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Alan Turing

May 24, 2023

"Turing" redirects here. For other uses, see Turing (disambiguation).

Alan Mathison Turing OBE FRS (/ˈtjʊərɪŋ/; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist.[6] Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer.[7][8][9] He is widely considered to be the father of theoretical computer science and artificial intelligence.[10]

Alan Turing

OBE FRS
Turing c. 1928
Born(1912-06-23)23 June 1912
Maida Vale, London, England
Died7 June 1954(1954-06-07) (aged 41)
Wilmslow, Cheshire, England
Cause of deathCyanide poisoning[note 1]
EducationSherborne School
Alma mater
Known for
PartnerJoan Clarke (engaged in 1941; did not marry)
AwardsSmith's Prize (1936)
Scientific career
Fields
Institutions
Thesis (1938)
Doctoral advisorAlonzo Church[2]
Doctoral students
InfluencesMax Newman[5]
Signature

Born in Maida Vale, London, Turing was raised in southern England. He graduated at King's College, Cambridge, with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation and defined a Turing machine, and went on to prove that the halting problem for Turing machines is undecidable. In 1938, he obtained his PhD from the Department of Mathematics at Princeton University. During the Second World War, Turing worked for the Government Code and Cypher School at Bletchley Park, Britain's codebreaking centre that produced Ultra intelligence. For a time he led Hut 8, the section that was responsible for German naval cryptanalysis. Here, he devised a number of techniques for speeding the breaking of German ciphers, including improvements to the pre-war Polish bomba method, an electromechanical machine that could find settings for the Enigma machine. Turing played a crucial role in cracking intercepted coded messages that enabled the Allies to defeat the Axis powers in many crucial engagements, including the Battle of the Atlantic.[11][12]

After the war, Turing worked at the National Physical Laboratory, where he designed the Automatic Computing Engine, one of the first designs for a stored-program computer. In 1948, Turing joined Max Newman's Computing Machine Laboratory, at the Victoria University of Manchester, where he helped develop the Manchester computers[13] and became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis[1] and predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, first observed in the 1960s. Despite these accomplishments, Turing was never fully recognised in Britain during his lifetime because much of his work was covered by the Official Secrets Act.[14]

Turing was prosecuted in 1952 for homosexual acts. He accepted hormone treatment with DES, a procedure commonly referred to as chemical castration, as an alternative to prison. Turing died on 7 June 1954, 16 days before his 42nd birthday, from cyanide poisoning. An inquest determined his death as a suicide, but it has been noted that the known evidence is also consistent with accidental poisoning. Following a public campaign in 2009, the British prime minister Gordon Brown made an official public apology on behalf of the British government for "the appalling way [Turing] was treated". Queen Elizabeth II granted a posthumous pardon in 2013. The term "Alan Turing law" is now used informally to refer to a 2017 law in the United Kingdom that retroactively pardoned men cautioned or convicted under historical legislation that outlawed homosexual acts.[15]

Turing has an extensive legacy with statues of him and many things named after him, including an annual award for computer science innovations. He appears on the current Bank of England £50 note, which was released on 23 June 2021, to coincide with his birthday. A 2019 BBC series, as voted by the audience, named him the greatest person of the 20th century.

Early life and education

Family

Turing was born in Maida Vale, London, while his father, Julius Mathison Turing was on leave from his position with the Indian Civil Service (ICS) of the British Raj government at Chatrapur, then in the Madras Presidency and presently in Odisha state, in India.[16][17] Turing's father was the son of a clergyman, the Rev. John Robert Turing, from a Scottish family of merchants that had been based in the Netherlands and included a baronet. Turing's mother, Julius's wife, was Ethel Sara Turing (née Stoney), daughter of Edward Waller Stoney, chief engineer of the Madras Railways. The Stoneys were a Protestant Anglo-Irish gentry family from both County Tipperary and County Longford, while Ethel herself had spent much of her childhood in County Clare.[18] Julius and Ethel married on 1 October 1907 at Batholomew's church on Clyde Road, in Dublin.[19]

Julius's work with the ICS brought the family to British India, where his grandfather had been a general in the Bengal Army. However, both Julius and Ethel wanted their children to be brought up in Britain, so they moved to Maida Vale,[20] London, where Alan Turing was born on 23 June 1912, as recorded by a blue plaque on the outside of the house of his birth,[21][22] later the Colonnade Hotel.[16][23] Turing had an elder brother, John Ferrier Turing, father of Sir John Dermot Turing, (12th Baronet of the Turing baronets).[24]

Turing's father's civil service commission was still active and during Turing's childhood years, his parents travelled between Hastings in the United Kingdom[25] and India, leaving their two sons to stay with a retired Army couple. At Hastings, Turing stayed at Baston Lodge, Upper Maze Hill, St Leonards-on-Sea, now marked with a blue plaque.[26] The plaque was unveiled on 23 June 2012, the centenary of Turing's birth.[27]

Very early in life, Turing showed signs of the genius that he was later to display prominently.[28] His parents purchased a house in Guildford in 1927, and Turing lived there during school holidays. The location is also marked with a blue plaque.[29]

School

Turing's parents enrolled him at St Michael's, a primary school at 20 Charles Road, St Leonards-on-Sea, from the age of six to nine. The headmistress recognised his talent, noting that she has "...had clever boys and hardworking boys, but Alan is a genius".[30]

Between January 1922 and 1926, Turing was educated at Hazelhurst Preparatory School, an independent school in the village of Frant in Sussex (now East Sussex).[31] In 1926, at the age of 13, he went on to Sherborne School,[32] a boarding independent school in the market town of Sherborne in Dorset, where he boarded at Westcott House. The first day of term coincided with the 1926 General Strike, in Britain, but Turing was so determined to attend that he rode his bicycle unaccompanied 60 miles (97 km) from Southampton to Sherborne, stopping overnight at an inn.[33]

 
Turing in July 1930, during his senior year at the Sherborne School. At the end of the term, Turing received the inaugural Cristopher Morcom prize.

Turing's natural inclination towards mathematics and science did not earn him respect from some of the teachers at Sherborne, whose definition of education placed more emphasis on the classics. His headmaster wrote to his parents: "I hope he will not fall between two stools. If he is to stay at public school, he must aim at becoming educated. If he is to be solely a Scientific Specialist, he is wasting his time at a public school".[34] Despite this, Turing continued to show remarkable ability in the studies he loved, solving advanced problems in 1927 without having studied even elementary calculus. In 1928, aged 16, Turing encountered Albert Einstein's work; not only did he grasp it, but it is possible that he managed to deduce Einstein's questioning of Newton's laws of motion from a text in which this was never made explicit.[35]

Christopher Morcom

At Sherborne, Turing formed a significant friendship with fellow pupil Christopher Collan Morcom (13 July 1911 – 13 February 1930),[36] who has been described[by whom?] as Turing's "first love".[This quote needs a citation] Their relationship provided inspiration in Turing's future endeavours, but it was cut short by Morcom's death, in February 1930, from complications of bovine tuberculosis, contracted after drinking infected cow's milk some years previously.[37][38][39]

The event caused Turing great sorrow. He coped with his grief by working that much harder on the topics of science and mathematics that he had shared with Morcom. In a letter to Morcom's mother, Frances Isobel Morcom (née Swan), Turing wrote:

I am sure I could not have found anywhere another companion so brilliant and yet so charming and unconceited. I regarded my interest in my work, and in such things as astronomy (to which he introduced me) as something to be shared with him and I think he felt a little the same about me ... I know I must put as much energy if not as much interest into my work as if he were alive, because that is what he would like me to do.[40]

Turing's relationship with Morcom's mother continued long after Morcom's death, with her sending gifts to Turing, and him sending letters, typically on Morcom's birthday.[41] A day before the third anniversary of Morcom's death (13 February 1933), he wrote to Mrs. Morcom:

I expect you will be thinking of Chris when this reaches you. I shall too, and this letter is just to tell you that I shall be thinking of Chris and of you tomorrow. I am sure that he is as happy now as he was when he was here. Your affectionate Alan.[42]

Some have speculated that Morcom's death was the cause of Turing's atheism and materialism.[43] Apparently, at this point in his life he still believed in such concepts as a spirit, independent of the body and surviving death. In a later letter, also written to Morcom's mother, Turing wrote:

Personally, I believe that spirit is really eternally connected with matter but certainly not by the same kind of body ... as regards the actual connection between spirit and body I consider that the body can hold on to a 'spirit', whilst the body is alive and awake the two are firmly connected. When the body is asleep I cannot guess what happens but when the body dies, the 'mechanism' of the body, holding the spirit is gone and the spirit finds a new body sooner or later, perhaps immediately.[44][45]

University and work on computability

After graduating from Sherborne, Turing studied the undergraduate course (Parts Ia, Ib and II of the Mathematical Tripos) from February 1931 to November 1934 at King's College, Cambridge where he was awarded first-class honours in mathematics. His dissertation, On the Gaussian error function, was written during his senior and delivered on November 1934 (with a deadline date of 6 December), in it, he proved a version of the central limit theorem. His dissertation was finally accepted in 16 March 1935. By spring of that same year, Turing started his master's course (Part III), -which he completed in 1937- and, at the same time, he published his first paper, a one-page article called Equivalence of left and right almost periodicity (sent on 23 April), featured in the tenth volume of the Journal of the London Mathematical Society.[46] Later that year, Turing was elected a Fellow of King's College on the strength of his dissertation. [47] However, and, unknown to Turing, this version of the theorem he proved in his paper, had already been proven, in 1922, by Jarl Waldemar Lindeberg. Despite this, the committee found Turing's methods original and so regarded the work worthy of consideration for the fellowship. Abram Besicovitch's report for the committee went so far as to say that if Turing's work had been published before Lindeberg's, it would have been "an important event in the mathematical literature of that year".[48][49][50]

 
Turing in 1935, at his parents' home garden.

Between the springs of 1935 and 1936, at the same time as Church, Turing worked on the decidability of problems, starting from Godel's incompleteness theorems. In mid-April 1936, Turing sent Max Newman the first draft typescript of his investigations. That same month, Alonzo Church published his An Unsolvable Problem of Elementary Number Theory, with similar conclusions to Turing's then-yet unpublished work. Finally, on 28 May of that year, he finished and delivered his 36-page paper for publication called "On Computable Numbers, with an Application to the Entscheidungsproblem".[51] 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.[52] 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 machines. 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 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".[53]

 
King's College, Cambridge, where Turing was an undergraduate in 1931 and became a Fellow in 1935. The computer room is named after him.

Although Turing's proof was published shortly after Alonzo Church's equivalent proof using his lambda calculus,[54] Turing's approach is considerably more accessible and intuitive than Church's.[55] 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.[56] To this day, Turing machines are a central object of study in theory of computation.

From September 1936 to July 1938, Turing spent most of his time studying under Church at Princeton University,[4] in the second year as a Jane Eliza Procter Visiting Fellow. In addition to his purely mathematical work, he studied cryptology and also built three of four stages of an electro-mechanical binary multiplier.[57] In June 1938, he obtained his PhD from the Department of Mathematics at Princeton;[58] his dissertation, Systems of Logic Based on Ordinals,[59][60] introduced the concept of ordinal logic and the notion of relative computing, in which Turing machines are augmented with so-called oracles, allowing the study of problems that cannot be solved by Turing machines. John von Neumann wanted to hire him as his postdoctoral assistant, but he went back to the United Kingdom.[61]

Career and research

When Turing returned to Cambridge, he attended lectures given in 1939 by Ludwig Wittgenstein about the foundations of mathematics.[62] The lectures have been reconstructed verbatim, including interjections from Turing and other students, from students' notes.[63] Turing and Wittgenstein argued and disagreed, with Turing defending formalism and Wittgenstein propounding his view that mathematics does not discover any absolute truths, but rather invents them.[64]

Cryptanalysis

During the Second World War, Turing was a leading participant in the breaking of German ciphers at Bletchley Park. The historian and wartime codebreaker Asa Briggs has said, "You needed exceptional talent, you needed genius at Bletchley and Turing's was that genius."[65]

From September 1938, Turing worked part-time with the Government Code and Cypher School (GC&CS), the British codebreaking organisation. He concentrated on cryptanalysis of the Enigma cipher machine used by Nazi Germany, together with Dilly Knox, a senior GC&CS codebreaker.[66] Soon after the July 1939 meeting near Warsaw at which the Polish Cipher Bureau gave the British and French details of the wiring of Enigma machine's rotors and their method of decrypting Enigma machine's messages, Turing and Knox developed a broader solution.[67] The Polish method relied on an insecure indicator procedure that the Germans were likely to change, which they in fact did in May 1940. Turing's approach was more general, using crib-based decryption for which he produced the functional specification of the bombe (an improvement on the Polish Bomba).[68]

 
Two cottages in the stable yard at Bletchley Park. Turing worked here in 1939 and 1940, before moving to Hut 8.

On 4 September 1939, the day after the UK declared war on Germany, Turing reported to Bletchley Park, the wartime station of GC&CS.[69] Like all others who came to Bletchley, he was required to sign the Official Secrets Act, in which he agreed not to disclose anything about his work at Bletchley, with severe legal penalties for violating the Act.[70]

Specifying the bombe was the first of five major cryptanalytical advances that Turing made during the war. The others were: deducing the indicator procedure used by the German navy; developing a statistical procedure dubbed Banburismus for making much more efficient use of the bombes; developing a procedure dubbed Turingery for working out the cam settings of the wheels of the Lorenz SZ 40/42 (Tunny) cipher machine and, towards the end of the war, the development of a portable secure voice scrambler at Hanslope Park that was codenamed Delilah.

By using statistical techniques to optimise the trial of different possibilities in the code breaking process, Turing made an innovative contribution to the subject. He wrote two papers discussing mathematical approaches, titled The Applications of Probability to Cryptography[71] and Paper on Statistics of Repetitions,[72] which were of such value to GC&CS and its successor GCHQ that they were not released to the UK National Archives until April 2012, shortly before the centenary of his birth. A GCHQ mathematician, "who identified himself only as Richard," said at the time that the fact that the contents had been restricted under the Official Secrets Act for some 70 years demonstrated their importance, and their relevance to post-war cryptanalysis:[73]

[He] said the fact that the contents had been restricted "shows what a tremendous importance it has in the foundations of our subject". ... The papers detailed using "mathematical analysis to try and determine which are the more likely settings so that they can be tried as quickly as possible". ... Richard said that GCHQ had now "squeezed the juice" out of the two papers and was "happy for them to be released into the public domain".

Turing had a reputation for eccentricity at Bletchley Park. He was known to his colleagues as "Prof" and his treatise on Enigma was known as the "Prof's Book".[74][75] According to historian Ronald Lewin, Jack Good, a cryptanalyst who worked with Turing, said of his colleague:

In the first week of June each year he would get a bad attack of hay fever, and he would cycle to the office wearing a service gas mask to keep the pollen off. His bicycle had a fault: the chain would come off at regular intervals. Instead of having it mended he would count the number of times the pedals went round and would get off the bicycle in time to adjust the chain by hand. Another of his eccentricities is that he chained his mug to the radiator pipes to prevent it being stolen.[76]

Peter Hilton recounted his experience working with Turing in Hut 8 in his "Reminiscences of Bletchley Park" from A Century of Mathematics in America:[77]

It is a rare experience to meet an authentic genius. Those of us privileged to inhabit the world of scholarship are familiar with the intellectual stimulation furnished by talented colleagues. We can admire the ideas they share with us and are usually able to understand their source; we may even often believe that we ourselves could have created such concepts and originated such thoughts. However, the experience of sharing the intellectual life of a genius is entirely different; one realizes that one is in the presence of an intelligence, a sensibility of such profundity and originality that one is filled with wonder and excitement. Alan Turing was such a genius, and those, like myself, who had the astonishing and unexpected opportunity, created by the strange exigencies of the Second World War, to be able to count Turing as colleague and friend will never forget that experience, nor can we ever lose its immense benefit to us.

Hilton echoed similar thoughts in the Nova PBS documentary Decoding Nazi Secrets.[78]

While working at Bletchley, Turing, who was a talented long-distance runner, occasionally ran the 40 miles (64 km) to London when he was needed for meetings,[79] and he was capable of world-class marathon standards.[80][81] Turing tried out for the 1948 British Olympic team, but he was hampered by an injury. His tryout time for the marathon was only 11 minutes slower than British silver medallist Thomas Richards' Olympic race time of 2 hours 35 minutes. He was Walton Athletic Club's best runner, a fact discovered when he passed the group while running alone.[82][83][84] When asked why he ran so hard in training he replied:

I have such a stressful job that the only way I can get it out of my mind is by running hard; it's the only way I can get some release.[85]

Due to the problems of counterfactual history, it is hard to estimate the precise effect Ultra intelligence had on the war.[86] However, official war historian Harry Hinsley estimated that this work shortened the war in Europe by more than two years and saved over 14 million lives.[87]

At the end of the war, a memo was sent to all those who had worked at Bletchley Park, reminding them that the code of silence dictated by the Official Secrets Act did not end with the war but would continue indefinitely.[70] Thus, even though Turing was appointed an Officer of the Order of the British Empire (OBE) in 1946 by King George VI for his wartime services, his work remained secret for many years.[88][89]

Bombe

Main article: Bombe

Within weeks of arriving at Bletchley Park,[69] Turing had specified an electromechanical machine called the bombe, which could break Enigma more effectively than the Polish bomba kryptologiczna, from which its name was derived. The bombe, with an enhancement suggested by mathematician Gordon Welchman, became one of the primary tools, and the major automated one, used to attack Enigma-enciphered messages.[90]

 
A working replica of a bombe now at The National Museum of Computing on Bletchley Park

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),[91] the bombe performed a chain of logical deductions based on the crib, implemented electromechanically.[92]

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.[93]

Action This Day

Main article: Action This Day (memo)

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.[94]

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.[94] As Andrew Hodges, biographer of Turing, later wrote, "This letter had an electric effect."[95] 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.[95] 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."[96] More than two hundred bombes were in operation by the end of the war.[97]

 
Statue of Turing holding an Enigma machine by Stephen Kettle at Bletchley Park, commissioned by Sidney Frank, built from half a million pieces of Welsh slate[98]

Hut 8 and the naval Enigma

Turing decided to tackle the particularly difficult problem of German naval Enigma "because no one else was doing anything about it and I could have it to myself".[99] In December 1939, Turing solved the essential part of the naval indicator system, which was more complex than the indicator systems used by the other services.[99][100]

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".[99] For this, he invented a measure of weight of evidence that he called the ban. Banburismus could rule out certain sequences of the Enigma rotors, substantially reducing the time needed to test settings on the bombes.[101] 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.[102]

Turing travelled to the United States in November 1942[103] and worked with US Navy cryptanalysts on the naval Enigma and bombe construction in Washington; he also visited their Computing Machine Laboratory in Dayton, Ohio.

Turing's reaction to the American bombe design was far from enthusiastic:

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.[104]

During this trip, he also assisted at Bell Labs with the development of secure speech devices.[105] He returned to Bletchley Park in March 1943. During his absence, 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.[106]

Alexander wrote of Turing's contribution:

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.[107]

Turingery

Main article: Turingery

In July 1942, Turing devised a technique termed Turingery (or jokingly Turingismus)[108] for use against the Lorenz cipher messages produced by the Germans' new Geheimschreiber (secret writer) machine. This was a teleprinter 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.[109] 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), and whose superior speed allowed the statistical decryption techniques to be applied usefully to the messages.[110] 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,[111][112] but he was not directly involved in the Colossus development.[113]

Delilah

Following his work at Bell Labs in the US,[114] 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 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.[115] 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.[116] 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.

Early computers and the Turing test

 
Plaque, 78 High Street, Hampton

Between 1945 and 1947, Turing lived in Hampton, London,[117] while he worked on the design of the ACE (Automatic Computing Engine) at the National Physical Laboratory (NPL). He presented a paper on 19 February 1946, which was the first detailed design of a stored-program computer.[118] 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".[119]

Although ACE was a feasible design, the effect of the 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.[120] 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.[121] 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.[122]

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.[123] 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).

In 1948, Turing was appointed reader in the 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 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.[124] During this time, he continued to do more abstract work in mathematics,[125] and in "Computing Machinery and Intelligence" (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.[126] 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 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, 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.[127] 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.[128] According to Garry Kasparov, Turing's program "played a recognizable game of chess".[129] The program lost to Turing's colleague Alick Glennie, although it is said that it won a game against Champernowne's wife, Isabel.[130]

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.[131]

Pattern formation and mathematical biology

When Turing was 39 years old in 1951, he turned to 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".[132] 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 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.[133]

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.[134] 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.[135][136][137] 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".[138] 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.[139] Later papers were not available until Collected Works of A. M. Turing was published in 1992.[140]

A study conducted in 2023 confirmed Turing's mathematical model hypothesis. Presented by the American Physical Society, the experiment involved growing chia seeds in even layers within trays, later adjusting the available moisture. Researchers experimentally tweaked the factors which appear in the Turing equations, and, as a result, patterns resembling those seen in natural environments emerged. This is believed to be the first time that experiments with living vegetation have verified Turing’s mathematical insight.[141][142]

Personal life

Engagement

In 1941, Turing proposed marriage to Hut 8 colleague Joan Clarke, a fellow mathematician and cryptanalyst, but their engagement was short-lived. After admitting his homosexuality to his fiancée, who was reportedly "unfazed" by the revelation, Turing decided that he could not go through with the marriage.[143]

Homosexuality and indecency conviction

In January 1952, Turing was 39 when he started a relationship with Arnold Murray, a 19-year-old unemployed man. Just before Christmas, Turing was walking along Manchester's Oxford Road when he met Murray just outside the Regal Cinema and invited him to lunch. On 23 January, Turing's house was burgled. Murray told Turing that he and the burglar were acquainted, and Turing reported the crime to the police. During the investigation, he acknowledged a sexual relationship with Murray. Homosexual acts were criminal offences in the United Kingdom at that time,[144] and both men were charged with "gross indecency" under Section 11 of the Criminal Law Amendment Act 1885.[145] Initial committal proceedings for the trial were held on 27 February during which Turing's solicitor "reserved his defence", i.e., did not argue or provide evidence against the allegations. The proceedings were held at the Sessions House in Knutsford.[146]

Turing was later convinced by the advice of his brother and his own solicitor, and he entered a plea of guilty.[147] The case, Regina v. Turing and Murray, was brought to trial on 31 March 1952.[148] Turing was convicted and given a choice between imprisonment and probation. His probation would be conditional on his agreement to undergo hormonal physical changes designed to reduce libido, known as "chemical castration".[149] He accepted the option of injections of what was then called stilboestrol (now known as diethylstilbestrol or DES), a synthetic oestrogen; this feminization of his body was continued for the course of one year. The treatment rendered Turing impotent and caused breast tissue to form,[150] fulfilling in the literal sense Turing's prediction that "no doubt I shall emerge from it all a different man, but quite who I've not found out".[151][152] Murray was given a conditional discharge.[153]

Turing's conviction led to the removal of his security clearance and barred him from continuing with his cryptographic consultancy for the Government Communications Headquarters (GCHQ), the British signals intelligence agency that had evolved from GC&CS in 1946, though he kept his academic job. He was denied entry into the United States after his conviction in 1952, but was free to visit other European countries.[154]

Treasure

In the 1940s, Turing became worried about losing his savings in the event of a German invasion. In order to protect it, he bought two silver bars weighing 3,200 oz (90 kg) and worth £250 (in 2022, £8,000 adjusted for inflation, £48,000 at spot price) and buried them in a wood near Bletchley Park.[155] Upon returning to dig them up, Turing found that he was unable to break his own code describing where exactly he had hidden them. This, along with the fact that the area had been renovated, meant that he never regained the silver.[156]

Death

 
A blue plaque on the house at 43 Adlington Road, Wilmslow where Turing lived and died[157]

On 8 June 1954, at his house at 43 Adlington Road, Wilmslow,[157] Turing's housekeeper found him dead. He had died the previous day at the age of 41. Cyanide poisoning was established as the cause of death.[158] When his body was discovered, an apple lay half-eaten beside his bed, and although the apple was not tested for cyanide,[159] it was speculated that this was the means by which Turing had consumed a fatal dose. An inquest determined his death to be a suicide.[149] Andrew Hodges and another biographer, David Leavitt, have both speculated that Turing was re-enacting a scene from the Walt Disney film Snow White and the Seven Dwarfs (1937), his favourite fairy tale. Both men noted that (in Leavitt's words) he took "an especially keen pleasure in the scene where the Wicked Queen immerses her apple in the poisonous brew".[160] Turing's remains were cremated at Woking Crematorium on 12 June 1954,[161] and his ashes were scattered in the gardens of the crematorium, just as his father's had been.[162]

Philosopher Jack Copeland has questioned various aspects of the coroner's historical verdict. He suggested an alternative explanation for the cause of Turing's death: the accidental inhalation of cyanide fumes from an apparatus used to electroplate gold onto spoons. The potassium cyanide was used to dissolve the gold. Turing had such an apparatus set up in his tiny spare room. Copeland noted that the autopsy findings were more consistent with inhalation than with ingestion of the poison. Turing also habitually ate an apple before going to bed, and it was not unusual for the apple to be discarded half-eaten.[163] Furthermore, Turing had reportedly borne his legal setbacks and hormone treatment (which had been discontinued a year previously) "with good humour" and had shown no sign of despondency before his death. He even set down a list of tasks that he intended to complete upon returning to his office after the holiday weekend.[163] Turing's mother believed that the ingestion was accidental, resulting from her son's careless storage of laboratory chemicals.[164] Biographer Andrew Hodges theorised that Turing deliberately left the nature of his death ambiguous in order to shield his mother from the knowledge that he had killed himself.[165]

 
Turing's OBE currently held in Sherborne School archives

It has been suggested that Turing's belief in fortune-telling may have caused his depressed mood.[162] 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.[162] According to the Greenbaums' daughter, Barbara:[166]

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.

Government apology and pardon

Main article: Alan Turing law

In August 2009, British programmer John Graham-Cumming started a petition urging the British government to apologise for Turing's prosecution as a homosexual.[167][168] The petition received more than 30,000 signatures.[169][170] The prime minister, Gordon Brown, acknowledged the petition, releasing a statement on 10 September 2009 apologising and describing the treatment of Turing as "appalling":[169][171]

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.[169][172]

In December 2011, William Jones and his member of Parliament, John Leech, created an e-petition[173] requesting that the British government pardon Turing for his conviction of "gross indecency":[174]

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.[173]

The petition gathered over 37,000 signatures,[173][175] and was submitted to Parliament by the Manchester MP John Leech but the request was discouraged by Justice Minister Lord McNally, who said:[176]

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.[177]

John Leech, the MP for Manchester Withington (2005–15), submitted several bills to Parliament[178] 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.[179] Leech continued to take the bill through Parliament and campaigned for several years, gaining the public support of numerous leading scientists, including Stephen Hawking.[180][181] 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.[182] 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.[183][184][185][186][187][188][189]

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.[190] 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.[191] The government indicated it would support the bill,[192][193][194] and it passed its third reading in the House of Lords in October.[195]

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,[196] but before the bill could be debated in the House of Commons,[197] 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.[198] 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.[175][199] The Queen officially pronounced Turing pardoned in August 2014.[200] The Queen's action is only the fourth royal pardon granted since the conclusion of the Second World War.[201] 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.[202]

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".[203][204] 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.[205]

Legacy

Main article: Legacy of Alan Turing
See also: List of things named after Alan Turing

Awards, honours, and tributes

 
The Alan Turing Building at the University of Manchester in 2008

Turing was appointed an officer of the Order of the British Empire in 1946.[89] He was also elected a Fellow of the Royal Society (FRS) in 1951.[7]

 
Turing memorial statue plaque in Sackville Park, Manchester

Turing has been honoured in various ways in Manchester, the city where he worked towards the end of his life. In 1994, a stretch of the A6010 road (the Manchester city intermediate ring road) was named "Alan Turing Way". A bridge carrying this road was widened, and carries the name Alan Turing Bridge. A statue of Turing was unveiled in Manchester on 23 June 2001 in Sackville Park, between the University of Manchester building on Whitworth Street and Canal Street. The memorial statue depicts the "father of computer science" sitting on a bench at a central position in the park, holding an apple. The cast bronze bench carries in relief the text "Alan Mathison Turing 1912–1954" and "IEKYF ROMSI ADXUO KVKZC GUBJ". The latter is described by the sculptor, Glyn Hughes, as "a motto as encoded by the German 'Enigma'".[206] The original message is often given as "Founder of Computer Science",[207][208][209] however this is unlikely as the Enigma ciphering system does not allow a letter to be enciphered to itself, while the fourteenth letter of that message (the "U" in "Computer") is the same as the fourteenth letter of the encoded inscription.[citation needed] A plaque at the statue's feet reads "Father of Computer Science, Mathematician, Logician, Wartime Codebreaker, Victim of Prejudice", followed by a Bertrand Russell quotation: "Mathematics, rightly viewed, possesses not only truth but supreme beauty, a beauty cold and austere like that of sculpture." The sculptor's own old Amstrad computer is buried under the statue as a tribute to "the godfather of all modern computer".[210]

In 1999, Time magazine named Turing as one of the 100 Most Important People of the 20th century and stated, "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."[8]

A blue plaque was unveiled at King's College, Cambridge on the centenary of his birth on 23 June 2012 and is now installed at the college's Keynes Building on King's Parade.[211][212] A 12-foot (3.7 m) high steel sculpture, designed in Turing's honour by Sir Antony Gormley, is planned to be installed at King's College, but Historic England deemed the sculpture too abstract for the setting, saying that it "would result in harm, of a less than substantial nature, to the significance of the listed buildings and landscape, and by extension the conservation area".[213]

On 25 March 2021, the Bank of England publicly unveiled the design for a new £50 note, featuring Turing's portrait, before its official issue on 23 June, Turing's birthday. Turing was selected as the new face of the note in 2019 following a public nomination process.[214]

Centenary celebrations

Main article: Alan Turing Year

To mark the 100th anniversary of Turing's birth, the Turing Centenary Advisory Committee (TCAC) co-ordinated the Alan Turing Year in 2012, a year-long programme of events around the world honouring Turing's life and achievements. The TCAC, chaired by S. Barry Cooper with Turing's nephew Sir John Dermot Turing acting as Honorary President, worked with the University of Manchester faculty members and a broad spectrum of people from Cambridge University and Bletchley Park.

Notes and references

Notes

  1. ^ Turing's death was officially determined as a suicide by an inquest, but this has been disputed.

References

  1. ^ a b Alan Turing publications indexed by Google Scholar  
  2. ^ a b Alan Turing at the Mathematics Genealogy Project
  3. ^ Gandy, Robin Oliver (1953). On axiomatic systems in mathematics and theories in physics (PhD thesis). University of Cambridge. doi:10.17863/CAM.16125. EThOS uk.bl.ethos.590164. from the original on 9 December 2017. Retrieved 9 December 2017.  
  4. ^ a b Bowen, Jonathan P. (2019). "The Impact of Alan Turing: Formal Methods and Beyond". In Bowen, Jonathan P.; Liu, Zhiming; Zhang, Zili (eds.). Engineering Trustworthy Software Systems. SETSS 2018 (PDF). Lecture Notes in Computer Science. Vol. 11430. Cham: Springer. pp. 202–235. doi:10.1007/978-3-030-17601-3_5. ISBN 978-3-030-17600-6. S2CID 121295850. Archived (PDF) from the original on 9 October 2022.
  5. ^ Grattan-Guinness, Ivor (2017). "Turing's mentor, Max Newman". In Copeland, B. Jack; Bowen, Jonathan P.; Wilson, Robin; Sprevak, Mark (eds.). The Turing Guide. Oxford University Press. ISBN 978-0-19-874782-6.
  6. ^ . The British Library. Archived from the original on 23 July 2019. Retrieved 29 July 2019.
  7. ^ a b Newman, M.H.A. (1955). "Alan Mathison Turing. 1912–1954". Biographical Memoirs of Fellows of the Royal Society. 1: 253–263. doi:10.1098/rsbm.1955.0019. JSTOR 769256. S2CID 711366.
  8. ^ a b Gray, Paul (29 March 1999). . Time. Archived from the original on 19 January 2011. Retrieved 10 January 2011. 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.
  9. ^ Sipser 2006, p. 137
  10. ^ Beavers 2013, p. 481
  11. ^ Copeland, Jack (18 June 2012). "Alan Turing: The codebreaker who saved 'millions of lives'". BBC News Technology. from the original on 11 October 2014. Retrieved 26 October 2014.
  12. ^ 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 (8 January 2015). . The Churchill Centre. Archived from the original on 17 February 2015. Retrieved 9 January 2015. and Hodges, Andrew. "Part 4: The Relay Race". Update to Alan Turing: The Enigma. from the original on 20 January 2015. Retrieved 9 January 2015. 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 (11 September 2009). "Profile: Alan Turing". BBC News. from the original on 13 December 2017. Retrieved 17 February 2015. 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 (1996) [1993], The Influence of ULTRA in the Second World War, Keith Lockstone's home page Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University
  13. ^ Leavitt 2007, pp. 231–233
  14. ^ Olinick, Michael (2021). "Chapter 15". Simply Turing. United States: Simply Charly.
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  22. ^ Plaque #381 on Open Plaques
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  25. ^ Hodges 1983, p. 6
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  31. ^ Alan Mathison (April 2016). "Alan Turing Archive – Sherborne School (ARCHON CODE: GB1949)" (PDF). Sherborne School, Dorset. (PDF) from the original on 26 December 2016. Retrieved 5 February 2017.
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  33. ^ Hofstadter, Douglas R. (1985). Metamagical Themas: Questing for the Essence of Mind and Pattern. Basic Books. p. 484. ISBN 978-0-465-04566-2. OCLC 230812136.
  34. ^ Hodges 1983, p. 26
  35. ^ Hodges 1983, p. 34
  36. ^ "The Shirburnian" (PDF). Archived (PDF) from the original on 9 October 2022.
  37. ^ Caryl, Christian (19 December 2014). "Poor Imitation of Alan Turing". New York Review of Books. from the original on 7 January 2015. Retrieved 9 January 2015.
  38. ^ Hassall, Rachel (2012–2013). (PDF). Vivat!. Archived from the original (PDF) on 15 April 2014.
  39. ^ Teuscher, Christof, ed. (2004). Alan Turing: Life and Legacy of a Great Thinker. Springer-Verlag. ISBN 978-3-540-20020-8. OCLC 53434737.
  40. ^ Hodges 1983, p. 61
  41. ^ Hodges, Andrew (2012). Alan Turing: The Enigma. Princeton University Press. p. 87. ISBN 978-0-691-15564-7.
  42. ^ Hodges, Andrew (2012). Alan Turing: The Enigma. Princeton University Press. p. 90. ISBN 978-0-691-15564-7.
  43. ^ Gray, Paul. . Time Magazine's Most Important People of the Century. p. 2. Archived from the original on 19 January 2011.
  44. ^ Hodges 1983, pp. 82–83
  45. ^ "Alan Turing and the 'Nature of Spirit'". oldshirburnian.org.uk. 15 August 2020.
  46. ^ "AMT-B-10 | the Turing Digital Archive".
  47. ^ Aldrich, John (December 2009). "England and Continental Probability in the Inter-War Years" (PDF). Electronic Journ@l for History of Probability and Statistics. 5 (2): 7–11.
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  49. ^ Hodges 1983, p. 113.
  50. ^ Zabell, S. L. (1995). "Alan Turing and the Central Limit Theorem". The American Mathematical Monthly. 102 (6): 483–494. doi:10.1080/00029890.1995.12004608.
  51. ^ Turing 1937
  52. ^ B. Jack Copeland; Carl J. Posy; Oron Shagrir (2013). Computability: Turing, Gödel, Church, and Beyond. MIT Press. p. 211. ISBN 978-0-262-01899-9.
  53. ^ Avi Wigderson (2019). Mathematics and Computation. Princeton University Press. p. 15. ISBN 978-0-691-18913-0.
  54. ^ Church 1936
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  57. ^ Hodges 1983, p. 138
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Further reading

Articles

  • Turing, Alan (1950). "Computing Machinery and Intelligence" (PDF). Mind. 49 (236): 433–460. doi:10.1093/mind/LIX.236.433. Archived (PDF) from the original on 9 October 2022.
  • Copeland, B. Jack (ed.). "The Mind and the Computing Machine: Alan Turing and others". The Rutherford Journal.
  • Copeland, B. Jack (ed.). "Alan Turing: Father of the Modern Computer". The Rutherford Journal.
  • Hodges, Andrew (2007). "Alan Turing". In Edward N. Zalta (ed.). Stanford Encyclopedia of Philosophy (Winter 2009 ed.). Stanford University. Retrieved 10 January 2011.
  • Hodges, Andrew (2004). "Turing, Alan Mathison". Oxford Dictionary of National Biography (online ed.). Oxford University Press. doi:10.1093/ref:odnb/36578. (Subscription or UK public library membership required.)
  • Gray, Paul (29 March 1999). . Time. Archived from the original on 16 October 2007.

Books

External links

  • 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 Year 17 February 2019 at the Wayback Machine
  • 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
  • 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 (11 December 2001). . System Toolbox. The Binary Freedom Project. Archived from the original on 3 August 2007.
  • – holds papers relating to Turing's time at Sherborne School
  • Alan Turing plaques recorded on openplaques.org
  • Alan Turing archive on New Scientist

May 24, 2023
alan, turing, turing, redirects, here, other, uses, turing, disambiguation, alan, mathison, turing, ʊər, june, 1912, june, 1954, english, mathematician, computer, scientist, logician, cryptanalyst, philosopher, theoretical, biologist, turing, highly, influenti. Turing redirects here For other uses see Turing disambiguation Alan Mathison Turing OBE FRS ˈ tj ʊer ɪ ŋ 23 June 1912 7 June 1954 was an English mathematician computer scientist logician cryptanalyst philosopher and theoretical biologist 6 Turing was highly influential in the development of theoretical computer science providing a formalisation of the concepts of algorithm and computation with the Turing machine which can be considered a model of a general purpose computer 7 8 9 He is widely considered to be the father of theoretical computer science and artificial intelligence 10 Alan TuringOBE FRSTuring c 1928Born 1912 06 23 23 June 1912Maida Vale London EnglandDied7 June 1954 1954 06 07 aged 41 Wilmslow Cheshire EnglandCause of deathCyanide poisoning note 1 EducationSherborne SchoolAlma materUniversity of Cambridge BA MA Princeton University PhD Known forCryptanalysis of the Enigma Turing s proof Turing machine Turing test Unorganised machine Turing pattern Turing reduction The Chemical Basis of Morphogenesis PartnerJoan Clarke engaged in 1941 did not marry AwardsSmith s Prize 1936 Scientific careerFieldsLogic Mathematics Cryptanalysis Computer science Mathematical and theoretical biology 1 InstitutionsUniversity of Manchester Government Code and Cypher School National Physical LaboratoryThesisSystems of Logic Based on Ordinals 1938 Doctoral advisorAlonzo Church 2 Doctoral studentsRobin Gandy 2 3 Beatrice Worsley 4 InfluencesMax Newman 5 SignatureBorn in Maida Vale London Turing was raised in southern England He graduated at King s College Cambridge with a degree in mathematics Whilst he was a fellow at Cambridge he published a proof demonstrating that some purely mathematical yes no questions can never be answered by computation and defined a Turing machine and went on to prove that the halting problem for Turing machines is undecidable In 1938 he obtained his PhD from the Department of Mathematics at Princeton University During the Second World War Turing worked for the Government Code and Cypher School at Bletchley Park Britain s codebreaking centre that produced Ultra intelligence For a time he led Hut 8 the section that was responsible for German naval cryptanalysis Here he devised a number of techniques for speeding the breaking of German ciphers including improvements to the pre war Polish bomba method an electromechanical machine that could find settings for the Enigma machine Turing played a crucial role in cracking intercepted coded messages that enabled the Allies to defeat the Axis powers in many crucial engagements including the Battle of the Atlantic 11 12 After the war Turing worked at the National Physical Laboratory where he designed the Automatic Computing Engine one of the first designs for a stored program computer In 1948 Turing joined Max Newman s Computing Machine Laboratory at the Victoria University of Manchester where he helped develop the Manchester computers 13 and became interested in mathematical biology He wrote a paper on the chemical basis of morphogenesis 1 and predicted oscillating chemical reactions such as the Belousov Zhabotinsky reaction first observed in the 1960s Despite these accomplishments Turing was never fully recognised in Britain during his lifetime because much of his work was covered by the Official Secrets Act 14 Turing was prosecuted in 1952 for homosexual acts He accepted hormone treatment with DES a procedure commonly referred to as chemical castration as an alternative to prison Turing died on 7 June 1954 16 days before his 42nd birthday from cyanide poisoning An inquest determined his death as a suicide but it has been noted that the known evidence is also consistent with accidental poisoning Following a public campaign in 2009 the British prime minister Gordon Brown made an official public apology on behalf of the British government for the appalling way Turing was treated Queen Elizabeth II granted a posthumous pardon in 2013 The term Alan Turing law is now used informally to refer to a 2017 law in the United Kingdom that retroactively pardoned men cautioned or convicted under historical legislation that outlawed homosexual acts 15 Turing has an extensive legacy with statues of him and many things named after him including an annual award for computer science innovations He appears on the current Bank of England 50 note which was released on 23 June 2021 to coincide with his birthday A 2019 BBC series as voted by the audience named him the greatest person of the 20th century Contents 1 Early life and education 1 1 Family 1 2 School 1 3 Christopher Morcom 1 4 University and work on computability 2 Career and research 2 1 Cryptanalysis 2 2 Bombe 2 2 1 Action This Day 2 3 Hut 8 and the naval Enigma 2 4 Turingery 2 5 Delilah 2 6 Early computers and the Turing test 2 7 Pattern formation and mathematical biology 3 Personal life 3 1 Engagement 3 2 Homosexuality and indecency conviction 3 3 Treasure 3 4 Death 3 5 Government apology and pardon 4 Legacy 4 1 Awards honours and tributes 4 2 Centenary celebrations 5 Notes and references 5 1 Notes 5 2 References 5 3 Sources 6 Further reading 6 1 Articles 6 2 Books 7 External linksEarly life and educationFamily Turing was born in Maida Vale London while his father Julius Mathison Turing was on leave from his position with the Indian Civil Service ICS of the British Raj government at Chatrapur then in the Madras Presidency and presently in Odisha state in India 16 17 Turing s father was the son of a clergyman the Rev John Robert Turing from a Scottish family of merchants that had been based in the Netherlands and included a baronet Turing s mother Julius s wife was Ethel Sara Turing nee Stoney daughter of Edward Waller Stoney chief engineer of the Madras Railways The Stoneys were a Protestant Anglo Irish gentry family from both County Tipperary and County Longford while Ethel herself had spent much of her childhood in County Clare 18 Julius and Ethel married on 1 October 1907 at Batholomew s church on Clyde Road in Dublin 19 Julius s work with the ICS brought the family to British India where his grandfather had been a general in the Bengal Army However both Julius and Ethel wanted their children to be brought up in Britain so they moved to Maida Vale 20 London where Alan Turing was born on 23 June 1912 as recorded by a blue plaque on the outside of the house of his birth 21 22 later the Colonnade Hotel 16 23 Turing had an elder brother John Ferrier Turing father of Sir John Dermot Turing 12th Baronet of the Turing baronets 24 Turing s father s civil service commission was still active and during Turing s childhood years his parents travelled between Hastings in the United Kingdom 25 and India leaving their two sons to stay with a retired Army couple At Hastings Turing stayed at Baston Lodge Upper Maze Hill St Leonards on Sea now marked with a blue plaque 26 The plaque was unveiled on 23 June 2012 the centenary of Turing s birth 27 Very early in life Turing showed signs of the genius that he was later to display prominently 28 His parents purchased a house in Guildford in 1927 and Turing lived there during school holidays The location is also marked with a blue plaque 29 School Turing s parents enrolled him at St Michael s a primary school at 20 Charles Road St Leonards on Sea from the age of six to nine The headmistress recognised his talent noting that she has had clever boys and hardworking boys but Alan is a genius 30 Between January 1922 and 1926 Turing was educated at Hazelhurst Preparatory School an independent school in the village of Frant in Sussex now East Sussex 31 In 1926 at the age of 13 he went on to Sherborne School 32 a boarding independent school in the market town of Sherborne in Dorset where he boarded at Westcott House The first day of term coincided with the 1926 General Strike in Britain but Turing was so determined to attend that he rode his bicycle unaccompanied 60 miles 97 km from Southampton to Sherborne stopping overnight at an inn 33 Turing in July 1930 during his senior year at the Sherborne School At the end of the term Turing received the inaugural Cristopher Morcom prize Turing s natural inclination towards mathematics and science did not earn him respect from some of the teachers at Sherborne whose definition of education placed more emphasis on the classics His headmaster wrote to his parents I hope he will not fall between two stools If he is to stay at public school he must aim at becoming educated If he is to be solely a Scientific Specialist he is wasting his time at a public school 34 Despite this Turing continued to show remarkable ability in the studies he loved solving advanced problems in 1927 without having studied even elementary calculus In 1928 aged 16 Turing encountered Albert Einstein s work not only did he grasp it but it is possible that he managed to deduce Einstein s questioning of Newton s laws of motion from a text in which this was never made explicit 35 Christopher Morcom At Sherborne Turing formed a significant friendship with fellow pupil Christopher Collan Morcom 13 July 1911 13 February 1930 36 who has been described by whom as Turing s first love This quote needs a citation Their relationship provided inspiration in Turing s future endeavours but it was cut short by Morcom s death in February 1930 from complications of bovine tuberculosis contracted after drinking infected cow s milk some years previously 37 38 39 The event caused Turing great sorrow He coped with his grief by working that much harder on the topics of science and mathematics that he had shared with Morcom In a letter to Morcom s mother Frances Isobel Morcom nee Swan Turing wrote I am sure I could not have found anywhere another companion so brilliant and yet so charming and unconceited I regarded my interest in my work and in such things as astronomy to which he introduced me as something to be shared with him and I think he felt a little the same about me I know I must put as much energy if not as much interest into my work as if he were alive because that is what he would like me to do 40 Turing s relationship with Morcom s mother continued long after Morcom s death with her sending gifts to Turing and him sending letters typically on Morcom s birthday 41 A day before the third anniversary of Morcom s death 13 February 1933 he wrote to Mrs Morcom I expect you will be thinking of Chris when this reaches you I shall too and this letter is just to tell you that I shall be thinking of Chris and of you tomorrow I am sure that he is as happy now as he was when he was here Your affectionate Alan 42 Some have speculated that Morcom s death was the cause of Turing s atheism and materialism 43 Apparently at this point in his life he still believed in such concepts as a spirit independent of the body and surviving death In a later letter also written to Morcom s mother Turing wrote Personally I believe that spirit is really eternally connected with matter but certainly not by the same kind of body as regards the actual connection between spirit and body I consider that the body can hold on to a spirit whilst the body is alive and awake the two are firmly connected When the body is asleep I cannot guess what happens but when the body dies the mechanism of the body holding the spirit is gone and the spirit finds a new body sooner or later perhaps immediately 44 45 University and work on computability After graduating from Sherborne Turing studied the undergraduate course Parts Ia Ib and II of the Mathematical Tripos from February 1931 to November 1934 at King s College Cambridge where he was awarded first class honours in mathematics His dissertation On the Gaussian error function was written during his senior and delivered on November 1934 with a deadline date of 6 December in it he proved a version of the central limit theorem His dissertation was finally accepted in 16 March 1935 By spring of that same year Turing started his master s course Part III which he completed in 1937 and at the same time he published his first paper a one page article called Equivalence of left and right almost periodicity sent on 23 April featured in the tenth volume of the Journal of the London Mathematical Society 46 Later that year Turing was elected a Fellow of King s College on the strength of his dissertation 47 However and unknown to Turing this version of the theorem he proved in his paper had already been proven in 1922 by Jarl Waldemar Lindeberg Despite this the committee found Turing s methods original and so regarded the work worthy of consideration for the fellowship Abram Besicovitch s report for the committee went so far as to say that if Turing s work had been published before Lindeberg s it would have been an important event in the mathematical literature of that year 48 49 50 Turing in 1935 at his parents home garden Between the springs of 1935 and 1936 at the same time as Church Turing worked on the decidability of problems starting from Godel s incompleteness theorems In mid April 1936 Turing sent Max Newman the first draft typescript of his investigations That same month Alonzo Church published his An Unsolvable Problem of Elementary Number Theory with similar conclusions to Turing s then yet unpublished work Finally on 28 May of that year he finished and delivered his 36 page paper for publication called On Computable Numbers with an Application to the Entscheidungsproblem 51 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 52 In this paper Turing reformulated Kurt Godel s 1931 results on the limits of proof and computation replacing Godel s universal arithmetic based formal language with the formal and simple hypothetical devices that became known as Turing machines 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 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 53 King s College Cambridge where Turing was an undergraduate in 1931 and became a Fellow in 1935 The computer room is named after him Although Turing s proof was published shortly after Alonzo Church s equivalent proof using his lambda calculus 54 Turing s approach is considerably more accessible and intuitive than Church s 55 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 56 To this day Turing machines are a central object of study in theory of computation From September 1936 to July 1938 Turing spent most of his time studying under Church at Princeton University 4 in the second year as a Jane Eliza Procter Visiting Fellow In addition to his purely mathematical work he studied cryptology and also built three of four stages of an electro mechanical binary multiplier 57 In June 1938 he obtained his PhD from the Department of Mathematics at Princeton 58 his dissertation Systems of Logic Based on Ordinals 59 60 introduced the concept of ordinal logic and the notion of relative computing in which Turing machines are augmented with so called oracles allowing the study of problems that cannot be solved by Turing machines John von Neumann wanted to hire him as his postdoctoral assistant but he went back to the United Kingdom 61 Career and researchWhen Turing returned to Cambridge he attended lectures given in 1939 by Ludwig Wittgenstein about the foundations of mathematics 62 The lectures have been reconstructed verbatim including interjections from Turing and other students from students notes 63 Turing and Wittgenstein argued and disagreed with Turing defending formalism and Wittgenstein propounding his view that mathematics does not discover any absolute truths but rather invents them 64 Cryptanalysis During the Second World War Turing was a leading participant in the breaking of German ciphers at Bletchley Park The historian and wartime codebreaker Asa Briggs has said You needed exceptional talent you needed genius at Bletchley and Turing s was that genius 65 From September 1938 Turing worked part time with the Government Code and Cypher School GC amp CS the British codebreaking organisation He concentrated on cryptanalysis of the Enigma cipher machine used by Nazi Germany together with Dilly Knox a senior GC amp CS codebreaker 66 Soon after the July 1939 meeting near Warsaw at which the Polish Cipher Bureau gave the British and French details of the wiring of Enigma machine s rotors and their method of decrypting Enigma machine s messages Turing and Knox developed a broader solution 67 The Polish method relied on an insecure indicator procedure that the Germans were likely to change which they in fact did in May 1940 Turing s approach was more general using crib based decryption for which he produced the functional specification of the bombe an improvement on the Polish Bomba 68 Two cottages in the stable yard at Bletchley Park Turing worked here in 1939 and 1940 before moving to Hut 8 On 4 September 1939 the day after the UK declared war on Germany Turing reported to Bletchley Park the wartime station of GC amp CS 69 Like all others who came to Bletchley he was required to sign the Official Secrets Act in which he agreed not to disclose anything about his work at Bletchley with severe legal penalties for violating the Act 70 Specifying the bombe was the first of five major cryptanalytical advances that Turing made during the war The others were deducing the indicator procedure used by the German navy developing a statistical procedure dubbed Banburismus for making much more efficient use of the bombes developing a procedure dubbed Turingery for working out the cam settings of the wheels of the Lorenz SZ 40 42 Tunny cipher machine and towards the end of the war the development of a portable secure voice scrambler at Hanslope Park that was codenamed Delilah By using statistical techniques to optimise the trial of different possibilities in the code breaking process Turing made an innovative contribution to the subject He wrote two papers discussing mathematical approaches titled The Applications of Probability to Cryptography 71 and Paper on Statistics of Repetitions 72 which were of such value to GC amp CS and its successor GCHQ that they were not released to the UK National Archives until April 2012 shortly before the centenary of his birth A GCHQ mathematician who identified himself only as Richard said at the time that the fact that the contents had been restricted under the Official Secrets Act for some 70 years demonstrated their importance and their relevance to post war cryptanalysis 73 He said the fact that the contents had been restricted shows what a tremendous importance it has in the foundations of our subject The papers detailed using mathematical analysis to try and determine which are the more likely settings so that they can be tried as quickly as possible Richard said that GCHQ had now squeezed the juice out of the two papers and was happy for them to be released into the public domain Turing had a reputation for eccentricity at Bletchley Park He was known to his colleagues as Prof and his treatise on Enigma was known as the Prof s Book 74 75 According to historian Ronald Lewin Jack Good a cryptanalyst who worked with Turing said of his colleague In the first week of June each year he would get a bad attack of hay fever and he would cycle to the office wearing a service gas mask to keep the pollen off His bicycle had a fault the chain would come off at regular intervals Instead of having it mended he would count the number of times the pedals went round and would get off the bicycle in time to adjust the chain by hand Another of his eccentricities is that he chained his mug to the radiator pipes to prevent it being stolen 76 Peter Hilton recounted his experience working with Turing in Hut 8 in his Reminiscences of Bletchley Park from A Century of Mathematics in America 77 It is a rare experience to meet an authentic genius Those of us privileged to inhabit the world of scholarship are familiar with the intellectual stimulation furnished by talented colleagues We can admire the ideas they share with us and are usually able to understand their source we may even often believe that we ourselves could have created such concepts and originated such thoughts However the experience of sharing the intellectual life of a genius is entirely different one realizes that one is in the presence of an intelligence a sensibility of such profundity and originality that one is filled with wonder and excitement Alan Turing was such a genius and those like myself who had the astonishing and unexpected opportunity created by the strange exigencies of the Second World War to be able to count Turing as colleague and friend will never forget that experience nor can we ever lose its immense benefit to us Hilton echoed similar thoughts in the Nova PBS documentary Decoding Nazi Secrets 78 While working at Bletchley Turing who was a talented long distance runner occasionally ran the 40 miles 64 km to London when he was needed for meetings 79 and he was capable of world class marathon standards 80 81 Turing tried out for the 1948 British Olympic team but he was hampered by an injury His tryout time for the marathon was only 11 minutes slower than British silver medallist Thomas Richards Olympic race time of 2 hours 35 minutes He was Walton Athletic Club s best runner a fact discovered when he passed the group while running alone 82 83 84 When asked why he ran so hard in training he replied I have such a stressful job that the only way I can get it out of my mind is by running hard it s the only way I can get some release 85 Due to the problems of counterfactual history it is hard to estimate the precise effect Ultra intelligence had on the war 86 However official war historian Harry Hinsley estimated that this work shortened the war in Europe by more than two years and saved over 14 million lives 87 At the end of the war a memo was sent to all those who had worked at Bletchley Park reminding them that the code of silence dictated by the Official Secrets Act did not end with the war but would continue indefinitely 70 Thus even though Turing was appointed an Officer of the Order of the British Empire OBE in 1946 by King George VI for his wartime services his work remained secret for many years 88 89 Bombe Main article Bombe Within weeks of arriving at Bletchley Park 69 Turing had specified an electromechanical machine called the bombe which could break Enigma more effectively than the Polish bomba kryptologiczna from which its name was derived The bombe with an enhancement suggested by mathematician Gordon Welchman became one of the primary tools and the major automated one used to attack Enigma enciphered messages 90 A working replica of a bombe now at The National Museum of Computing on Bletchley ParkThe 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 91 the bombe performed a chain of logical deductions based on the crib implemented electromechanically 92 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 93 Action This Day Main article Action This Day memo 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 94 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 94 As Andrew Hodges biographer of Turing later wrote This letter had an electric effect 95 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 95 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 96 More than two hundred bombes were in operation by the end of the war 97 Statue of Turing holding an Enigma machine by Stephen Kettle at Bletchley Park commissioned by Sidney Frank built from half a million pieces of Welsh slate 98 Hut 8 and the naval Enigma Turing decided to tackle the particularly difficult problem of German naval Enigma because no one else was doing anything about it and I could have it to myself 99 In December 1939 Turing solved the essential part of the naval indicator system which was more complex than the indicator systems used by the other services 99 100 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 99 For this he invented a measure of weight of evidence that he called the ban Banburismus could rule out certain sequences of the Enigma rotors substantially reducing the time needed to test settings on the bombes 101 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 102 Turing travelled to the United States in November 1942 103 and worked with US Navy cryptanalysts on the naval Enigma and bombe construction in Washington he also visited their Computing Machine Laboratory in Dayton Ohio Turing s reaction to the American bombe design was far from enthusiastic 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 104 During this trip he also assisted at Bell Labs with the development of secure speech devices 105 He returned to Bletchley Park in March 1943 During his absence 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 106 Alexander wrote of Turing s contribution 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 107 Turingery Main article Turingery In July 1942 Turing devised a technique termed Turingery or jokingly Turingismus 108 for use against the Lorenz cipher messages produced by the Germans new Geheimschreiber secret writer machine This was a teleprinter 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 109 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 and whose superior speed allowed the statistical decryption techniques to be applied usefully to the messages 110 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 111 112 but he was not directly involved in the Colossus development 113 Delilah Following his work at Bell Labs in the US 114 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 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 115 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 116 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 Early computers and the Turing test Plaque 78 High Street Hampton Between 1945 and 1947 Turing lived in Hampton London 117 while he worked on the design of the ACE Automatic Computing Engine at the National Physical Laboratory NPL He presented a paper on 19 February 1946 which was the first detailed design of a stored program computer 118 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 119 Although ACE was a feasible design the effect of the 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 120 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 121 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 122 According to the memoirs of the German computer pioneer Heinz Billing from the Max Planck Institute for Physics published by Genscher Dusseldorf there was a meeting between Turing and Konrad Zuse 123 It took place in Gottingen 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 In 1948 Turing was appointed reader in the 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 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 124 During this time he continued to do more abstract work in mathematics 125 and in Computing Machinery and Intelligence 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 126 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 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 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 127 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 128 According to Garry Kasparov Turing s program played a recognizable game of chess 129 The program lost to Turing s colleague Alick Glennie although it is said that it won a game against Champernowne s wife Isabel 130 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 131 Pattern formation and mathematical biology When Turing was 39 years old in 1951 he turned to 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 132 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 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 133 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 134 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 135 136 137 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 138 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 139 Later papers were not available until Collected Works of A M Turing was published in 1992 140 A study conducted in 2023 confirmed Turing s mathematical model hypothesis Presented by the American Physical Society the experiment involved growing chia seeds in even layers within trays later adjusting the available moisture Researchers experimentally tweaked the factors which appear in the Turing equations and as a result patterns resembling those seen in natural environments emerged This is believed to be the first time that experiments with living vegetation have verified Turing s mathematical insight 141 142 Personal lifeEngagement In 1941 Turing proposed marriage to Hut 8 colleague Joan Clarke a fellow mathematician and cryptanalyst but their engagement was short lived After admitting his homosexuality to his fiancee who was reportedly unfazed by the revelation Turing decided that he could not go through with the marriage 143 Homosexuality and indecency conviction In January 1952 Turing was 39 when he started a relationship with Arnold Murray a 19 year old unemployed man Just before Christmas Turing was walking along Manchester s Oxford Road when he met Murray just outside the Regal Cinema and invited him to lunch On 23 January Turing s house was burgled Murray told Turing that he and the burglar were acquainted and Turing reported the crime to the police During the investigation he acknowledged a sexual relationship with Murray Homosexual acts were criminal offences in the United Kingdom at that time 144 and both men were charged with gross indecency under Section 11 of the Criminal Law Amendment Act 1885 145 Initial committal proceedings for the trial were held on 27 February during which Turing s solicitor reserved his defence i e did not argue or provide evidence against the allegations The proceedings were held at the Sessions House in Knutsford 146 Turing was later convinced by the advice of his brother and his own solicitor and he entered a plea of guilty 147 The case Regina v Turing and Murray was brought to trial on 31 March 1952 148 Turing was convicted and given a choice between imprisonment and probation His probation would be conditional on his agreement to undergo hormonal physical changes designed to reduce libido known as chemical castration 149 He accepted the option of injections of what was then called stilboestrol now known as diethylstilbestrol or DES a synthetic oestrogen this feminization of his body was continued for the course of one year The treatment rendered Turing impotent and caused breast tissue to form 150 fulfilling in the literal sense Turing s prediction that no doubt I shall emerge from it all a different man but quite who I ve not found out 151 152 Murray was given a conditional discharge 153 Turing s conviction led to the removal of his security clearance and barred him from continuing with his cryptographic consultancy for the Government Communications Headquarters GCHQ the British signals intelligence agency that had evolved from GC amp CS in 1946 though he kept his academic job He was denied entry into the United States after his conviction in 1952 but was free to visit other European countries 154 Treasure In the 1940s Turing became worried about losing his savings in the event of a German invasion In order to protect it he bought two silver bars weighing 3 200 oz 90 kg and worth 250 in 2022 8 000 adjusted for inflation 48 000 at spot price and buried them in a wood near Bletchley Park 155 Upon returning to dig them up Turing found that he was unable to break his own code describing where exactly he had hidden them This along with the fact that the area had been renovated meant that he never regained the silver 156 Death A blue plaque on the house at 43 Adlington Road Wilmslow where Turing lived and died 157 On 8 June 1954 at his house at 43 Adlington Road Wilmslow 157 Turing s housekeeper found him dead He had died the previous day at the age of 41 Cyanide poisoning was established as the cause of death 158 When his body was discovered an apple lay half eaten beside his bed and although the apple was not tested for cyanide 159 it was speculated that this was the means by which Turing had consumed a fatal dose An inquest determined his death to be a suicide 149 Andrew Hodges and another biographer David Leavitt have both speculated that Turing was re enacting a scene from the Walt Disney film Snow White and the Seven Dwarfs 1937 his favourite fairy tale Both men noted that in Leavitt s words he took an especially keen pleasure in the scene where the Wicked Queen immerses her apple in the poisonous brew 160 Turing s remains were cremated at Woking Crematorium on 12 June 1954 161 and his ashes were scattered in the gardens of the crematorium just as his father s had been 162 Philosopher Jack Copeland has questioned various aspects of the coroner s historical verdict He suggested an alternative explanation for the cause of Turing s death the accidental inhalation of cyanide fumes from an apparatus used to electroplate gold onto spoons The potassium cyanide was used to dissolve the gold Turing had such an apparatus set up in his tiny spare room Copeland noted that the autopsy findings were more consistent with inhalation than with ingestion of the poison Turing also habitually ate an apple before going to bed and it was not unusual for the apple to be discarded half eaten 163 Furthermore Turing had reportedly borne his legal setbacks and hormone treatment which had been discontinued a year previously with good humour and had shown no sign of despondency before his death He even set down a list of tasks that he intended to complete upon returning to his office after the holiday weekend 163 Turing s mother believed that the ingestion was accidental resulting from her son s careless storage of laboratory chemicals 164 Biographer Andrew Hodges theorised that Turing deliberately left the nature of his death ambiguous in order to shield his mother from the knowledge that he had killed himself 165 Turing s OBE currently held in Sherborne School archives It has been suggested that Turing s belief in fortune telling may have caused his depressed mood 162 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 162 According to the Greenbaums daughter Barbara 166 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 Government apology and pardon Main article Alan Turing law In August 2009 British programmer John Graham Cumming started a petition urging the British government to apologise for Turing s prosecution as a homosexual 167 168 The petition received more than 30 000 signatures 169 170 The prime minister Gordon Brown acknowledged the petition releasing a statement on 10 September 2009 apologising and describing the treatment of Turing as appalling 169 171 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 169 172 In December 2011 William Jones and his member of Parliament John Leech created an e petition 173 requesting that the British government pardon Turing for his conviction of gross indecency 174 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 173 The petition gathered over 37 000 signatures 173 175 and was submitted to Parliament by the Manchester MP John Leech but the request was discouraged by Justice Minister Lord McNally who said 176 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 177 John Leech the MP for Manchester Withington 2005 15 submitted several bills to Parliament 178 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 179 Leech continued to take the bill through Parliament and campaigned for several years gaining the public support of numerous leading scientists including Stephen Hawking 180 181 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 182 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 183 184 185 186 187 188 189 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 190 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 191 The government indicated it would support the bill 192 193 194 and it passed its third reading in the House of Lords in October 195 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 196 but before the bill could be debated in the House of Commons 197 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 198 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 175 199 The Queen officially pronounced Turing pardoned in August 2014 200 The Queen s action is only the fourth royal pardon granted since the conclusion of the Second World War 201 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 202 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 203 204 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 205 LegacyMain article Legacy of Alan Turing See also List of things named after Alan Turing Awards honours and tributes The Alan Turing Building at the University of Manchester in 2008 Turing was appointed an officer of the Order of the British Empire in 1946 89 He was also elected a Fellow of the Royal Society FRS in 1951 7 Turing memorial statue plaque in Sackville Park Manchester Turing has been honoured in various ways in Manchester the city where he worked towards the end of his life In 1994 a stretch of the A6010 road the Manchester city intermediate ring road was named Alan Turing Way A bridge carrying this road was widened and carries the name Alan Turing Bridge A statue of Turing was unveiled in Manchester on 23 June 2001 in Sackville Park between the University of Manchester building on Whitworth Street and Canal Street The memorial statue depicts the father of computer science sitting on a bench at a central position in the park holding an apple The cast bronze bench carries in relief the text Alan Mathison Turing 1912 1954 and IEKYF ROMSI ADXUO KVKZC GUBJ The latter is described by the sculptor Glyn Hughes as a motto as encoded by the German Enigma 206 The original message is often given as Founder of Computer Science 207 208 209 however this is unlikely as the Enigma ciphering system does not allow a letter to be enciphered to itself while the fourteenth letter of that message the U in Computer is the same as the fourteenth letter of the encoded inscription citation needed A plaque at the statue s feet reads Father of Computer Science Mathematician Logician Wartime Codebreaker Victim of Prejudice followed by a Bertrand Russell quotation Mathematics rightly viewed possesses not only truth but supreme beauty a beauty cold and austere like that of sculpture The sculptor s own old Amstrad computer is buried under the statue as a tribute to the godfather of all modern computer 210 In 1999 Time magazine named Turing as one of the 100 Most Important People of the 20th century and stated 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 8 A blue plaque was unveiled at King s College Cambridge on the centenary of his birth on 23 June 2012 and is now installed at the college s Keynes Building on King s Parade 211 212 A 12 foot 3 7 m high steel sculpture designed in Turing s honour by Sir Antony Gormley is planned to be installed at King s College but Historic England deemed the sculpture too abstract for the setting saying that it would result in harm of a less than substantial nature to the significance of the listed buildings and landscape and by extension the conservation area 213 On 25 March 2021 the Bank of England publicly unveiled the design for a new 50 note featuring Turing s portrait before its official issue on 23 June Turing s birthday Turing was selected as the new face of the note in 2019 following a public nomination process 214 Centenary celebrations Main article Alan Turing Year To mark the 100th anniversary of Turing s birth the Turing Centenary Advisory Committee TCAC co ordinated the Alan Turing Year in 2012 a year long programme of events around the world honouring Turing s life and achievements The TCAC chaired by S Barry Cooper with Turing s nephew Sir John Dermot Turing acting as Honorary President worked with the University of Manchester faculty members and a broad spectrum of people from Cambridge University and Bletchley Park Notes and referencesNotes Turing s death was officially determined as a suicide by an inquest but this has been disputed References This article has an unclear citation style The references used may be made clearer with a different or consistent style of citation and footnoting April 2022 Learn how and when to remove this template message a b Alan Turing publications indexed by Google Scholar a b Alan Turing at the Mathematics Genealogy Project Gandy Robin Oliver 1953 On axiomatic systems in mathematics and theories in physics PhD thesis University of Cambridge doi 10 17863 CAM 16125 EThOS uk bl ethos 590164 Archived from the original on 9 December 2017 Retrieved 9 December 2017 a b Bowen Jonathan P 2019 The Impact of Alan Turing Formal Methods and Beyond In Bowen Jonathan P Liu Zhiming Zhang Zili eds Engineering Trustworthy Software Systems SETSS 2018 PDF Lecture Notes in Computer Science Vol 11430 Cham Springer pp 202 235 doi 10 1007 978 3 030 17601 3 5 ISBN 978 3 030 17600 6 S2CID 121295850 Archived PDF from the original on 9 October 2022 Grattan Guinness Ivor 2017 Turing s mentor Max Newman In Copeland B Jack Bowen Jonathan P Wilson Robin Sprevak Mark eds The Turing Guide Oxford University Press ISBN 978 0 19 874782 6 Alan Turing The British Library Archived from the original on 23 July 2019 Retrieved 29 July 2019 a b Newman M H A 1955 Alan Mathison Turing 1912 1954 Biographical Memoirs of Fellows of the Royal Society 1 253 263 doi 10 1098 rsbm 1955 0019 JSTOR 769256 S2CID 711366 a b Gray Paul 29 March 1999 Computer Scientist Alan Turing Time Archived from the original on 19 January 2011 Retrieved 10 January 2011 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 p 137 Beavers 2013 p 481 Copeland Jack 18 June 2012 Alan Turing The codebreaker who saved millions of lives BBC News Technology Archived from the original on 11 October 2014 Retrieved 26 October 2014 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 8 January 2015 Myths gt Churchill Said Turing Made the Single Biggest Contribution to Allied Victory The Churchill Centre Archived from the original on 17 February 2015 Retrieved 9 January 2015 and Hodges Andrew Part 4 The Relay Race Update to Alan Turing The Enigma Archived from the original on 20 January 2015 Retrieved 9 January 2015 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 11 September 2009 Profile Alan Turing BBC News Archived from the original on 13 December 2017 Retrieved 17 February 2015 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 1996 1993 The Influence of ULTRA in the Second World War Keith Lockstone s home page Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University Leavitt 2007 pp 231 233 Olinick Michael 2021 Chapter 15 Simply Turing United States Simply Charly Alan Turing law Thousands of gay men to be pardoned BBC News 20 October 2016 Archived from the original on 20 October 2016 Retrieved 20 October 2016 a b Hodges 1983 p 5 The Alan Turing Internet Scrapbook Alan Turing The Enigma Archived from the original on 14 June 2012 Retrieved 2 January 2012 Maguire Phil 23 June 2012 An Irishman s Diary The Irish Times p 5 Irish Marriages 1845 1958 Dublin South Dublin Ireland Group Registration ID 1990366 SR District Reg Area Dublin South London Blue Plaques English Heritage 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2013 Retrieved 31 October 2013 Cawthorne Nigel 2014 Alan Turing the enigma man London p 18 ISBN 978 1 78404 535 7 OCLC 890938716 Alan Mathison April 2016 Alan Turing Archive Sherborne School ARCHON CODE GB1949 PDF Sherborne School Dorset Archived PDF from the original on 26 December 2016 Retrieved 5 February 2017 Alan Turing OBE PhD FRS 1912 1954 The Old Shirburnian Society 1 September 2016 Retrieved 10 October 2020 Hofstadter Douglas R 1985 Metamagical Themas Questing for the Essence of Mind and Pattern Basic Books p 484 ISBN 978 0 465 04566 2 OCLC 230812136 Hodges 1983 p 26 Hodges 1983 p 34 The Shirburnian PDF Archived PDF from the original on 9 October 2022 Caryl Christian 19 December 2014 Poor Imitation of Alan Turing New York Review of Books Archived from the original on 7 January 2015 Retrieved 9 January 2015 Hassall Rachel 2012 2013 The Sherborne Formula The Making of Alan Turing PDF Vivat Archived from the original PDF on 15 April 2014 Teuscher Christof ed 2004 Alan Turing Life and Legacy of a Great Thinker Springer Verlag ISBN 978 3 540 20020 8 OCLC 53434737 Hodges 1983 p 61 Hodges Andrew 2012 Alan Turing The Enigma Princeton University Press p 87 ISBN 978 0 691 15564 7 Hodges Andrew 2012 Alan Turing The Enigma Princeton University Press p 90 ISBN 978 0 691 15564 7 Gray Paul Alan Turing Time Magazine s Most Important People of the Century p 2 Archived from the original on 19 January 2011 Hodges 1983 pp 82 83 Alan Turing and the Nature of Spirit oldshirburnian org uk 15 August 2020 AMT B 10 the Turing Digital Archive Aldrich John December 2009 England and Continental Probability in the Inter War Years PDF Electronic Journ l for History of Probability and Statistics 5 2 7 11 Turing Dermot 2015 Prof Alan Turing Decoded The History Press p 69 ISBN 9781841656434 Hodges 1983 p 113 Zabell S L 1995 Alan Turing and the Central Limit Theorem The American Mathematical Monthly 102 6 483 494 doi 10 1080 00029890 1995 12004608 Turing 1937 B Jack Copeland Carl J Posy Oron Shagrir 2013 Computability Turing Godel Church and Beyond MIT Press p 211 ISBN 978 0 262 01899 9 Avi Wigderson 2019 Mathematics and Computation Princeton University Press p 15 ISBN 978 0 691 18913 0 Church 1936 Grime James February 2012 What Did Turing Do for Us NRICH University of Cambridge Archived from the original on 4 March 2016 Retrieved 28 February 2016 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 p 138 Turing A M 1939 Systems of Logic Based on Ordinals Proceedings of the London Mathematical Society s2 45 161 228 doi 10 1112 plms s2 45 1 161 hdl 21 11116 0000 0001 91CE 3 Turing Alan 1938 Systems of Logic Based on Ordinals PhD thesis Princeton University doi 10 1112 plms s2 45 1 161 hdl 21 11116 0000 0001 91CE 3 ProQuest 301792588 Turing A M 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Conversation with Sir John Dermot Turing New Orleans The National WWII Museum Retrieved 24 August 2021 Turing Alan c 1941 The Applications of Probability to Cryptography The National Archives United Kingdom HW 25 37 Archived from the original on 7 April 2015 Retrieved 25 March 2015 Turing Alan c 1941 Paper on Statistics of Repetitions The National Archives United Kingdom HW 25 38 Archived from the original on 8 April 2015 Retrieved 25 March 2015 Vallance Chris 19 April 2012 Alan Turing papers on code breaking released by GCHQ BBC News Archived from the original on 4 October 2012 Retrieved 20 April 2012 Hodges 1983 p 208 Turing Alan M 1940 The Prof s Book Turing s Treatise on the Enigma In late 1940 Alan Turing wrote a report describing the methods he and his colleagues at Bletchley Park had used to break into the German Enigma cipher systems At Bletchley it was known as the Prof s Book A copy of this handbook was at last released from secrecy by the American National Security Agency in April 1996 under the title Turing s Treatise on the Enigma Subsequently a much better original copy was released by the British National Archives box HW 25 3 This also revealed a title which had been lost in the American copy Mathematical theory of ENIGMA machine Though oddly the report does not actually have any mathematical theory Lewin 1978 p 57 Hilton Peter A Century of Mathematics in America Part 1 Reminiscences of Bletchley Park PDF Archived PDF from the original on 29 August 2019 Hilton Peter NOVA Transcripts Decoding Nazi Secrets PBS PBS Archived from the original on 29 August 2019 Brown Anthony Cave 1975 Bodyguard of Lies The Extraordinary True Story Behind D Day The Lyons Press ISBN 978 1 59921 383 5 Graham Cumming John 10 March 2010 An Olympic honour for Alan Turing The Guardian London Archived from the original on 1 December 2016 Retrieved 10 December 2016 Butcher Pat 14 September 2009 In Praise of Great Men Globe Runner Archived from the original on 18 August 2013 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from the original on 7 July 2018 Retrieved 21 June 2018 a b This month in history Alan Turing and the Enigma code thegazette co uk Archived from the original on 26 June 2019 Retrieved 6 February 2019 Welchman Gordon 1997 1982 The Hut Six story Breaking the Enigma codes Cleobury Mortimer England M amp M Baldwin p 81 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 Retrieved 18 March 2021 Oakley 2006 p 40 03B a b Hodges 1983 p 218 a b Hodges 1983 p 221 Copeland The Essential Turing pp 336 337 Archived 18 February 2015 at the Wayback Machine Copeland Jack Proudfoot Diane May 2004 Alan Turing Codebreaker and Computer Pioneer alanturing net Archived from the original on 9 July 2007 Retrieved 27 July 2007 Bletchley Park Unveils Statue Commemorating Alan Turing Archived from the original on 30 June 2007 Retrieved 30 June 2007 a b c Mahon 1945 p 14 Leavitt 2007 pp 184 186 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Retrieved 6 February 2019 Hodges 1983 pp 488 489 Vincent Dowd 6 June 2014 What was Alan Turing really like BBC Archived from the original on 17 January 2019 Retrieved 16 January 2019 Thousands call for Turing apology BBC News 31 August 2009 Archived from the original on 31 August 2009 Retrieved 31 August 2009 Petition seeks apology for Enigma code breaker Turing CNN 1 September 2009 Archived from the original on 5 October 2009 Retrieved 1 September 2009 a b c Davies Caroline 11 September 2009 PM s apology to codebreaker Alan Turing we were inhumane The Guardian UK Archived from the original on 4 February 2017 Retrieved 10 December 2016 The petition was only open to UK citizens PM apology after Turing petition BBC News 11 September 2009 Archived from the original on 31 May 2012 Retrieved 11 September 2009 Full text of the Prime Minister s apology Archived from the original on 9 November 2012 a b c Grant a pardon to Alan Turing 6 December 2011 Archived from the original on 10 January 2012 Petition to pardon computer pioneer Alan Turing started BBC News 6 December 2011 Archived from the original on 19 June 2018 Retrieved 21 June 2018 a b Wright Oliver 23 December 2013 Alan Turing gets his royal pardon for gross indecency 61 years after he poisoned himself The Independent London Archived from the original on 24 December 2013 Retrieved 21 August 2017 Wainwright Martin 7 February 2012 Government rejects a pardon for computer genius Alan Turing The Guardian Archived from the original on 4 February 2017 Retrieved 10 December 2016 hansard Parliament of the United Kingdom 2 February 2012 Archived from the original on 6 July 2017 Retrieved 29 August 2017 Stevenson Alex 24 December 2013 Better late than never Alan Turing is finally pardoned politics co uk Archived from the original on 16 August 2016 Retrieved 25 September 2016 Fitzgerald Todd 24 September 2016 Alan Turing s court convictions go on display for the first time manchestereveningnews co uk Archived from the original on 25 September 2016 Retrieved 25 September 2016 Britton Paul 24 December 2013 Alan Turing pardoned by The Queen for his unjust and discriminatory conviction for homosexuality Manchester Evening News Archived from the original on 24 June 2018 Retrieved 24 June 2018 MP calls for pardon for computer pioneer Alan Turing BBC News 1 February 2012 Archived from the original on 2 July 2016 Retrieved 25 September 2016 My proudest day as a Liberal Democrat Liberal Democrat Voice Archived from the original on 24 June 2018 Retrieved 24 June 2018 Manchester computer pioneer Alan Turing announced as face of new 50 note 15 July 2019 Archived from the original on 19 July 2019 Retrieved 19 July 2019 John Leech secures historic deal with Government on Alan Turing Law outnewsglobal com 20 October 2016 Elliott Larry Halliday Josh eds 15 July 2019 Alan Turing to feature on new 50 banknote The Guardian via www theguardian com Bloom Dan 23 October 2016 Tory refuses to apologise for killing bad law pardoning thousands of gay men mirror 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 31 January 2017 Bank of England honours Alan Turing on 50 note QNews 15 July 2019 Bill Parliament of the United Kingdom 26 July 2012 Archived from the original on 2 November 2013 Retrieved 31 October 2013 Pearse Damian 13 December 2012 Alan Turing should be pardoned argue Stephen Hawking and top scientists The Guardian Archived from the original on 4 February 2017 Retrieved 15 December 2012 Watt Nicholas 19 July 2013 Enigma codebreaker Alan Turing to be given posthumous pardon The Guardian London Archived from the original on 4 January 2017 Retrieved 10 December 2016 Worth Dan 30 October 2013 Alan Turing pardon sails through House of Lords V3 Archived from the original on 24 December 2013 Retrieved 24 December 2013 Alan Turing Statutory Pardon Bill Archived from the original on 5 July 2013 Retrieved 20 July 2013 Roberts Scott 2 December 2013 Lib Dem MP John Leech disappointed at delay to Alan Turing pardon bill Pink News Archived from the original on 25 December 2013 Retrieved 24 December 2013 Roberts Scott 2 December 2013 Lib Dem MP John Leech disappointed at delay to Alan Turing pardon bill PinkNews Archived from the original on 12 June 2018 Retrieved 20 June 2018 Alan Turing Statutory Pardon Bill Archived from the original on 2 November 2013 Retrieved 24 December 2013 Swinford Steven 23 December 2013 Alan Turing granted Royal pardon by the Queen The Daily Telegraph Archived from the original on 2 May 2018 Retrieved 5 April 2018 Royal pardon for codebreaker Alan Turing BBC News 24 December 2013 Archived from the original on 24 December 2013 Retrieved 24 December 2013 With Queen s Decree Alan Turing Is Now Officially Pardoned Advocate com 22 August 2014 Archived from the original on 1 November 2014 Retrieved 1 November 2014 Pardoned Alan Turing Computing patriarch Time Magazine Vol 183 no 1 13 January 2014 p 14 Davies Caroline 24 December 2013 Codebreaker Turing is given posthumous royal pardon The Guardian London pp 1 6 Government committed to Alan Turing gay pardon law BBC News 22 September 2016 Archived from the original on 22 September 2016 Retrieved 22 September 2016 Cowburn Ashley 21 September 2016 Theresa May committed to introducing the Alan Turing Law The Independent Archived from the original on 22 September 2016 Retrieved 22 September 2016 Policing and Crime Act 2017 Government of the United Kingdom Archived from the original on 5 March 2019 Retrieved 6 February 2019 Hughes Glyn ALAN MATHISON TURING 1912 Archived from the original on 13 August 2010 Retrieved 20 January 2023 Wyke Terry Cocks Harry 2004 Public Sculpture of Greater Manchester Liverpool University Press pp 123 125 ISBN 0853235678 Retrieved 20 January 2023 The philanthropy of Alan Turing Science and Engineering The University of Manchester 20 November 2019 Retrieved 20 January 2023 Shena Simon Campus The Mancester College 12 August 2021 Retrieved 20 January 2023 Computer buried in tribute to genius Manchester Evening News 17 February 2007 Archived from the original on 4 November 2013 Retrieved 7 December 2014 Blue plaque to commemorate Alan Turing King s College Cambridge Archived from the original on 7 December 2018 Retrieved 8 December 2018 Turing plaque fixed in place King s College Cambridge Archived from the original on 9 December 2018 Retrieved 8 December 2018 Reid Smith Tris 1 May 2020 Heritage watchdog objects to statue of gay hero Alan Turing at Kings College Cambridge Gay Star News Archived from the original on 9 January 2022 Retrieved 8 May 2020 Pylas Pan 25 March 2021 WWII codebreaker Alan Turing honoured on new UK bank note AP News Associated Press Retrieved 25 March 2021 Sources Agar Jon 2001 Turing and the Universal Machine Duxford Icon ISBN 978 1 84046 250 0 Agar Jon 2003 The government machine a revolutionary history of the computer Cambridge Massachusetts MIT Press 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 2013 Alan Turing Mathematical Mechanist In Cooper S Barry van Leeuwen Jan eds Alan Turing His Work and Impact Waltham Elsevier pp 481 485 ISBN 978 0 12 386980 7 Beniger James 1986 The control revolution technological and economic origins of the information society Cambridge Massachusetts Harvard University Press ISBN 978 0 674 16986 9 Babbage Charles 1864 Campbell Kelly Martin ed Passages from the life of a philosopher Rough Draft Printing published 2008 ISBN 978 1 60386 092 5 Bodanis David 2005 Electric Universe How Electricity Switched on the Modern World New York Three Rivers Press ISBN 978 0 307 33598 2 OCLC 61684223 Bruderer Herbert 2012 Die Maschinen von Charles Babbage Alan Turing und John von Neumann Konrad Zuse und die Schweiz Wer hat den Computer erfunden in German Munchen Oldenbourg Wissenschaftsverlag doi 10 1524 9783486716658 ISBN 978 3 486 71366 4 Campbell Kelly Martin Aspray William 1996 Computer A History of the Information Machine New York Basic Books ISBN 978 0 465 02989 1 Ceruzzi Paul E 1998 A History of Modern Computing Cambridge Massachusetts and London MIT Press ISBN 978 0 262 53169 6 Chandler Alfred 1977 The Visible Hand The Managerial Revolution in American Business Cambridge Massachusetts Belknap Press ISBN 978 0 674 94052 9 Church Alonzo 1936 An Unsolvable Problem of Elementary Number Theory American Journal of Mathematics 58 2 345 363 doi 10 2307 2371045 ISSN 0002 9327 JSTOR 2371045 Cooper S Barry van Leeuwen Jan 2013 Alan Turing His Work and Impact New York Elsevier ISBN 978 0 12 386980 7 Copeland B Jack 2004a Colossus Its Origins and Originators IEEE Annals of the History of Computing 26 4 38 45 doi 10 1109 MAHC 2004 26 S2CID 20209254 Copeland B Jack ed 2004b The Essential Turing Oxford Oxford University Press ISBN 978 0 19 825079 1 OCLC 156728127 Copeland B Jack ed 2005 Alan Turing s Automatic Computing Engine Oxford Oxford University Press ISBN 978 0 19 856593 2 OCLC 224640979 Copeland B Jack 2006 Colossus The secrets of Bletchley Park s code breaking computers Oxford University Press ISBN 978 0 19 284055 4 Hilton Peter 2006 Living with Fish Breaking Tunny in the Newmanry and Testery Colussus in Copeland 2006 pp 189 203 Edwards Paul N 1996 The closed world computers and the politics of discourse in Cold War America Cambridge Massachusetts MIT Press ISBN 978 0 262 55028 4 Gannon Paul 2007 2006 Colossus Bletchley Park s Greatest Secret London Atlantic Books ISBN 978 1 84354 331 2 Hodges Andrew 1983 Alan Turing the enigma London Burnett Books ISBN 978 0 09 152130 1 Hochhuth Rolf 1988 Alan Turing en berattelse Symposion ISBN 978 91 7868 109 9 Leavitt David 2007 The man who knew too much Alan Turing and the invention of the computer Phoenix ISBN 978 0 7538 2200 5 Levin Janna 2006 A Madman Dreams of Turing Machines New York Knopf ISBN 978 1 4000 3240 2 Lewin Ronald 1978 Ultra Goes to War The Secret Story Classic Military History Classic Penguin ed London Hutchinson amp Co published 2001 ISBN 978 1 56649 231 7 Lubar Steven 1993 Infoculture Boston Massachusetts and New York Houghton Mifflin ISBN 978 0 395 57042 5 Mahon A P 1945 The History of Hut Eight 1939 1945 UK National Archives Reference HW 25 2 Retrieved 10 December 2009 Oakley Brian ed 2006 The Bletchley Park War Diaries July 1939 August 1945 2 6 ed Wynne Press O Connell H Fitzgerald M 2003 Did Alan Turing have Asperger s syndrome Irish Journal of Psychological Medicine Irish Institute of Psychological Medicine 20 1 28 31 doi 10 1017 s0790966700007503 ISSN 0790 9667 PMID 30440230 S2CID 53563123 O Connor John J Robertson Edmund F Alan Mathison Turing MacTutor History of Mathematics archive University of St Andrews 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 2006 Introduction to the Theory of Computation PWS Publishing 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 1937 Delivered to the Society November 1936 On Computable Numbers with an Application to the Entscheidungsproblem PDF Proceedings of the London Mathematical Society 2 Vol 42 pp 230 65 doi 10 1112 plms s2 42 1 230 and Turing A M 1938 On Computable Numbers with an Application to the Entscheidungsproblem A correction Proceedings of the London Mathematical Society 2 Vol 43 published 1937 pp 544 46 doi 10 1112 plms s2 43 6 544 Turing Sara Stoney 1959 Alan M Turing W Heffer 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 1988 Breaking the code S French 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 1997 Turing s Legacy A history of computing at the National Physical Laboratory 1945 1995 London London Science Museum ISBN 978 0 901805 94 2 OCLC 123794619 Further readingArticles Turing Alan 1950 Computing Machinery and Intelligence PDF Mind 49 236 433 460 doi 10 1093 mind LIX 236 433 Archived PDF from the original on 9 October 2022 Copeland B Jack ed The Mind and the Computing Machine Alan Turing and others The Rutherford Journal Copeland B Jack ed Alan Turing Father of the Modern Computer The Rutherford Journal Hodges Andrew 2007 Alan Turing In Edward N Zalta ed Stanford Encyclopedia of Philosophy Winter 2009 ed Stanford University Retrieved 10 January 2011 Hodges Andrew 2004 Turing Alan Mathison Oxford Dictionary of National Biography online ed Oxford University Press doi 10 1093 ref odnb 36578 Subscription or UK public library membership required Gray Paul 29 March 1999 Computer Scientist Alan Turing Time Archived from the original on 16 October 2007 Books Bernhardt Chris 2017 Turing s Vision The Birth of Computer Science MIT Press ISBN 978 0 262 53351 5 Copeland B Jack Bowen Jonathan P Wilson Robin Sprevak Mark 2017 The Turing Guide Oxford University Press ISBN 978 0 19 874783 3 Dyson George 2012 Turing s Cathedral The Origins of the Digital Universe Vintage ISBN 978 1 4000 7599 7 Gleick James 2011 The Information A History a Theory a Flood New York Pantheon ISBN 978 0 375 42372 7 Hodges Andrew 2014 Alan Turing The Enigma Princeton University Press ISBN 978 0 691 16472 4 originally published in 1983 basis of the film The Imitation Game Turing Sara 2012 Alan M Turing Cambridge University Press ISBN 978 1 107 02058 0 originally published in 1959 by W Heffer amp Sons Ltd External linksAlan Turing at Wikipedia s sister projects Media from Commons News from Wikinews Quotations from Wikiquote Texts from Wikisource 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 Year Archived 17 February 2019 at the Wayback Machine 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 11 December 2001 Alan Turing Towards a Digital Mind Part 1 System Toolbox The Binary Freedom Project Archived from the original on 3 August 2007 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 Portals Biography England LGBT Greater Manchester Mathematics Computer programming World War II Retrieved from https en wikipedia org w index php title Alan Turing amp oldid 1155989857, wikipedia, wiki, book, books, library,

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