Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  And here I must warn you that in order to deceive and baffle the enemy as well as to exercise the forces, there will be many false alarms, many feints, and many dress rehearsals. We may also ourselves be the object of new forms of attack from the enemy. Britain can take it. She has never flinched or failed. And when the signal is given, the whole circle of avenging nations will hurl themselves upon the foe and batter out the life of the cruellest tyranny which has ever sought to bar the progress of mankind.

  It was not very good policy to test the Delilah with the same recording over and over again, because even when in the spring of 1945 they got it to work, it still helped to know the words when listening to the output. The deciphered speech had to compete with a noisy background,* and a 4000 Hz whistle. The latter arose from a 4000 Hz signal used to synchronise sender and receiver, and which was only imperfectly filtered out of the final speech output. But the Delilah actually worked - that was the joy of it, for all its deficiencies. Alan had created a sophisticated piece of electronic technology out of nothing, and it worked. They did go as far as making a proper sixteen-inch disc recording of the effect, which entailed a trip to the black broadcasting studios at Simpson, since Hanslope lacked the requisite equipment. While they were there, Alan’s braces burst. Harold Robin, the chief engineer of the organisation, produced some bright red cord from an American packing case. Alan used it every day thereafter as his normal way of keeping his trousers up.

  As the chief goose would surely have guessed, Churchill’s prophecies had owed something to the continued supply of golden eggs, and so did the fact that by the time the Delilah was enciphering them, the words had come true. The pre-invasion ‘feint’ had succeeded in outwitting the German command, as they had been able to tell by listening in. At the critical points of the Normandy campaign, they had enjoyed the advantage of hearing the story from the other side. But he might well have wondered why it was taking so appallingly long to finish the war.

  As month after over-confident month passed, the technological developments at Bletchley became less and less relevant to fighting the war. If Sigint continued to help with the general knowledge, it failed resoundingly at critical points. For all the wonders of the electronic revolution, the Allies had been taken completely by surprise in December 1944 when the front, already held far longer than anyone expected, threatened to settle into another and more gruesome 1917. There had been a radio silence. It was perhaps more the fault of the military that no serious assessment had been made of the German forces at Arnhem. But there was a limit to what Sigint could do. Knowledge of the ‘new forms of attack’ from the pilotless VI and rocket-propelled V2 had not sufficed to stop them. And most remarkably, even the U-boat war, pre-eminently the war of information, was no walkover for the Allies. One factor was a political one: the RAF insisted on its role as an independent war-winning organisation, and devoted itself to the devastation of German cities rather than to the careful elimination of U-boats. But an increasing use of radio silence made cryptanalysis almost irrelevant at the end. The extraordinary fact was that when Dönitz took over from Hitler in April 1945, he still commanded a powerful, if suicidal, force. More U-boats were patrolling the American coasts than at any time since the mid-war winter, and new types of true submarines – rather than submersible boats – were in service. They were too late, like the new Enigmas that were ready but never came into service, but not very much too late.

  The tapes whizzed round, the rotors spun, the Wrens followed their decision trees, but in the last months the mathematicians, finally given everything they wanted, had whizzed on into a world of their own. (Though what was real, and what absurd, would now be hard to tell.) Brute force, rather than wit and ingenuity, characterised the final Allied effort. This was not Alan Turing’s war. The achievement of his work was more the defensive one, rather appropriate for him, who only wanted to be left in peace. There had been no repetition of the Atlantic of 1917, and the almost impossible had been made possible in time, just before German science and industry was being used seriously. As for the Europe of 1945, the Dresden of his friend, the Warsaw where it had begun, was this the victory of anyone’s intelligence? Had the poker game of 1941 done anything for this? It did not bear thinking about.

  Indeed, hardly anyone was permitted to think about it. The ‘cracking from within’ of 1918 had often filled British strategists of the Second World War with comforting delusions of easy victory, but it had also created a betrayal myth on which the Nazi party had capitalised. The great crack in logical control achieved by Bletchley Park no doubt had its influence upon the strategists of its aftermath, but this time there was no popular impact. It was completely hushed up. The victorious western governments had a common interest, for obvious reasons, in concealing the fact that the world’s most sophisticated communication system had been mastered.

  No one questioned that this had to be so. Those who knew a part of their story transferred it to a sealed compartment of the mind, so that the whole war became a blank out of which only stories about bicycles could emerge. The Bletchley vision had taken a few people on a time travel trip, into a world of Our Ford where science had an answer for everything. Now they had to come back to the mid-1940s. Some, of course, had been grappling with the grimy reality of the 1940s all the time, and knew how almost impossible it had been to bridge the gap. Alan Turing, however, had been able more than most to protect himself from the abrasion. It would not be easy for him to adjust. And as one acquainted with a wider span of knowledge than any other of the ‘men of the Professor type’, it meant a particularly acute mind-splitting operation. On VE day, 8 May 1945, he joined Robin Gandy, Don Bayley and Alan Wesley for a walk in the nearby woods at Paulerspury. ‘Well, the war is over, now you can tell all,’ said Don, not very seriously. ‘Don’t be bloody silly,’ said Alan – and that was the last word.

  The Delilah was finished at about the same time as the German surrender. There was no particular drive to improve standards for the Japanese war, nor for future purposes, and its fundamental advance met with little enthusiasm. Radley and another engineer, R.J. Halsey, came to Hanslope to inspect it in somewhat perplexed fashion. The Post Office did have some system of their own under development – possibly based on the Vocoder, on which they had requested and received information in 1941. Their main concern was that the crackly output of the Delilah was too poor to be commercially acceptable, as indeed it was. They showed no sign of interest in the potential of the principle. Alan then spent some time himself at Dollis Hill in the summer of 1945, where he explained his system to a somewhat sceptical Flowers.

  It was all over except the details – and Alan was never good at bothering with the last details. He was happy to leave it for Don Bayley to work on. For he had other ideas in mind. He had several times discussed with Don the question of his plans for peacetime, and had said that he was expecting to return to his King’s fellowship and a cut back to £300 per annum. There were eighteen months of his 1938 fellowship still to run, but beyond this he now had a longer period assured, since on 27 May 1944, making a rather special gesture of confidence, King’s had prolonged the tenure of his fellowship by a further three years. He could go back as if the war had never happened, and continue from where he had left off in 1939. A university lectureship might soon come his way.16 And yet the war had happened, and everything had changed. It had not simply been an interruption to the course of his intellectual career, as for some of the ‘professor type’ it might have been. It had mobilised his inner life. His ideas had been enmeshed with its critical developments, and they had been able to grow with the scale of the war itself. The world had learned to think big, and so had he. For though expecting to return to Cambridge, Alan had also told Don Bayley from the start of their collaboration that he wanted ‘to build a brain’.

  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 ‘st
ates 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.