SciTech Tuesday: Alan Turing Submits “On Computable Numbers” for Publication | The National WWII...

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Images:
1. 30P Stamp for British Commonwealth island St Helena Alan M. Turing, codebreaker and an Enigma Code Machine.
2. The back of a huge contraption known as the Bombe, which the Bletchley Park code breakers used to break ciphers created by Nazi Germany’s Enigma machine.
3. English Mathematician and Logician Alan Matheson Turing finishing second in a three-mile race at Dorking, England.
4. Turing and colleagues working on the Ferranti Mark I Computer in 1951. It was based on a prototype built five years earlier at the University of Manchester

Background from {[https://mathshistory.st-andrews.ac.uk/Biographies/Turing/]}
Alan Mathison Turing
________________________________________
Quick Info
Born 23 June 1912 at London, England
Died 7 June 1954 at Wilmslow, Cheshire, England
________________________________________
Summary
Alan Turing's work was fundamental in the theoretical foundations of computer science.

Biography
Alan Turing was born at Paddington, London. His father, Julius Mathison Turing, was a British member of the Indian Civil Service and he was often abroad. Alan's mother, Ethel Sara Stoney, was the daughter of the chief engineer of the Madras railways and Alan's parents had met and married in India. When Alan was about one year old his mother rejoined her husband in India, leaving Alan in England with friends of the family. Alan was sent to school but did not seem to be obtaining any benefit so he was removed from the school after a few months.

Next he was sent to Hazlehurst Preparatory School where he seemed to be an 'average to good' pupil in most subjects but was greatly taken up with following his own ideas. He became interested in chess while at this school and he also joined the debating society. He completed his Common Entrance Examination in 1926 and then went to Sherborne School. Now 1926 was the year of the general strike and when the strike was in progress Turing cycled 60 miles to the school from his home, not too demanding a task for Turing who later was to become a fine athlete of almost Olympic standard. He found it very difficult to fit into what was expected at this public school, yet his mother had been so determined that he should have a public school education. Many of the most original thinkers have found conventional schooling an almost incomprehensible process and this seems to have been the case for Turing. His genius drove him in his own directions rather than those required by his teachers.

He was criticised for his handwriting, struggled at English, and even in mathematics he was too interested with his own ideas to produce solutions to problems using the methods taught by his teachers. Despite producing unconventional answers, Turing did win almost every possible mathematics prize while at Sherborne. In chemistry, a subject which had interested him from a very early age, he carried out experiments following his own agenda which did not please his teacher. Turing's headmaster wrote (see for example [6]):-
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.
This says far more about the school system that Turing was being subjected to than it does about Turing himself. However, Turing learnt deep mathematics while at school, although his teachers were probably not aware of the studies he was making on his own. He read Einstein's papers on relativity and he also read about quantum mechanics in Eddington's The nature of the physical world.

An event which was to greatly affect Turing throughout his life took place in 1928. He formed a close friendship with Christopher Morcom, a pupil in the year above him at school, and the two worked together on scientific ideas. Perhaps for the first time Turing was able to find someone with whom he could share his thoughts and ideas. However Morcom died in February 1930 and the experience was a shattering one to Turing. He had a premonition of Morcom's death at the very instant that he was taken ill and felt that this was something beyond what science could explain. He wrote later (see for example [6]):-
It is not difficult to explain these things away - but, I wonder!
Despite the difficult school years, Turing entered King's College, Cambridge, in 1931 to study mathematics. This was not achieved without difficulty. Turing sat the scholarship examinations in 1929 and won an exhibition, but not a scholarship. Not satisfied with this performance, he took the examinations again in the following year, this time winning a scholarship. In many ways Cambridge was a much easier place for unconventional people like Turing than school had been. He was now much more able to explore his own ideas and he read Russell's Introduction to mathematical philosophy in 1933. At about the same time he read von Neumann's 1932 text on quantum mechanics, a subject he returned to a number of times throughout his life.

The year 1933 saw the beginnings of Turing's interest in mathematical logic. He read a paper to the Moral Science Club at Cambridge in December of that year of which the following minute was recorded (see for example [6]):-
A M Turing read a paper on "Mathematics and logic". He suggested that a purely logistic view of mathematics was inadequate; and that mathematical propositions possessed a variety of interpretations of which the logistic was merely one.
Of course 1933 was also the year of Hitler's rise in Germany and of an anti-war movement in Britain. Turing joined the anti-war movement but he did not drift towards Marxism, nor pacifism, as happened to many.

Turing graduated in 1934 then, in the spring of 1935, he attended Max Newman's advanced course on the foundations of mathematics. This course studied Gödel's incompleteness results and Hilbert's question on decidability. In one sense 'decidability' was a simple question, namely given a mathematical proposition could one find an algorithm which would decide if the proposition was true of false. For many propositions it was easy to find such an algorithm. The real difficulty arose in proving that for certain propositions no such algorithm existed. When given an algorithm to solve a problem it was clear that it was indeed an algorithm, yet there was no definition of an algorithm which was rigorous enough to allow one to prove that none existed. Turing began to work on these ideas.

Turing was elected a fellow of King's College, Cambridge, in 1935 for a dissertation On the Gaussian error function which proved fundamental results on probability theory, namely the central limit theorem. Although the central limit theorem had recently been discovered, Turing was not aware of this and discovered it independently. In 1936 Turing was a Smith's Prizeman.

Turing's achievements at Cambridge had been on account of his work in probability theory. However, he had been working on the decidability questions since attending Newman's course. In 1936 he published On Computable Numbers, with an application to the Entscheidungsproblem. It is in this paper that Turing introduced an abstract machine, now called a "Turing machine", which moved from one state to another using a precise finite set of rules (given by a finite table) and depending on a single symbol it read from a tape.

The Turing machine could write a symbol on the tape, or delete a symbol from the tape. Turing wrote [13]:-
Some of the symbols written down will form the sequences of figures which is the decimal of the real number which is being computed. The others are just rough notes to "assist the memory". It will only be these rough notes which will be liable to erasure.
He defined a computable number as real number whose decimal expansion could be produced by a Turing machine starting with a blank tape. He showed that π was computable, but since only countably many real numbers are computable, most real numbers are not computable. He then described a number which is not computable and remarks that this seems to be a paradox since he appears to have described in finite terms, a number which cannot be described in finite terms. However, Turing understood the source of the apparent paradox. It is impossible to decide (using another Turing machine) whether a Turing machine with a given table of instructions will output an infinite sequence of numbers.

Although this paper contains ideas which have proved of fundamental importance to mathematics and to computer science ever since it appeared, publishing it in the Proceedings of the London Mathematical Society did not prove easy. The reason was that Alonzo Church published An unsolvable problem in elementary number theory in the American Journal of Mathematics in 1936 which also proves that there is no decision procedure for arithmetic. Turing's approach is very different from that of Church but Newman had to argue the case for publication of Turing's paper before the London Mathematical Society would publish it. Turing's revised paper contains a reference to Church's results and the paper, first completed in April 1936, was revised in this way in August 1936 and it appeared in print in 1937.

A good feature of the resulting discussions with Church was that Turing became a graduate student at Princeton University in 1936. At Princeton, Turing undertook research under Church's supervision and he returned to England in 1938, having been back in England for the summer vacation in 1937 when he first met Wittgenstein. The major publication which came out of his work at Princeton was Systems of Logic Based on Ordinals which was published in 1939. Newman writes in [13]:-
This paper is full of interesting suggestions and ideas. ... [It] throws much light on Turing's views on the place of intuition in mathematical proof.
Before this paper appeared, Turing published two other papers on rather more conventional mathematical topics. One of these papers discussed methods of approximating Lie groups by finite groups. The other paper proves results on extensions of groups, which were first proved by Reinhold Baer, giving a simpler and more unified approach.

Perhaps the most remarkable feature of Turing's work on Turing machines was that he was describing a modern computer before technology had reached the point where construction was a realistic proposition. He had proved in his 1936 paper that a universal Turing machine existed [13]:-
... which can be made to do the work of any special-purpose machine, that is to say to carry out any piece of computing, if a tape bearing suitable "instructions" is inserted into it.
Although to Turing a "computer" was a person who carried out a computation, we must see in his description of a universal Turing machine what we today think of as a computer with the tape as the program.

While at Princeton Turing had played with the idea of constructing a computer. Once back at Cambridge in 1938 he starting to build an analogue mechanical device to investigate the Riemann hypothesis, which many consider today the biggest unsolved problem in mathematics. However, his work would soon take on a new aspect for he was contacted, soon after his return, by the Government Code and Cypher School who asked him to help them in their work on breaking the German Enigma codes.

When war was declared in 1939 Turing immediately moved to work full-time at the Government Code and Cypher School at Bletchley Park. Although the work carried out at Bletchley Park was covered by the Official Secrets Act, much has recently become public knowledge. Turing's brilliant ideas in solving codes, and developing computers to assist break them, may have saved more lives of military personnel in the course of the war than any other. It was also a happy time for him [13]:-
... perhaps the happiest of his life, with full scope for his inventiveness, a mild routine to shape the day, and a congenial set of fellow-workers.
Together with another mathematician W G Welchman, Turing developed the Bombe, a machine based on earlier work by Polish mathematicians, which from late 1940 was decoding all messages sent by the Enigma machines of the Luftwaffe. The Enigma machines of the German navy were much harder to break but this was the type of challenge which Turing enjoyed. By the middle of 1941 Turing's statistical approach, together with captured information, had led to the German navy signals being decoded at Bletchley.

From November 1942 until March 1943 Turing was in the United States liaising over decoding issues and also on a speech secrecy system. Changes in the way the Germans encoded their messages had meant that Bletchley lost the ability to decode the messages. Turing was not directly involved with the successful breaking of these more complex codes, but his ideas proved of the greatest importance in this work. Turing was awarded the O.B.E. in 1945 for his vital contribution to the war effort.

At the end of the war Turing was invited by the National Physical Laboratory in London to design a computer. His report proposing the Automatic Computing Engine (ACE) was submitted in March 1946. Turing's design was at that point an original detailed design and prospectus for a computer in the modern sense. The size of storage he planned for the ACE was regarded by most who considered the report as hopelessly over-ambitious and there were delays in the project being approved.

Turing returned to Cambridge for the academic year 1947-48 where his interests ranged over many topics far removed from computers or mathematics; in particular he studied neurology and physiology. He did not forget about computers during this period, however, and he wrote code for programming computers. He had interests outside the academic world too, having taken up athletics seriously after the end of the war. He was a member of Walton Athletic Club winning their 3 mile and 10 mile championship in record time. He ran in the A.A.A. Marathon in 1947 and was placed fifth.

By 1948 Newman was the professor of mathematics at the University of Manchester and he offered Turing a readership there. Turing resigned from the National Physical Laboratory to take up the post in Manchester. Newman writes in [13] that in Manchester:-
... work was beginning on the construction of a computing machine by F C Williams and T Kilburn. The expectation was that Turing would lead the mathematical side of the work, and for a few years he continued to work, first on the design of the subroutines out of which the larger programs for such a machine are built, and then, as this kind of work became standardised, on more general problems of numerical analysis.
In 1950 Turing published Computing machinery and intelligence in Mind. It is another remarkable work from his brilliantly inventive mind which seemed to foresee the questions which would arise as computers developed. He studied problems which today lie at the heart of artificial intelligence. It was in this 1950 paper that he proposed the Turing Test which is still today the test people apply in attempting to answer whether a computer can be intelligent [1]:-
... he became involved in discussions on the contrasts and similarities between machines and brains. Turing's view, expressed with great force and wit, was that it was for those who saw an unbridgeable gap between the two to say just where the difference lay.
Turing did not forget about questions of decidability which had been the starting point for his brilliant mathematical publications. One of the main problems in the theory of group presentations was the question: given any word in a finitely presented groups is there an algorithm to decide if the word is equal to the identity. Post had proved that for semigroups no such algorithm exist. Turing thought at first that he had proved the same result for groups but, just before giving a seminar on his proof, he discovered an error. He was able to rescue from his faulty proof the fact that there was a cancellative semigroup with insoluble word problem and he published this result in 1950. Boone used the ideas from this paper by Turing to prove the existence of a group with insoluble word problem in 1957.

Turing was elected a Fellow of the Royal Society of London in 1951, mainly for his work on Turing machines in 1936. By 1951 he was working on the application of mathematical theory to biological forms. In 1952 he published the first part of his theoretical study of morphogenesis, the development of pattern and form in living organisms.

Turing was arrested for violation of British homosexuality statutes in 1952 when he reported to the police details of a homosexual affair. He had gone to the police because he had been threatened with blackmail. He was tried as a homosexual on 31 March 1952, offering no defence other than that he saw nothing wrong in his actions. Found guilty he was given the alternatives of prison or oestrogen injections for a year. He accepted the latter and returned to a wide range of academic pursuits.

Not only did he press forward with further study of morphogenesis, but he also worked on new ideas in quantum theory, on the representation of elementary particles by spinors, and on relativity theory. Although he was completely open about his sexuality, he had a further unhappiness which he was forbidden to talk about due to the Official Secrets Act.

The decoding operation at Bletchley Park became the basis for the new decoding and intelligence work at GCHQ. With the cold war this became an important operation and Turing continued to work for GCHQ, although his Manchester colleagues were totally unaware of this. After his conviction, his security clearance was withdrawn. Worse than that, security officers were now extremely worried that someone with complete knowledge of the work going on at GCHQ was now labelled a security risk. He had many foreign colleagues, as any academic would, but the police began to investigate his foreign visitors. A holiday which Turing took in Greece in 1953 caused consternation among the security officers.

Turing died of potassium cyanide poisoning while conducting electrolysis experiments. The cyanide was found on a half eaten apple beside him. An inquest concluded that it was self-administered but his mother always maintained that it was an accident."

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Alan Turing - BBC Horizon Documentary
The Strange Life and Death of Dr Turing (full vídeo)
https://www.youtube.com/watch?v=Z-sTs2o0VuY

Images:
1. Alan Turing superimposed _BIT_TuringTest
2. Portrait of Alan Turing, 1928
3. The first demonstration of the pilot ACE at NPL December 1950 Alan Matheson Turing.
4. Statue of Alan Turingin in Sackville Park in Manchester, England,

Background from {[https://history.computer.org/pioneers/turing.html]}
Born June 23, 1912, London, England; died June 7, 1954, Manchester, England, creator of the concept of the "universal machine," the concepts of early computational machines, and computer logic.
Education: Sherborne School, 1926-1931; wrangler, mathematics tripos, Kings College, Cambridge; PhD, Princeton University, 1938.

Professional Experience: fellow, King's College, 1935-1945; Princeton University, 1936-1938; British Foreign Office, Bletchley Park, 1939-1945; National Physical Laboratory, 1945-1948; University of Manchester, 1948-1954.

Honors and Awards: Smith's Prize, Cambridge University, 1936; Order of the British Empire (OBE), 1946; fellow, Royal Society, 1951.

Alan Turing's interest in science began early and never wavered. Both at his preparatory schools and later at Sherborne, which he entered in 1926, the contrast between his absorbed interest in science and mathematics, and his indifference to Latin and "English subjects," perplexed and distressed his teachers, bent on giving him a well-balanced education. Many of the characteristics that were strongly marked in his later life can already be clearly seen in remembered incidents of this time: his particular delight in problems, large or small, that enabled him to combine theory with the kind of experiments he could carry out with his own hands, with the help of whatever apparatus was at hand; and his strong preference for working everything out from first principles instead of borrowing from others--a habit which gave freshness and independence to his work, but also undoubtedly slowed him down, and later on made him a difficult author to read.

In 1931 he entered King's College, Cambridge, as a mathematical scholar. A second class in Part I of the tripos showed him still determined not to spend time on subjects that did not interest him. In Part II he was a wrangler, with "b*," and he won a Smith's Prize in 1936. He was elected a fellow of King's in 1935 for a dissertation on the central limit theorem of probability (which he discovered anew, in ignorance of recent previous work).

It was in 1935 that he first began to work in mathematical logic, and almost immediately started on the investigation that was to lead to his best known results, on computable numbers and the "Turing machine." The paper attracted attention as soon as it appeared and the resulting correspondence led to his spending the next two years (1936-1938) in Princeton, the second of them as Procter Fellow, working with Professor Alonzo Church.

In 1938 Turing returned to Cambridge; in 1939 the war broke out. For the next six years he was fully occupied with his work at the Government Code and Cypher School, otherwise known as Bletchley Park. His application of logic to code breaking has still not been well documented, though his influence on the development of Colossus is well known. But the loss to his published scientific work of the years between the ages of 27 and 33 was a cruel one. 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 Bletchley Park he was awarded the OBE.

At the end of the war many circumstances combined to turn his attention to the new automatic computing machines. They were in principle realizations of the "universal machine" which he had described in the 1937 paper for the purpose of a logical argument, although their designers did not yet know of Turing's work. Besides this theoretical link, there was a strong attraction in the many-sided nature of the work, ranging from electric circuit design to the entirely new field of organizing mathematical problems for a machine. He decided to decline an offer of a Cambridge University lectureship, and join the group that was being formed at the National Physical Laboratory for the design, construction, and use of a large automatic computing machine. In the three years (1945-1948) that this association lasted, he made the first plan of the ACE, [Automatic Computing Engine.] the NPL's automatic computer, and did a great deal of pioneering work in the design of subroutines. The machine was still incomplete when he left.

In 1948 he was appointed to a readership in the University of Manchester, where work was beginning on the construction of a computing machine by F.C. Williams and T. Kilburn. The expectation was that Turing would lead the mathematical side of the work, and for a few years he continued to work, first on the design of the subroutines out of which the larger programs for such a machine are built, and then, as this kind of work became standardized, on more general problems of numerical analysis. From 1950 onward he turned back for a while to mathematics and finally to his biological theory. But he remained in close contact with the Computing Machine Laboratory, whose members found him ready to tackle the mathematical problems that arose in their work, and what is more, to find the answers, by that combination of powerful mathematical analysis and intuitive shortcuts that showed him at heart more of an applied than a pure mathematician.

After the war, feeling in need of violent exercise, he took to long distance running, and found that he was very successful at it. He won the 3-mile and 10-mile championships of his club (the Walton Athletic Club), both in record time, and was placed fifth in the Amateur Athletic Association Marathon race in 1947. He thought it quite natural to put this accomplishment to practical use from time to time, for example, by running some 9 miles from Teddington to a technical conference at the Post Office Research Station in North London, when the public transport proved tedious.

In conversation he had a gift for comical but brilliantly apt analogies, which found its full scope in the discussions on "brains v. machines" of the late 1940s. He delighted in confounding those who, as he thought, too easily assumed that the two things are separated by an impassable gulf, by challenging them to produce an examination paper that could be passed by a man, but not by a machine.

Robin Addie and Maurice Wilkes were students together at Cambridge University in the years before World War II. They were both active in the Cambridge University Wireless Society, and were both keen radio hams. Their later careers took different directions. Addie held a Royal Signals commission in the Territorial Army Volunteer Reserve, and was mobilized soon after the outbreak of the war on, September 3, 1939. He found himself, at the age of 23, in command of the Wireless Section of the 52nd (Lowland) Divisional Signals in France. Later in the war, when attached to the "Y" service, Addie met Alan Turing:

One of my wartime activities was to be involved in the planning, design, and construction of a large radio receiving station at Hanslope Park a few miles from Bletchley. It was known as a 'Y' station and was intended for the interception of enemy radio signals. The project was aimed at setting a new standard for intercept stations. It was a green field exercise involving a new station building, and much of the equipment for it had to be specially designed and made. To this end, workshop and laboratory space was provided. The antenna system consisted of numbers of 3-wire rhombics spaced radially round the main building which housed banks of receivers fed from wide band amplifiers to whose inputs selected antennas could be connected. Dedicated land lines fed outgoing signals to Bletchley Park, which was only a few miles away, and to other places. The engineering section, with which I was associated, undertook all constructional and maintenance work in the technical field.

It was in 1944, when the station was operational, that I was asked to provide facilities for Alan Turing so that he might pursue his ideas on speech encryption. Thus I came to know him well and appreciate his intellectual qualifies, which clearly dwarfed those of us who were trying to help him.

His aim was to develop active elements for his computer ideas, largely NOR/AND gates, etc. I gave him room and assistants, and supplied him with chassis, components, power supplies, etc.

My vivid memories are of a man of medium build with a round head of crewcut hair bending over what we used to describe as an "electrified bird's nest" of resistors, capacitors, and odd components insecurely fixed to a prototype chassis. All components were held aloft by little blobs of solder, hence the "nest." At one end was a power supply delivering several hundreds of volts. I would watch fascinated as Turing plunged a hot soldering iron in the midst of this wonderwork. Needless to say, calamities happened; sparks flew, fuses blew, and things got hot, but Turing just pressed on in the sure knowledge of what he wished to achieve. Working on experimental gear with the power on was a common practice in those days, but not everybody was as reckless as Turing.

It had been arranged to find him digs locally, to and from which he rode an ancient bicycle. He seemed impervious to weather and, on more than one occasion, arrived soaked to the skin. On these occasions, he was coaxed into removing his trousers and given a lab coat in which he marched throughout the complex, regardless of his hairy legs and sock suspenders (garters) being on general view. He decided that our impregnating oven was the place to dry his garments, and on one occasion, with his mind on other weightier matters, he caused a minor fire. Clothes were then rationed in the UK, and we had to have a collection of ration coupons to help him buy a new pair of trousers.

In the Mess, he was both lively and amusing, and would engage in all manner of discussions on all kinds of diverse topics. I recall a most interesting tete-à-tete between Turing and Professor Stratton (the astrophysicist), then Colonel Stratton, which went on for a long time, way above my head, as can be imagined.

Turing was indeed a most dedicated man, totally oblivious of the wherewithal required for his own comfort. He took it for granted that all would somehow be provided, and we did provide it as far as we could. The girls at Hanslope took him in hand, calling him "prof," which he seemed to like. He was pleasant to me, and I always kept close touch with the work he did, and showed that I was interested. He always took trouble to explain his thoughts, which I appreciated.

Unfortunately, I did not see the outcome of Turing's experiments, since I was posted to the Far East to help mastermind the communications for Mountbatten in India and beyond. I was particularly distressed at the manner of his death in 1954, and the utter waste of a brilliant mind.

Much has been made of the homosexuality of Alan Turing. The biography by Andrew Hodges was initially intended (according to the publishers) to be a celebration of his sexual preference, but they were able to convince Hodges that there was more to the story than just that aspect of his life. Similarly, the play by Hugh Whitemore makes homosexuality the central theme, and a recent (1992) video play by the British Broadcasting Corporation, entitled "The Strange Life and Death of Dr. Turing," followed the same thread.

In a set of interviews in 1992 with I. Jack Good and Donald Michie, [Sponsored in part by the National Science Foundation.] both colleagues of Turing during his Bletchley Park sojourn, I led them to discuss their knowledge of Turing's homosexuality:

Good: ...when we walked down King's Parade [in 1947] that was the first time I discovered that he was homosexual. That was when he said that he was going to Paris to "see a boy." It was obvious that he was admitting or proclaiming his homosexuality.

Lee: He was very open about it?
Good: Yes, at that time.

Michie: He certainly wasn't during the war, for some of us, including both of us, were quite unaware.... I took quite seriously his engagement to ...
Good: Joan Clarke?

Lee: Peter Hilton [1991] quotes you, Jack, as saying, 'It was fortunate that the authorities did not know during the war that Turing was a homosexual, otherwise the Allies might have lost the war."
Good: Yes.

Michie: Oh but that's absolute nonsense, because Bletchley had some flamboyant homosexuals--Peter's ideas that security people were down on homosexuality itself, is absolute nonsense. I can't think how he could write that. The most flamboyant case was Angus Wilson--he later became a very successful novelist, and he had a boyfriend called Beverly, and these two, Angus was about that high [indicating small] with flowing yellow hair (I remember it went white later) and Beverly (I forget his second name) was very "weed-like," very tall. They could be seen shambling along the horizon, a daily sight, as they took their walk around lawns after lunch.
Good: I never knew that. I know that Angus Wilson ran around the pond in the nude, when he had a nervous breakdown.

Michie: He was also said to have poured ink on his head on another occasion; it was the first sign he was going nuts again. I had not heard about the nude bit.
Good: I assumed they were down on homosexuality.

Michie: I think that's a retrospective coloring actually. Because Henry Reed. [Reed was a poet who had composed a poem entitled "Naming of Parts"--see Lewin, Ronald, 1978, Ultra Goes to War, Hutchinson & Co., Ltd., London, 490 pp.] You remember Henry Reed, you knew he was a homosexual didn't you?
Good: No!

Michie: I must have known him better than you. He was always complaining to me about how his current affair was, or was not, prospering.
Good: Well, I was in digs with him, and with David Rees ... He never said anything about his affairs.

Michie: I had some links to a more literary set. There was a literary set in Bletchley, and I was fresh from a wholly arts education. There were these two cultures--the mathematicians' culture was another-I worked all my time in the mathematicians' culture but I retained, certainly for a year or two, quite a lot of social links to various classics dons and literary people like Henry Reed. And in that group, things like whether Henry Reed was a homosexual-everybody knew. And the same with Angus Wilson.
Good: I had no idea.

In 1952 Turing was convicted by a British court for his involvement in "unnatural acts" and was required to take female hormones in an effort to rid him of his preferences. The physical result was the development of Turing's breasts, and apparently his accompanying depression. This was the time of Turing's life when he was studying the chemical theory of morphogenesis. His "experimental methodology" was what Newman termed his "rules of the game," in which he attempted to solve problems using only the materials immediately at hand or which he could construct in his mind. Turing died by his own hand in 1954 by eating an apple dipped in strychnine. It is unknown whether this was an experiment which had an unfortunate result or whether his death was intentional. Either way, the world lost a mathematical genius at the height of his intellectual power.

QUOTATION
"It is of course important that some efforts be made to verify the correctness of the assertions that are made about a routine. There are essentially two types of method available, the theoretical and the experimental. In the extreme form of the theoretical method a watertight mathematical proof is provided for the assertion. In the extreme form of the experimental method the routine is tried out on the machine with a variety of initial conditions and is pronounced fit if the assertions hold in each case. Both methods have their weaknesses." (Manchester Mark I Programming Manual, 1951)

BIBLIOGRAPHY
Biographical
Addie, Robin, "Memories of Alan Turing," Ann. Hist. Comp., Vol. 15, No. 1, 1992, pp. 59-60.

Aspray, William F., From Mathematical Constructivity to Computer Science: Alan Turing, John von Neumann, and the Origins of Computer Science in Mathematical Logic, unpublished PhD dissertation, University of Wisconsin, Madison, 1980.

Britton, J.L., ed., Pure Mathematics; with a Section on Turing's Statistical Work by I.J. Good, North-Holland, Amsterdam, 1992.

Campbell-Kelly, Martin, "Programming the Pilot ACE: Early Programming Activity at the National Physical Laboratory," Ann. Hist. Comp., Vol. 3, No. 2, 1981, pp. 133-162.

Carpenter, B.E., and R.W. Doran, eds., A.M. Turing's ACE Report of 1946 and Other Papers, MIT Press, Cambridge, Mass., 1986.

Herken, Rolf, ed., The Universal Turing Machine: A Half-Century Survey, Oxford Univ. Press, Oxford, UK, 1988.

Hilton, Peter, "Working with Alan Turing," Mathematical Intelligencer, Vol. 13, No. 4, 199 1, pp. 22-25.

Hinsley, Sir Harry H., and Alan Stripp, Code Breakers: The Inside Story of Bletchley Park, Oxford Univ. Press, Oxford, UK, 1993.

Hodges, Andrew, Alan Turing: The Enigma, Simon and Schuster, New York, 1983.

Huskey, Harry, "From ACE to G-15," Ann. Hist. Comp., Vol. 6, No. 4, Oct. 1984, pp. 350-371.

Lavington, Simon, Early British Computers, Digital Press, Bedford, Mass., 1980; see Chapter 5: "The ACE, the British National Computer," and Chapter 8: "The NPL Pilot ACE."

Michie, D., "Machines that Play and Plan," Science Journal, Oct. 1968, pp. 83-88.

Michie, D., "The Disaster of Alan Turing's Buried Treasure," Letter to the editor, Computer Weekly, Mar. 1977, p. 10.

Michie, D., "Turing and the Origins of the Computer," New Scientist, Vol. 85, No. 1195, 1980, pp. 580-583.

Newman, M.H.A., "Alan Mathison Turing, 1912-1954," Biographical Memoirs of Fellows of the Royal Society, Vol. 1, 1955, pp. 253-263.

Randell, Brian, "The Colossus," in Metropolis, N., J. Howlett, and Gian-Carlo Rota, A History of Computing in the Twentieth Century, Academic Press, New York, 1980, pp. 47-92.

Ritchie, David, The Computer Pioneers, Simon and Schuster, New York, 1986.

Slater, Robert, Portraits in Silicon, MIT Press, Cambridge, Mass., 1987

Turing, Sara, Alan M. Turing, W. Heffer & Sons, Cambridge, UK, 1959.

Wilkinson, J.H., "Turing's Work at the National Physical Laboratory and the Construction of Pilot ACE, DEUCE, and ACE," in Metropolis, N., J. Howlett, and Gian-Carlo Rota, A History of Computing in the Twentieth Century, Academic Press, New York, 1980, pp. 101-114.

Whitemore, Hugh, Breaking the Code, A Play in Two Acts, Samuel French, New York, 1987

Significant Publications
Carpenter, B.E., and R.W. Doron, eds., A.M. Turing's ACE Report of 1946 and Other Papers, MIT Press, Cambridge, Mass., 1986.

Morris, F.L., and C.B. Jones, "An Early Program Proof by Alan Turing," Ann. Hist. Comp., Vol. 6. No. 2, Apr. 1984, pp. 139-143.

Turing, Alan M., "On Computable Numbers with an Application to the Entscheidungs-problem", [This paper defined the concept of the universal machine.] Proc. London Math. Soc., Vol. 42, 1937, pp. 230-265.

Turing, Alan M., "Machine Intelligence," submitted to National Physical Laboratory, reprinted in Meltzer, Bernard, and Donald Michie, eds., Machine Intelligence 5, Halstead Press, John Wiley & Sons, New York, 1970, pp. 3-23.

Turing, Alan M., "Computing Machinery and Intelligence,&quot [It is in this paper that Turing proposed the test of intelligence which we now know as the "Turing Test."] Mind, Vol. 59, 1950, pp. 433-460.

Turing, Alan M., Proposal for the Development of an Electronic Computer, Nat'l. Phys. Lab. Report, Computer Science 57, London; reprint from original with foreword by D.W. Davies, 1972."
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Alan Turing, Cybernetics and the Secrets of Life
https://www.youtube.com/watch?v=rPLvj-GcfSU

Images:
1. Alan Turing in 1951
2. Statue of Alan Turing in in Sackville Park in Manchester, England,
3. Ratio Club at Cambridge 1952, Giles Brindley (yellow), Donald MacKay (red), Alan Turing (green)
4. Statue of Turing by Stephen Kettle at Bletchley Park, commissioned by Sidney Frank, built from half a million pieces of Welsh slate


Background from {[ https://www.nytimes.com/2019/06/05/obituaries/alan-turing-overlooked.html]}
Overlooked No More: Alan Turing, Condemned Code Breaker and Computer Visionary
His ideas led to early versions of modern computing and helped win World War II. Yet he died as a criminal for his homosexuality.

Though he is regarded today as one the most innovative thinkers of the 20th century, at his death many of his wartime accomplishments were classified. Credit...Godrey Argent Studio, via The Royal Society
June 5, 2019
Overlooked is a series of obituaries about remarkable people whose deaths, beginning in 1851, went unreported in The Times. This month we’re adding the stories of important L.G.B.T.Q. figures.
By Alan Cowell
LONDON — His genius embraced the first visions of modern computing and produced seminal insights into what became known as “artificial intelligence.” As one of the most influential code breakers of World War II, his cryptology yielded intelligence believed to have hastened the Allied victory.
But, at his death several years later, much of his secretive wartime accomplishments remained classified, far from public view in a nation seized by the security concerns of the Cold War. Instead, by the narrow standards of his day, his reputation was sullied.
On June 7, 1954, Alan Turing, a British mathematician who has since been acknowledged as one the most innovative and powerful thinkers of the 20th century — sometimes called the progenitor of modern computing — died as a criminal, having been convicted under Victorian laws as a homosexual and forced to endure chemical castration. Britain didn’t take its first steps toward decriminalizing homosexuality until 1967.
Only in 2009 did the government apologize for his treatment.
“We’re sorry — you deserved so much better,” said Gordon Brown, then the prime minister. “Alan and the many thousands of other gay men who were convicted, as he was, under homophobic laws were treated terribly.”
And only in 2013 did Queen Elizabeth II grant Turing a royal pardon, 59 years after a housekeeper found his body at his home at Wilmslow, near Manchester, in northwest England.
A coroner determined that he had died of cyanide poisoning and that he had taken his own life “while the balance of his mind was disturbed.”
At his side lay a half-eaten apple. Biographers speculated that he had ingested the poison by dousing the apple with cyanide and eating it to disguise the toxin’s taste. Some of those who studied his personality or knew him, most notably his mother, Ethel Turing, challenged the official verdict of suicide, arguing that he had poisoned himself accidentally.
To this day Turing is recognized in his own country and among a broad society of scientists as a pillar of achievement who had fused brilliance and eccentricity, had moved comfortably in the abstruse realms of mathematics and cryptography but awkwardly in social settings, and had been brought low by the hostile society into which he was born.
“He was a national treasure, and we hounded him to his death,” said John Graham-Cumming, a computer scientist who campaigned for Turing to be pardoned.
Above all, Turing’s name is associated for many people with the top-secret wartime operations of Britain’s code-breakers at Bletchley Park, a sprawling estate north of London, where he oversaw and inspired the effort to decrypt ciphers generated by Nazi Germany’s Enigma machine, which had once seemed impenetrable. The Germans themselves regarded the codes as unbreakable.
At the time, German submarines were prowling the Atlantic, hunting Allied ships carrying vital cargo for the war effort. The convoys were critical for building military strength in Britain and eventually enabled the Allies to undertake the D-Day landings in Normandy in 1944, heralding the collapse of Nazi Germany the next year.
Only by charting the submarines’ movements could Allied forces change the course of their convoys, and for that they relied on the cryptologists of Bletchley Park to decode messages betraying the Germans’ deployments.
The enduring fascination with Turing’s story inspired the 2014 movie “The Imitation Game,” starring Benedict Cumberbatch and Keira Knightley. But his scientific range went far beyond the limits of cinematic drama: He laid down principles that have molded the historical record of the relationship between humans and the machines they have created to solve their problems.

Even before World War II, Turing was making breakthroughs.
Credit for the creation of the first functioning computer in 1946 went to the researchers John Presper Eckert and John W. Mauchly for their machine the Electronic Numerical Integrator and Computer, or Eniac, which they had developed at the University of Pennsylvania during World War II.
But Turing’s notions preceded the Eniac. He conceived what became known as the universal Turing machine, which envisioned “one machine for all possible tasks” — essentially computers as we know them today, Andrew Hodges, Turing’s biographer, wrote in a condensed version of his 1983 book, “Alan Turing: The Enigma.”
Turing’s vision, Hodges said, was that one machine could “be turned to any well-defined task by being supplied with the appropriate program.”
He added, “The universal Turing machine naturally exploits what was later seen as the ‘stored program’ concept essential to the modern computer: It embodies the crucial 20th century insight that symbols representing instructions are no different in kind from symbols representing numbers.”
Later, technology that emerged from the Manhattan Project, the United States-led effort to develop the atom bomb, also relied on Turing’s ideas.
“What had begun as a British idea was scaled up to industrial size by the Americans,” David Kaiser, a professor at the Massachusetts Institute of Technology, wrote in 2012 in The London Review of Books.
Turing’s postwar work at the University of Manchester, on the first functioning British computers, was also significant: It reflected the emerging power of electronic computing in the Cold War race for nuclear supremacy. And he remained fascinated by the interplay between human thought processes and their computerized inventions. Even in 1944, Hodges wrote, Turing had spoken to a colleague about “building a brain.”

In an article published in 1950 in the academic journal Mind, Turing developed a method that came to be known as the “Turing Test,” a sort of thought experiment to determine whether a computer could pass as a human. As part of his experiment, a human interrogator would ask questions and try to figure out whether the answers had come from a computer or a human.
Many years later, on a visit to London, President Barack Obama placed Turing in a trans-Atlantic pantheon of innovation and discovery, saying, “From Newton and Darwin to Edison and Einstein, from Alan Turing to Steve Jobs, we have led the world in our commitment to science and cutting-edge research.”
Alan Mathison Turing was born in London on June 23, 1912, the second of two sons of Ethel Sara Stoney and Julius Mathison Turing, who had met in imperial India, where his father was a senior colonial administrator. After Alan’s birth they left him and his brother, John, in the care of foster parents in England while they returned to India so that Alan’s father could continue his work.
“Alan Turing’s story was not one of family or tradition but of an isolated and autonomous mind,” Hodges wrote.
In his early days, Turing’s education reflected the overwhelming social requisite of his class to secure a place at a reputable private boarding school. Alan, at age 13, enrolled at Sherborne School, in southern England, where his fascination with science raised alarms in an educational system based on the study of what were called the classics — works in Latin and ancient Greek.
“If he is to be solely a scientific specialist, he is wasting his time at a public school,” Nowell Smith, Sherborne’s headmaster, wrote to his parents, as recorded in Hodges’s book.

Nonetheless, he secured a place at King’s College in Cambridge to study mathematics, graduating in 1934 with a first class honors degree. With remarkable academic precocity he was made a fellow of the college in 1935. A year later, he published the groundbreaking paper “On Computable Numbers, With an Application to the Entscheidungsproblem” (or “decidability problem”), a reference in German to a celebrated riddle that the American logician Alonzo Church had also explained.
Both Turing and Church reached the same conclusion — a basis for computer science — that there is no single algorithm that could determine the truth or falsity of any statement in formal logic (though Turing’s thinking was more direct).
Turing completed a doctoral thesis at Princeton in 1938 before returning to Cambridge. With Britain’s declaration of war on Germany in September 1939, he joined the Bletchley Park code breakers at the Government Code and Cypher School, working in makeshift huts clustered around a mansion.
Their greatest initial challenge was figuring out the method of encryption of the German Enigma device, which was invented 20 years earlier by Arthur Scherbius, a German electrical engineer who had patented it as a civilian machine to encrypt commercial messages. The machine worked by entering letters on a typewriter-like keyboard and then encoding them through a series of rotors to a light board, which showed the coded equivalents. The machine was said to be capable of generating almost 159 quintillion permutations.
The British were helped initially by a Polish mathematician who had been studying the Enigma machine and had provided vital details after Hitler’s forces invaded Poland in 1939. But under the direction of Turing and another Cambridge-educated mathematician, W.G. Welchman, the Bletchley Park code breakers greatly expanded and accelerated those early efforts. Using a huge contraption called the Bombe, they mimicked the operations of the Enigma machine to break its codes.

“The critical factor was Turing’s brilliant mechanization of subtle logical deductions,” the biographer Hodges wrote.
In 1942, Turing was assigned to visit the United States for several months of high-level consultations on the encryption of conversations between President Franklin D. Roosevelt and Winston S. Churchill. His wartime work earned him a high civilian award, and he was named an Officer of the Most Excellent Order of the British Empire.
In the postwar years, Turing’s fascination with computers led him to design the Automatic Computing Engine. Although it was never built, Turing believed that “the computer would offer unlimited scope for practical progress toward embodying intelligence in an artificial form,” Hodges wrote.
In October 1948, Turing began working at Manchester University’s computing laboratory. He bought a house in nearby Wilmslow in 1950. Among his enthusiasms were his work on various scientific themes, including morphogenesis, the theory of growth and form in biology; his continued secret ties to Britain’s postwar code breakers; and long-distance running.
He was also, Hodges said, beginning to explore the homosexual identity he had hidden when he proposed marriage in 1941 to Joan Clarke, a Bletchley Park cryptanalyst. He later withdrew the offer after explaining his sexuality to her, and the two remained friends.
About 10 years later, the police were investigating a burglary at his home when he admitted to having had a physical relationship with a man named Arnold Murray. Murray told Turing that he knew the thief’s identity, and detectives, in their questioning, asked Turing about his relationship to Murray.
In March 1952, Turing and Murray were charged with “gross indecency,” and both pleaded guilty in court. Murray was given a conditional discharge, but Turing was ordered to undergo chemical castration by taking doses of the female hormone estrogen to reduce sex drive.
Two years later, the motive for his apparent suicide, at age 41, remained unclear and left many questions. At the time, Hodges wrote, known homosexuals were denied security clearances, which meant that Turing could not be involved in secret work during the Cold War, leaving him excluded and embittered. While a coroner deemed the death a suicide, the telltale apple at Turing’s side was never forensically examined."


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