Alan Turing

Alan Mathison Turing OBE FRS (/ˈtjʊərɪŋ/; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist.[5] 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.[6][7][8] Turing is widely considered to be the father of theoretical computer science and artificial intelligence.[9] Despite these accomplishments, he was never fully recognised in his home country during his lifetime, due to his homosexuality, which was then a crime in the UK.

During the Second World War, Turing worked for the Government Code and Cypher School (GC&CS) 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 bombe method, an electromechanical machine that could find settings for the Enigma machine.

Turing played a pivotal role in cracking intercepted coded messages that enabled the Allies to defeat the Nazis in many crucial engagements, including the Battle of the Atlantic, and in so doing helped win the war.[10][11] Counterfactual history is difficult with respect to the effect Ultra intelligence had on the length of the war,[12] but at the upper end it has been estimated that this work shortened the war in Europe by more than two years and saved over 14 million lives.[10]

After the war, Turing worked at the National Physical Laboratory, where he designed the Automatic Computing Engine, which was 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.

Turing was prosecuted in 1952 for homosexual acts; the Labouchere Amendment had mandated that "gross indecency" was a criminal offence in the UK. He accepted chemical castration treatment, with DES, as an alternative to prison. Turing died in 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.[14]

In 2009, following an Internet campaign, British Prime Minister Gordon Brown made an official public apology on behalf of the British government for "the appalling way he was treated". Queen Elizabeth II granted Turing a posthumous pardon in 2013.[15][16][17] The Alan Turing law is now an informal term for a 2017 law in the United Kingdom that retroactively pardoned men cautioned or convicted under historical legislation that outlawed homosexual acts.[18]

Alan Turing

Alan Turing Aged 16
Turing aged 16
Born
Alan Mathison Turing

23 June 1912
Maida Vale, London, England
Died7 June 1954 (aged 41)
Wilmslow, Cheshire, England
Cause of deathSuicide (disputed) by cyanide poisoning
Resting placeAshes scattered in gardens of Woking Crematorium
ResidenceWilmslow, Cheshire, England
EducationKing's College, Cambridge (BA, MA)
Princeton University (PhD)
Known for
AwardsSmith's Prize (1936)
Scientific career
Fields
Institutions
ThesisSystems of Logic Based on Ordinals (1938)
Doctoral advisorAlonzo Church[2]
Doctoral studentsRobin Gandy[2][3]
InfluencesMax Newman[4]
Signature
Alan Turing signature

Early life and education

Family

Turing was born in Maida Vale, London,[5] while his father, Julius Mathison Turing (1873–1947), was on leave from his position with the Indian Civil Service (ICS) at Chatrapur, then in the Madras Presidency and presently in Odisha state, in India.[19][20] 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' wife, was Ethel Sara Turing (née Stoney 1881–1976),[5] 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.[21]

Julius' 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,[22] 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,[23][24] later the Colonnade Hotel.[19][25] Turing had an elder brother, John (the father of Sir John Dermot Turing, 12th Baronet of the Turing baronets).[26]

Turing's father's civil service commission was still active and during Turing's childhood years Turing's parents travelled between Hastings in England[27] 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.[28] The plaque was unveiled on 23 June 2012, the centenary of Turing's birth.[29]

Very early in life, Turing showed signs of the genius that he was later to display prominently.[30] 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.[31]

School

Turing's parents enrolled him at St Michael's, a day school at 20 Charles Road, St Leonards-on-Sea, at the age of six. The headmistress recognised his talent early on, as did many of his subsequent teachers.

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).[32] In 1926, at the age of 13, he went on to Sherborne School, a boarding independent school in the market town of Sherborne in Dorset. The first day of term coincided with the 1926 General Strike in Britain, but he 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'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 Morcom (1911 – 1930), who has been described as Turing's "first love". 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.[36][37][38]

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 Turing said:

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.[39]

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 birthdays.[40] A day before the third anniversary of Morcom's death (12 February, 1933), he wrote to Mrs. Morcom: {quote|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. [41]

Some have speculated that Morcom's death was the cause of Turing's atheism and materialism.[42] 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 said:

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.[43]

University and work on computability

After Sherborne, Turing studied as an undergraduate from 1931 to 1934 at King's College, Cambridge,[5] where he was awarded first-class honours in mathematics. In 1935, at the age of 22, he was elected a fellow of King's on the strength of a dissertation in which he proved the central limit theorem.[44] Unknown to the committee, the theorem had already been proven, in 1922, by Jarl Waldemar Lindeberg.[45] A blue plaque at the college was unveiled on the centenary of his birth on 23 June 2012 and is now installed at the college's Keynes Building on King's Parade.[46][47]

In 1936, Turing published his paper "On Computable Numbers, with an Application to the Entscheidungsproblem" (1936).[48] 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.

20130808 Kings College Front Court Fountain Crop 03
King's College, Cambridge, where Turing was a student 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,[49] Turing's approach is considerably more accessible and intuitive than Church's.[50] 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.[51] 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, 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.[52] In June 1938, he obtained his PhD from the Department of Mathematics at Princeton;[53] his dissertation, Systems of Logic Based on Ordinals,[54][55] introduced the concept of ordinal logic and the notion of relative computing, where 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 England.[56]

Career and research

When Turing returned to Cambridge, he attended lectures given in 1939 by Ludwig Wittgenstein about the foundations of mathematics.[57] The lectures have been reconstructed verbatim, including interjections from Turing and other students, from students' notes.[58] 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.[59]

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."[60] From September 1938, Turing had been working part-time with the GC&CS, the British codebreaking organisation. He concentrated on cryptanalysis of the Enigma with Dilly Knox, a senior GC&CS codebreaker.[61] Soon after the July 1939 Warsaw meeting at which the Polish Cipher Bureau had provided the British and French with the details of the wiring of Enigma rotors and their method of decrypting Enigma code messages, Turing and Knox started to work on a less fragile approach to the problem.[62] The Polish method relied on an insecure indicator procedure that the Germans were likely to change, which they 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 of the Polish Bomba).[63]

Turing flat
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.[64] 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 for making much more efficient use of the bombes dubbed Banburismus; developing a procedure for working out the cam settings of the wheels of the Lorenz SZ 40/42 (Tunny) dubbed Turingery 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[65] and Paper on Statistics of Repetitions,[66] 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 for some 70 years demonstrated their importance, and their relevance to post-war cryptanalysis:[67]

[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".[68] 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.[69]

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,[70] and he was capable of world-class marathon standards.[71][72] 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.[73][74][75]

In 1946, Turing was appointed an Officer of the Order of the British Empire (OBE) by King George VI for his wartime services, but his work remained secret for many years.[76][77]

Bombe

Within weeks of arriving at Bletchley Park,[64] 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.[78]

Bombe-rebuild
A complete and 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),[79] the bombe performed a chain of logical deductions based on the crib, implemented electromechanically.

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.[80]

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.[81]

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.[81] As Andrew Hodges, biographer of Turing, later wrote, "This letter had an electric effect."[82] 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.[82] 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."[83] More than two hundred bombes were in operation by the end of the war.[84]

Turing-statue-Bletchley 14
Statue of Turing by Stephen Kettle at Bletchley Park, commissioned by Sidney Frank, built from half a million pieces of Welsh slate.[85]

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".[86] 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.[86][87]

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."[86] 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.

Turing travelled to the United States in November 1942[88] 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.[89]

During this trip, he also assisted at Bell Labs with the development of secure speech devices.[90] 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.

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.[91]

Turingery

In July 1942, Turing devised a technique termed Turingery (or jokingly Turingismus)[92] 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.[93] 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.[94] 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,[95][96] but he was not directly involved in the Colossus development.[97]

Delilah

Following his work at Bell Labs in the US,[98] Turing pursued the idea of electronic enciphering of speech in the telephone system. In the latter part of the war, he moved in order 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.[99] 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.[100] 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

Alan Turing 78 High Street Hampton blue plaque
Plaque, 78 High Street, Hampton

Between 1945 and 1947, Turing lived in Hampton, London,[101] 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.[102] 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".[103] Although ACE was a feasible design, the secrecy surrounding the wartime work at Bletchley Park 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.[104] 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.[105]

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.[106] 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.[107] During this time, he continued to do more abstract work in mathematics,[108] 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.[109] In the paper, Turing suggested that rather than building a program to simulate the adult mind, it would be better rather 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 Turbochamp.[110] 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.[111] According to Garry Kasparov, Turing's program "played a recognizable game of chess."[112] The program lost to Turing's colleague Alick Glennie, although it is said that it won a game against Champernowne's wife, Isabel.[113]

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.[114] He also invented the LU decomposition method in 1948,[108] used today for solving matrix equations.[115]

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. Among other things, he wanted to understand Fibonacci phyllotaxis, the existence of Fibonacci numbers in plant structures.[116] 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".[117] 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.[118]

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.[119] 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.[120][121][122] 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."[123] 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.[124] Later papers were not available until Collected Works of A. M. Turing was published in 1992.[125]

Personal life

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.[126]

Conviction for indecency

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,[127] and both men were charged with "gross indecency" under Section 11 of the Criminal Law Amendment Act 1885.[128] 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.

Turing was later convinced by the advice of his brother and his own solicitor, and he entered a plea of guilty.[129] The case, Regina v. Turing and Murray, was brought to trial on 31 March 1952.[130] Turing was convicted and given a choice between imprisonment and probation, which would be conditional on his agreement to undergo hormonal treatment designed to reduce libido. He accepted the option of treatment via injections of what was then called stilboestrol (now known as diethylstilbestrol or DES), a synthetic oestrogen; this treatment was continued for the course of one year. The treatment rendered Turing impotent and caused gynaecomastia,[131] 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".[132][133] Murray was given a conditional discharge.[134]

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. Turing was never accused of espionage but, in common with all who had worked at Bletchley Park, he was prevented by the Official Secrets Act from discussing his war work.[135]

Death

On 8 June 1954, Turing's housekeeper found him dead; he had died the previous day. Cyanide poisoning was established as the cause of death.[136] When his body was discovered, an apple lay half-eaten beside his bed, and although the apple was not tested for cyanide,[137] it was speculated that this was the means by which Turing had consumed a fatal dose. An inquest determined that he had committed suicide. 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."[138] Turing's remains were cremated at Woking Crematorium on 12 June 1954[139] and his ashes were scattered in the gardens of the crematorium, just as his father's had been.[140]

Philosophy professor 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.[141] In addition, 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 prior to his death. He even set down a list of tasks that he intended to complete upon returning to his office after the holiday weekend.[141] Turing's mother believed that the ingestion was accidental, resulting from her son's careless storage of laboratory chemicals.[142] Biographer Andrew Hodges theorised that Turing arranged the delivery of the equipment in order to deliberately allow his mother plausible deniability in regard to any suicide claims.[143]

Alan Turing OBE
Turing's OBE currently held in Sherborne School archives

Conspiracy theorists pointed out that Turing was the cause of intense anxiety to the British authorities at the time of his death. The secret services feared that communists would entrap prominent homosexuals and use them to gather intelligence. Turing was still engaged in highly classified work when he was also a practising homosexual who holidayed in European countries near the Iron Curtain. It is possible that the secret services considered him too great a security risk and assassinated one of the most brilliant minds in their employ.[144]

Turing believed in extrasensory perception,[145][146] and it has been suggested that his belief in fortune-telling may have caused his depressed mood. As a youth, Turing had been told by a gypsy fortune-teller that he would be a genius.[140] Shortly before his death, during a day-trip to St Annes-on Sea with the Greenbaum family, Turing again decided to consult a fortune-teller.[140] According to the Greenbaums' daughter, Barbara:

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."[147]

Government apology and pardon

In August 2009, British programmer John Graham-Cumming started a petition urging the British government to apologise for Turing's prosecution as a homosexual.[148][149] The petition received more than 30,000 signatures.[150][151] The Prime Minister, Gordon Brown, acknowledged the petition, releasing a statement on 10 September 2009 apologising and describing the treatment of Turing as "appalling":[150][152]

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.[150][153]

In December 2011, William Jones created an e-petition[154] requesting that the British government pardon Turing for his conviction of "gross indecency":[155]

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.[154]

The petition gathered over 37,000 signatures,[17][154] and was supported by Manchester MP John Leech but the request was discouraged by Justice Minister Lord McNally, who said:[156]

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.[157]

John Leech, the MP for Manchester Withington (2005–15), submitted several bills to Parliament[158] and campaigned with Jones 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.[159] Leech continued to take the bill through Parliament and campaigned for several years until it was passed.[160]

At the UK 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.[161] His campaign turned to acquiring pardons for the 75,000 other men convicted of the same crime. Leech's campaign gained public support from leading scientists, including Stephen Hawking.[162]

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.[163] 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.[164] The government indicated it would support the bill,[165][166][167] and it passed its third reading in the Lords in October.[168]

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,[169] but before the bill could be debated in the House of Commons,[170] 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.[16] 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.[15][17] The Queen officially pronounced Turing pardoned in August 2014.[171] The Queen's action is only the fourth royal pardon granted since the conclusion of the Second World War.[172] 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.[173]

In a letter to the Prime Minister, David Cameron, human rights advocate Peter Tatchell criticised the decision to single out Turing due to his fame and achievements when thousands of others convicted under the same law have not received pardons.[174] Tatchell also called for a new investigation into Turing's death:

A new inquiry is long overdue, even if only to dispel any doubts about the true cause of his death—including speculation that he was murdered by the security services (or others). I think murder by state agents is unlikely. There is no known evidence pointing to any such act. However, it is a major failing that this possibility has never been considered or investigated.[175]

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".[176][177] 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.[178]

Awards, honours, and tributes

Alan Turing Building 1
The Alan Turing Building at the University of Manchester in 2008

Turing was appointed an officer of the Order of the British Empire 1946.[77] He was also elected a Fellow of the Royal Society (FRS) in 1951.[6] Several things are named in his honour:

Posthumous tributes

Various institutions have paid tribute to Turing by naming things after him including:

A biography published by the Royal Society shortly after Turing's death,[6] while his wartime work was still subject to the Official Secrets Act, recorded:

Three remarkable papers written just before the war, on three diverse mathematical subjects, show the quality of the work that might have been produced if he had settled down to work on some big problem at that critical time. For his work at the Foreign Office he was awarded the OBE.[6]

Since 1966, the Turing Award has been given annually by the Association for Computing Machinery for technical or theoretical contributions to the computing community. It is widely considered to be the computing world's highest honour, equivalent to the Nobel Prize.[203]

On 23 June 1998, on what would have been Turing's 86th birthday, his biographer, Andrew Hodges, unveiled an official English Heritage blue plaque at his birthplace in Warrington Crescent, London, later the Colonnade Hotel.[204][205] To mark the 50th anniversary of his death, a memorial plaque was unveiled on 7 June 2004 at his former residence, Hollymeade, in Wilmslow, Cheshire.[206]

Turing Plaque
A blue plaque marking Turing's home at Wilmslow, Cheshire

On 13 March 2000, Saint Vincent and the Grenadines issued a set of postage stamps to celebrate the greatest achievements of the 20th century, one of which carries a portrait of Turing against a background of repeated 0s and 1s, and is captioned: "1937: Alan Turing's theory of digital computing". On 1 April 2003, Turing's work at Bletchley Park was named an IEEE Milestone.[207] On 28 October 2004, a bronze statue of Turing sculpted by John W. Mills was unveiled at the University of Surrey in Guildford, marking the 50th anniversary of Turing's death; it portrays him carrying his books across the campus.[181]

Turing was one of four mathematicians examined in the BBC documentary entitled Dangerous Knowledge (2008).[208] The Princeton Alumni Weekly named Turing the second most significant alumnus in the history of Princeton University, second only to President James Madison. A 1.5-ton, life-size statue of Turing was unveiled on 19 June 2007 at Bletchley Park. Built from approximately half a million pieces of Welsh slate, it was sculpted by Stephen Kettle, having been commissioned by the American billionaire Sidney Frank.[209]

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. Turing is shown holding an apple. The cast bronze bench carries in relief the text 'Alan Mathison Turing 1912–1954', and the motto 'Founder of Computer Science' as it could appear if encoded by an Enigma machine: 'IEKYF ROMSI ADXUO KVKZC GUBJ'. However, the meaning of the coded message is disputed, as the 'u' in 'computer' matches up with the 'u' in 'ADXUO'. As a letter encoded by an enigma machine can not appear as itself, the actual message behind the code is uncertain.[210]

Sackville Park Turing plaque
Turing memorial statue plaque in Sackville Park, Manchester

A plaque at the statue's feet reads 'Father of computer science, mathematician, logician, wartime codebreaker, victim of prejudice'. There is also 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 buried his own old Amstrad computer under the plinth as a tribute to "the godfather of all modern computers".[211]

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."[7]

In 2002, Turing was ranked twenty-first on the BBC's poll of the 100 Greatest Britons following a UK-wide vote.[212] In 2006, British writer and mathematician Ioan James chose Turing as one of twenty people to feature in his book about famous historical figures who may have had some of the traits of Asperger syndrome.[213] In 2010, actor/playwright Jade Esteban Estrada portrayed Turing in the solo musical, Icons: The Lesbian and Gay History of the World, Vol. 4. In 2011, in The Guardian's "My hero" series, writer Alan Garner chose Turing as his hero and described how they had met while out jogging in the early 1950s. Garner remembered Turing as "funny and witty" and said that he "talked endlessly".[214] In 2006, Turing was named with online resources as an LGBT History Month Icon.[215] In 2006, Boston Pride named Turing their Honorary Grand Marshal.[216]

Alan Turing Memorial Closer
Turing memorial statue in Sackville Park, Manchester

The logo of Apple Inc. is often erroneously referred to as a tribute to Turing, with the bite mark a reference to his death.[217] Both the designer of the logo[218] and the company deny that there is any homage to Turing in the design.[219][220] Stephen Fry has recounted asking Steve Jobs whether the design was intentional, saying that Jobs' response was, "God, we wish it were."[221] In February 2011, Turing's papers from the Second World War were bought for the nation with an 11th-hour bid by the National Heritage Memorial Fund, allowing them to stay at Bletchley Park.[222]

In 2012, Turing was inducted into the Legacy Walk, an outdoor public display that celebrates LGBT history and people.[223][224]

The song "Alan et la Pomme", by francophone singer-songwriter Salvatore Adamo, is a tribute to Turing.[225] Turing's life and work featured in a BBC children's programme about famous scientists, Absolute Genius with Dick and Dom, first broadcast on 12 March 2014.

On 17 May 2014, the world's first work of public art to recognise Turing as gay was commissioned in Bletchley, close by to Bletchley Park where his war-time work was carried out. The commission was announced to mark International Day Against Homophobia and Transphobia. The work was unveiled at a ceremony on Turing's birthday, 23 June 2014, and is placed alongside busy Watling Street, the old main road to London, where Turing himself would have passed by on many occasions. On 22 October 2014, Turing was inducted into the NSA Hall of Honor.[226][227]

In February 2019, in the BBC eight-part series Icons: The Greatest Person of the 20th Century, Turing was voted by viewers to be the Greatest Person.[228]

Centenary celebrations

David Chalmers, delivering a talk at De La Salle University-Manila, March 27, 2012
David Chalmers on stage for an Alan Turing Year conference at De La Salle University, Manila, 27 March 2012

To mark the 100th anniversary of Turing's birth, the Turing Centenary Advisory Committee (TCAC) co-ordinated the Alan Turing Year, 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.

On 23 June 2012, Google featured an interactive doodle where visitors had to change the instructions of a Turing Machine, so when run, the symbols on the tape would match a provided sequence, featuring "Google" in Baudot-Murray code.[229]

The Bletchley Park Trust collaborated with Winning Moves to publish an Alan Turing edition of the board game Monopoly. The game's squares and cards have been revised to tell the story of Turing's life, from his birthplace in Maida Vale to Hut 8 at Bletchley Park.[230] The game also includes a replica of an original hand-drawn board created by William Newman, son of Turing's mentor, Max Newman, which Turing played on in the 1950s.[231]

In the Philippines, the Department of Philosophy at De La Salle University-Manila hosted Turing 2012, an international conference on philosophy, artificial intelligence, and cognitive science from 27 to 28 March 2012 to commemorate the centenary birth of Turing.[232][233] Madurai, India held celebrations with a programme attended by 6,000 students.[234]

Alan Turing Olympic Torch
The London 2012 Olympic Torch flame was passed on in front of Turing's statue in Manchester on his 100th birthday.

There was a three-day conference in Manchester in June, the Alan Turing Centenary Conference, a two-day conference in San Francisco, organised by the ACM, and a birthday party and Turing Centenary Conference in Cambridge organised at King's College, Cambridge, and the University of Cambridge, the latter organised by the association Computability in Europe.[235]

The Science Museum in London launched a free exhibition devoted to Turing's life and achievements in June 2012, to run until July 2013.[236] In February 2012, the Royal Mail issued a stamp featuring Turing as part of its "Britons of Distinction" series.[237] The London 2012 Olympic Torch flame was passed on in front of Turing's statue in Sackville Gardens, Manchester, on the evening of 23 June 2012, the 100th anniversary of his birth.

On 22 June 2012 Manchester City Council, in partnership with the Lesbian and Gay Foundation, launched the Alan Turing Memorial Award, which will recognise individuals or groups who have made a significant contribution to the fight against homophobia in Manchester.[238]

At the University of Oxford, a new course in Computer Science and Philosophy was established to coincide with the centenary of Turing's birth.[239]

Previous events have included a celebration of Turing's life and achievements, at the University of Manchester, arranged by the British Logic Colloquium and the British Society for the History of Mathematics on 5 June 2004.[240]

Portrayal

In theatre

Benedict Cumberbatch 2013 TIFF (headshot)
Benedict Cumberbatch portrayed Turing in the 2014 film The Imitation Game
  • Breaking the Code is a 1986 play by Hugh Whitemore about Turing. The play ran in London's West End beginning in November 1986 and on Broadway from 15 November 1987 to 10 April 1988. In these performances Turing was played by Derek Jacobi. The Broadway production was nominated for three Tony Awards including Best Actor in a Play, Best Featured Actor in a Play, and Best Direction of a Play, and for two Drama Desk Awards, for Best Actor and Best Featured Actor. Turing was again portrayed by Jacobi in the 1996 television film adaptation of Breaking the Code.[241]
  • In 2012, in honour of the Turing Centennial, American Lyric Theater commissioned an operatic exploration of the life and death of Turing from composer Justine F. Chen and librettist David Simpatico.[242] Titled The Life and Death(s) of Alan Turing, the opera is a historical fantasia on the life of Turing. In November 2014, the opera and several other artistic works inspired by Turing's life were featured on Studio 360.[243] The opera received its first public performance in January 2017.[244]

In literature

In music

  • Electronic music duo Matmos released an EP titled For Alan Turing in 2006, which was based on material commissioned by Dr. Robert Osserman and David Elsenbud of the Mathematical Sciences Research Institute.[252] In one of its tracks, an original Enigma Machine is sampled.[253]
  • In 2012, Spanish group Hidrogenesse dedicated their LP Un dígito binario dudoso. Recital para Alan Turing (A dubious binary digit. Concert for Alan Turing) to the memory of the mathematician.[254]
  • A musical work inspired by Turing's life, written by Neil Tennant and Chris Lowe of the Pet Shop Boys, entitled A Man from the Future, was announced in late 2013.[255] It was performed by the Pet Shop Boys and Juliet Stevenson (narrator), the BBC Singers, and the BBC Concert Orchestra conducted by Dominic Wheeler at the BBC Proms in the Royal Albert Hall on 23 July 2014.[256]
  • Codebreaker is also the title of a choral work by the composer James McCarthy. It includes settings of texts by the poets Wilfred Owen, Sara Teasdale, Walt Whitman, Oscar Wilde and Robert Burns that are used to illustrate aspects of Turing's life. It was premiered on 26 April 2014 at the Barbican Centre in London, where it was performed by the Hertfordshire Chorus, who commissioned the work, led by David Temple with the soprano soloist Naomi Harvey providing the voice of Turing's mother.[257][258]

In film

  • Codebreaker, original UK title Britain's Greatest Codebreaker, is a TV film that aired on 21 November 2011 by Channel 4 about Turing's life. It had a limited release in the US beginning on 17 October 2012. The story is told as a discussion between Turing and his psychiatrist Dr. Franz Greenbaum. The story is based on journals maintained by Greenbaum and others who have studied Turing's life as well as some of his colleagues.[259]
  • The historical drama film The Imitation Game, directed by Morten Tyldum and starring Benedict Cumberbatch as Turing and Keira Knightley as Joan Clarke, was released in the UK on 14 November 2014 and released theatrically in the US on 28 November 2014. The story concentrates on the period of Turing’s life where he breaks the Enigma code with other codebreakers in Bletchley Park.[260][261][262][263] It received the academy award for best adapted screenplay in 2015. It was a tremendous success, bringing in $233.6 million[264] for a production cost of $14 million[265].

See also

References

  1. ^ a b Alan Turing publications indexed by Google Scholar Edit this at Wikidata
  2. ^ a b Alan Turing at the Mathematics Genealogy Project
  3. ^ Gandy, Robin Oliver (1953). On axiomatic systems in mathematics and theories in physics. repository.cam.ac.uk (PhD thesis). University of Cambridge. doi:10.17863/CAM.16125. EThOS uk.bl.ethos.590164. Free to read
  4. ^ Grattan-Guinness, Ivor, Chapter 40, Turing's mentor, Max Newman. In Copeland, B. Jack; Bowen, Jonathan P.; Wilson, Robin; Sprevak, Mark (2017). The Turing Guide. Oxford University Press. ISBN 978-0-19-874782-6.
  5. ^ a b c d Anon (2017). Turing, Alan Mathison. ukwhoswho.com. Who's Who (online Oxford University Press ed.). A & C Black, an imprint of Bloomsbury Publishing plc. doi:10.1093/ww/9780199540884.013.U243891. closed access (subscription required)
  6. ^ a b c d Newman, M.H.A. (1955). "Alan Mathison Turing. 1912–1954" (PDF). Biographical Memoirs of Fellows of the Royal Society. 1: 253–263. doi:10.1098/rsbm.1955.0019. JSTOR 769256.
  7. ^ a b Gray, Paul (29 March 1999). "Alan Turing – Time 100 People of the Century". Time. 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.
  8. ^ Sipser 2006, p. 137
  9. ^ Beavers 2013, p. 481
  10. ^ a b Copeland, Jack (18 June 2012). "Alan Turing: The codebreaker who saved 'millions of lives'". BBC News Technology. Retrieved 26 October 2014.
  11. ^ A number of sources state that Winston Churchill said that Turing made the single biggest contribution to Allied victory in the war against Nazi Germany. However, both The Churchill Centre and Turing's biographer Andrew Hodges have said they know of no documentary evidence to support this claim nor of the date or context in which Churchill supposedly said it, and the Churchill Centre lists it among their Churchill 'Myths', see Schilling, Jonathan. "Churchill Said Turing Made the Single Biggest Contribution to Allied Victory". The Churchill Centre: Myths. Retrieved 9 January 2015. and Hodges, Andrew. "Part 4: The Relay Race". Update to Alan Turing: The Enigma. 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. Update 13 February 2015
  12. ^ See for example Richelson, Jeffery T. (1997). A Century of Spies: Intelligence in the Twentieth Century. New York: Oxford University Press. p. 296. and Hartcup, Guy (2000). The Effect of Science on the Second World War. Basingstoke, Hampshire: Macmillan Press. pp. 96–99.
  13. ^ Leavitt 2007, pp. 231–233
  14. ^ Pease, Roland (26 June 2012). "Alan Turing: Inquest's suicide verdict 'not supportable'". BBC News. Retrieved 25 December 2013.
  15. ^ a b "Royal pardon for codebreaker Alan Turing". BBC News. 24 December 2013. Retrieved 24 December 2013.
  16. ^ a b Swinford, Steven (23 December 2013). "Alan Turing granted Royal pardon by the Queen". The Daily Telegraph.
  17. ^ a b c Wright, Oliver (23 December 2013). "Alan Turing gets his royal pardon for 'gross indecency' – 61 years after he poisoned himself". The Independent. London.
  18. ^ "'Alan Turing law': Thousands of gay men to be pardoned". BBC News. 20 October 2016. Retrieved 20 October 2016.
  19. ^ a b Hodges 1983, p. 5
  20. ^ "The Alan Turing Internet Scrapbook". Alan Turing: The Enigma. Retrieved 2 January 2012.
  21. ^ Phil Maguire, "An Irishman's Diary", p. 5. The Irish Times, 23 June 2012.
  22. ^ "London Blue Plaques". English Heritage. Archived from the original on 13 September 2009. Retrieved 10 February 2007.
  23. ^ The Scientific Tourist In London: #17 Alan Turing's Birth Place, Nature. London Blog
  24. ^ Plaque #381 on Open Plaques.
  25. ^ "The Alan Turing Internet Scrapbook". Retrieved 26 September 2006.
  26. ^ Sir John Dermot Turing on the Bletchley Park website.
  27. ^ Hodges 1983, p. 6
  28. ^ "Plaque unveiled at Turing's home in St Leonards". Hastings & St. Leonards Observer. 29 June 2012. Retrieved 3 July 2017.
  29. ^ "St Leonards plaque marks Alan Turing's early years". BBC News. 25 June 2012. Retrieved 3 July 2017.
  30. ^ Jones, G. James (11 December 2001). "Alan Turing – Towards a Digital Mind: Part 1". System Toolbox. Archived from the original on 3 August 2007. Retrieved 27 July 2007.
  31. ^ "Guildford Dragon NEWS". The Guildford Dragon. 29 November 2012. Retrieved 31 October 2013.
  32. ^ Alan Mathison (April 2016). "Alan Turing Archive – Sherborne School (ARCHON CODE: GB1949)" (PDF). Sherborne School, Dorset. Retrieved 5 February 2017.
  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. ^ Caryl, Christian (19 December 2014). "Poor Imitation of Alan Turing". New York Review of Books.
  37. ^ Rachel Hassall, 'The Sherborne Formula: The Making of Alan Turing' 'Vivat!' 2012/13
  38. ^ Teuscher, Christof (ed.) (2004). Alan Turing: Life and Legacy of a Great Thinker. Springer-Verlag. ISBN 978-3-540-20020-8. OCLC 53434737.CS1 maint: Extra text: authors list (link)
  39. ^ Hodges 1983, p. 61
  40. ^ Hodges, Andrew (2012). Alan Turing: The Enigma. p. 87. ISBN 978-0-691-15564-7.
  41. ^ Hodges, Andrew (2012). Alan Turing: The Enigma. p. 90. ISBN 978-0-691-15564-7.
  42. ^ Paul Gray, Alan Turing Time Magazine's Most Important People of the Century, p. 2
  43. ^ Hodges 1983, pp. 82–83
  44. ^ See Section 3 of John Aldrich, "England and Continental Probability in the Inter-War Years", Journal Electronique d'Histoire des Probabilités et de la Statistique, vol. 5/2 Decembre 2009 Journal Electronique d'Histoire des Probabilités et de la Statistique
  45. ^ Hodges 1983, pp. 88, 94
  46. ^ "Blue plaque to commemorate Alan Turing". King's College, Cambridge. Retrieved 8 December 2018.
  47. ^ "Turing plaque fixed in place". King's College, Cambridge. Retrieved 8 December 2018.
  48. ^ Turing 1937
  49. ^ Church 1936
  50. ^ Grime, James (February 2012). "What Did Turing Do for Us?". NRICH. University of Cambridge. Retrieved 28 February 2016.
  51. ^ "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.
  52. ^ Hodges 1983, p. 138
  53. ^ 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.
  54. ^ Turing, Alan (1938). Systems of Logic Based on Ordinals (PhD thesis). Princeton University. doi:10.1112/plms/s2-45.1.161.
  55. ^ Turing, A.M. (1938). "Systems of Logic Based on Ordinals" (PDF).
  56. ^ John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More, Norman MacRae, 1999, American Mathematical Society, Chapter 8
  57. ^ Hodges 1983, p. 152
  58. ^ Cora Diamond (ed.), Wittgenstein's Lectures on the Foundations of Mathematics, University of Chicago Press, 1976
  59. ^ Hodges 1983, pp. 153–154
  60. ^ Briggs, Asa (21 November 2011). Britain's Greatest Codebreaker (TV broadcast). UK Channel 4.
  61. ^ Copeland, Jack, "Colossus and the Dawning of the Computer Age", p. 352 in Action This Day, 2001.
  62. ^ Copeland 2004a, p. 217
  63. ^ Clark, Liat (18 June 2012). "Turing's achievements: codebreaking, AI and the birth of computer science (Wired UK)". Wired. Retrieved 31 October 2013.
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  • 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. 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. 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 reading

Articles

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External links

Alan Turing (sculpture)

Alan Turing, sometimes spelled Allen Turing and also known as Allen Turing Gargoyle, is an outdoor 1988 hammered copper sheet sculpture of Alan Turing by Wayne Chabre, installed on the exterior of Deschutes Hall on the University of Oregon campus in Eugene, Oregon, in the United States. The portrait face in high relief measures approximately 3 feet (0.91 m) x 1.5 feet (0.46 m) x 1.5 feet (0.46 m) and cost $2,500. Its condition was undetermined when the Smithsonian Institution surveyed the work as part of its "Save Outdoor Sculpture!" program in March 1993.

Alan Turing Building

The Alan Turing Building, named after the mathematician and founder of computer science Alan Turing, is a building at the University of Manchester, in Manchester, England. It houses the School of Mathematics, the Photon Science Institute and the Jodrell Bank Centre for Astrophysics (part of the School of Physics and Astronomy). The building is located in the Chorlton-on-Medlock district of Manchester, on Upper Brook Street, and is adjacent to University Place and the Henry Royce Institute. While under construction the project was known as AMPPS : Astronomy, Mathematics, Physics and Photon Science. The building was shortlisted for the Greater Manchester Building of the Year 2008 prize, which is awarded by the Greater Manchester Chamber of Commerce. The manager of the building project was awarded a silver medal in the Chartered Institute of Building "Construction Manager of the Year" awards.

Alan Turing Institute

The Alan Turing Institute is the United Kingdom's national institute for data science and artificial intelligence, founded in 2015. It is named after Alan Turing, the British mathematician and computing pioneer.

Alan Turing Memorial

The Alan Turing Memorial, situated in Sackville Park in Manchester, England, is in memory of Alan Turing, a pioneer of modern computing. Turing is believed to have committed suicide in 1954 two years after being convicted of gross indecency (i.e. homosexual acts). As such he is as much a gay icon as an icon of computing, and it is no coincidence that this memorial is situated near Canal Street, Manchester's gay village.Turing is depicted sitting on a bench situated in a central position in the park. On Turing's left is the University of Manchester and on his right is Canal Street.

The statue was unveiled on 23 June, Turing's birthday, in 2001. It was conceived by Richard Humphry, a barrister from Stockport, who set up the Alan Turing Memorial Fund in order to raise the necessary funds. Humphry had come up with the idea of a statue after seeing Hugh Whitemore's play Breaking the Code, starring Sir Derek Jacobi. Jacobi became the patron of the Fund. Glyn Hughes, an industrial sculptor from Adlington near Westhoughton, was commissioned to sculpt the statue. Roy Jackson (who had previously raised funds for HIV/AIDS and Gay Awareness in Manchester) was asked to assist in the funding raising to make the memorial happen. Within 12 months, through donations and a "village lottery", the money was raised. This allowed the statue to be cast in China. Glyn Hughes had found contacts that could manufacture and ship an identical bronze statue to that which would have cost c. £50,000 in the UK. The cost of the memorial was achieved with the £16,000 raised.

Turing is shown holding an apple. The cast bronze bench carries in relief the text "Alan Mathison Turing 1912–1954" and the motto "Founder of Computer Science" as it would appear if encoded by an Enigma machine; 'IEKYF RQMSI ADXUO KVKZC GUBJ'. However this appears to be an "artist's impression" of an ENIGMA encryption, rather than an actual one. ENIGMA could not encode a letter as itself and there is a letter "U" at position 14 of both the plain-text and the cipher.

A plaque at the statue's feet says "Father of computer science, mathematician, logician, wartime codebreaker, victim of prejudice". There is also a Bertrand Russell quotation saying "Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture."

Alan Turing Year

The Alan Turing Year, 2012, marked the celebration of the life and scientific influence of Alan Turing during the centenary of his birth on 23 June 1912. Turing had an important influence on computing, computer science, artificial intelligence, developmental biology, and the mathematical theory of computability and made important contributions to code-breaking during the Second World War. The Alan Turing Centenary Advisory committee (TCAC) was originally set up by Professor Barry CooperThe international impact of Turing's work is reflected in the list of countries in which Alan Turing Year was celebrated, including: Bolivia, Brazil, Canada, China, Czech Republic, France, Germany, India, Israel, Italy, Netherlands, Mexico, New Zealand, Norway, Philippines, Portugal, Spain, Switzerland, U.K. and the U.S.A. 41+ countries were involved.

Alan Turing law

The "Alan Turing law" is 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 pardon men who were cautioned or convicted under historical legislation that outlawed homosexual acts. The provision is named after Alan Turing, the World War II codebreaker and computing pioneer, who was convicted of gross indecency in 1952. Turing received a royal pardon (posthumously) in 2013. The law applies in England and Wales.

Several proposals had been put forward for an Alan Turing law, and introducing such a law has been government policy since 2015. To implement the pardon, the British Government announced on 20 October 2016 that it would support an amendment to the Policing and Crime Act that would provide a posthumous pardon, also providing an automatic formal pardon for living people who had had such offences removed from their record. A rival bill to implement the Alan Turing law, in second reading at the time of the government announcement, was filibustered. The bill received royal assent on 31 January 2017, and the pardon was implemented that same day. The law only provides pardons for men convicted of acts that are no longer offences; those convicted under the same laws of offences that would now be classified as cottaging, underage sex, or rape will not be pardoned.Manchester Withington MP John Leech, often described as 'the architect' of The Alan Turing Law, led a high profile campaign to pardon Turing and submitted several bills to parliament, leading to the eventual posthumous pardon.

Andrew Hodges

Andrew Hodges (; born 1949) is a British mathematician and author.

Breaking the Code

Breaking the Code is a 1986 play by Hugh Whitemore about British mathematician Alan Turing, who was a key player in the breaking of the German Enigma code at Bletchley Park during World War II and a pioneer of computer science. The play thematically links Turing's cryptographic activities with his attempts to grapple with his homosexuality.

It was adapted as a 1996 television film directed by Herbert Wise, with Derek Jacobi reprising his stage role as Turing.

Computing Machine Laboratory

The Computing Machine Laboratory at the University of Manchester in the north of England was established by Max Newman shortly after the end of World War II, around 1946.The Laboratory was funded through a grant from the Royal Society, which was approved in the summer of 1946. He recruited the engineers Frederic Calland Williams and Thomas Kilburn where they built the world's first electronic stored-program digital computer, which came to be known as the Manchester Baby, based on Alan Turing's ideas. Their prototype ran its first program on 21 June 1948.

Entscheidungsproblem

In mathematics and computer science, the Entscheidungsproblem (pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm], German for "decision problem") is a challenge posed by David Hilbert in 1928. The problem asks for an algorithm that takes as input a statement of a first-order logic (possibly with a finite number of axioms beyond the usual axioms of first-order logic) and answers "Yes" or "No" according to whether the statement is universally valid, i.e., valid in every structure satisfying the axioms. By the completeness theorem of first-order logic, a statement is universally valid if and only if it can be deduced from the axioms, so the Entscheidungsproblem can also be viewed as asking for an algorithm to decide whether a given statement is provable from the axioms using the rules of logic.

In 1936, Alonzo Church and Alan Turing published independent papers showing that a general solution to the Entscheidungsproblem is impossible, assuming that the intuitive notion of "effectively calculable" is captured by the functions computable by a Turing machine (or equivalently, by those expressible in the lambda calculus). This assumption is now known as the Church–Turing thesis.

Recursively enumerable language

In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i.e., if there exists a Turing machine which will enumerate all valid strings of the language.

Recursively enumerable languages are known as type-0 languages in the Chomsky hierarchy of formal languages. All regular, context-free, context-sensitive and recursive languages are recursively enumerable.

The class of all recursively enumerable languages is called RE.

The Chemical Basis of Morphogenesis

"The Chemical Basis of Morphogenesis" is an article written by the English mathematician Alan Turing in 1952 describing the way in which natural patterns such as stripes, spots and spirals may arise naturally out of a homogeneous, uniform state. The theory, which can be called a reaction–diffusion theory of morphogenesis, has served as a basic model in theoretical biology.

The Imitation Game

The Imitation Game is a 2014 American historical drama film directed by Morten Tyldum and written by Graham Moore, based on the biography Alan Turing: The Enigma by Andrew Hodges. It stars Benedict Cumberbatch as British cryptanalyst Alan Turing, who decrypted German intelligence codes for the British government during the Second World War. Keira Knightley, Matthew Goode, Rory Kinnear, Charles Dance, and Mark Strong also star.

The screenplay topped the annual Black List for best unproduced Hollywood scripts in 2011. The Weinstein Company acquired the film for $7 million in February 2014, the highest amount ever paid for U.S. distribution rights at the European Film Market. It was released theatrically in the United States on 28 November 2014.

The Imitation Game grossed over $233 million worldwide on a $14 million production budget, making it the highest-grossing independent film of 2014. It received eight nominations at the 87th Academy Awards, winning for Best Adapted Screenplay, five nominations in the 72nd Golden Globe Awards, and three nominations at the 21st Screen Actors Guild Awards. It also received nine BAFTA nominations and won the People's Choice Award at the 39th Toronto International Film Festival.

The film was criticised by some for its inaccurate portrayal of historical events and for downplaying Turing's homosexuality. However, the LGBT civil rights advocacy organization the Human Rights Campaign honoured it for bringing Turing's legacy to a wider audience.

The Innovators (book)

The Innovators: How a Group of Hackers, Geniuses, and Geeks Created the Digital Revolution is an overview of the history of computer science and the Digital Revolution. It was written by Walter Isaacson, and published in 2014 by Simon & Schuster.

The book summarizes the contributions of several innovators who have made pivotal breakthroughs in computer technology and its applications—from the world's first computer programmer, Ada Lovelace, and Alan Turing's work in artificial intelligence, through the Information Age of the present. Although his book's focus is on individuals, Isaacson reminds readers that innovations are often the product of group collaboration.

Innovators discussed in the book include Charles Babbage, Ada Lovelace, Vannevar Bush, Konrad Zuse, Alan Turing, Grace Hopper, John Mauchly, John von Neumann, J. C. R. Licklider, Doug Engelbart, Robert Noyce of Intel, Bill Gates and Paul Allen of Microsoft, Steve Wozniak and Steve Jobs of Apple, Tim Berners-Lee, Larry Page of Google, Jimmy Wales of Wikipedia, and Lee Felsenstein of Osborne.

The Turing Test (novel)

The Turing Test is a BBC Books original novel written by Paul Leonard and based on the long-running British science fiction television series Doctor Who. It features the Eighth Doctor.

The story is in three parts, written as if by three historical figures: mathematician Alan Turing and novelists Graham Greene and Joseph Heller respectively.

Turing Award

The ACM A.M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) to an individual selected for contributions "of lasting and major technical importance to the computer field". The Turing Award is generally recognized as the highest distinction in computer science and the "Nobel Prize of computing".The award is named after Alan Turing, a British mathematician and reader in mathematics at the University of Manchester. Turing is often credited as being the key founder of theoretical computer science and artificial intelligence. From 2007 to 2013, the award was accompanied by an additional prize of US $250,000, with financial support provided by Intel and Google. Since 2014, the award has been accompanied by a prize of US $1 million, with financial support provided by Google.The first recipient, in 1966, was Alan Perlis, of Carnegie Mellon University. The first female recipient was Frances E. Allen of IBM in 2006.

Turing College, Kent

Turing College is the University of Kent's sixth college.

Named in honour of the mathematician and codebreaker Alan Turing, the college's residential accommodations are divided into "Turing Houses" and "Turing Flats". The dining area, "Hut 8", is named after Turing's section at Bletchley Park.

Turing test

The Turing test, developed by Alan Turing in 1950, is a test of a machine's ability to exhibit intelligent behavior equivalent to, or indistinguishable from, that of a human. Turing proposed that a human evaluator would judge natural language conversations between a human and a machine designed to generate human-like responses. The evaluator would be aware that one of the two partners in conversation is a machine, and all participants would be separated from one another. The conversation would be limited to a text-only channel such as a computer keyboard and screen so the result would not depend on the machine's ability to render words as speech. If the evaluator cannot reliably tell the machine from the human, the machine is said to have passed the test. The test results do not depend on the machine's ability to give correct answers to questions, only how closely its answers resemble those a human would give.

The test was introduced by Turing in his 1950 paper, "Computing Machinery and Intelligence", while working at the University of Manchester (Turing, 1950; p. 460). It opens with the words: "I propose to consider the question, 'Can machines think?'" Because "thinking" is difficult to define, Turing chooses to "replace the question by another, which is closely related to it and is expressed in relatively unambiguous words." Turing's new question is: "Are there imaginable digital computers which would do well in the imitation game?" This question, Turing believed, is one that can actually be answered. In the remainder of the paper, he argued against all the major objections to the proposition that "machines can think".Since Turing first introduced his test, it has proven to be both highly influential and widely criticised, and it has become an important concept in the philosophy of artificial intelligence. Some of these criticisms, such as John Searle's Chinese room, are controversial in their own right.

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