Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game

by Andrew Hodges

  There was another throwback to 1939, for Bob was getting married. He had settled in Manchester, first doing some wartime cotton research, and then becoming an industrial chemist. Alan went to Cumberland for the wedding on 2 October, giving the couple a generous present. Then he went to Manchester himself, to take up his new life. His plans had been wrecked, but then the era of planning, if ever it had existed at all, was now over. The government would do well if it could manage to look one move ahead. Alan Turing likewise would have to make the best of a bad job.

  * * *

  * Curiously, they did not think of what later became magnetic core storage. They knew all about the properties of toroidal magnetic cores, wound with current-carrying wire, because they were used in the wide-band radio frequency transformers which Donald Bayley often had to break away from work on Delilah in order to design. The cores for this work were chosen for their low hysteresis, meaning that they would respond rapidly and accurately without loss of signal. It never occurred to them that the ‘less satisfactory’ types shown in the manufacturers’ catalogue, whose response was not so linear, and which would tend to remain either ‘north’ or ‘south’, could be used in the discrete ‘on or off’ manner required for storage.

  * As a branch of mathematics, however, numerical analysis probably ranked the lowest, even below the theory of statistics, in terms of what most university mathematicians found interesting.

  * In the passage already quoted on page 368.

  * A typical circumlocution necessary for ‘the computer’.

  * The work done at RCA on the ‘lconoscope’ was closely related to the American commercial development of television, and as such was much more technically ambitious than the use of ‘ordinary’ cathode ray tubes familiar in radar displays, such as Alan favoured.

  * Or as he put it, ‘it is not thought wise to design for higher speeds than this as yet.’

  * In decimal floating point, the sequence 2658 13 would be used to represent the number 2.658 × 1013 or 26580000000000; the computer would normally use a binary equivalent of this.

  * The standard image, more illuminating, came to be that of the stack, holding the ‘return addresses’ of the ‘sub-routines’ entered.

  * But Zuse, in Germany, had also worked out some highly advanced ideas by this time, under the name Plankalkül.

  * Perhaps, however, he had been made aware that symbols could indifferently represent data or instructions when at his first school he misunderstood the instruction to omit ‘the’.

  * A figure similar to that on page 345.

  * W. T. Tutte had worked on this pure-mathematical problem.

  * The Department of Scientific and Industrial Research, through which the NPL was funded.

  † Travis had already received a knighthood.

  * They wanted the ACE for ‘shell, bombs, rockets and guided missiles’. The MoS was assured by E. S. Hiscocks, Secretary of the NPL, on 20 March that ‘we certainly hope that it will be freely available for the types of purpose mentioned in your letter….’

  * Actually on 31 August.

  * Speech encipherment caught up with the Delilah in fifteen years or so.

  * The Times printed their letters under the headline ELECTRONIC BRAIN – a subtle mixture of data and instructions.

  * By ‘ACE’, Wilkes meant ‘a computer’.

  * But not Norbert Wiener, whose refusal to attend this conference marked his public dissociation from all military-funded science.

  * ‘EDVAC-type machine’ was another example of a phrase used to indicate ‘a computer’. Although people spoke of the EDVAC as though it were already a thing, it was still as much at the planning stage as the ACE.

  * In the passages quoted earlier.

  * There was, however, at least one scientist who may have been over-exposed to fall-out: John von Neumann, who watched the Bikini tests of July 1946.

  * This criterion in itself marked a difference in attitude and policy. For someone from an ENIAC background it was obvious that the function of a computer was to do numerical calculation. Indeed Huskey cheerfully jettisoned the logical functions included in the ACE as ‘not needed in most computing problems’. But who knew what computing problems would or could be? Alan Turing’s scheme had reflected the fact that he had spent the war on non-numerical problems – but he was in no position to argue for the significance of this fact.

  * In November 1946 he had also tried to retrieve a spare Delilah power pack from the Cypher Policy Board: ‘Do you think it could be spared and sent down to me here? It is an old friend whose tricks I am used to.’ But this was almost certainly unsuccessful.

  * As further illustration, it is noteworthy that irrespective of Alan’s reports, Womersley continued to assume that the Americans held all the trumps. In April 1947 he daringly suggested that Darwin, currently attending meetings of the United Nations in New York, should call at Princeton to negotiate for the latest news in EDVAC engineering. This proposal was ill-timed; in May the NPL was declared by the American armed services to be ‘unsuitable’ for the receipt of such (commercially valuable) information. The ruling was relaxed later in 1947: information could be passed to Britain provided it was used only for military purposes.

  * Giving the whole £400 was generous, but illogical. It was put in trust for his nieces.

  * He also received reduced pay at the rate of £630 per annum for the sabbatical period. Darwin had offered full pay, but Alan told him he would prefer half-pay, saying that on full pay he would feel that ‘I ought not to play tennis in the morning, when I want to.’

  * Higher than that of ‘lecturer’, but not as high as a true ‘Prof’.

  * The actual words he used were ‘Universal Practical Computing Machine’.

  * A false prophecy.

  * He meant what has here throughout been called ‘cryptanalysis’, as the following passage shows.

  * i.e. ‘infinity’. This was mathematical shorthand for the fact that a Babbage-like machine could in principle be fed with an unlimited quantity of data and instructions from an external source – the price being, of course, an unlimited time delay.

  * A remark very characteristic of his post-war life – but there is no evidence as to how this particular contact had come about.

  † As The Times put it on 9 August, the public would ‘put the true high value on the near misses of the British men and women.’

  * As it happened, Alan and his mother had seen Noyce as a boy, passing him when walking in the Welsh hills in 1927.

  7 The Greenwood Tree

  Unseen buds, infinite, hidden well,

  Under the snow and ice, under the darkness, in every square or cubic inch,

  Germinal, exquisite, in delicate lace, microscopic, unborn,

  Like babes in wombs, latent, folded, compact, sleeping;

  Billions of billions, and trillions of trillions of them waiting,

  (On earth and in the sea – the universe – the stars there in the heavens,)

  Urging slowly, surely forward, forming endless,

  And waiting ever more, forever more behind.

  What Alan Turing did not know was that a number of changes had been made at Manchester University since his appointment in May. He had been created ‘Deputy Director’ of the ‘Royal Society Computing Laboratory’ when Newman was supposed to be directing it, and the Royal Society funding it. But by October it had become clear that F. C. Williams had need neither of a ‘Director’ nor of the Royal Society.

  In the development of electronic hardware, the important factor had been that Williams’s ingenuity was backed by a cosy relationship with TRE, which allowed him to draw upon their supplies, and to have two assistants seconded from the government establishment. One of these was a young engineer with a Cambridge mathematics degree, T. Kilburn. The second, after a short interval, came to be G. C. Tootill, another young TRE man from the same wartime Cambridge year.

  As for the development of a logical design, the first step had be
en taken by Newman. He had explained the principle of storing numbers and instructions, which according to Williams1 ‘took all of half an hour’, favouring the von Neumann type of design.* In late 1947 the plans had rapidly evolved in the hands of Williams and his two assistants. They were not detained by the prospect of ‘formidable mathematical difficulties’, but had pressed on, as Williams put it,* ‘without stopping to think too much’. The result was the tiny computer of whose existence Alan had learned in the summer, whose store consisted of just one cathode ray tube.

  The advantage of the cathode ray tube over the delay line was that, in both senses, it eliminated delay. It was essentially an ordinary piece of equipment, not requiring precision engineering as did the mercury delay line, and could be taken ‘off the shelf’. In practice this virtue was tempered by the fact that most tubes contained too many impurities in the screen to be used, but its ‘home-made’ quality was still of value in getting the project off the ground. In operation it was not particularly fast – indeed it would take ten microseconds to read a digit as compared with the one microsecond intended for the ACE – but this was compensated by the fact that the information stored on the tube was directly available, without the long period of waiting for a pulse to emerge from a delay line. Continuing his ‘papyrus scroll’ analogy, Alan compared it3 to ‘a number of sheets of paper exposed to the light on a table, so that any particular word or symbol becomes visible as soon as the eye focusses on it.’

  They had been able to store 2048 spots on the tube by the principle of regenerating them periodically, but in the end had settled on using just 1024, arranged in thirty-two ‘lines’ each of thirty-two spots. Each line would represent either an instruction or a number. A second cathode ray tube served as the logical control, storing the instruction currently being executed, and the address of that instruction. A third acted as the accumulator, the shunting station for the arithmetical operations. It was a ‘one-address’ system, so that each act of shunting in, or of shunting out, constituted a full instruction – an arrangement entirely different to that envisaged for the ACE. Arithmetic was, however, reduced to the barest minimum for the sake of demonstrating that it was possible at all – the operations of copying and subtraction, together with a simple form of conditional branching. It amounted to far less than Huskey’s ‘Test Assembly’ would have done, had that abortive NPL effort been completed. Physically, the Manchester computer was embodied in a straggly jumble of racks and valves and wires,* with three screens glowing in the gloom of a room with dirty brown tiles which Williams was fond of describing as ‘late lavatorial’ in style.

  It was, in fact, the most obvious feature of the cathode ray tube storage system that one could actually see the numbers and instructions held in the machine, as bright spots on the three monitor tubes. Indeed, at this stage it was essential to see them, for there was no other output mechanism. Nor was there any form of input but that of hand switches, used to insert digits one at a time into the storage tube.

  But this was enough. As Williams described4 the day of triumph:

  When first built, a program was laboriously inserted and the start switch pressed. Immediately the spots on the display tube entered a mad dance.

  In early trials it was a dance of death leading to no useful result, and what was even worse, without yielding any clue as to what was wrong. But one day it stopped and there, shining brightly in the expected place, was the expected answer.

  This happened on 21 June 1948, and the world’s first working program on an electronic stored-program computer, to find the highest factor of an integer by crude brute force trial, had been written by Kilburn.

  Nothing was ever the same again. We knew that only time and effort were needed to make a machine of meaningful size. We doubled our effort immediately by taking on a second technician.

  It was in these circumstances that Kilburn mentioned to Tootill a few days later that ‘there’s a chap called Turing coming here, he’s written a program.’ Williams knew about Alan because of his dealings with the NPL. Kilburn vaguely knew of him. Tootill, who had not heard of him at all, worked on the program. He was astonished (and naturally, smugly pleased) to discover it not only to be inefficient but to contain an error.

  At Manchester they had a machine which actually worked, and this simple fact counted for more than did ingenious or impressive plans. It meant that while Alan had been away on his holidays, political considerations had transformed the Manchester set-up. Already in July, Sir Henry Tizard, then Chief Scientific Adviser to the Ministry of Defence, had seen the machine and considered it5

  of national importance that the development should go on as speedily as possible, so as to maintain the lead which this country has thus acquired in the field of big computing machines, in spite of the large amount of effort and material that have been put into similar projects in America. He promised full support both in supply of material and in obtaining necessary priorities.

  To the engineers it was a gratifying verdict, but it was one which had no connection whatever with the ‘fundamental research in mathematics’ that was Newman’s object, and the purpose of the Royal Society grant.

  It was not surprising that Tizard should take this view. In 1948 (although he changed his mind in 1949, saying that Britain should admit it was no longer a Great Power), he supported the policy of building a British atomic bomb. In August 1946 the MacMahon Act had prevented the United States government from sharing atomic knowledge with Britain, and at the beginning of 1947, the British government had, in great secrecy, decided upon an independent development. The government’s interest in a working electronic computer was then refreshed by at least two other experts: Sir David Brunt the meteorologist and successor to R. V. Jones in Scientific Intelligence, and Sir Ben Lockspeiser the Government Chief Scientist. A few days after Lockspeiser’s visit, the Ministry of Supply placed an order with Ferranti Ltd, the Manchester-based weapons and electronics manufacturers, which according to the letter dated 26 October 1948 was simply ‘to construct an electronic calculating machine to the instructions of Professor F. C. Williams.’

  About £100,000 was thus spent by the government, whose rapid, almost panicky move made a strong contrast with the stately progress of Planned Science at the NPL. It had more to do with events in Berlin and Prague than with the intentions of the Royal Society. (It was in that same month of October 1948 that the demolition of air-raid shelters was suddenly stopped.) It certainly had nothing to do with Alan, the pawn in the Great Game. For that matter the carte blanche contract made no reference to Newman or Blackett. Newman’s motives had been entirely those of a pure mathematician, one who wistfully thought of what the talent at Bletchley could have achieved had it been applied to his subject. He had originally wanted to buy a machine and get on with the mathematics, and by this time had realised that it could not be so; the development of the hardware was going to be a dominating feature, and his interest had accordingly waned. He therefore did not object to the project being taken away. Blackett, however, was distinctly annoyed, perhaps the more so as he opposed the atomic weapon development.

  But even apart from the politics of the machine, Alan had come too late to direct its development. Already the important decision had been taken to adopt, for use as a large, slow, backing store, a rotating magnetic drum such as A. Booth of Birkbeck College, London, had developed for use with a relay calculator. With digits stored on tracks around the drum to be read off by a head, this was equivalent to providing a large number of slow, cheap, delay lines for the storage of data and instructions not immediately in use. Another innovation in the design, a modification originally suggested by Newman, was that of the ‘B-tube’. (It was so called because the arithmetic and control tubes were naturally ‘A’ and ‘C’ tubes respectively.) This additional cathode ray tube had the property of modifying the instructions held in the control; in particular it could be used when working along a sequence of numbers, in such a way that the idea of the ‘next’ n
umber did not have to be rendered into laborious programming.* As such it was contrary to the general policy that Alan had pursued on the ACE design, that of using instructions rather than hardware as far as possible.

  But more generally, the design and development had all been decided by others. They called it the ‘baby machine’ – but it was someone else’s baby. Williams had turned the tables, for while Darwin had hoped for him to build to Alan Turing’s instructions, now Alan had the task of making Williams’ machine work. With the best will in the world, there was room for conflict; the more so as the engineers had no intention of being ‘directed’ by anyone. The line between ‘mathematicians’ and ‘engineers’ was demarcated very clearly, and if not quite an Iron Curtain, it was a barrier as awkward as the MacMahon Act. This would never be Alan Turing’s machine, as the ACE would have been, and correspondingly, he withdrew as much as possible from any administrative responsibility for it. But he could foster it, and there was the prospect of using it. His position also attracted the salary of some £1200 per annum (increased to £1400 in June 1949), and very considerable freedom.

  So he stuck with Manchester, not as a ‘Deputy Director’ but as a freelance ‘Prof’ (as people still called him, perhaps to the slight annoyance of the true professors). There was a conventional sense in which Manchester, compared with Cambridge, was a come-down. It was largely the technical university of the North, producing doctors and engineers, rather than abstract ideas. However, Manchester prided itself on its standards, and Newman had built up a mathematics department which rivalled that of Cambridge. So although Alan was a bigger fish in a smaller pond, he was not a fish out of water. Certainly the physical setting of the university was grim. Its late Victorian gothic buildings, black with soot from the first industrial revolution, faced across the tram-tracks of Oxford Road on to the Temperance Society and expanses of slumland, whose holes and shored-up corners marked where the bombers had got through. Alan also commented on the low standard of male physique, not surprising in a city still recovering from the Depression. But the industrial landscape had some pleasures too: when Malcolm MacPhail from Princeton days visited in 1950, he was taken to see where the Duke of Bridgwater’s canal crossed the Manchester Ship Canal, having first been challenged to work out how this was achieved.