Alan Turing at the end of his (real) lifeI began with a 1946 picture of Alan Turing running, as on this Scrapbook Page.
In 1946, at 34, Alan Turing's head was full of the greatest Anglo-American secrets of the war, and full of plans for the computer of the future. But he died on 7 June 1954 at the age of 41. It is an unanswerable question as to what he would have done if he had lived. His life was full of surprises at every turn, and was unpredictable. But I shall use this counterfactual theme to discuss what he was doing and thinking at his death in 1954, and to survey some other unfinished threads in his life.
This last phase of his life has been dramatised in the play and TV film Breaking the Code. It began with his arrest on the first day of Queen Elizabeth's reign, 7 February 1952 (this is my contribution to the current Golden Jubilee celebrations!) It was notable for his holidays abroad in 1952 and 1953 which, as he explained, were to escape the English law.
Here I showed a page of Turing's 'Ibsen5' machine-code program, as on this Scrapbook Page. I referred to the talk earlier in the day where Jonathan Swinton had illustrated Alan Turing's morphogenesis work with some of his Manchester machine-code programming. He had shown a page of KJELL theory, explaining that this was a reference to Turing's Norwegian holiday in 1952 and the young man he met there.
Breaking the machine code: IBSEN was just another Norwegian allusion. The choice of Norway was in fact Alan Turing's response to news of the first open European gay movement in Scandinavia, twenty years ahead of his time as usual. In March 1953, Kjell tried to visit him in Manchester, and this caused a second major crisis for Turing with the police keeping watch on him. This doesn't surprise me, because he had so much top-secret knowledge at the height of the cold war. We do not know how matters developed between then and his death on 7 June 1954, and this period remains full of mystery.
Where his theory of life might have ledWhat we do know, from Jonathan Swinton's talk, is that in his last year he was exploring many varied avenues in his morphogenesis. The Fibonacci problem was probably less tractable than he hoped. But there were many other directions in which his biological theory might have moved if he had lived longer:
Word problemsBut Turing had by no means abandoned pure mathematics. He had probably lost interest in mathematical logic. But in 1949 he had done work on decidability problems in semigroups, and he might well have gone on to contribute to other decision questions within mathematics. There was, for instance, the outstanding question (Hilbert's Tenth Problem) of the solvability of Diophantine equations, not settled until 1970. (In the real world, Martin Davis had a prominent role in this story, though he was too modest to mention this when he referred to the Tenth Problem in his talk!). Turing described P. S. Novikov's new result on the undecidability of the word problem for groups in a popular article which appeared in 1954.
He explained a 'word problem' in terms of a problem in knot theory. This illustration itself pointed to another fascinating and growing area in post-war mathematics, and also reflected the more geometrical turn of his interests. The 1954 article went on to explain Gödel's theorem This was perhaps the first popular article on the subject, which was not at all well known in those days. (Douglas Hofstadter's Gödel, Escher, Bach did not appear until 25 years later!) So this article also suggests another role that a longer-lived Alan Turing might have taken — a great communicator of mathematics and science to a wide audience.
Computer Science and Machine IntelligenceWhat about the future of his work in computer science? Immediately after Turing's death in 1954, his student and friend Robin Gandy wrote to Max Newman with an account of what struck him as unfinished in Turing's work (this letter is published in the fourth volume of the Collected Works.) Jonathan Swinton has already referred to Gandy's letter, in quoting his remarks on the state of the morphogenesis work. In fact, Gandy wrote comments under eight different headings. Only one of them, the sixth, was in computer science:
I always hoped he would return one day to the practical problems of making a machine learn. There should be somewhere a copy of the report he wrote on this after his sabbatical year at Cambridge from the NPL.
Now, the report he wrote for the NPL, Intelligent Machinery, is the basis for the work which has brought us all here today, thanks to Christof Teuscher! I'm sure there will be more to come, extending the exploration of Turing's models.
The computer scientist John McCarthy would have invited Turing to Dartmouth College in 1956, for what is wrongly thought of as the conference that began Artificial Intelligence. What would Turing have said? Well, I hope he would have been living witness to the fact that Artificial Intelligence had started well before 1956, as Prof. Copeland rightly said in his talk. I like also to think he would have advocated avoiding the separation of 'top-down' from 'bottom-up' research that was in fact to develop so strongly for the next 30 years (as Christof Teuscher brought out so clearly in his talk.) In contrast, Turing in 1948 and again in 1950 described both approaches together, saying that both approaches should be tried.
But it is worth noting Gandy's message that Turing had shown little interest in pursuing this work. And I'm not sure he would have accepted the invitation to Dartmouth College. He didn't like conferences much! But he would have enjoyed THIS one, I assured the audience, with quite enough handome young men to please him... he wouldn't have changed at 90...
When he had the 1951 Manchester computer at his disposal, he had not used it to follow up his bottom-up ideas on networks, nor his top-down ideas on chess-playing. So it is by no means obvious that a longer life would have led him to continue with AI research. He seemed to prefer to leave it to others.
The same goes for his ideas for programming theory. It is very striking that he continued to write raw machine code for the Manchester machine, although he of all people knew that the machine itself could have been made to do the routine work. In 1946, years ahead of others, he had seen the potential of the stored program for interpreters, compilers and scripts:
The process of constructing instruction table should be very fascinating. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself.
In 1947 he explicitly recognised the general nature of programming languages.
...one could communicate with these machines in any language provided it was an exact language, i.e. in principle one should be able to communicate in any symbolic logic, provided that the machine were given instruction tables which would allow it to interpret that logical system.
In 1950 his M.Sc. student Audrey Bates worked on putting a small part of Church's lambda-calculus in a form where it could be mechanised by the Manchester computer. This is a small snippet of her thesis:
This work could have led to LISP programming, which was also inspired by the lambda-calculus, but he never followed it up. The same is true of the work he did on program proofs in 1949; this was never taken up and had to wait for others in the 1960s.
He preferred making the first attack at a new idea and then leaving details to others. Of course, Christof Teuscher knows there may be an enormous amount of work in sorting out such so-called details!
To speculate a little more wildly, there is another obvious arena where his knowledge of mathematical logic might have been brought into practical computer science: this is what we have known as complexity theory since the 1970s.
Tony Sale's talk showed how practical time constraints on algorithmic solutions formed a vital aspect of Turing's wartime work. It seems quite possible to me that he was consulted by GCHQ after 1948 about the use of computers for large-scale problems, such as the famous Venona problem of Soviet messages which was the top Anglo-American priority in that period. If so it is quite possible that researches in large-scale efficient computer-based searching and sorting would have brought him to complexity-theory ideas.
CONTINUE to Part 2 of the lecture