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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.
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.
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.
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.
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.
Despite this, Turing continued to show remarkable ability in the studies he loved, solving advanced problems in 1927 without having studied even elementary calculus.
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.
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.
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.
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.
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.
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).
In addition to his purely mathematical work, he studied cryptology and also built three of four stages of an electro-mechanical binary multiplier.
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.
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.
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.
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.
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:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.'
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
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.
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).
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.
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.
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.
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.
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'.
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.
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.
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.
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'.
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.
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.
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.
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.'
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.
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'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.
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'.
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.
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.
Biographer Andrew Hodges theorised that Turing arranged the delivery of the equipment in order to deliberately allow his mother plausible deniability with regard to any suicide claims.
According to the conspiracy theory, 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.
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 ...
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.
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.
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.
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.
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.
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.
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).
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'.
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.
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.
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'.
plaque at the statue's feet reads 'Father of computer science, mathematician, logician, wartime codebreaker, victim of prejudice'.
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.'
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.
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 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.
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.
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.
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.
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.
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