Alan Turing: The Enigma (90 page)

Another old score, that of the Enigma, was also paid off at about this time:
²⁰

I have set up on the Manchester computer a small programme using only 1000 units of storage, whereby the machine supplied with one sixteen figure number replies with another within two seconds. I would defy anyone to learn from these replies sufficient about the programme to be able to predict any replies to untried values.

He had, in other words, devised a cipher system which he reckoned impregnable even with the help of known plain-text. The lumbering wheels of the Second World War were already heading towards the same obsolescence as that of his zeta-function machine.

There were some other hints of a continued interest in cryptology. Another item that he demanded from the engineers as a hardware function of the Mark I Ferranti machine was what they called a ‘sideways adder’. It would count the number of ‘1’ pulses in a 40-bit sequence. This would have no application in a numerical program, but would be very useful in one where the digits coded ‘yes’ or ‘no’ answers to some Boolean question, and it was required to count the ‘yes’ answers – just what the Colossus had done. Such applications might possibly have been spare-time interests of his own. However, it was during this period, as the international situation hardened, that he found himself consulted by GCHQ. It would indeed have been remarkable had they
not
consulted the person who knew more about cryptology and the potential of electronic computers than did anyone else. And had he not described cryptanalysis as the most ‘rewarding’ field for the application of programming? Few, however, were in a position to perceive this fact, the subject being more secret than ever.

A hark-back to cryptology also featured in his discussions with a young American, David Sayre, in this
period. A graduate of the wartime MIT Radiation Laboratory, Sayre was now at Oxford studying molecular biology with Dorothy Hodgkin. Having worked with F.C. Williams during the war, he made a visit to Manchester to see the computer, explaining that it might help in X-ray crystallography, Williams passed him on to Alan, who showed an unusual kindness and geniality, making Sayre
²¹
‘perfectly at ease with him’. They talked for two and a half days, interrupted only when ‘the telephone would ring to say that the machine was free for a few minutes in case he wanted to use it, and he would gather up sheaves of paper and ribbons of punched paper tapes …and disappear for a bit.’

David Sayre was able to guess that Alan had worked on cryptological problems during the war. The point was that X-ray crystallography, which was now being applied to the problem of determining the structure of proteins, was remarkably similar in nature to cryptanalysis. The X-rays would leave a diffraction pattern, which could be regarded as the encipherment of the molecular structure. Performing the decipherment process was closely analogous to the problem of finding both plain-text and key, given the cipher-text alone.
^*
The result of this analogy was that

…Before we finished he had re-invented by himself most of the methods which crystallographers, up to that time, had worked out. He had, for this purpose, a breadth of knowledge greatly surpassing that of any crystallographer I have known, and I am confident that he would have advanced the crystallographic situation very decidedly if he had worked in it seriously for a time. As it was, he may have had hold of one line which in 1949 had not yet appeared in crystallography, concerned with establishing quantitatively how much information it is necessary to have on hand at the outset of a search for a solution to ensure that a solution can be found.

Alan told him about the Shannon theorem which he had exploited for the Delilah, and Sayre made
use of it in a paper
²²
which much advanced the theory of the subject. But Alan did not decide to work seriously in this area, although he encouraged young Sayre to return and use the Manchester machine for computations; this was a branch of science where exciting progress was being made, and yet for him it would perhaps have been too much a research into things past, like all these other 1949 encounters. Or perhaps it would have been too crowded and competitive a field. He always wanted something that would be self-contained.

Claude Shannon was himself another visitor. Since 1943, their discussions on machines and minds, information and communication, had been opened up to all. In September 1950 there was a London symposium
²³
on ‘information theory’, at which Shannon was the star guest. His paper
²⁴
on chess-playing, which explained the principles of minimax play and tree searching, had just appeared. Someone reviewed it and made a remark that Alan thought had confused cause and effect, or in typical Turing language, it was

… like taking a statistical analysis of the laundry of men in various positions and deciding, from the data collected, that an infallible method of getting ahead in life was to send a large number of shirts to the wash each week.

Afterwards, Shannon went to Manchester to see the prototype machine, then in its last days, and Alan told him all about the zeta-function calculation.
^*

The conference which gave occasion to this visit was a manifestation of the ‘cybernetics’ movement. Another was that in July 1949, following a talk by K. Lorenz at Cambridge on animal behaviour, an informal cybernetics discussion group had been started, meeting in London about once a month over a dinner. It was called the Ratio Club. McCulloch who with Wiener was one of the original high priests of cybernetics, addressed the first meeting. (He also travelled to Manchester to see Alan, who thought him ‘a charlatan’.) Alan was not in the Ratio Club’s founding group, but at the first meeting, his name was put forward
²⁵
by Gold and the biologist John Pringle, who had been Alan’s undergraduate contemporary at King’s.

Thereafter Alan used to go to meetings every few months, and found them good entertainment. Robin Gandy went to some meetings later, and Jack Good joined after attending Alan’s talk on ‘Educating a Digital Computer’ in December 1950. Uttley from TRE and the philosophical physicist D. Mackay, were also very interested in machine intelligence, while W. Grey Walter and W. Ross Ashby, neurologists who both brought
out early and influential books
²⁶
on cybernetic ideas, were keen members. (Grey Walter made some motorised ‘tortoises’ which could recharge themselves when their batteries were low.) The meetings were held at the National Hospital for Nervous Diseases, whose John Bates acted as secretary and galvaniser. There was a lot of enthusiasm, though it fell off over the next few years, as it was found that cybernetics offered no immediate solutions to the problems posed by human beings.

In some ways it was an attempt to revive the democratic association of young scientists which had characterised the war years. They excluded those of professorial rank, and Alan’s light touch went down well. Many of the Ratio Club had worked at TRE, where they had held what were called Sunday Soviets, according to the illusions of the day – much the same way as each section worked at Bletchley. It was just a faint ghost of the ‘creative anarchy’.

As it happened, Peter Hilton from Bletchley days had left Oxford to join the Manchester mathematics department in 1948, and Alan took him to see the machine which in some ways had grown out of their experiences. Peter Hilton was also present at a discussion in the department in 1949 which also touched upon subjects in Alan’s remoter past, the two fields of group theory and mathematical logic which had set his professional career in motion.

The discussion concerned the ‘word problem’ for groups. This was like the Hilbert
Entscheidungs problem
that
Computable Numbers
had settled, but instead of asking for a ‘definite method’ for deciding whether or not a given theorem was provable, it asked for a definite method for determining whether or not some given product of group elements was equal to some other given product; that is, whether some given sequence of operations would have the same effect as some other sequence.
^*
Emil Post had given the first new result in this direction in 1943, by showing that the word problem for ‘semi-groups’ was insoluble.
^†
The question for groups still remained open. Peter Hilton was amazed because
²⁷

Turing claimed he had never heard of this problem, and found it a very interesting problem, and so, though at that time his principal work was in machines, he went away and about ten days later announced that he had proved that the word problem was unsolvable. And so a seminar was arranged at which Turing would give his proof. And a few days before the seminar he said: ‘No, there was something a little wrong in the argument, but the argument would work for cancellation semigroups.’ And so he in fact gave his proof for cancellation semigroups.
^‡

The proof required quite new methods,
technically more difficult than those of
Computable Numbers
, in order to relate the ideas of doing and undoing operations to the action of a Turing machine. It showed that at any time, even though he was so out of touch, he could revert to being ‘a logician’. It was a great comeback, and yet for him it would not have been coming back, but going back. He spent some more time on the original problem for groups, but did not dedicate himself to it. It offered the innocence of the work of his twenties, before he had got mixed up with the world’s affairs. But it did not offer the direction in which to move onward.

Alan submitted his results
²⁸
to von Neumann’s journal, where it was received on 13 August 1949, and elicited a reply
²⁹
from the big man himself:

September 13 1949

Dear Alan,

… Our machine project is moving along quite satisfactorily, but we aren’t yet at the point where you are. I think that the machine will be physically complete early next year. What are the problems on which you are working now, and what is your program for the immediate future?

With best regards, Yours sincerely, John

Von Neumann’s machine at the IAS was lagging years behind because the Iconoscope, upon which such hopes had been placed, could not be made to work. The first American computers to be completed were Eckert and Mauchly’s BINAC, used for aircraft engineering, in August 1950, and then the CSAW’s cryptanalytic ATLAS in December 1950. But by late September 1949 the Soviet Union had tested its atomic bomb, and this encouraged the American decision in early 1950 to construct a thermonuclear weapon. The IAS machine and its copy MANIAC at Los Alamos were then pushed ahead, although even so it was 1952 before they were completed. The 1950-52 calculation for H-bomb feasibility was performed by 1930s methods, with slide rules and desk calculators, absorbing years of human work. In the end they had to scrap the special Iconoscope and use Williams’ ordinary cathode ray tubes. With two assistants, he had beaten American industry. It was still possible for British ingenuity to ‘jump in ahead of the Americans’.

But where did this leave Alan? What was his programme for the immediate future? It was a very pertinent question that the Wizard posed to Dorothy – not least because the facilities of the Manchester computer, when completed, would not match the ambitions spelt out by Alan in 1948 for ‘learning’ and ‘teaching’ and ‘searching’. He had to reconcile himself to the fact that those ideas were dreams on the edge of reality, and find some new way in which to continue.

Meanwhile the claims of cybernetics had attracted the attentions of
philosophers more weighty than Jefferson, and Alan was drawn into a more professional defence of his views. The motive force was supplied by Michael Polany., the Hungarian emigré who had held the Chair of Physical Chemistry at Manchester from 1933 to 1948, since when he had occupied a new Chair of ‘social studies’, specially created to facilitate his philosophical ambitions.

Polanyi had long led an opposition to the notions of Planned Science. Even during the war he had founded a ‘Society for Freedom in Science’, and after the war attempted to combine political and scientific philosophy, marshalling a variety of arguments against various kinds of determinism. In particular, he seized on Gödel’s theorem as a proof that mind would do something that was beyond any mechanical system. It was this subject that most engaged Alan and Polanyi in discussion. Alan would run over to the Polanyi home, which was not far from his lodgings at Hale. (Once Polanyi visited Alan, only to find him practising the violin in freezing cold, not bothering or not daring to ask the landlady for proper heat.) But Polanyi had many other suggestions up his sleeve. He rejected Eddington’s argument for free will from the Uncertainty Principle. But, unlike Eddington, he thought that the mind could interfere with the motions of molecules, writing that
³⁰
‘some enlarged, laws of nature may make possible the realization of operational principles acting by consciousness,’ and that the mind might ‘exercise power over the body merely by sorting out the random impulses of the ambient thermal agitation.’

Polanyi also favoured an extension of the ‘Jabberwocky’ argument, that science was all in the mind anyway, and had no meaning apart from the ‘semantic function’ which the human mind alone could supply. Karl Popper, who held similar views, said in 1950
³¹
that ‘It is only our human brain which may lend significance to the calculators’ senseless powers of producing truths.’ Popper and Polanyi both held that people had an inalienable ‘responsibility’, and that science only existed by virtue of conscious, responsible decisions. Polanyi held that science should rest on a moral basis. ‘My opposition to a universal mechanical interpretation of things,’ he wrote, ‘… also implies some measure of dissent from the absolute moral neutrality of science.’ There was a schoolmasterish tone to this ‘responsibility’ that was rather different from gentle Eddington’s vision of Mind-stuff perceiving the spiritual world. There was also a powerful Cold War thread to it. Polanyi attacked the Laplacian picture on the grounds that it ‘induces the teaching that material welfare … is the supreme good’ and that ‘political action is necessarily shaped by force.’ These unpalatable doctrines he associated with the Soviet government rather than with that of the other Great Power, complaining at the suggestion that ‘all cultural activities should subserve the power of the State in transforming society for the achievement of welfare.’ Alan liked the point that all measurements ultimately involved an element of decision, and produced for
Polanyi a photograph of a horse-race finish, in which of two neck-and-neck horses one could be said to have won if a jet of spittle were counted as part of its body, and not otherwise – a contingency not allowed for in the rules.
³²
But the thrust of the Christian philosopher’s arguments lay in a very different direction from his own.