Alan Turing: The Enigma (84 page)

Wittgenstein also liked to talk about learning and teaching. But
his
ideas derived not from the example of an English public school, but from his experience in an Austrian elementary school, where he had explicitly tried to get away from the repressive rote-learning that Alan had endured. By this time Alan had compared his school experience with Robin, who had had a much happier time at Abbotsholme, the progressive boys’ boarding school where Edward Carpenter’s ideas had enjoyed an influence, and ‘Dear Love of Comrades’ was the school song. Alan, speaking to Robin of Sherborne, had said: ‘The great thing about a public school education is that afterwards, however miserable you are, you know it can never be quite so bad again’,
^†
But there was no trace of his criticism of the Sherborne process
in this essay, except inasmuch as he was enjoying a sally at the pompous old masters by talking of replacing them by machines. There was a gap here, a certain lack of seriousness. It was rather like Samuel Butler in
Erewhon
, wittily transposing the values attached to ‘sin’ and to ‘sickness’ in order to tease the official Victorian mentality, yet never questioning that beatings would be the appropriate ‘treatment’ for ‘sin’.

But in other ways, he certainly did recognise that his machine model of the brain was deprived of some very significant features of human reality. This was where he began to question the isolated puzzle-solver as a model for the understanding of Mind:

…in so far as a man is a machine he is one that is subject to very much interference. In fact interference will be the rule rather than the exception. He is in frequent communication with other men, and is continually receiving visual and other stimuli which themselves constitute a form of interference. It will only be when the man is ‘concentrating’ with a view to eliminating these stimuli or ‘distractions’ that he approximates a machine without interference … although a man when concentrating may behave like a machine without interference, his behaviour when concentrating is largely determined by the way he has been conditioned by previous interference.

In a soaring flight of imagination, he supposed it possible to equip a machine with ‘television cameras, microphones, loudspeakers, wheels and “handling servo-mechanisms” as well as some sort of “electronic brain’”. Tongue in cheek, he proposed that it should ‘roam the countryside’ so that it ‘should have a chance of finding things out for itself’, on the human analogy, and perhaps thinking of his own country walks at Bletchley, where his odd behaviour had attracted the spy-conscious citizen’s suspicion. But he admitted that even so well-equipped a robot would still ‘have no contact with food, sex, sport, and many other things of interest to the human being’ – and certainly of interest to Alan Turing. His conclusion was that it was necessary to investigate what

can be done with a ‘brain’ which is more or less without a body, providing at most organs of sight speech and hearing. We are then faced with the problem of finding suitable branches of thought for the machine to exercise its powers in.

The suggestions he made were simply the activities that had been pursued on and off duty in Hut 8 and Hut 4, rather surprisingly brought into the open:

(i) Various games e.g. chess, noughts and crosses, bridge, poker

(ii) The learning of languages

(iii) Translation of languages

(iv) Cryptography
^*

(v) Mathematics.

Of these (i), (iv) and to a lesser extent (iii) and (v) are good in that they require little contact with the outside world. For instance in order
that the machine should be able to play chess its only organs need be ‘eyes’ capable of distinguishing the various positions on a specially made board, and means for announcing its own moves. Mathematics should preferably be restricted to branches where diagrams are not much used. Of the above possible fields the learning of languages would be the most impressive, since it is the most human of these activities. This field seems however to depend rather too much on sense organs and locomotion to be feasible.

The field of cryptography will perhaps be the most rewarding. There is a remarkably close parallel between the problems of the physicist and those of the cryptographer. The system on which a message is enciphered corresponds to the laws of the universe, the intercepted messages to the evidence available, the keys for a day or a message to important constants which have to be determined. The correspondence is very close, but the subject matter of cryptography is very easily dealt with by discrete machinery, physics not so easily.

There was more to
Intelligent Machinery
than this. One feature was that he laid down definitions of what was meant by ‘machine’, in such a way that it connected the 1936 Turing machine with the real world. He distinguished first:

’Discrete
^*
and ‘Continuous’ machinery
. We may call a machine ‘discrete’ when it is natural to describe its possible states as a discrete set. …The states of ‘continuous’ machinery on the other hand form a continuous manifold. …All machinery can be regarded as continuous, but when it is possible to regard it as discrete it is usually best to do so.

and then:

‘Controlling’ and ‘Active’ machinery
. Machinery may be described as ‘controlling’ if it only deals with information. In practice this condition is much the same as saying that the magnitude of the machine’s effects may be as small as we please. … ‘Active’ machinery is intended to produce some definite physical effect.

He then gave examples:

A ‘Brunsviga’ was a standard make of desk calculator, and the point was that such a machine, like an Enigma, a Bombe, a Colossus, the ENIAC or the planned ACE was best
regarded as
a ‘controlling’ device. In practice it would have a physical embodiment, but the nature of the embodiment, and the magnitude of its physical effects, were essentially irrelevant. The
Turing machine was the abstract version of such a ‘discrete controlling’ machine, and the cipher machines and decipherment machines were physical versions of them. They had taken up much of his working life. And the fundamental thesis of
Intelligent Machinery
was that the brain could also be ‘best regarded as’ a machine of this kind.

The paper also included a short calculation which bridged the two descriptions of a machine such as a computer, the logical description and the physical description. He showed that in a job taking more than 10
¹⁰
steps, a physical storage mechanism would be virtually certain to jump into the ‘wrong’ discrete state, because of the ever-present effects of random thermal noise. This was hardly a practical constraint. He might have made a similar calculation regarding the effect of quantum indeterminacy, and the upshot would have been the same. The determinism of the logical machine, although it could never be rendered with absolute perfection, was still effectively independent of all the ‘Jabberwocky’ of physics. This part of the paper integrated his several interests in logic and physics, mapped out where his own work stood within a wider framework, and summed up a long chapter of unfulfilled ambitions.

A final section suggested approaches to ‘intelligent machinery’ which were not based on this crude ‘teaching’, but upon his real experience as a pure mathematician. He considered the process of transforming problems from one formulation into another, solving a problem by proving a theorem in some other logical system, and translating the result back into the original form. This corresponded closely with the real work of mathematics, that of detecting analogies, and searching for openings towards a proof within some framework of ideas. ‘Further research into intelligence of machinery will probably be very greatly concerned with “searches” of this kind,’ he wrote. ‘We may perhaps call such searches “intellectual searches”. They might very briefly be defined as “searches carried out by brains for combinations with particular properties”.’ Of course, this was not exactly unrelated to the task of cryptanalysis, that of finding patterns in the apparently patternless. He drew a Darwinian parallel:

It may be of interest to mention two other kinds of search in this connection. There is the genetical or evolutionary search by which a combination of genes is looked for, the criterion being survival value. The remarkable success of this search confirms to some extent the idea that intellectual activity consists mainly of various kinds of search.

The remaining form of search is what I should like to call the ‘cultural search’. As I have mentioned, the isolated man does not develop any intellectual power. It is necessary for him to be immersed in an environment of other men, whose techniques he absorbs during the first twenty years of his life. He may then perhaps do a little research of his own and make a very few discoveries which are passed on to other men. From this point of view the search for new techniques
must be regarded as carried out by the human community as a whole, rather than by individuals.

This was a rare revelation of his self-perception. It was a dignified and generous response to the lessons of 1937 and 1945, when others had come forward with ideas equivalent to his own – so much more realistic than the usual worrying about ‘priority’, with its implicit fear of cheating and copying, and so free of the male competitiveness which was by 1948 becoming more and more evident in science.
⁵⁴
He never claimed more than that ‘some years ago I made an investigation into what could be done by a rule-of-thumb process,’ when referring to his own part. And of course this had been yet another of the lessons of 1941, that it was the search of the whole Bletchley community that mattered so much. But that very fact might perhaps have made him wonder more as to whether the operation of the brain ‘without interference’ was really the right way in which to focus attention. The very existence of these social or cultural levels of description was an indication that individual ‘intelligence’ was not the whole story. This question was not developed in this essay. Meanwhile, his ability to stand back from the individual struggle was certainly required in adjusting himself to work with the rival computer that had been developed at Manchester.

He wrote off to F.C. Williams for information, and received a reply probably on 8 July. By this time, the fact was that they had already, on 21 June 1948, successfully run the first program on the first working stored program electronic digital computer in the world. Darwin had talked about ‘formidable mathematical difficulties’, but at Manchester they had just got on with it, and produced a computer behind Darwin’s back. It used, for storage, the cathode ray tube that Williams had developed, and at this point the total store consisted of just 1024 binary digits stored on one tube. Alan drew attention to this figure in a table of ‘memory capacities’ in this report:

It was a pointed contrast between one machine still merely ‘proposed’, and another that actually worked. But the figures also pointed to the fact that F.C. Williams had pursued his project in a more modest way. The Manchester computer was small, and might even be called small-minded. But it was the first embodiment of a Universal Turing Machine, albeit with a very short ‘tape’. Alan wrote out a little routine
⁵⁵
to perform long division, and posted it north immediately.

Jack Good and Donald Michie looked
in on Alan at King’s, and rather annoyed him by peeping at the uncompleted version of
Intelligent Machinery
while he was out. Afterwards, walking along King’s Parade, Alan dropped a very deliberate remark to Jack Good about a boy in Paris.
^*
His drift got across to Jack, who had not known before. They were also in correspondence during this summer period. Jack wrote:

25 July 48

Dear Prof,

When I was last in Oxford I met a lecturer in physiology who said that he thought the number of neurons in the brain was only about two million. This seems amazingly little to me even allowing [for] the fact that the number of processes from each neuron is something like 40. I wonder if you could tell me the right answer, with or without a reference.

I understand that by next October we’ll have swapped towns, Judging by the international situation I think you’ve had the better of the bargain

How near were you to getting into the Olympics?

Jack was leaving his Manchester lectureship to join the branch of the Civil Service now known as the Government Communications Headquarters, and located at Eastcote, in north-west London. As for the international situation, the new lines were rapidly hardening. Yugoslavia had been expelled from the Cominform – a break which led Robin, like many other sympathisers with the pre-war USSR, to move much further away from the Communist party. The airlift to West Berlin was under way, and for the first time there was serious talk of war with Russia.