The Alan Turing Internet Scrapbook


Growth, Form and Crisis
1951-1952, anticipating 2006-2009

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Non-linear Life

Alan Turing opened the second half of the twentieth century with his own, completely original, mathematical theory of morphogenesis: the theory of how biological growth occurs. His work can now be seen as one of the foundations of the huge field of non-linear systems as well as pioneering work at the interface of mathematics and biology.

Rather than investigating non-linearity in general, Turing's own working and writing was closely focussed on explaining specific biological phenomena. His idea was that non-linear partial differential equations could describe and explain the development of an initially homogeneous mixture of chemicals into the asymmetrical forms seen in biological structures.

Such equations could only be attacked by numerical methods and so demanded the use of a computer.

There is an edition of Turing's published and unpublished papers on this work in the Collected Works. See the Bibliography.

The mathematical biologist Jonathan Swinton has a website showing his detailed study of Turing's biological work.

A personal computer

As described on another Scrapbook page, Manchester University had the world's first working computer in 1948. In February 1951 a fully engineered version, the Ferranti Mark 1, came into operation. The result was that Turing was in the one place in the world where he could get personal use of a computer to work on his new theory of life.

The engineers at Manchester had triumphed through finding a way to use cathode ray tubes as its fast storage system. (There was a slower magnetic drum as well --- ancestor of the hard disk.)

The screen of the tube actually was the storage system itself, and the fact that it gave a visual display was regarded as incidental. Other people disapproved of 'peeping' at the progress of the program. But Turing liked watching what was happening to his calculations simulating non-linear dynamic effects. So, ahead of his time as usual, he became the first to be glued to a screen as a computer graphics user.


A hard place

The Computer Laboratory at Manchester remained dominated by the hardware skills of the electronic engineers, and after 1950 Alan Turing lost interest in the field of what was to become computer science. He never revived his early ideas for developing computer languages. He wrote machine code in base-32 arithmetic for his own work.


Culture clash: the soft machine in a hard place.

Behind the Scenes

Besides being used for the frantic atomic bomb programme, which culminated in the British test of October 1952, a copy of the Manchester machine went to GCHQ, successor to the Bletchley Park organisation. It was based at Eastcote in north-west London until moving to Cheltenham in 1952. After 1948 Turing was consulted, possibly on some aspect of the Venona problem of decrypting Soviet traffic. This appears to have been the dominant Anglo-American priority of the time, and played an important role in identifying Soviet agents.

It seems very likely that Turing did some work on the Manchester computer for GCHQ. The engineers were surprised when he specified the need for a 'sideways adder' in the hardware, and this may well have been with codebreaking in mind.

Breaking the Codebook of Nature

Alan Turing's programme for mathematical biology was so far ahead that only in the 1980s did computers really become fast enough to do justice to what he had in mind. Even now, people are investigating models not much more complicated than those he set out.

There is a very clear account of morphogenetic theory in a University of Calgary research overview which takes you from Turing's first paper to present-day work. On the right is a sea-shell pattern that emerged from 'cooking' on a modern computer screen.

There are many more beautiful pictures to be seen on this site.

On the Caltech Xmorphia website, unfortunately no longer available on the Web, you could see the results of using a supercomputer on the equations

which were essentially those Turing wrote down for development on a two-dimensional surface. F and k are two numerical parameters. (The Xmorphia site has been reincarnated here.)

The Manchester computer took hours to evolve a system like this with just one set of parameters, but a modern computer can do it over and over again for many parameter values and bring to light the different regions of parameter space where stable or chaotic evolution ensues.
Since 2000, desk-top computers have run about as fast as the supercomputer which did the work in 1993. So now at last Turing's theory is truly in the domain of the personal computer, something Turing would have been happy to see. I owe this remark to John E. Pearson who was a pioneer in this work at Los Alamos.

Here is an example (reduced to low-resolution quality) of what comes out for one particular choice of parameter values:

Suprisingly complex structures arise out of very simple equations — that is the essence of Alan Turing's idea.

In this case the equations have been solved on a torus, which means you could use this or one of the many other examples of evolution for tiling the screen on a Web page. Roy Williams and Bruce Sears, who created the Xmorphia site, set up another page for just this purpose, called The Wallpaper Machine. I used it for papering the pages of the short Turing biography on this site.

Fifty Years Ahead

John Pearson has a histogram of the citations made to Turing's work, dramatically illustrating how far ahead of his time Turing was. It only runs to 1999, but since then there has been a major development.

In the journal Science, 1 December 2006, a European group of biological researchers (Stefanie Sick, Stefan Reinker, Jens Timmer, Thomas Schlake) found the first direct physical evidence for Turing's theory of pattern formation.

An accompanying paper by Philip Maini and his collaborators (opening paragraph shown at left) explains the significance of their discovery, which came 55 years after Turing's paper was submitted.


Alan Mathison Turing, FRS

In 1951 Alan Turing was elected to a Fellowship of the Royal Society, the main scientific academy of the United Kingdom.

He had almost become respectable at last, at 39.

This is when he sat for formal portrait photographs.

See the Archive page for information about this and other images.


Then it happened

In December 1951, just after he had submitted for publication his first results on non-linear theory, Alan Turing met a 19-year-old man at a pick-up spot in Oxford Street, Manchester. You can see some pictures of the area as it is today on this Scrapbook page.

Manchester is now a lively city with a huge student population and a big gay scene, immortalised in 1999 in the drama series Queer as Folk on Channel Four Television. But it was very different in 1951.

As usual, Alan Turing walked into another culture clash, this time the most dramatic of all.

A complicated sequence of events developed, told in my book, and subsequently dramatised in the play Breaking the Code. It resulted in them both being arrested on 7 February 1952, the day of Queen Elizabeth's accession. Their crime — three occasions of consenting sex in Alan Turing's house in Wilmslow. The trial followed on 31 March 1952.




From the local newspaper, the Alderley Edge and Wilmslow Advertiser, 4 April 1952.

It was argued in court that the importance of his research work meant he could be allowed to take injections of oestrogen as an alternative to a prison sentence. This concession — chemical castration — was called 'organo-therapic treatment'. It had to continue for a year.

He was reported as protesting to the police that a 'Royal Commission was sitting to legalise it.' If so, he was quite mistaken. The Wolfenden commission did not exist until 1954, reporting in 1957. Even when English law was changed in 1967, what Alan Turing had done remained a crime, for the 'age of consent' was set at 21, and was only changed to 18 in 1994. See the Stonewall campaign organisation for further news.

Behind the scenes, there was something else very serious for Alan Turing: the question of his secret work for GCHQ. Now he was revealed as a homosexual and so automatically a 'security risk' by post-war American standards. His work was stopped.

Change in the concept of homosexuals as 'security risks' only came in the 1990s. In the USA, the National Organization of Gay and Lesbian Scientists and Technical Professionals (NOGLSTP) has worked on this and President Clinton signed an anti-discrimination order. In the UK, job advertisements for GCHQ now assert that there is no discrimination on grounds of sexual orientation.

It was very different in 1952: Alan Turing's revealed homosexuality became an unspeakable and terrifying issue of national security.

A Government apology, after 50 years

These events shocked and traumatised everyone involved. No-one spoke of them; there was public silence. When I learned of them in 1973, from some of the very few people who knew something of them, they became a call to action. In 1977 I embarked on the full-scale biography of Alan Turing in an attempt to do full justice to what had happened. In 1986, the playwright Hugh Whitemore made the arrest into the central dramatic action of his play Breaking the Code.

Twenty years later, many more people felt that shock and a wish that something could somehow be done about it. In 2009 a British computer scientist, John Graham-Cumming, started a petition on the webspace set up by the British government, calling on the Prime Minister to apologise to Turing for the prosecution in 1952. It gained wide support, with Richard Dawkins a notable contributor. The Independent newspaper, with more letters here, BBC News, and Channel Four Television news gave sympathetic coverage. Particularly strong grass-roots support came from Manchester, but calls for signatures appeared in many other media, from logicians' messageboards to gay sex chatlines. Of course, the story also went round the world.

On 10 September 2009, the Prime Minister responded with a full personal statement of apology.

The statement went further and deeper than the petition asked for, making it clear that Alan Turing's prosecution and punishment was only one aspect what could and did happen under the law as it was, blighting millions of lives. Apology is due to all who thus suffered, and not just him. Quite correctly, the Prime Minister observed that since 1997, the Labour government had substantially changed British law in letter and in spirit. Such effective government action has spoken louder than symbolic words, and is very much what Alan Turing would have wanted, even if fifty years too late.

It is worth pointing out that this change of political culture was marked by an event in 1998, when Chris Smith (now Lord Smith), a prominent government minister, made a public statement that 'Alan Turing did more for his country and for the future of science than almost anyone. He was dishonourably persecuted during his life; today let us wipe that national shame clean by honouring him properly.'

Since 2009 there have been further developments: see the Parliamentary debate, 27 June 2012, on the occasion of the centenary.

Alan Turing's reaction?

In summer 1952, a holiday in Norway. See the next Scrapbook page.




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Andrew Hodges