The Alan Turing Internet Scrapbook

Wondrous Light


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Not Going Linear

Alan Turing tried as best he could to make a joke of the trial and the injurious and humiliating effect of the hormones on his body, He talked openly about it in the computing laboratory, refusing to show any shame or remorse, or to see the law except as an absurdity.

He made more of his friends, and found some new ones.

He went in for Jungian analysis, writing down all his dreams.

He continued to develop the theory of morphogenesis. His numerical treatment of non-linear equations was work of the future, not followed by anyone else until the 1970s.

For a vignette of this period see 'My hero: Alan Turing, by Alan Garner.

The Dream Machine

Here is a page of his base-32 machine-code programming of Morphogenesis theory simulation, reduced to half-size.

The letters U, U2, V, UV, at the lower right-hand corner refer to variables in the morphogenetic theory, just as in the modern Xmorphia equations (see this Scrapbook page).

The name of his programme is Ibsen5 (after the Norwegian playwright).

There is a story to this: he used Norwegian names after his holiday in Norway in summer 1952.

The Scandinavian Connection

He had been attracted to Scandinavia on hearing rumours of its dances 'for men only'.

On 23 June 1948 a modern gay organisation, F-48, had been founded in Denmark and it had since branched into Norway and Sweden. There had been pictures in the press of dances in Copenhagen.

There is a personal website on the history of F-48, with a page on Norwegian activism in 1951 and pictures of the dancing in Copenhagen, 1951, which 'caused a sensation in Scandinavia.'

Alan Turing must have thought the future had already arrived: he was wrong. (In 1955 the authorities stamped on F-48 with arrests and show trials.)

His holiday was not completely disappointing, and some of his programs were named after a young Norwegian man, Kjell...

Watching the Daisies Grow

Other programs were given names like 'fircone' because he had a particular goal of showing that his theory would explain the appearance of the Fibonacci series of numbers, beginning

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...

These numbers are to be found in the leaf spirals of many plants. The fircone gives an easy way of seeing the spirals, and so do the centres of large flowers like sunflowers and daisies.

One of Alan Turing's more complete pieces of work was headed 'Outline of the Development of the Daisy'.

In his early life Alan Turing had been sketched watching the daisies grow.

A page in the Calgary overview of modern morphogenetic theory shows work on plant patterns today, together with a picture of a daisy:

You can count on it: 13 right-turning spirals and 21 left-turning spirals.

Alan Turing's work on this theory has still not been fully explored by modern researchers.

See the website of Jonathan Swinton for the latest survey of what Turing was doing.

Messages from the Unseen World

Robin Gandy, (see this Scrapbook Page) was both his research student and an intimate friend. In March 1953 Robin was just about to submit his Ph.D. thesis. Alan Turing wrote about arrangements for his viva. He got the Manchester computer to print it out, and then posted it. (This was the nearest you could get to an email in 1953.)

...[should] be no possible objection to making it say 4.30 if you find this more convenient. HR is probably thinking of your getting back the same day. If you really are going skiing no doubt it could be delayed till April or May though I may have forgotten about it by then mostly.

Your last letter arrived in the middle of a crisis about 'Den Norske Gutt' so I have not been able to give my attention yet to the....

Turing never fully explained this crisis about Kjell, the young Norwegian, but told Robin later that 'for sheer incident' it rivalled the arrest and trial in 1952.

Kjell had arrived at Newcastle from Norway, and police ('the poor sweeties' as Turing called them) were watching his house, and were deployed all over the North of England to intercept him.

There was something serious going on that his friends never realised: they did not think of Alan Turing as the repository of the greatest state secrets.

Explorers and Exiles

We do not know Alan Turing's dreams, but he certainly needed escape from the Britain of the Fifties. Unable to travel to the future to where he belonged, only travel abroad offered the chance of freedom.

He remained very interested in learning Danish and Norwegian. He mentioned in 1953 the possibility of getting a job in France, but nothing came of it.

In summer 1953 he took a holiday in Corfu, Athens and Paris. He came back with a list of men he had met (which I saw in 1978 before it was destroyed by a censorious employee of the Atomic Weapons Research Establishment.)

These were the days of panic in the Cold War. The first British atomic bomb (thanks to the Manchester computer) was successfully tested in October 1952. The first Soviet H-bomb was tested in August 1953; the 14-megaton American H-bomb was detonated in March 1954... and that parallel figure Robert Oppenheimer was effectively on trial...

Alan Turing had no holiday in summer 1954.

I suspect this would have been too much for the unseen world of British intelligence to allow.

Back to the Future

In March 1954 Alan Turing sent four

Messages from the Unseen World

on postcards to Robin Gandy. The fourth read:

Hyperboloids of wondrous Light
Rolling for aye through Space and Time
Harbour there Waves which somehow Might
Play out God's holy pantomime.

Another Country

The reference to 'the unseen world' was a shared joke with Robin Gandy about the religious standpoint of the mathematical physicist and astronomer Arthur Eddington, whose book The Nature of the Physical World had started Alan Turing thinking about fundamental physical theory in 1930.

It was parody of the hymns of Sherborne School chapel, but perhaps also a serious reference back to his first wondering about mind and matter.

It was also very strangely suggestive of mathematical developments in relativity barely starting in 1954: ideas in which the geometry of light rays was fundamental. Roger Penrose's twistor theory, which started in 1964, was to take this viewpoint to the extreme.

Alan Turing also described to Robin Gandy the problem he saw in the foundations of quantum mechanics as it stood — which is the same problem as stands today, central to Roger Penrose's ideas: when does the non-linear process of 'reduction' take place? He wrote to Robin, '...I'm trying to invent a new Quantum Mechanics but it won't really work. How about coming here next week and making it work for me?'

We shall never know what he had in mind... Read more by me about
What would Alan Turing have done after 1954?

His last postcard also joked about the Heisenberg Exclusion Principle, 'laid down for the benefit of the electrons themselves, who might be tempted if allowed to associate too freely...'

Exclusion principle? Who knows what he had in mind?

Other visions:

The house in 1992
Alan Turing's house near Wilmslow, Cheshire,

where he took his own life on 7 June 1954,
just ten years after D-Day.

He took potassium cyanide.

He left a half-eaten apple; symbol of lost innocence.


  Over the Rainbow  

It is often stated as a matter of established fact that the Apple Macintosh logo was drawn from the story of Alan Turing's death. But according to Apple Inc., whose name was chosen in 1976, the logo was designed in 1977 to allude to Newton but also to 'the symbol of lust and knowledge, the colors of the rainbow in the wrong order.. hope and anarchy.' See this full discussion, and the designer's account. It should be remembered that in 1977 Alan Turing's story was very little known. Even if it had been known, suicide would hardly have been a happy allusion for the young Apple company to evoke.

And yet, it's one of those extraordinary things which seem to make Alan Turing's life resonate far beyond his death.

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Andrew Hodges