算。
他之後繼續證明決定性問題無解,一開始是提出停機問題是圖靈機的決定性問題,不可能通過算法判斷圖靈機會不會停止。這篇論文被認為「很容易成為歷史上最有影響力的數學論文」[51]。
![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/46/20130808_Kings_College_Front_Court_Fountain_Crop_03.jpg/220px-20130808_Kings_College_Front_Court_Fountain_Crop_03.jpg)
圖靈證明發表前不久,阿隆佐·邱奇才自己的Λ演算法提出等價的證據[52],但圖靈的方法比邱奇更簡單、更直觀[53]。圖靈在證明中構思一種了「通用機」,也就是現在的通用圖靈機,認為這種機器能執行其他計算機器的任務(這一點邱奇的Λ演算法確實能做到)。根據邱奇-圖靈論題,圖靈機和Λ演算法能夠計算一切可計算的事物。約翰·馮·諾伊曼認為現代計算機的中央思想源於圖靈的論文[54]。時至今日,圖靈機仍是計算理論研究領域的重點課題。
1936年9月到1938年7月,圖靈大部分時間都在普林斯頓大學師從邱奇[4],第二年出任簡·伊麗莎·普羅克特訪問學者。除了單純研究數學,圖靈還鑽研密碼學,完成了電動乘法器四個建造階段的前三個[55]。1938年6月,獲普林斯頓大學數學系博士學位[56],其論文《基於序數的邏輯系統》[57][58]介紹了序數邏輯概念及相對的計算方法。約翰·馮·諾伊曼想請他當博士後助理,但他回到了英國[59]。
研究
[編輯]當圖靈回到劍橋時,他參加了1939年路德維希·維特根斯坦關於數學基礎的講座。[60]講座已根據學生的筆記逐字重建,包括圖靈和其他學生的感嘆詞。[61]圖靈和維特根斯坦爭論不休,圖靈為數學形式辯護,而維特根斯坦提出他的觀點,即數學不發現任何絕對真理,而是發明它們。[62]
密碼分析
[編輯]在第二次世界大戰期間,圖靈是在布萊切利園破解德國密碼的主要參與者。歷史學家和戰時密碼破譯者Asa Briggs曾說過:「你需要非凡的才能,你需要布萊切利的天才,而圖靈就是那個天才。」[63]
1938年9月起,圖靈在英國密碼破譯機構政府密碼學校兼職,與高級密碼破解員第利·諾克斯專責對納粹德國的恩尼格瑪機進行密碼解析[64]。1939年7月,波蘭密碼局在華沙附近召集會議,向英國和法國提供了恩尼格瑪機轉子的接線,以及他們解碼恩尼格瑪密碼機信息的方法。圖靈和諾克斯依照這些信息,開發出更為廣泛的方案[65]。波蘭的方法依賴並不安全的分析儀手段,這個環節德國人很容易更改,實際上他們在1940年5月改過一次。圖靈的方法更加通用,用的是基於嬰兒床的破解方法(「嬰兒床」為布萊切利園對任何已知明文或可疑明文的代稱),並以此開發出炸彈機(波蘭炸彈機的改良版)的功能參數[66]。
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Turing_flat.jpg/220px-Turing_flat.jpg)
1939年9月4日,英國對德國宣戰的第二天,圖靈來到政府密碼學校的戰時站點布萊切利園報道[67]。和其他來報道的人一樣,他需要簽署《官方保密法》,同意不透露布萊切利園的工作內容,否則因違反法律而面臨嚴重的法律處罰[68]。
指明炸彈機是圖靈在戰時為密碼分析學取得的其中一項重大進展,另外四項為推導德國海軍使用的分析儀程序、開發代號班布里莫斯的統計程序提供密碼機運作效率、開發代號圖靈里的程序找出洛倫茲 SZ 40/42密碼機凸輪的設置,以及在戰爭快結束的時候為漢斯洛普園開發代號「大麗花」的加密語音加擾器。
圖靈在解密過程中,利用統計技術優化對不同概率的試驗,為這一課題作出突出貢獻。他在《概率在密碼學中的應用》(The Applications of Probability to Cryptography)[69]和《關於重複的統計論文》(Paper on Statistics of Repetitions)[70]兩篇文章中討論的數學方法,受到密碼學校和後來的政府通信總部重視,相關內容直到圖靈百歲誕辰2012年4月前才由英國國家檔案館公開。僅自稱「理查德」(Richard)的政府通信總部數學家當時曾說,這些內容按照《官方保密法》被保密約70年,足以證明其重要性及對戰後密碼分析學的關聯性[71]:
他表示,這些內容一直被限制,『證明它對我們學科的基礎有着非常大的重要性』......這些論文詳細記述用『數學分析找出最有可能的設定,方便破譯人員儘可能迅速地進行嘗試』的方法......理查德說政治通信總部現在已經『榨乾了(兩篇論文)的果汁』,『願意把他們放上公有領域』。
圖靈在布萊切利園是出了名的古怪,同事一般叫他『教授』,把他對恩尼格瑪機的內容稱為「教授的著作」[72]。根據歷史學家羅納德·勒溫,曾和圖靈共事的密碼分析師傑克·古德回憶道:
每年六月第一個禮拜,他都會患上嚴重的花粉症。他騎自行車去辦公室的時候,都會戴上軍用防毒面具,防止吸入花粉。他的自行車有個毛病,就是鏈條會定期鬆脫,但他不拿去修理,而是依照踏板轉動次數算出它什麼時候會掉下來,那到時候,他就會親手換鏈條了。他還有個毛病,就是把馬克杯用鐵鏈拴在暖氣管上,防止別人偷走[73]。
彼得·希爾頓在《美國百年數學史》一書的文章《布萊切利園的回憶》中,提到自己和圖靈共事的經歷[74]:
遇見真正的天才是一種很罕見的體驗。我們這些生活在學術世界的人,都很熟悉被才華橫溢的同事醍醐灌頂的體驗。我們可以欣賞他們的想法,一般也能理解他們的想法從何而來。我們甚至經常以為自己也能提出這樣的概念,誕生這樣的想法。但是,和天才頭腦碰撞的體驗是完全不同的,就像一個人意識到自己站在天才的面前,對方又有着深度和獨創性非常高的敏感性,會變得訝異和興奮,而艾倫·圖靈就是那樣的天才。而像我一樣,因為第二次世界大戰的詭異緊張興奮得到驚人且意想不到的機會,和圖靈做同事和朋友的人們,永遠不會忘記那段經歷,永遠不會丟失他給我們帶來的深厚影響。
希爾頓在公共廣播電視公司Nova紀錄片《解碼納粹秘密》(Decoding Nazi Secrets)也提到類似的想法[75]。
在布萊切利園工作期間,身為長跑健將的圖靈經常跑40英里(64公里)的路去倫敦開會[76],跑步水平達到世界級馬拉松標準[77][78]圖靈參加1948年英國奧運代表隊試訓,但因為受傷退出。他的馬拉松試訓成績只比憑藉2小時35分鐘獲得銀牌的英國選手托馬斯·理查德(Thomas Richards)慢了11分鐘。圖靈是沃爾頓競技俱樂部(Walton Athletic Club)的最佳跑手,這個事實是他在超越大部隊獨自奔跑時發現的[79][80][81]。
被問到為什麼這麼努力地練跑步,他說:
我的工作很緊張,只有在努力跑步的時候才能忘掉,這是我釋放壓力的唯一方式[82]。
由於一些反事實歷史的問題,Ultra情報部門在二戰期間發揮的確切作用很難估計[83]。但是,官方戰爭歷史學家哈里·欣斯利估計這項研究將歐洲的戰事縮短了兩年多,拯救了1400萬人[84]。
戰爭結束時,布萊切利園的員工都收到一份備忘錄,提醒他們《官方保密法》的效力並不會隨着戰爭結束而失效,而是一直持續下去[68]。正因為如此,圖靈1946年因戰時的工作獲國王喬治六世頒發大英帝國勳章後,其研究成果仍被保密許多年[85][86]。
解碼器「炸彈」
[編輯]在到達布萊切利園的幾週內[67],圖靈優化波蘭解碼器「炸彈」,成功加速破解納粹德國的恩尼格瑪密碼機,從而設計出自己的同名機電裝置「炸彈」,不過波蘭的解碼器名是波蘭語的炸彈 bomba,而圖靈則是以法語將他的解碼器命名為 bombe。接受了數家Gordon Welchman的建議而做出修正之後,圖靈的「炸彈」成為了衝擊恩尼格瑪密碼機加密資訊最重要的手段之一,也成為最主要的所有自動化工具。[87]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Bombe-rebuild.jpg/220px-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: 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),[88] the bombe performed a chain of logical deductions based on the crib, implemented electromechanically.[89]
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.[90]
By late 1941, Turing and his fellow cryptanalysts Gordon Welchman, Hugh Alexander and Stuart Milner-Barry were frustrated. Building on the 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.[91]
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.[91] As Andrew Hodges, biographer of Turing, later wrote, "This letter had an electric effect."[92] Churchill wrote a memo to 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.[92] 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."[93] More than two hundred bombes were in operation by the end of the war.[94]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Turing-statue-Bletchley_14.jpg/170px-Turing-statue-Bletchley_14.jpg)
8號營房與海軍恩尼格瑪機
[編輯]圖靈決定解決德國海軍謎團這一困難問題,"因為沒有人在做這方面的工作,我可以自己來做。"」。[96] 1939年12月,圖靈解決了海軍指示系統的基本部分,它比其他部門使用的指示系統更複雜。[96][97]
同一天晚上,他還構思了 Banburismus的想法,這是一種順序統計技術(沃德·亞伯拉罕後來稱之為順序分析),以協助破解海軍英格瑪,"儘管我不確定它在實踐中是否可行,事實上,直到有些日子真的破解了才確定。[96] 為此,他發明了一種衡量證據重要性的標準,他稱之為禁令 (單位)。禁令可以排除恩尼格瑪機轉子的某些序列,大大減少了在炸彈上測試設置所需的時間。[98] 後來,這種用分班(禁令的十分之一)積累足夠的證據重量的順序過程被用於洛倫茲密碼的加密分析。[99]
1942年11月,圖靈前往美國[100],在華盛頓與美國海軍的密碼學家一起研究海軍的英尼碼和轟炸機的構造;他還參觀了他們在俄亥俄州代頓的電腦實驗室。
圖靈對美國轟炸機設計算不上有興趣:
美國的轟炸機計劃是要生產336架轟炸機,每個輪子都有一個。我曾經對這一方案所隱含的炸彈人小屋程序的概念暗自發笑,但認為指出我們不會真正以這種方式使用它們,並沒有什麼特別的目的。 他們的測試(換向器)很難被認為是完成品,因為他們沒有用電子止動器來測試反彈。似乎沒有人被告知 rods or offiziers or banburismus ,除非有意改進。[101]
在這次旅行中,他還在貝爾實驗室協助開發安全語音設備[102] 他於1943年3月返回布萊切利莊園。在他離開期間,Hugh Alexander正式擔任了8號小屋的負責人,儘管亞歷山大在一段時間內一直是事實上的負責人(圖靈對該部門的日常運作興趣不大)。圖靈成為布萊切利莊園密碼分析的一般顧問。[103]
亞歷山大在談到圖靈的貢獻時寫道。:
任何人都不應該懷疑,圖靈的工作是Hut 8成功的最大因素。在早期,他是唯一認為這個問題值得解決的密碼學家,他不僅主要負責小屋內的主要理論工作,而且他還與韋爾奇曼和基恩分享了發明炸彈的主要功勞。要說誰是 "絕對不可缺少的 "總是很困難的,但如果說誰是第八小屋不可缺少的,那就是圖靈。當經驗和例行公事後來使一切看起來都很容易時,先驅者的工作總是傾向於被遺忘,而我們第8小屋的許多人認為,圖靈的貢獻之大從未被外部世界充分認識。[104]
圖靈方法
[編輯]1942年7月,圖靈設計了一種被稱為 Turingery(或開玩笑說是Turingismus)[105]的技術,用於對付德國人新的秘密作家(德語:Geheimschreiber)機器產生的 洛倫茲密碼 密碼信息。這是在布萊切利莊園的一個teleprinter rotor cipher attachment的密碼附件,代號為Tunny。Turingery是一種wheel-breaking的方法 i.e., a procedure for working out the cam settings of Tunny's wheels.[106]他還將Tunny團隊介紹給了Tommy Flowers即是在Max Newman的指導下,Max Newman,建造巨人計算機的學者,巨人計算機是世界上第一台可編程的數字電子計算機,它取代了之前更簡單的機器(the Heath Robinson),其卓越的速度使統計解密技術能夠有效地應用於信息。[107]有些人錯誤地認為圖靈是巨人計算機計算機設計中的關鍵人物。圖靈里和班伯里斯的統計方法無疑為洛倫茲密碼的密碼分析提供了思路,cryptanalysis of the Lorenz cipher,[108][109]但他沒有直接參與Colossus的開發。[110]
黛利拉
[編輯]圖靈在貝爾實驗室工作後,[111] 致力於對電話系統中的語音進行加密。戰爭後期,他轉到漢斯洛普公園的特勤局無線電安全處 (即後來的HMGCC)。 在工程師Donald Bayley的協助下,他進一步學習了電子方面的知識,並一起設計製造了一個代號為Delilah的便攜式安全語音通訊機。[112] 這台機器適應於多種不同的用途,但它缺乏長距離無線電傳輸的能力。 無論如何,Delilah都發明得太遲,無法在戰爭期間使用。 儘管該系統完全可以運作,圖靈也向官員展示過——用它來加密和解密邱吉爾的演講錄音,Delilah仍然並未被採用。[113]圖靈也與貝爾實驗室協商開發 SIGSALY,這是一種在戰爭末期使用的安全語音系統。
雛形計算機與圖靈測試
[編輯]![](http://upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Alan_Turing_78_High_Street_Hampton_blue_plaque.jpg/220px-Alan_Turing_78_High_Street_Hampton_blue_plaque.jpg)
在1945和1947年間,圖靈在漢普頓 (倫敦)居住,[114] 其時他在英國國家物理實驗室研究自動計算機(Automatic Computing Engine)的設計。 他在1946年2月19日發表了一片論文,它是存儲程序計算機的第一個細節的設計。[115]馮·諾伊曼 不完整的「EDVAC報告書的第一份草案」比圖靈的論文早,但它的細節少很多,並且,根據NPL 數學部主管John R. Womersley,它「包含一些圖靈自己的想法」。[116]
雖然ACE是一個可行的設計,但是圍繞布萊切利園戰時工作的Official Secrets Act使得圖靈不可能解釋他分析包括人類操作者的計算機安裝的基礎。.[117] 這導致了項目開始的延遲,他的幻想破滅了。在1947年末,他返回了劍橋,度過了一個休假年。在此期間,他創作了一部關於智能機械的開創性工作,它在圖靈的有生之年裡沒有出版。[118] 當他在劍橋時,沒有他的情況下建造了Pilot ACE。它在1950年5月10日運行了第一個程序,世界各地的許多後來的計算機都歸功於它,包括English Electric DEUCE 和美國的 Bendix G-15。圖靈的ACE的完整版本直到他去世也沒有被建造。[119]
根據Genscher, Düsseldorf發表的德國計算機先驅者,馬克斯·普朗克物理學研究所的Heinz Billing回憶錄,圖靈和康拉德·楚澤曾經有過一次見面。[120] 它在1947年哥廷根發生。審問採用座談會的形式。 參與者是來自英格蘭的 Womersley、Turing、Porter 和一些德國研究人員,如 Zuse、Walther 和 Billing(更多詳細信息請參見 Herbert Bruderer、Konrad Zuse und die Schweiz)。
1948年,圖靈被任命為曼徹斯特維多利亞大學數學系reader。一年後,他成為了計算機器實驗室副主任,他在其研究最早的馮·諾伊曼結構計算機之一,曼切斯特1型的軟件。圖靈撰寫了這台機器的第一版程序員手冊,並被 Ferranti 聘為他們商業化機器 Ferranti Mark 1 開發的顧問。直到他去世,Ferranti 仍然繼續向他支付諮詢費。.[121]在這段時間,他繼續做更加抽象的數學工作, [122] 在「Computing Machinery and Intelligence」(Mind,1950 年 10 月)中,圖靈解決了人工智能的問題,並提出了一個後來被稱為圖靈測試的實驗,試圖為稱為「智能」的機器定義一個標準。想法是一台計算機可以被認為「思考」,如果一個人類審問者不能通過談話將其與一個人類分開。[123]論文中,圖靈建議與其建立一個模擬成年人意識的程序,不如先建立一個模擬孩童思想的程序,然後讓它接受教育。一個圖靈測試的反向形式在因特網上被廣泛地使用;驗證碼測試是為了確定用戶是人類還是機器人。
在1948年,圖靈與他的前本科同事 D.G. Champernowne 工作,開始為一個尚不存在的電腦編寫一個國際象棋程序。到了1950年,程序已經完成,並被稱為Turochamp。[124]在1952年,他嘗試在Ferranti Mark 1上實現它,但是計算機由於缺乏足夠功率,無法運行程序。替代地,圖靈通過在棋盤上執行算法的指令,每次移動大約半小時,「運行」了程序。這場棋局被記錄下來。[125] 根據加里·基莫維奇·卡斯帕羅夫,圖靈的程序「下了一盤有辨識度的國際象棋。」[126]程序輸給了圖靈的同事Alick Glennie,雖然說它跟Champernowne的妻子Isabel贏了一局。[127]
他的圖靈測試對關於人工智能的辯論做出了重要的、典型的、刺激的和持久的貢獻,這場辯論在半個多世紀後仍在繼續。[128]
圖靈斑圖與數理生物學
[編輯]1951年,圖靈39歲,他轉向數理生物學,終於在1952年1月,發表名篇〈形態發生的化學基礎〉。圖靈有志研究形態發生,即生物體的形態、圖案如何產生。他提出,一個反應-擴散系統,即若干種化學物質一邊互相反應,一邊擴散而形成的系統,可以解釋「形態發生的主要現象」("the main phenomena of morphogenesis")。[129]他探用偏微分方程組,為有催化的化學反應建模。例如,若某化學反應需要催化劑甲才發生,但該反應本身亦產生催化劑甲,則稱該反應自催化,是個正回饋系統,可以用非線性微分方程描述。圖靈發現,若反應不僅產生催化劑甲,還同時產生抑制劑乙,抑劑甲的產生,而兩者以不同的速率在容器中擴散,則可以有某些區域由甲佔主導,另一些區域由乙主導,從而產生圖案。若要準確模擬此現象,需要強大的電腦,但在1951年不易取用,所以圖靈僅能考慮方程的線性近似,以紙筆解出。其計算給出正確的定性結論,例如推斷出由某種均勻混合物開始,可以出奇地產生固定間距的紅點。俄國生化學家鮑里斯·別洛烏索夫曾得出類似的實驗結果,但未能發表論文,因為當時的成見認為,任何此種現象必然違反熱力學第二定律。別氏未曾知道圖靈在《自然科學會報》發表了論文。[130]:126
雖然圖靈發表論文的時間,尚早於學界明白DNA結構和功用的時間,但圖靈對形態發生的研究,至21世紀仍具意義,在數理生物領域被視為具開創性。[131]作為該論文的早期應用,詹姆士·莫瑞解釋了大小貓科動物的毛如何形成斑點與條紋。[132]:80[133][130]:134後續研究指出,生物之所以長出「羽毛、毛囊、肺的分枝結構」,甚至為何有「將心臟置於左胸的左右不對稱性」,皆可由圖靈的論文部分解釋。[134]2012年,舍思等人發現,移除鼠的同源異形基因,會增加指頭的數目,而不改變肢體的整體大小,推論該種基因控制指頭生長的機制,是藉由調校某個圖靈斑圖的波長(即前段機制中,圖案的間距)。[135]此後圖靈的論文,要待1992年《圖靈文集》(Collected Works of A. M. Turing)出版,才見諸市面。[136]
個人生活
[編輯]訂婚
[編輯]1941年,圖靈向Hut 8的同事、數學家和密碼分析師Joan Clarke求婚,然而他們的訂婚很短暫。在向未婚妻承認了自己的同性戀身份後,圖靈決定不再繼續這段婚姻,據報道其未婚妻對這一消息「泰然自若」。[137]
猥褻罪
[編輯]1952年1月,39歲的圖靈與19歲無業男子阿諾德·穆雷(Arnold Murray)相戀。在上一年聖誕節前夕,圖靈走在曼徹斯特的牛津路,在富豪電影院門外遇到穆雷,遂請他共進午餐。1月23日,圖靈家遭竊,穆雷說自己和盜竊犯是熟人,圖靈則向警方報告案件。調查期間,圖靈承認自己愛上穆雷。然而同性戀當時在英國屬於刑事犯罪[138],兩人最終按照《1885年刑法修正案》第11條被控「嚴重猥褻罪」[139]。案件預審於同年2月27日舉行,期間圖靈律師「保留辯護權利」,即沒有就相關指控提出證據或進行辯護。
後來在哥哥及辯護律師的說服下,圖靈選擇認罪[140]。案件最終以「女王訴圖靈及穆雷案」的名義於1952年3月31日正式開審[141]。圖靈選擇認罪,可以在服刑及緩刑之間做出選擇,而緩刑的條件是同意進行激素的治療,以降低性衝動。圖靈選擇注射當時叫做芪雌酚(也就是現在的己烯雌酚)的合成雌性激素,身體會在之後一年產生雌性反應,包括出現勃起功能障礙、乳房組織發育[142]。這種感受直接和圖靈的預測相吻合:「毫無疑問我會變成一個完全不同的男人,還沒有遇到過的那種[143][144]。」與此同時,穆雷獲得有條件假釋[145]。
被判刑後,圖靈從事安全工作的資格被撤銷,無法在英國信號情報機構政府通信總部擔任密碼學顧問,但他可以繼續從事學術工作。除此之外,圖靈也無法進入美國,但可以自由前往其他歐洲國家[146]。
死亡
[編輯]![](http://upload.wikimedia.org/wikipedia/commons/thumb/1/19/Turing_Plaque.jpg/220px-Turing_Plaque.jpg)
1954年6月8日,圖靈於威姆斯洛艾靈頓路43號的家中[147]被其管家發現已經身亡,時年41歲。他的死被判定為是由氰化物中毒導致[148]。當他的屍體被發現時,其床邊有一個吃了一半的蘋果。雖然蘋果本身沒有驗出氰化物[149],仍然有猜測認為圖靈通過進食這個蘋果吸取了致命劑量的氰化物。隨後進行的死因研訊斷定圖靈是自殺。霍奇斯及另一名傳記作者大衛·萊維特皆推測圖靈是在重演華特·迪士尼在1937年製作的《白雪公主》電影的一幕,因為該故事是圖靈最喜愛的童話。萊維特在著作中提到他與霍奇斯皆認為圖靈「特別為故事中壞王后把蘋果浸進毒藥的一幕著迷」[150]。
圖靈的遺體在1954年6月12日[151]於沃金火葬場火化。與其父一樣,圖靈的骨灰被散到火葬場花園內的每一角落[152]。
哲學家傑克·科普蘭對有關當局的結論感到質疑,並對提出了另一個解釋:圖靈可能是意外吸入電鍍裝置釋出的氰化物氣體而死。當時圖靈在一個小房間裏設置了一個在餐匙上鍍金的實驗裝置,而氰化鉀因為能溶解金而成為這個實驗的必需品。科普蘭指出,圖靈的驗屍報告顯示他較可能是吸入毒氣而非服用毒物。此外,圖靈睡前有進食蘋果的習慣,而他沒吃完蘋果就把它放下也是很正常的事[15]。與此同時,從已知的紀錄顯示,圖靈本人對他被定罪和被迫服食荷爾蒙的事「一笑置之」(而且在他去世時,他已經停止服藥達一年),而他去世前亦沒有任何抑鬱跡象。他甚至寫下了一個在度假後打算完成的事項清單,顯示他十分期待自己恢復工作[15]。圖靈的母親亦相信兒子是意外身亡,因為他並不謹慎處理實驗用的化學物品[16]。為圖靈作傳的安德魯·霍奇斯則認為圖靈故意在母親面前安排運送實驗器材,讓她得知人們指稱他是自殺而死時,可加以否認[17]。
![](http://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Alan_Turing_OBE.jpg/220px-Alan_Turing_OBE.jpg)
It has been suggested that Turing's belief in fortune-telling may have caused his depressed mood.[152] As a youth, Turing had been told by a fortune-teller that he would be a genius. In mid-May 1954, shortly before his death, Turing again decided to consult a fortune-teller during a day-trip to St Annes-on-Sea with the Greenbaum family.[152] According to the Greenbaums' daughter, Barbara:[153]
But it was a lovely sunny day and Alan was in a cheerful mood and off we went... Then he thought it would be a good idea to go to the Pleasure Beach at Blackpool. We found a fortune-teller's tent[,] and Alan said he'd like to go in[,] so we waited around for him to come back... And this sunny, cheerful visage had shrunk into a pale, shaking, horror-stricken face. Something had happened. We don't know what the fortune-teller said[,] but he obviously was deeply unhappy. I think that was probably the last time we saw him before we heard of his suicide.
政府道歉與赦免
[編輯]In August 2009, British programmer John Graham-Cumming started a petition urging the British government to apologise for Turing's prosecution as a homosexual.[154][155] The petition received more than 30,000 signatures.[156][157] The Prime Minister, Gordon Brown, acknowledged the petition, releasing a statement on 10 September 2009 apologising and describing the treatment of Turing as "appalling":[156][158]
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 ... 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.[156][159]
In December 2011, William Jones and his Member of Parliament, John Leech, created an e-petition[160] requesting that the British government pardon Turing for his conviction of "gross indecency":[161]
We ask the HM Government to grant a pardon to Alan Turing for the conviction of "gross indecency". In 1952, he was convicted of "gross indecency" with another man and was forced to undergo so-called "organo-therapy"—chemical castration. Two years later, he killed himself with cyanide, aged just 41. Alan Turing was driven to a terrible despair and early death by the nation he'd done so much to save. This remains a shame on the British government and British history. A pardon can go some way to healing this damage. It may act as an apology to many of the other gay men, not as well-known as Alan Turing, who were subjected to these laws.[160]
The petition gathered over 37,000 signatures,[160][162] and was submitted to Parliament by the Manchester MP John Leech but the request was discouraged by Justice Minister Lord McNally, who said:[163]
A posthumous pardon was not considered appropriate as Alan Turing was properly convicted of what at the time was a criminal offence. He would have known that his offence was against the law and that he would be prosecuted. It is tragic that Alan Turing was convicted of an offence that now seems both cruel and absurd—particularly poignant given his outstanding contribution to the war effort. However, the law at the time required a prosecution and, as such, long-standing policy has been to accept that such convictions took place and, rather than trying to alter the historical context and to put right what cannot be put right, ensure instead that we never again return to those times.[164]
John Leech, the MP for Manchester Withington (2005–15), submitted several bills to Parliament[165] and led a high-profile campaign to secure the pardon. Leech made the case in the House of Commons that Turing's contribution to the war made him a national hero and that it was "ultimately just embarrassing" that the conviction still stood.[166] Leech continued to take the bill through Parliament and campaigned for several years, gaining the public support of numerous leading scientists, including Stephen Hawking.[167][168] At the British premiere of a film based on Turing's life, The Imitation Game, the producers thanked Leech for bringing the topic to public attention and securing Turing's pardon.[169] Leech is now regularly described as the "architect" of Turing's pardon and subsequently the Alan Turing Law which went on to secure pardons for 75,000 other men and women convicted of similar crimes.[170][171][172][173][174][175][176][177][178][179][180]
On 26 July 2012, a bill was introduced in the House of Lords to grant a statutory pardon to Turing for offences under section 11 of the Criminal Law Amendment Act 1885, of which he was convicted on 31 March 1952.[181] Late in the year in a letter to The Daily Telegraph, the physicist Stephen Hawking and 10 other signatories including the Astronomer Royal Lord Rees, President of the Royal Society Sir Paul Nurse, Lady Trumpington (who worked for Turing during the war) and Lord Sharkey (the bill's sponsor) called on Prime Minister David Cameron to act on the pardon request.[182] The government indicated it would support the bill,[183][184][185] and it passed its third reading in the House of Lords in October.[186]
At the bill's second reading in the House of Commons on 29 November 2013, Conservative MP Christopher Chope objected to the bill, delaying its passage. The bill was due to return to the House of Commons on 28 February 2014,[187] but before the bill could be debated in the House of Commons,[188] the government elected to proceed under the royal prerogative of mercy. On 24 December 2013, Queen Elizabeth II signed a pardon for Turing's conviction for "gross indecency", with immediate effect.[189] Announcing the pardon, Lord Chancellor Chris Grayling said Turing deserved to be "remembered and recognised for his fantastic contribution to the war effort" and not for his later criminal conviction.[162][190] The Queen officially pronounced Turing pardoned in August 2014.[191] The Queen's action is only the fourth royal pardon granted since the conclusion of the Second World War.[192] Pardons are normally granted only when the person is technically innocent, and a request has been made by the family or other interested party; neither condition was met in regard to Turing's conviction.[193]
In September 2016, the government announced its intention to expand this retroactive exoneration to other men convicted of similar historical indecency offences, in what was described as an "Alan Turing law".[194][195] The Alan Turing law is now an informal term for the law in the United Kingdom, contained in the Policing and Crime Act 2017, which serves as an amnesty law to retroactively pardon men who were cautioned or convicted under historical legislation that outlawed homosexual acts. The law applies in England and Wales.[196]
影響
[編輯]獎項與榮譽
[編輯]![](http://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Alan_Turing_Building_1.jpg/220px-Alan_Turing_Building_1.jpg)
圖靈在1946年被授予大英帝國勳章官佐勳章[86],後在1951年當選為皇家學會院士[8]。 曼徹斯特作為圖靈自工作直至離世所居住的城市,用了各種方式來紀念他。1994年,曼徹斯特中的一段環路以其名字命名,這條路所行經的橋拓寬後亦以他爲名。在2001年6月23日,圖靈雕像在曼徹斯特大學和運河街附近的公園落成,這位「計算機科學之父」坐在公園中心位置的一張長椅上,手中還拿著一個象徵其自殺時使用的蘋果,身後的長椅鑄有據信為「計算機科學開創者」英文經恩尼格瑪密碼機加密後的字樣:「IEKYF ROMSI ADXUO KVKZC GUBJ」[d][197]。
![](http://upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Alan_Turing_Memorial.jpg/220px-Alan_Turing_Memorial.jpg)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Sackville_Park_Turing_plaque.jpg/220px-Sackville_Park_Turing_plaque.jpg)
雕像腳下的牌匾上寫著「計算機科學之父、數學家、邏輯學家、戰時密碼破譯者、偏見的受害者」。以及伯特蘭·羅素的名言:「數學,正確看待時,不僅具有真理,還具有至高的美—一種冷而嚴峻的美,一種如雕塑一般屹立不搖的美。」這位雕塑家將他自己的舊 Amstrad 計算機埋在了基座下,以此向「所有現代計算機的教父」致敬[198]。
1999年,《時代雜誌》提名圖靈爲時代100人:本世紀最重要的人物,並評價道:「時至今日,現在每個人敲擊鍵盤、打開電子表格或文字處理程序,都仍在使用所謂的圖靈機。」 [9] 2012 年 6 月 23 日,圖靈誕辰一百週年之際,一塊藍色牌匾在國王學院揭幕,現在安裝在該學院位於 King's Parade 的凱恩斯大樓 [199][200]。
2021 年 3 月 25 日,英格蘭銀行公佈了新版 50 英鎊紙幣的設計,背面印有圖靈的肖像,並在圖靈誕辰 6 月 23 日正式發行。圖靈於 2019 年經過公開提名被選為新肖像人選 [201]。
百年誕辰
[編輯]為紀念圖靈誕辰 100 週年,圖靈百年紀念諮詢委員會 (TCAC) 協調了艾倫圖靈年,這是一項為期一年的全球活動計劃,旨在紀念圖靈的生平和成就。 TCAC 由 S. Barry Cooper擔任主席,圖靈的侄子約翰·德莫特·圖靈爵士擔任名譽主席,合作者包括曼徹斯特大學的教職員工以及來自劍橋大學和布萊切利公園的人士。
鋼雕塑爭議
[編輯]2020年5月,據Gay Star News報道,為紀念圖靈,英國雕塑家Antony Gormley設計了一座 12英尺(3.7公尺) 的鋼製雕塑。Antony Gormley提案把雕塑建造在劍橋大學國王學院,但英格蘭歷史遺產保護局稱一座19塊鋼板組成的抽象雕塑「…與學院現有的特徵不符。這樣對於景觀和保護建築,以及對保護區的擴展都會造成一些不那麼具實質性的損害。」[202]
注釋
[編輯]參考資料
[編輯]- ^ 1.0 1.1 由Google學術搜索索引的艾倫·圖靈出版物。
- ^ 2.0 2.1 艾倫·圖靈在數學譜系計畫的資料。
- ^ Gandy, Robin Oliver. On axiomatic systems in mathematics and theories in physics (PhD論文). University of Cambridge. 1953 [2017-12-09]. doi:10.17863/CAM.16125. EThOS uk.bl.ethos.590164. (原始內容存檔於2017-12-09).
- ^ 4.0 4.1 喬納森·P·鮑文. The Impact of Alan Turing: Formal Methods and Beyond. 喬納森·P·鮑文; 劉志明; 張自立 (編). Engineering Trustworthy Software Systems. SETSS 2018 (PDF). 計算機科學講義 11430. Cham: Springer. 2019: 202–235. ISBN 978-3-030-17600-6. S2CID 121295850. doi:10.1007/978-3-030-17601-3_5. (原始內容存檔 (PDF)於2022-10-09) (英語).
- ^ Ivor Grattan-Guinness, Chapter 40, Turing's mentor, Max Newman. In Copeland, B. Jack; Bowen, Jonathan P.; Wilson, Robin; Sprevak, Mark. The Turing Guide. Oxford University Press. 2017. ISBN 978-0-19-874782-6.
- ^ Who was Alan Turing?. The British Library. [2019-07-29]. (原始內容存檔於2019-07-23).
- ^ 7.0 7.1 7.2 Anon. Turing, Alan Mathison
. 英国名人录. ukwhoswho.com 牛津大學出版社在線版 (布盧姆斯伯里出版公司旗下A & C Black). 2017. doi:10.1093/ww/9780199540884.013.U243891. 需要訂閱或英國公共圖書館會員資格
- ^ 8.0 8.1 Newman, M.H.A. Alan Mathison Turing. 1912–1954. Biographical Memoirs of Fellows of the Royal Society. 1955, 1: 253–263. JSTOR 769256. S2CID 711366. doi:10.1098/rsbm.1955.0019
.
- ^ 9.0 9.1 Gray, Paul. Alan Turing – Time 100 People of the Century. Time. 1999-03-29 [2011-01-10]. (原始內容存檔於2011-01-19) (英語).
Providing a blueprint for the electronic digital computer. The fact remains that everyone who taps at a keyboard, opening a spreadsheet or a word-processing program, is working on an incarnation of a Turing machine.
- ^ Sipser 2006,第137頁
- ^ Beavers 2013,第481頁
- ^ Copeland, Jack. Alan Turing: The codebreaker who saved 'millions of lives'. BBC News Technology. 2012-06-18 [2014-10-26]. (原始內容存檔於2014-10-11).
- ^ A number of sources state that Winston Churchill said that Turing made the single biggest contribution to Allied victory in the war against Nazi Germany. However, both The Churchill Centre and Turing's biographer Andrew Hodges have stated they know of no documentary evidence to support this claim, nor of the date or context in which Churchill supposedly said it, and the Churchill Centre lists it among their Churchill 'Myths', see Schilling, Jonathan. Churchill Said Turing Made the Single Biggest Contribution to Allied Victory. The Churchill Centre: Myths. 2015-01-08 [2015-01-09]. (原始內容存檔於2015-02-17). and Hodges, Andrew. Part 4: The Relay Race. Update to Alan Turing: The Enigma. [2015-01-09]. (原始內容存檔於2015-01-20). A BBC News profile piece that repeated the Churchill claim has subsequently been amended to say there is no evidence for it. See Spencer, Clare. Profile: Alan Turing. BBC News. 2009-09-11 [2015-02-17]. (原始內容存檔於2017-12-13).
Update 13 February 2015
Official war historian Harry Hinsley estimated that this work shortened the war in Europe by more than two years but added the caveat that this did not account for the use of the atomic bomb and other eventualities.Hinsley, Harry, The Influence of ULTRA in the Second World War, 1996 [1993] Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University - ^ Olinick, M. (2021). Simply Turing. United States: Simply Charly, ch. 15.
- ^ 15.0 15.1 15.2 Pease, Roland. Alan Turing: Inquest's suicide verdict 'not supportable'. BBC News. 2012-06-23 [2012-06-23]. (原始內容存檔於2012-06-23).
We have ... been recreating the narrative of Turing's life, and we have recreated him as an unhappy young man who committed suicide. But the evidence is not there.
- ^ 16.0 16.1 TURING, Ethel Sara (1881–1976, mother of Alan Turing). Series of 11 autograph letters to Robin Gandy, Guilford, 28 July 1954 – 11 June 1971 (most before 1959), altogether 29 pages, 8vo (2 letters dated 17 May and 26 May 1955 incomplete, lacking continuation leaves, occasional light soiling). christies.com. [2019-02-06]. (原始內容存檔於2019-02-07).
- ^ 17.0 17.1 Hodges 1983,第488, 489頁
- ^ 18.0 18.1 Hodges 1983,第5頁
- ^ The Alan Turing Internet Scrapbook. Alan Turing: The Enigma. [2012-01-02]. (原始內容存檔於2012-10-14).
- ^ Phil Maguire, "An Irishman's Diary", p. 5. The Irish Times, 23 June 2012.
- ^ London Blue Plaques. English Heritage. [2007-02-10]. (原始內容存檔於2009-09-03).
- ^ The Alan Turing Internet Scrapbook. [2006-09-26]. (原始內容存檔於2011-07-20).
- ^ The Scientific Tourist In London: #17 Alan Turing's Birth Place 網際網路檔案館的存檔,存檔日期2013-09-21., Nature. London Blog
- ^ Plaque #381 on Open Plaques.
- ^ Sir John Dermot Turing 網際網路檔案館的存檔,存檔日期2017-10-18. on the Bletchley Park website.
- ^ Hodges 1983,第6頁
- ^ Plaque unveiled at Turing's home in St Leonards. Hastings & St. Leonards Observer. 2012-06-29 [2017-07-03]. (原始內容存檔於2017-09-12).
- ^ St Leonards plaque marks Alan Turing's early years. BBC News. 2012-06-25 [2017-07-03]. (原始內容存檔於2017-12-03).
- ^ Jones, G. James. Alan Turing – Towards a Digital Mind: Part 1. System Toolbox. 2001-12-11 [2007-07-27]. (原始內容存檔於2007-08-03).
- ^ Guildford Dragon NEWS. The Guildford Dragon. 2012-11-29 [2013-10-31]. (原始內容存檔於2013-10-19).
- ^ Cawthorne, Nigel. Alan Turing : the enigma man. London. 2014: 18. ISBN 978-1-78404-535-7. OCLC 890938716.
- ^ Alan Mathison. Alan Turing Archive – Sherborne School (ARCHON CODE: GB1949) (PDF). Sherborne School, Dorset. April 2016 [2017-02-05]. (原始內容存檔 (PDF)於2016-12-26).
- ^ Alan Turing OBE, PhD, FRS (1912–1954). The Old Shirburnian Society. 2016-09-01 [2020-10-10] (英國英語).
- ^ Hofstadter, Douglas R. Metamagical Themas: Questing for the Essence of Mind and Pattern. Basic Books. 1985: 484. ISBN 978-0-465-04566-2. OCLC 230812136.
- ^ Hodges 1983,第26頁
- ^ Hodges 1983,第34頁
- ^ The Shirburnian
- ^ Caryl, Christian. Poor Imitation of Alan Turing. New York Review of Books. 2014-12-19 [2015-01-09]. (原始內容存檔於2015-01-07). 參數
|newspaper=
與模板{{cite web}}
不匹配(建議改用{{cite news}}
或|website=
) (幫助) - ^ Rachel Hassall, 'The Sherborne Formula: The Making of Alan Turing' 網際網路檔案館的存檔,存檔日期2014-04-15. 'Vivat!' 2012/13
- ^ Teuscher, Christof (編). Alan Turing: Life and Legacy of a Great Thinker. Springer-Verlag. 2004. ISBN 978-3-540-20020-8. OCLC 53434737.
- ^ Hodges 1983,第61頁
- ^ Hodges, Andrew. Alan Turing: The Enigma
. Princeton University Press. 2012: 87. ISBN 978-0-691-15564-7.
- ^ Hodges, Andrew. Alan Turing: The Enigma
. Princeton University Press. 2012: 90. ISBN 978-0-691-15564-7.
- ^ Paul Gray, Alan Turing 網際網路檔案館的存檔,存檔日期2011-01-19. Time Magazine's Most Important People of the Century, p. 2
- ^ Hodges 1983,第82–83頁
- ^ The Old Shirburnian Society
- ^ 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 網際網路檔案館的存檔,存檔日期2018-04-21. Journal Electronique d'Histoire des Probabilités et de la Statistique
- ^ Hodges 1983,第88, 94頁
- ^ Turing 1937
- ^ B. Jack Copeland; Carl J. Posy; Oron Shagrir. Computability: Turing, Gödel, Church, and Beyond. MIT Press. 2013: 211. ISBN 978-0-262-01899-9.
- ^ Avi Wigderson. Mathematics and Computation. Princeton University Press. 2019: 15. ISBN 978-0-691-18913-0.
- ^ Church 1936
- ^ Grime, James. What Did Turing Do for Us?. NRICH. University of Cambridge. February 2012 [2016-02-28]. (原始內容存檔於2016-03-04).
- ^ "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.
- ^ Hodges 1983,第138頁
- ^ Turing, A.M. Systems of Logic Based on Ordinals. Proceedings of the London Mathematical Society. 1939, s2–45: 161–228. doi:10.1112/plms/s2-45.1.161. hdl:21.11116/0000-0001-91CE-3
.
- ^ Turing, Alan. Systems of Logic Based on Ordinals (PhD論文). Princeton University. 1938. doi:10.1112/plms/s2-45.1.161. hdl:21.11116/0000-0001-91CE-3
. ProQuest 301792588.
- ^ Turing, A.M. Systems of Logic Based on Ordinals (PDF). 1938 [2012-02-04]. (原始內容 (PDF)存檔於2012-10-23).
- ^ John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More, Norman MacRae, 1999, American Mathematical Society, Chapter 8
- ^ Hodges 1983,第152頁
- ^ Cora Diamond (ed.), Wittgenstein's Lectures on the Foundations of Mathematics, University of Chicago Press, 1976
- ^ Hodges 1983,第153–154頁
- ^ Briggs, Asa. Britain's Greatest Codebreaker (TV broadcast). UK Channel 4. 2011-11-21.
- ^ Copeland, Jack. Colossus and the Dawning of the Computer Age. Smith, Michael; Erskine, Ralph (編). Action This Day. Bantam. 2001: 352. ISBN 978-0-593-04910-5.
- ^ Copeland 2004a,第217頁
- ^ Clark, Liat. Turing's achievements: codebreaking, AI and the birth of computer science (Wired UK). Wired. 2012-06-18 [2013-10-31]. (原始內容存檔於2013-11-02).
- ^ 67.0 67.1 Copeland, 2006 p. 378.
- ^ 68.0 68.1 Collins, Jeremy. Alan Turing and the Hidden Heroes of Bletchley Park: A Conversation with Sir John Dermot Turing. nationalww2museum.org. New Orleans: The National WWII Museum. 2020-06-24 [2021-08-24].
- ^ Turing, Alan. The Applications of Probability to Cryptography. c. 1941 [2015-03-25]. The National Archives (United Kingdom): HW 25/37. (原始內容存檔於2015-04-07).
- ^ Turing, Alan. Paper on Statistics of Repetitions. c. 1941 [2015-03-25]. The National Archives (United Kingdom): HW 25/38. (原始內容存檔於2015-04-08).
- ^ Vallance, Chris. Alan Turing papers on code breaking released by GCHQ. BBC News. 2012-04-19 [2012-04-20]. (原始內容存檔於2012-10-04).
- ^ Hodges 1983,第208頁
- ^ Lewin 1978,第57頁
- ^ Hilton, Peter. A Century of Mathematics in America, Part 1, Reminiscences of Bletchley Park (PDF). (原始內容存檔 (PDF)於2019-08-29).
- ^ Hilton, Peter. NOVA | Transcripts | Decoding Nazi Secrets | PBS. (原始內容存檔於2019-08-29).
- ^ Brown, Anthony Cave. Bodyguard of Lies: The Extraordinary True Story Behind D-Day. The Lyons Press. 1975. ISBN 978-1-59921-383-5.
- ^ Graham-Cumming, John. An Olympic honour for Alan Turing. The Guardian (London). 2010-03-10 [2016-12-10]. (原始內容存檔於2016-12-01).
- ^ Butcher, Pat. In Praise of Great Men. Globe Runner. 2009-09-14 [2012-06-23]. (原始內容存檔於2013-08-18).
- ^ Hodges, Andrew. Alan Turing: a short biography. Alan Turing: The Enigma. [2014-06-12]. (原始內容存檔於2013-09-14).
- ^ Graham-Cumming, John. Alan Turing: a short biography. The Guardian. 2010-03-10 [2014-06-12]. (原始內容存檔於2014-11-08).
- ^ Butcher, Pat. Turing as a runner. The MacTutor History of Mathematics archive. December 1999 [2014-06-12]. (原始內容存檔於2014-11-13).
- ^ Kottke, Jason. Turing was an excellent runner. kottke.org.
- ^ See for example Richelson, Jeffery T. A Century of Spies: Intelligence in the Twentieth Century. New York: Oxford University Press. 1997: 296. and Hartcup, Guy. The Effect of Science on the Second World War. Basingstoke, Hampshire: Macmillan Press. 2000: 96–99.
- ^ Hinsley, Harry, The Influence of ULTRA in the Second World War, 1996 [1993] Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University
- ^ Alan Turing: Colleagues share their memories. BBC News. 2012-06-23 [2018-06-21]. (原始內容存檔於2018-07-07).
- ^ 86.0 86.1 This month in history: Alan Turing and the Enigma code. thegazette.co.uk. [2019-02-06]. (原始內容存檔於2019-06-26).
- ^ Welchman, Gordon, The Hut Six story: Breaking the Enigma codes, Cleobury Mortimer, England: M&M Baldwin: 81, 1997 [1982], ISBN 978-0-947712-34-1
- ^ Jack Good in "The Men Who Cracked Enigma", 2003: with his caveat: "if my memory is correct".
- ^ The Turing-Welchman Bombe. The National Museum of Computing. [2021-03-18].
- ^ Oakley 2006,第40/03B頁
- ^ 91.0 91.1 Hodges 1983,第218頁
- ^ 92.0 92.1 Hodges 1983,第221頁
- ^ Copeland, The Essential Turing, pp. 336–337 網際網路檔案館的存檔,存檔日期2015-02-18..
- ^ Copeland, Jack; Proudfoot, Diane. Alan Turing, Codebreaker and Computer Pioneer. alanturing.net. May 2004 [2007-07-27]. (原始內容存檔於2007-07-09).
- ^ Bletchley Park Unveils Statue Commemorating Alan Turing. [2007-06-30]. (原始內容存檔於2007-06-30).
- ^ 96.0 96.1 96.2 Mahon 1945,第14頁
- ^ Leavitt 2007,第184–186頁
- ^ Gladwin, Lee. Alan Turing, Enigma, and the Breaking of German Machine Ciphers in World War II (PDF). Prologue Magazine. Fall 1997,. Fall 1997: 202–217 [2019-04-13]. (原始內容存檔 (PDF)於2019-06-26) –透過National Archives.
- ^ Good, Jack; Michie, Donald; Timms, Geoffrey, General Report on Tunny: With Emphasis on Statistical Methods, Part 3 Organisation: 38 Wheel-breaking from Key, Page 293, 1945 [2019-04-13], UK Public Record Office HW 25/4 and HW 25/5, (原始內容存檔於2019-04-21)
- ^ Hodges 1983,第242–245頁
- ^ Turing, Alan M. Visit to National Cash Register Corporation of Dayton, Ohio. Cryptologia. 2001, 25 (1): 1–10. S2CID 14207094. doi:10.1080/0161-110191889734.
- ^ Hodges 1983,第245–253頁
- ^ Marshall Legacy Series: Codebreaking – Events. marshallfoundation.org. [2019-04-07]. (原始內容存檔於2019-04-07).
- ^ Alexander & circa 1945,第42頁
- ^ Copeland 2006,第380頁
- ^ Copeland 2006,第381頁
- ^ Copeland 2006,第72頁
- ^ Gannon 2007,第230頁
- ^ Hilton 2006,第197–199頁
- ^ Copeland 2006,第382, 383頁
- ^ Hodges 1983,第245–250頁
- ^ Hodges 1983,第273頁
- ^ Hodges 1983,第346頁
- ^ Plaque #1619 on Open Plaques.
- ^ Copeland 2006,第108頁
- ^ Randell, Brian. A History of Computing in the Twentieth Century: Colossus (PDF). 1980 [2012-01-27]. (原始內容存檔 (PDF)於2012-01-27). citing Womersley, J.R. 'ACE' Machine Project. Executive Committee, National Physical Laboratory, Teddington, Middlesex. 1946-02-13.
- ^ Hodges, Andrew. Alan Turing: The Enigma. Princeton University Press. 2014: 416. ISBN 978-0-691-16472-4.
- ^ See Copeland 2004b,第410–432頁
- ^ Turing at NPL. [2015-07-03]. (原始內容存檔於2015-07-05).
- ^ Bruderer, Herbert. Did Alan Turing interrogate Konrad Zuse in Göttingen in 1947? (PDF). [2013-02-07]. (原始內容存檔 (PDF)於2013-05-21).
- ^ Swinton, Jonathan. Alan Turing's Manchester. Manchester: Infang Publishing. 2019 [2019-03-18]. ISBN 978-0-9931789-2-4. (原始內容存檔於2019-02-17).
- ^ Turing, A.M. Rounding-Off Errors in Matrix Processes. The Quarterly Journal of Mechanics and Applied Mathematics. 1948, 1: 287–308. doi:10.1093/qjmam/1.1.287. hdl:10338.dmlcz/103139.
- ^ Harnad, Stevan (2008) The Annotation Game: On Turing (1950) on Computing, Machinery and Intelligence 網際網路檔案館的存檔,存檔日期2017-10-18.. In: Epstein, Robert & Peters, Grace (Eds.) Parsing the Turing Test: Philosophical and Methodological Issues in the Quest for the Thinking Computer. Springer
- ^ Clark, Liat. Turing's achievements: codebreaking, AI and the birth of computer science. Wired. [2013-11-11]. (原始內容存檔於2013-11-02).
- ^ Alan Turing vs Alick Glennie (1952) "Turing Test" 網際網路檔案館的存檔,存檔日期2006-02-19. Chessgames.com
- ^ Kasparov, Garry, Smart machines will free us all, The Wall Street Journal, 15–16 April 2017, p. c3
- ^ O'Connor, J.J.; Robertson, E.F. David Gawen Champernowne. MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland. [2018-05-22]. (原始內容存檔於2017-10-19).
- ^ Pinar Saygin, A.; Cicekli, I.; Akman, V. Turing Test: 50 Years Later. Minds and Machines. 2000, 10 (4): 463–518. S2CID 990084. doi:10.1023/A:1011288000451. hdl:11693/24987
.
- ^ Turing, Alan M. The Chemical Basis of Morphogenesis. Philosophical Transactions of the Royal Society of London B. 1952-08-14, 237 (641): 37–72. Bibcode:1952RSPTB.237...37T. S2CID 120437796. doi:10.1098/rstb.1952.0012.
- ^ 130.0 130.1 Gribbin, John. Deep Simplicity. Random House. 2004.
- ^ Turing's Last, Lost work. [2011-11-28]. (原始內容存檔於2003-08-23).
- ^ Murray, James. How the leopard gets its spots. Scientific American. 1988-03, 258 (3): 80–87. JSTOR 24989019.
- ^ Murray, James D. 6. Reaction Kinetics. Mathematical Biology. I: An Introduction. Springer Verlag. 2002. doi:10.1007/b98868.
- ^ Vogel, G. Turing Pattern Fingered for Digit Formation. Science. 2012, 338 (6113): 1406. Bibcode:2012Sci...338.1406V. PMID 23239707. doi:10.1126/science.338.6113.1406.
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.
- ^ Sheth, R.; Marcon, L.; Bastida, M.F.; Junco, M.; Quintana, L.; Dahn, R.; Kmita, M.; Sharpe, J.; Ros, M.A. Hox Genes Regulate Digit Patterning by Controlling the Wavelength of a Turing-Type Mechanism. Science. 2012, 338 (6113): 1476–1480. Bibcode:2012Sci...338.1476S. PMC 4486416
. PMID 23239739. doi:10.1126/science.1226804.
- ^ Andrew Hodges. The Alan Turing Bibliography. turing.org.uk: morphogenesis. [2015-07-27]. (原始內容存檔於2015-09-05).
- ^ Leavitt 2007,第176–178頁
- ^ Hodges 1983,第458頁
- ^ Leavitt 2007,第268頁
- ^ Hodges, Andrew. Alan Turing: The Enigma
. Princeton University Press. 2012: 463. ISBN 978-0-691-15564-7.
- ^ Hodges, Andrew. Alan Turing: The Enigma
. Princeton University Press. 2012: 471. ISBN 978-0-691-15564-7.
- ^ Hodges, Andrew. Alan Turing: The Enigma The Centenary Edition. Princeton University. 2012.
- ^ Turing, Alan. Letters of Note: Yours in distress, Alan. 1952 [2012-12-16]. (原始內容存檔於2013-01-20).
- ^ Hodges, Andrew. Alan Turing: The Enigma
. Princeton University Press. 2012: xxviii. ISBN 978-0-691-15564-7.
- ^ Hodges 1983,第473頁
- ^ Copeland 2006,第143頁
- ^ 147.0 147.1 Anon. Turing's House: Copper Folly, 43 Adlington Road, Wilmslow, Cheshire, SK9 2BJ (PDF). savills.com. 2021. (原始內容 (PDF)存檔於2021-07-03).
- ^ Alan Turing. Biography, Facts, & Education. Encyclopædia Britannica. [2017-10-11]. (原始內容存檔於2017-10-11).
- ^ Hodges 1983,第488頁
- ^ Leavitt 2007,第140頁及Hodges 1983,第149, 489頁
- ^ Hodges 1983,第529頁
- ^ 152.0 152.1 152.2 Hodges, Andrew. Alan Turing: The Enigma. Random House. 2012 [2019-01-16]. ISBN 978-1-4481-3781-7. (原始內容存檔於2019-01-17).
- ^ Vincent Dowd. What was Alan Turing really like?. BBC. 2014-06-06 [2019-01-16]. (原始內容存檔於2019-01-17).
- ^ Thousands call for Turing apology. BBC News. 2009-08-31 [2009-08-31]. (原始內容存檔於2009-08-31).
- ^ Petition seeks apology for Enigma code-breaker Turing. CNN. 2009-09-01 [2009-09-01]. (原始內容存檔於2009-10-05).
- ^ 156.0 156.1 156.2 Davies, Caroline. PM's apology to codebreaker Alan Turing: we were inhumane. The Guardian (UK). 2009-09-11 [2016-12-10]. (原始內容存檔於2017-02-04).
- ^ The petition was only open to UK citizens.
- ^ PM apology after Turing petition. BBC News. 2009-09-11 [2009-09-11]. (原始內容存檔於2012-05-27).
- ^ Full text of the Prime Minister's apology 網際網路檔案館的存檔,存檔日期2012-11-09..
- ^ 160.0 160.1 160.2 Grant a pardon to Alan Turing. 2011-12-06. (原始內容存檔於2012-01-10).
- ^ Petition to pardon computer pioneer Alan Turing started. BBC News. 2011-12-06 [2018-06-21]. (原始內容存檔於2018-06-19).
- ^ 162.0 162.1 Wright, Oliver. Alan Turing gets his royal pardon for 'gross indecency' – 61 years after he poisoned himself. The Independent (London). 2013-12-23 [2017-08-21]. (原始內容存檔於2013-12-24).
- ^ Wainwright, Martin. Government rejects a pardon for computer genius Alan Turing. The Guardian. 2012-02-07 [2016-12-10]. (原始內容存檔於2017-02-04).
- ^ hansard. Parliament of the United Kingdom. 2012-02-02 [2017-08-29]. (原始內容存檔於2017-07-06).
- ^ Stevenson, Alex. Better late than never, Alan Turing is finally pardoned. politics.co.uk. 2013-12-24 [2016-09-25]. (原始內容存檔於2016-08-16).
- ^ Fitzgerald, Todd. Alan Turing's court convictions go on display for the first time. manchestereveningnews.co.uk. 2016-09-24 [2016-09-25]. (原始內容存檔於2016-09-25).
- ^ Britton, Paul. Alan Turing pardoned by The Queen for his 'unjust and discriminatory' conviction for homosexuality. Manchester Evening News. 2013-12-24 [2018-06-24]. (原始內容存檔於2018-06-24).
- ^ MP calls for pardon for computer pioneer Alan Turing. BBC News. 2012-02-01 [2016-09-25]. (原始內容存檔於2016-07-02).
- ^ My proudest day as a Liberal Democrat. Liberal Democrat Voice. [2018-06-24]. (原始內容存檔於2018-06-24).
- ^ Manchester computer pioneer Alan Turing announced as face of new £50 note. 2019-07-15 [2019-07-19]. (原始內容存檔於2019-07-19).
- ^ Alan Turing announced as face of new £50 banknote. 2019-07-15 [2019-07-19]. (原始內容存檔於2019-07-16).
- ^ John Leech secures historic deal with Government on 'Alan Turing Law'. outnewsglobal.com. 2016-10-20.
- ^ Barlow, Nigel. Turing on £50 note will be painful reminder of what we lost. 2018-11-03.
- ^ Alan Turing announced as face of new £50 banknote. 2019-07-15.
- ^ Elliott, Larry; Halliday, Josh (編). Alan Turing to feature on new £50 banknote. 2019-07-15 –透過www.theguardian.com.
- ^ This is who is on the new £50 note. www.thegayuk.com. 2019-07-15.
- ^ Bloom, Dan. Tory refuses to apologise for 'killing bad law' pardoning thousands of gay men. mirror. 2016-10-23.
- ^ Alan Turing's 'fearless approach to problems and intellectual curiosity' praised. Dunfermline Press.
- ^ The Alan Turing Law finally pardons thousands of unfairly convicted gay and bisexual men. University of Manchester. 2017-01-31.
- ^ Bank of England honours Alan Turing on £50 note. QNews. 2019-07-15.
- ^ Bill. Parliament of the United Kingdom. 2012-07-26 [2013-10-31]. (原始內容存檔於2013-11-02).
- ^ Pearse, Damian, "Alan Turing should be pardoned, argue Stephen Hawking and top scientists" 網際網路檔案館的存檔,存檔日期2017-02-04., The Guardian, 13 December 2012. Retrieved 15 December 2012.
- ^ Watt, Nicholas. Enigma codebreaker Alan Turing to be given posthumous pardon. The Guardian (London). 2013-07-19 [2016-12-10]. (原始內容存檔於2017-01-04).
- ^ Worth, Dan. Alan Turing pardon sails through House of Lords. V3. 2013-10-30 [2013-12-24]. (原始內容存檔於2013-12-24).
- ^ Alan Turing (Statutory Pardon) Bill. [2013-07-20]. (原始內容存檔於2013-07-05).
- ^ Roberts, Scott. Lib Dem MP John Leech disappointed at delay to Alan Turing pardon bill. Pink News. 2013-12-02 [2013-12-24]. (原始內容存檔於2013-12-25).
- ^ Roberts, Scott. Lib Dem MP John Leech disappointed at delay to Alan Turing pardon bill. PinkNews. 2013-12-02 [2018-06-20]. (原始內容存檔於2018-06-12).
- ^ Alan Turing (Statutory Pardon) Bill. [2013-12-24]. (原始內容存檔於2013-11-02).
- ^ Swinford, Steven. Alan Turing granted Royal pardon by the Queen. The Daily Telegraph. 2013-12-23 [2018-04-05]. (原始內容存檔於2018-05-02).
- ^ Royal pardon for codebreaker Alan Turing. BBC News. 2013-12-24 [2013-12-24]. (原始內容存檔於2013-12-24).
- ^ With Queen's Decree, Alan Turing Is Now Officially Pardoned. Advocate.com. 2014-08-22 [2014-11-01]. (原始內容存檔於2014-11-01).
- ^ Pardoned: Alan Turing, Computing patriarch. Time Magazine, vol. 183, no. 1, 13 January 2014, p. 14. Retrieved 6 January 2014.
- ^ Davies, Caroline. Codebreaker Turing is given posthumous royal pardon. The Guardian (London). 2013-12-24: 1, 6.
- ^ Government 'committed' to Alan Turing gay pardon law. BBC News. 2016-09-22 [2016-09-22]. (原始內容存檔於2016-09-22).
- ^ Cowburn, Ashley. Theresa May committed to introducing the 'Alan Turing Law'. The Independent. 2016-09-21 [2016-09-22]. (原始內容存檔於2016-09-22).
- ^ Participation, Expert. Policing and Crime Act 2017. Government of the United Kingdom. [2019-02-06]. (原始內容存檔於2019-03-05).
- ^ What does the code on the Alan Turing Memorial actually say?. Random Hacks. 2010-09-23 [2018-06-28]. (原始內容存檔於2018-06-28).
- ^ Computer buried in tribute to genius. Manchester Evening News. 2007-02-17 [2014-12-07]. (原始內容存檔於2013-11-04) (英語).
- ^ Blue plaque to commemorate Alan Turing. King's College, Cambridge. [2018-12-08]. (原始內容存檔於2018-12-07) (英語).
- ^ Turing plaque fixed in place. 劍橋大學國王學院. [2018-12-08]. (原始內容存檔於2018-12-09) (英語).
- ^ Pylas, Pan. WWII codebreaker Alan Turing honored on new UK bank note. AP News. Associated Press. 2021-03-25 [2021-03-25] (英語).
- ^ Reid-Smith, Tris. Heritage watchdog objects to statue of gay hero Alan Turing at Kings College Cambridge. Gay Star News. 2020-05-01 [2020-05-08].
來源
[編輯]- Agar, Jon. Turing and the Universal Machine. Duxford: Icon. 2001. ISBN 978-1-84046-250-0.
- Agar, Jon. The government machine: a revolutionary history of the computer. Cambridge, Massachusetts: MIT Press. 2003. ISBN 978-0-262-01202-7.
- Alexander, C. Hugh O'D. Cryptographic History of Work on the German Naval Enigma. The National Archives, Kew, Reference HW 25/1.
- Beavers, Anthony. Alan Turing: Mathematical Mechanist. Cooper, S. Barry; van Leeuwen, Jan (編). Alan Turing: His Work and Impact. Waltham: Elsevier. 2013: 481–485. ISBN 978-0-12-386980-7.
- Beniger, James. The control revolution: technological and economic origins of the information society. Cambridge, Massachusetts: Harvard University Press. 1986. ISBN 978-0-674-16986-9.
- Babbage, Charles. Campbell-Kelly, Martin , 編. Passages from the life of a philosopher. Rough Draft Printing. 18642008. ISBN 978-1-60386-092-5.
- Bodanis, David. Electric Universe: How Electricity Switched on the Modern World. New York: Three Rivers Press. 2005. ISBN 978-0-307-33598-2. OCLC 61684223.
- Bruderer, Herbert: Konrad Zuse und die Schweiz. Wer hat den Computer erfunden? Charles Babbage, Alan Turing und John von Neumann Oldenbourg Verlag, München 2012, XXVI, 224 Seiten, ISBN 978-3-486-71366-4
- Campbell-Kelly, Martin; Aspray, William. Computer: A History of the Information Machine. New York: Basic Books. 1996. ISBN 978-0-465-02989-1.
- Ceruzzi, Paul E. A History of Modern Computing. Cambridge, Massachusetts, and London: MIT Press. 1998. ISBN 978-0-262-53169-6.
- Chandler, Alfred. The Visible Hand: The Managerial Revolution in American Business. Cambridge, Massachusetts: Belknap Press. 1977. ISBN 978-0-674-94052-9.
- Church, Alonzo. An Unsolvable Problem of Elementary Number Theory. American Journal of Mathematics. 1936, 58 (2): 345–363. ISSN 0002-9327. JSTOR 2371045. doi:10.2307/2371045.
- Cooper, S. Barry; van Leeuwen, Jan. Alan Turing: His Work and Impact. New York: Elsevier. 2013. ISBN 978-0-12-386980-7.
- Copeland, B. Jack. Colossus: Its Origins and Originators. IEEE Annals of the History of Computing. 2004a, 26 (4): 38–45. S2CID 20209254. doi:10.1109/MAHC.2004.26.
- Copeland, B. Jack (編). The Essential Turing. Oxford: Oxford University Press. 2004b. ISBN 978-0-19-825079-1. OCLC 156728127.
- Copeland, B. Jack (編). Alan Turing's Automatic Computing Engine
. Oxford: Oxford University Press. 2005. ISBN 978-0-19-856593-2. OCLC 224640979.
- Copeland, B. Jack. Colossus: The secrets of Bletchley Park's code-breaking computers. Oxford University Press. 2006. ISBN 978-0-19-284055-4.
- Hilton, Peter. Living with Fish: Breaking Tunny in the Newmanry and Testery. Colussus. 2006. in Copeland 2006,第189–203頁
- Edwards, Paul N. The closed world: computers and the politics of discourse in Cold War America. Cambridge, Massachusetts: MIT Press. 1996. ISBN 978-0-262-55028-4.
- Gannon, Paul. Colossus: Bletchley Park's Greatest Secret. London: Atlantic Books. 2007 [2006]. ISBN 978-1-84354-331-2.
- Hodges, Andrew. Alan Turing : the enigma. London: Burnett Books. 1983. ISBN 978-0-09-152130-1.
- Hochhuth, Rolf. Alan Turing: en berättelse. Symposion. 1988. ISBN 978-91-7868-109-9.
- Leavitt, David. The man who knew too much: Alan Turing and the invention of the computer. Phoenix. 2007. ISBN 978-0-7538-2200-5.
- Levin, Janna. A Madman Dreams of Turing Machines. New York: Knopf. 2006. ISBN 978-1-4000-3240-2.
- Lewin, Ronald. Ultra Goes to War: The Secret Story. Classic Military History Classic Penguin. London: Hutchinson & Co. 19782001. ISBN 978-1-56649-231-7.
- Lubar, Steven. Infoculture. Boston, Massachusetts and New York: Houghton Mifflin. 1993. ISBN 978-0-395-57042-5.
- Mahon, A.P. The History of Hut Eight 1939–1945. UK National Archives Reference HW 25/2. 1945 [2009-12-10].
- Oakley, Brian (編). The Bletchley Park War Diaries: July 1939 – August 1945 2.6. Wynne Press. 2006.
- O'Connell, H; Fitzgerald, M. Did Alan Turing have Asperger's syndrome?. Irish Journal of Psychological Medicine (Irish Institute of Psychological Medicine). 2003, 20 (1): 28–31. ISSN 0790-9667. PMID 30440230. S2CID 53563123. doi:10.1017/s0790966700007503.
- 約翰·J·奧康納; 埃德蒙·F·羅伯遜, Alan Mathison Turing, MacTutor數學史檔案 (英語)
- Petzold, Charles (2008). "The Annotated Turing: A Guided Tour through Alan Turing's Historic Paper on Computability and the Turing Machine". Indianapolis: Wiley Publishing. ISBN 978-0-470-22905-7
- Smith, Roger (1997). Fontana History of the Human Sciences. London: Fontana.
- Sipser, Michael. Introduction to the Theory of Computation. PWS Publishing. 2006. ISBN 978-0-534-95097-2.
- Weizenbaum, Joseph (1976). Computer Power and Human Reason. London: W.H. Freeman. ISBN 0-7167-0463-3
- Turing, A.M. On Computable Numbers, with an Application to the Entscheidungsproblem (PDF). Proceedings of the London Mathematical Society. 2 42. 1937: 230–65 [Delivered to the Society November 1936]. doi:10.1112/plms/s2-42.1.230. and Turing, A.M. On Computable Numbers, with an Application to the Entscheidungsproblem: A correction. Proceedings of the London Mathematical Society. 2 43. 1938: 544–461937. doi:10.1112/plms/s2-43.6.544.
- Turing, Sara Stoney. Alan M Turing. W Heffer. 1959. Turing's mother, who survived him by many years, wrote this 157-page biography of her son, glorifying his life. It was published in 1959, and so could not cover his war work. Scarcely 300 copies were sold (Sara Turing to Lyn Newman, 1967, Library of St John's College, Cambridge). The six-page foreword by Lyn Irvine includes reminiscences and is more frequently quoted. It was re-published by Cambridge University Press in 2012, to honour the centenary of his birth, and included a new foreword by Martin Davis, as well as a never-before-published memoir by Turing's older brother John F. Turing.
- Whitemore, Hugh; Hodges, Andrew. Breaking the code. S. French. 1988. This 1986 Hugh Whitemore play tells the story of Turing's life and death. In the original West End and Broadway runs, Derek Jacobi played Turing and he recreated the role in a 1997 television film based on the play made jointly by the BBC and WGBH, Boston. The play is published by Amber Lane Press, Oxford, ASIN: B000B7TM0Q
- Williams, Michael R. (1985) A History of Computing Technology, Englewood Cliffs, New Jersey: Prentice-Hall, ISBN 0-8186-7739-2
- Yates, David M. Turing's Legacy: A history of computing at the National Physical Laboratory 1945–1995. London: London Science Museum. 1997. ISBN 978-0-901805-94-2. OCLC 123794619.
延伸閱讀
[編輯]文章
[編輯]- Turing, Alan. Computing Machinery and Intelligence (PDF). Mind. 1950, 49 (236): 433–460. doi:10.1093/mind/LIX.236.433.
- Copeland, B. Jack (編). The Mind and the Computing Machine: Alan Turing and others. The Rutherford Journal.
- Copeland, B. Jack (編). Alan Turing: Father of the Modern Computer. The Rutherford Journal.
- Hodges, Andrew. Alan Turing. 扎爾塔, 愛德華·N (編). 《史丹佛哲学百科全书》 2009年冬.
- Hodges, Andrew. Turing, Alan Mathison. 《牛津國家人物傳記大辭典》 線上版. 牛津大學出版社. 2004. doi:10.1093/ref:odnb/36578. 需要訂閱或英國公共圖書館會員資格
- Gray, Paul. Computer Scientist: Alan Turing. Time. 1999-03-29. (原始內容存檔於2007-10-16).
著作
[編輯]- Bernhardt, Chris, Turing's Vision: The Birth of Computer Science, MIT Press, 2017, ISBN 978-0-262-53351-5
- Copeland, B. Jack; Bowen, Jonathan P.; Wilson, Robin; Sprevak, Mark. The Turing Guide. Oxford University Press. 2017. ISBN 978-0-19-874783-3.
- Dyson, George. Turing's Cathedral: The Origins of the Digital Universe. Vintage. 2012. ISBN 978-1-4000-7599-7.
- Gleick, James. The Information: A History, a Theory, a Flood. New York: Pantheon. 2011. ISBN 978-0-375-42372-7.
- Hodges, Andrew. Alan Turing: The Enigma. Princeton University Press. 2014. ISBN 978-0-691-16472-4. (originally published in 1983); basis of the film The Imitation Game
- Turing, Sara. Alan M. Turing. Cambridge University Press. 2012. ISBN 978-1-107-02058-0. (originally published in 1959 by W. Heffer & Sons, Ltd)
外部連結
[編輯]- Oral history interview with Nicholas C. Metropolis, Charles Babbage Institute, University of Minnesota. Metropolis was the first director of computing services at Los Alamos National Laboratory; topics include the relationship between Turing and John von Neumann
- How Alan Turing Cracked The Enigma Code Imperial War Museums
- Alan Turing RKBExplorer
- Alan Turing Year
- CiE 2012: Turing Centenary Conference
- Science in the Making Alan Turing's papers in the Royal Society's archives
- Alan Turing site maintained by Andrew Hodges including a short biography
- AlanTuring.net – Turing Archive for the History of Computing by Jack Copeland
- The Turing Archive – contains scans of some unpublished documents and material from the King's College, Cambridge archive
- Alan Turing Papers – University of Manchester Library, Manchester
- Jones, G. James. Alan Turing – Towards a Digital Mind: Part 1. System Toolbox (The Binary Freedom Project). 2001-12-11. (原始內容存檔於2007-08-03).
- Sherborne School Archives – holds papers relating to Turing's time at Sherborne School
- Alan Turing plaques recorded on openplaques.org
- Alan Turing archive on New Scientist
- 在Find a Grave上的艾倫·圖靈
|