Alan Turing: The Enigma (65 page)

His use of the word ‘brain’ was entirely consistent with his bold appeal to ‘states of mind’ ten years before. If the states of a Turing machine could be compared with ‘states of mind’, then its physical embodiment could be compared with a brain. One important aspect of this comparison, important to anyone who was concerned with the mystery of mind, the apparent paradox of free will and determinism, was that the Turing machine model was one independent of physics. The argument from Laplacian physical determinism could be shrugged aside with the observation that no such prediction could ever be performed in practice. This rebuttal could not be applied to a Turing machine, in which everything that happened could be described in terms of a finite set of symbols, and worked out with complete precision in terms of discrete states. Later he would articulate this himself:
¹⁷

The prediction which we are considering is however rather nearer to practicability than that considered by Laplace. The system of the ‘universe as a whole’ is such that quite small errors in the initial conditions can have an overwhelming effect at a later time. The displacement of a single electron by a billionth of a centimetre at one moment might make the difference between a man being killed by an avalanche a year later, or escaping. It is an essential property of the mechanical systems which we have called ‘discrete state machines’ that this phenomenon does not occur.

To understand the Turing model
of ‘the brain’, it was crucial to see that it regarded physics and chemistry, including all the arguments about quantum mechanics to which Eddington had appealed, as essentially irrelevant. In his view, the physics and chemistry were relevant only in as much as they sustained the medium for the embodiment of discrete ‘states’, ‘reading’ and ‘writing’. Only the
logical
pattern of these ‘states’ could really matter. The claim was that whatever a brain did, it did by virtue of its structure as a logical system, and not because it was inside a person’s head, or because it was a spongy tissue made up of a particular kind of biological cell formation. And if this were so, then its logical structure could just as well be represented in some other medium, embodied by some other physical machinery. It was a materialist view of mind, but one that did not confuse logical patterns and relations with physical substances and thing, as so often people did.

In particular it was a different claim from that of behaviourist psychology, which spoke of reducing psychology to physics. The Turing model did not seek to explain one kind of phenomenon, that of mind, in terms of another. It did not expect to ‘reduce’ psychology to anything. The thesis was that ‘mind’ or psychology could properly be described in terms of Turing machines because they both lay on the
same
level of description of the world, that of discrete logical systems. It was not a reduction, but an attempt at transference, when he imagined embodying such systems in an artificial ‘brain’.

Alan probably did not know much in 1945 about the actual physiology of human brains: quite possibly no more than from jolly pictures of the brain as a humming telephone exchange in the
Children’s Encyclopaedia
, or from the passage in
Natural Wonders
describing the ‘small thinking place in the brain’:

Directly over the ear, a place that you can almost cover with your thumb, lies the most important part of all, the place where we remember and handle words. At the bottom of this word spot, we remember how words sound. An inch farther up and toward the back, we remember how words look in print. A little farther up and forward lies the ‘speech center’ from which, when we want to talk, we direct the tongue and lips what to say. Thus we get our word-hearing, our word-seeing, and our word-speaking centers close together, so that when we speak we have close by and handy our memory of what we have heard in words, and of what we have read.

But that would have been
quite sufficient. He would have seen pictures of nerve cells (there were a few in
Natural Wonders
), but at the level at which he was approaching the description of mind, the details were not important. In speaking of ‘building a brain’ he did not mean that the components of his machine should resemble the components of a brain, or that their connections should imitate the manner in which the regions of the brain were connected. That the brain stored words, pictures, skills in
some
definite way, connected with input signals from the senses and output signals to the muscles, was almost all he needed. But ten years before, he had also had to fight his own way through to the crucial idea that Brewster glossed over; he had rejected the idea of a ‘we’ behind the brain that somehow ‘did’ this signalling and organising of the memory. The signalling and the organisation had to be all that there was.

But in describing the Turing machines ten years before, he had also justified his formalisation of the idea of ‘mechanical’ with a complementary argument, that of the ‘instruction note’. This put the emphasis not on the internal workings of the brain, but upon the explicit instructions that a human worker could follow blindly. In 1936 such ‘instruction notes’ had entered his experience through the rules of Sherborne School, other social conventions, and of course in the mathematical formulae that one could apply ‘without thinking’. But in 1945 a great deal of water had flowed under the bridge, and the ‘instruction notes’ that had been somewhat fanciful in 1936, just as were the theoretical logical machines, had become exceedingly concrete and practical. The cornucopian abundance was one of messages ‘based on a machine and broken on a machine’, and these machines were
Turing
machines, in which the logical transformation of symbols was what mattered, not physical power. And in designing such machines, and in working out processes that could be given to people acting like machines – the ‘slaves’ – they had effectively been writing elaborate ‘instruction notes’.

This was a different, but not incompatible, approach to the idea of ‘brain’. It was the interplay between the two approaches that perhaps fascinated Alan most – just as at Bletchley there had been a constant play between human intelligence, and the use of machines or ‘slave’ methods. His ‘weight of evidence’ theory had shown how to transfer certain kinds of human recognition, judgment and decision into an ‘instruction note’ form. His chess-playing methods did the same thing – as did the games on the Colossi – and posed the question as to where a line could be drawn between the ‘intelligent’ and the ‘mechanical’. His view, expressed in terms of the imitation principle, was that there was
no
such line, and neither did he ever draw a sharp distinction between the ‘states of mind’ approach and the ‘instruction note’ approach to the problem of reconciling the appearances of freedom and of determinism.

All these questions remained to be explored, for the exigencies of the German cipher machines had barely scratched the surface of what could be
done. It was yet to be seen how much could be achieved by writing ‘instruction notes’, and yet to be seen whether a machine could behave like a brain in developing ‘thinking spots’ for itself. As he had stressed in his discussions with Donald Michie, it had to be shown that a machine could
learn
. To explore these questions it would be necessary to have machines on which to experiment. But the almost incredible fact was that it would require only
one
machine, for the performance of any and all such experiments. For a
universal
Turing machine could imitate the behaviour of any Turing machine whatever.

In 1936 the Universal Turing Machine had played a purely theoretical part in his attack upon the Hilbert
Entscheidungs problem
. But in 1945 it had a very much more practical potential. For the Bombes and Colossi and all the other machines and mechanical processes were parasitic beasts, dependent upon the whims and blindness of the German cryptographers. A change of mind on the other side of the Channel would mean that all the engineering that had been required to construct them would suddenly become useless. It had happened right from the start, with the Polish ‘fingerprint’ file, their perforated sheets and their simple Bombe, and it had nearly led to catastrophe in the blackout of 1942. The construction of special machines had led the cryptanalysts into one problem after another with the acquisition and application of new technology. But a
universal
machine, if only it could be realised in practice, would require no fresh engineering, only fresh tables, encoded as ‘description numbers’ and placed upon its ‘tape’. Such a machine could replace not only Bombes, Colossi, decision trees and all the other mechanical Bletchley tasks, but the whole laborious work of computation into which mathematicians had been conscripted by the war. The zeta function machine, the calculation of roots of seventh order equations, the large sets of equations arising in electrical circuit theory – they could all alike be performed by a single machine. It was a vision beyond the comprehension of most people in 1945, but not beyond Alan Turing. As he would write later in 1945:
¹⁸

There will positively be no internal alterations to be made even if we wish suddenly to switch from calculating the energy levels of the neon atom to the enumeration of groups of order 720.

or as he would put it in 1948,
¹⁹

We do not need to have an infinity of different machines doing different jobs. A single one will suffice. The engineering problem of producing various machines for various jobs is replaced by the office work of ‘programming’ the universal machine to do these jobs.

From this point of view, a ‘brain’ would not be just some bigger or better machine, some superior kind of Colossus. It did not develop out of an experience of things, but out of a consciousness of underlying ideas. A
universal machine would not just be a machine; it would
be all
machines. It would replace not only the physical Bletchley machinery, but all that was routine – almost all that those ten thousand people had been doing. And not even the ‘intelligent’ work of the high-level analysts would be sacrosanct. For a universal machine could also play out the workings of human brains. Whatever a brain did,
any
brain, could in principle be placed as a ‘description number’ on the tape of a Universal Machine. This was his vision.

But there was nothing in the paper design of the Universal Turing Machine that suggested it could be made a practical proposition. In particular, there was nothing about its speed of operation. The tables of
Computable Numbers
could be realised by people sending postcards to each other, without affecting the theoretical argument. But if a universal machine were to be of any practical use, it would have to be able to run through millions of steps in a reasonable tune. This demand for speed could only be met by electronic components. And this was where the revolution of 1943 had made all the difference in the world.

More precisely, the point was that electronic components could be regarded as operating upon
discrete
, on-or-off, quantities, and so could realise a Turing machine. This he had learnt in 1942, and thereafter he had known all about the Robinsons, the X-system, and the Rockex; he had also picked up a fund of radar knowledge from his new friends at Hanslope. But above all there were the two developments that had begun in 1943. Whatever its usefulness to the war effort, the technical success of the Colossi told him that thousands of electronic valves could be used in conjunction – something that few could have believed in until it had been done. And then he had worked with his own bare hands on the Delilah. There had been a method in his madness all along. By working in these second-rate conditions, on a device that officialdom had not called for, he had proved that he could carry off an electronic project of his own. Coordinated with his theoretical ideas and his experience of mechanical methods, this direct knowledge of electronic technology formed the last link in his plans. He had learned how to build a brain – not an
electric
brain, as he might possibly have imagined before the war – but an
electronic
brain. It was thus that ‘round about 1944’, Alan’s mother heard him talking
²⁰
about ‘his plans for the construction of a universal [machine] and of the service such a machine might render to psychology in the study of the human brain.’

There was a further fundamental consideration besides that of discreteness, reliability and speed: that of sheer size. There would have to be room on the ‘tape’ of a universal machine both for the ‘description numbers’ of the machines it had to imitate, and its workings. The abstract universal machine of 1936 was equipped with a ‘tape’ of
infinite
length, meaning that although at any stage the amount of tape used would be finite, it was assumed that as more space was required it could always be made available.

In a practical machine, space would
always be limited in extent – and for that reason no physical machine could actually realise a truly universal machine. Still, Alan had suggested in
Computable Numbers
that human memory was finite in extent. If this were so then the human brain itself could hold only a limited number of ‘tables of behaviour’, and a sufficiently large tape could contain them all. The finiteness of any practical machine would not, on this argument, debar it from having a brain-like quality. The question was, however, how much ‘tape’ would be required for a machine that could actually be built: enough to make it interesting, but not more than would be technically feasible. And how could such storage be arranged without inconceivable expense in terms of electronic valves?

This practical question was one more up Don Bayley’s street. As the European war ground to its end, and the problems of the Delilah were essentially solved, it became clear that Alan’s interest had turned to ‘the brain’. He described to his assistant the universal machine of
Computable Numbers
, and its ‘tape’ on which instructions would be stored. They began thinking together about ways in which to realise a ‘tape’ that could store such information. And thus it was that in this remote station of the new Sigint empire, working with one assistant in a small hut, and thinking in his spare time, an English homosexual atheist mathematician had conceived of the
computer
^*