Alan Turing: The Enigma

6 Mercury Delayed

As I walk these broad majestic days of peace,

(For the war, the struggle of blood finish’d, wherein, O terrific Ideal.

Against vast odds erewhile having gloriously won,

Now thou stridest on, yet perhaps in time toward denser wars,

Perhaps to engage in time in still more dreadful contests, dangers,

Longer campaigns and crises, labors beyond all others,)

Around me I hear that eclat of the world, politics, produce,

The announcements of recognized things, science,

The approved growth of cities and the spread of inventions.

I see the ships, (they will last a few years,)

The vast factories with their foremen and workmen,

And hear the indorsement of all, and do not object to it.

But I too announce solid things,

Science, ships, politics, cities, factories, are not nothing,

Like a grand procession to music of distant bugles pouring,

triumphantly moving, and grander heaving in sight,

They stand for realities – all is as it should be.

Then my realities;

What else is so real as mine?

Libertad and the divine average, freedom to every slave

on the face of the earth,

The rapt promises and luminè of seers, the spiritual world,

these centuries-lasting songs,

And our visions, the visions of poets, the most solid

announcements of any.

Alan Turing did not wait to take up the NPL post before thinking about the practical construction of his universal machine. In particular he discussed with Don Bayley the problem which dominated its engineering – that of the storage mechanism, or ‘tape’. They discussed every form of discrete storage that they could think of. For instance, they considered magnetic recording. They had seen a captured German Army ‘Magnetophon’, the first successful tape recorder, but rejected the idea essentially because magnetic tape was too much like the tape of the theoretical Universal Turing Machine – it would require so much physical moving to and fro.* Instead, they favoured another solution with which Alan was by now well acquainted – that of the ‘acoustic delay line.’

The idea was based on the fact that the time taken for a sound wave to travel along a few feet of pipe was of the order of a thousandth of a second. The pipe could be regarded as storing the sound wave for that period. The principle had already been applied in radar, using information stored in the delay line to cancel out all the radar echoes which had not changed since the last scanning. In that way the radar screen could be made to show only new, or changing, objects. It was Eckert of the ENIAC team who had suggested the use of a delay line to store the pulses of an electronic computer. There were several ideas involved. The pipe, or delay line, would have to cope with pulses separated by only a millionth of a second, and to transmit them unsmudged. It was also necessary that the pulses should be stored not just for a thousandth of a second, but indefinitely, which required recirculating them through the delay line again and again. If this were done naively then the pulses would soon become too blurred to be distinguishable. So electronics had to be devised to detect the existence of a (somewhat degenerated) pulse arriving at the end of the line, and to start off a clean pulse at the beginning – the electronic equivalent of the relay used as a telegraph repeater. This would have to be combined with the facility to accept pulses from the rest of the computer and to feed them back in as required. It was well known that it was advantageous to use a medium other than air for the sound waves, and mercury was already being employed in radar applications. This appropriate element, associated with the classical deity of speed and communication, was to haunt the developments of the next few years.

This was an attractively cheap solution within the existing technology, and had been provisionally adopted in the Draft Report on the EDVAC. In this September 1945 period, they tried out the principle in the Hanslope hut. Don Bayley rigged up a cardboard tube, eight inches across and the whole ten feet of the hut in length, and Alan designed a super-regenerative amplifier (a particularly sensitive form of amplifier fashionable at the time.) They connected the amplifier to a microphone at one end of the tube and a loudspeaker at the other. The idea was simply to get a feel for the problem by recycling a sound wave in air on the delay line principle, clapping at one end and hoping to set up a hundred artificial echoes thereafter. They did not get it to work before Alan left Hanslope to take up his NPL post, which officially began on 1 October 1945. But it meant that he arrived full of ideas both logical and physical, and was far from being the pure mathematician of 1938.

In setting up the new Mathematics Division, Womersley had been able to recruit from the experts in the field of numerical computation, as it had been developed for the war effort. His division took over the highly regarded Admiralty Computing Service as the nucleus of what was the most high-powered group in the western world, the rival being the American equivalent at the National Bureau of Standards. It was not that they were good at doing large sums, although indeed they were doing sums on desk calculators. Their problems were roughly analogous to those that faced Alan in calculating the Riemann zeta-function in 1938. When the resources of pure mathematics had been fully exploited, there might still remain a formula, or system of equations, into which actual numbers had to be substituted. Actually doing such substitutions on desk calculators was not very interesting; but the problem of how best to organise the work was a more abstract question, one constituting the branch of mathematics called ‘numerical analysis’.* One particular problem was that although equations and formulae would generally relate ‘real numbers’ of infinite precision, practical computation would work with quantities defined only to so many decimal places, thus introducing an error into every step. Deducing the effect of such errors and minimising them was an important aspect of numerical analysis. The existence of such problems was partly what made Alan say that automatic computers would not make mathematicians redundant.

The section doing such work was headed by E.T. ‘Charles’ Goodwin, a fellow B-star of 1934 who recognised Alan from undergraduate days. Two other sections, ‘Statistics’ and ‘Punched cards’ were also related to the Turing interest, and the existence of punched-card machinery on the premises was to decide the choice of input mechanism for his machine. A fourth section consisted of the staff of the Hartree differential analyser, and remained for the time being at Manchester. The fifth section consisted of Alan Turing alone. By the end of the year there were twenty-seven staff in the Division, which was thus roughly equivalent to a large university department.

Two Victorian houses, Teddington Hall and Cromer House, on the perimeter of the existing NPL territory, had been acquired in March, and in October the whole new Division was housed in Cromer House, where Alan had a little room in the north wing. Charles Goodwin and his colleague Leslie Fox were across the way and working on the problem of how best to find the ‘eigenvalues’ of matrices, in connection with the problem of finding the resonant frequencies of an aircraft design. In these autumn months they would hear his typewriter banging jerkily away.

Alan lived in a guest house in nearby Hampton Hill, on the edge of Bushy Park, and generally continued to live out of a suitcase just as in wartime. The transition from war to peace was marked by the fact that now, instead of being under the administration of military officers, he was under the direction of scientists. This was not as much of a change as he might have expected. For Womersley, to whom he would grimly refer as ‘my boss’, as indeed he was, had turned out to be the epitome of what Alan despised as ‘bogus’. Although a man of some dynamism and vision, he lacked the solid grasp of scientific knowledge that Alan considered essential for a person in his position. Thus it transpired that Womersley’s lengthy and expensive tour of the United States earlier in 1945 had been a technical failure, since he had lacked the expertise to make detailed notes on what he had been allowed to see. Flowers and Chandler had been obliged to make a visit of their own in September and October to see the ENIAC in connection with work they were doing on special-purpose calculators for the military, instead of using Womersley’s notes. Womersley’s gifts of management: a mastery of name-dropping, a genial enthusiasm, a pleasant office manner to important visitors, a diplomatic sense of what to report, were not skills that Alan Turing ranked highly; not just because he lacked them himself, but because he still could not understand why anyone should need weapons other than rational argument. Before long, Alan was openly rude to Womersley in the office, saying ‘What do you want?’ and turning his back if Womersley dared to intrude upon some discussion. Later on there was a bet arranged among the staff of the Division, which depended upon someone coming out of Womersley’s office with ‘an equation, no matter how trivial’; it was abandoned and conceded, Alan reported, ‘for lack of entries’. Conversely, Womersley would show visitors round Cromer House, pointing at the Turing office from afar with exaggerated awe, and saying ‘Ah, that’s Turing, we mustn’t disturb him,’ as of some rare zoological exhibit.

A stronger scientific intellect, with an independent view of how computers should be built, might have hindered rather than helped Alan’s plans, which at least found in Womersley no technical resistance. On the contrary, Womersley was all too liable to agree with whatever had last been suggested. Womersley also coined a more happy acronym for the Turing electronic computer project than the soulless ENIAC and EDVAC. It was to be called the Automatic Computing Engine – a reference to Babbage’s ‘engine’. It would be the ACE. Alan was fond of saying that this was Womersley’s only contribution to the project. It reminded him of old George Johnstone Stoney, who had not discovered the electron, but gave it its name. In fact, Womersley had displayed considerable political skill in getting the project approved. It was not for nothing that he had a copy of How to Win Friends and Influence People on his desk. But Alan was blind to that. He was still the least political person.

Alan’s first task was to write a report 1, setting out a detailed design of an electronic universal machine, and an account of its operation. Surprisingly, the report that he submitted did not contain mention of Computable Numbers. Instead, it referred to the Draft Report on the EDVAC, with which his report was to be read ‘in conjunction’. However, the ACE proposal was effectively self-contained, and its roots lay not in the EDVAC, but in his own universal machine. Some fragmentary notes², dating from this early period, made this clear:

…In ‘Computable Numbers’ it was assumed that all the stored material was arranged linearly, so that in effect the accessibility time was directly proportional to the amount of material stored, being essentially the digit time multiplied by the number of digits stored. This was the essential reason why the arrangement in ‘Computable Numbers’ could not be taken over as it stood to give a practical form of machine.

It was also implicit in an opening paragraph of the report he now wrote, which explained how new problems would be ‘virtually only a matter of paper work’, with examples,^* and said:

It may appear somewhat surprising that this can be done. How can one expect a machine to do all this multitudinous variety of things? The answer is that we should consider the machine as doing something quite simple, namely carrying out orders given to it in a standard form which it is able to understand.

But he considerably amplified this idea in a talk given a year later in February 1947,³ in words which explained the origin of the ACE as he himself perceived it:

Some years ago I was researching on what might now be described as an investigation of the theoretical possibilities and limitations of digital computing machines. I considered a type of machine which had a central mechanism and an infinite memory which was contained on an infinite tape. This type of machine appeared to be sufficiently general. One of my conclusions was that the idea of a ‘rule of thumb’ process and a ‘machine process’ were synonymous. The expression ‘machine process’ of course means one which could be carried out by the type of machine I was considering… Machines such as the ACE^† may be regarded as practical versions of this same type of machine. There is at least a very close analogy.

Digital computing machines all have a central mechanism or control and some very extensive form of memory. The memory does not have to be infinite, but it certainly needs to be very large. In general the arrangement of the memory on an infinite tape is unsatisfactory in a practical machine, because of the large amount of time which is liable to be spent in shifting up and down the tape to reach the point at which a particular piece of information required at the moment is stored. Thus a problem might easily need a storage of three million entries, and if each entry was equally likely to be the next required the average journey up the tape would be through a million entries, and this would be intolerable. One needs some form of memory with which any required entry can be reached at short notice. This difficulty presumably used to worry the Egyptians when their books were written on papyrus scrolls. It must have been slow work looking up references in them, and the present arrangement of written matter in books which can be opened at any point is greatly to be preferred. We may say that storage on tape and papyrus scrolls is somewhat inaccessible. It takes a considerable time to find a given entry. Memory in book form is a good deal better, and is certainly highly suitable when it is to be read by the human eye. We could even imagine a computing machine that was made to work with a memory based on books. It would not be very easy but would be immensely preferable to the single long tape. Let us for the sake of argument suppose that the difficulties involved in using books as memory were overcome, that is to say that mechanical devices for finding the right book and opening it at the right page, etc. etc. had been developed, imitating the use of human hands and eyes. The information contained in the books would still be rather inaccessible because of the time occupied in the mechanical motions. One cannot turn a page over very quickly without tearing it, and if one were to do much book transportation, and do it fast, the energy involved would be very great. Thus if we moved one book every millisecond and each were moved ten metres and weighed 200 grams, and if the kinetic energy were wasted each time, we should consume 10¹⁰ watts, about half the country’s power consumption. If we are to have a really fast machine then we must have our information, or at any rate a part of it, in a more accessible form than can be obtained with books.

After this flight of fancy, very typical of his conversation, he discussed various more serious proposals for storage, and commented that ‘the provision of proper storage is the key to the problem of the digital computer.’

In my opinion this problem of making a large memory available at reasonably short notice is much more important than that of doing operations such as multiplication at high speed. Speed is necessary if the machine is to work fast enough for the machine to be commercially valuable, but a large storage is necessary if it is to be capable of anything more than rather trivial operations. The storage capacity is therefore the more fundamental requirement.

He then continued to give a succinct definition of ‘building a brain’:

Let us now return to the analogy of the theoretical computing machines with an infinite tape. It can be shown that a single special machine of that type can be made to do the work of all. It could in fact be made to work as a model of any other machine. The special machine may be called the universal machine; it works in the following quite simple manner. When we have decided what machine we wish to imitate, we punch a description of it on the tape of the universal machine. This description explains what the machine would do in every configuration in which it might find itself. The universal machine has only to keep looking at this description in order to find out what it should do at each stage. Thus the complexity of the machine to be imitated is concentrated in the tape and does not appear in the universal machine proper in any way.

If we take the properties of the universal machine in combination with the fact that machine processes and rule of thumb processes are synonymous, we may say that the universal machine is one which, when supplied with the appropriate instructions, can be made to do any rule of thumb process. This feature is parallelled in digital computing machines such as the ACE. They are in fact practical versions of the universal machine. There is a certain central pool of electronic equipment, and a large memory. When any particular problem has to be handled the appropriate instructions for the computing process involved are stored in the memory of the ACE and it is then ‘set up’ for carrying out that process.

His priorities were a large, fast memory, and then a hardware system that would be as simple as possible. The latter requirement was reminiscent of his ‘desert island^’ mentality, doing everything with the least waste. But both features were to exploit the universality of the machine. His idea was always that anything in the way of refinement or convenience for the user, could be performed by thought and not by machinery, by instructions and not by hardware.

In his philosophy it was almost an extravagance to supply addition and multiplication facilities as hardware, since in principle they could be replaced by instructions applying only the more primitive logical operations of OR, AND, and NOT. Indeed, the Colossus, when it was ‘almost’ programmed to do multiplication, had done just that. Since these primitive logical operations (absent from the EDVAC draft design) were incorporated in his plan for the ACE, he could indeed have omitted adders and multipliers, and still have had a universal machine. In reality, he did include special hardware to perform arithmetical tasks, but even there he decomposed the arithmetical operations into small pieces so that he could economise on hardware at the cost of more stored instructions. The whole conception was very puzzling to his contemporaries, to whom a computer was a machine to do sums, and a multiplier the very essence of its function. To Alan Turing, the multiplier was a rather tiresome technicality; the heart lay in the logical control, which took the instructions from the memory, and put them into operation.

This last statement sounds quite paradoxical, but it is a simple consequence of the fact that these machines can be made to do any rule of thumb process by remembering suitable instructions. In particular it can be made to do binary decimal conversion. For example in the case of the ACE the provision of the converter involves no more than adding two extra delay lines to the memory. This situation is very typical of what happens with the ACE. There are many fussy little details which have to be taken care of, and which according to normal engineering practice would require special circuits. We are able to deal with these points without modification of the machine itself, by pure paperwork, eventually resulting in feeding in appropriate instructions.

Logical as this was, and certainly comprehensible to mathematicians, who had been familiar with binary numbers for three hundred years at least, the fact was that ‘fussy little details’ such as this were more of a headache for other people. To an engineer, in particular, it would come as a revelation that the concept of number could be separated from its representation in decimal form. Many people would see the ‘binary’ arithmetic of the ACE as itself a weird and wonderful innovation. Whilst he was perfectly correct in seeing this as a detail, it was a good example of his difficulties in communication with the kind of people who might fund, organise, and build his machine.

But with such details disposed of, he concentrated his report upon the two really important things: the memory and the control.

Considering the storage problem, he listed every form of discrete store that he and Don Bayley had thought of, including film, plugboards, wheels, relays, paper tape, punched cards, magnetic tape, and ‘cerebral cortex’, each with an estimate, in some cases obviously fanciful, of access time, and of the number of digits that could be stored per pound sterling. At one extreme, the storage could all be on electronic valves, giving access within a microsecond, but this would be prohibitively expensive. As he put it in his 1947 elaboration, ‘To store the content of an ordinary novel by such means would cost many millions of pounds.’ It was necessary to make a trade-off between cost and speed of access. He agreed with von Neumann, who in the EDVAC report had referred to the future possibility of developing a special ‘Iconoscope’ or television screen,* for storing digits in the form of a pattern of spots. This he described as ‘much the most hopeful scheme, for economy combined with speed.’ But in a prescient paragraph of the ACE report he also suggested an approach more on the home-made, ‘least waste of energy’ line:

It seems probable that a suitable storage system can be developed without involving any new types of tube, using in fact an ordinary cathode ray tube with tin-foil over the screen to act as a signal plate. It will be necessary to furbish up the charge pattern from time to time, as it will tend to become dissipated. …It will be necessary to stop the beam from scanning in the refurbishing cycle, switch to the point from which the information required is to be taken, do some scanning there, replace the information removed by the scanning, and return to refurbishing from the point left off. Arrangements must also be made to make sure that refurbishing does not get neglected for too long because of more pressing duties. None of this involves any fundamental difficulty, but no doubt it will take time to develop.

Lacking such cathode ray tube storage, he had to plump for the mercury delay lines, not with any great enthusiasm, but because they were already working. They held the obvious disadvantage, from the point of view of accessibility, of involving a delay. His plan was for a delay line to hold a sequence of 1024 pulses, so it was like chopping up the ‘tape’ of the Universal Turing Machine into segments each of 1024 squares in length. It would take an average of 512 units of time to reach a given entry. However, this was an improvement upon the ‘papyrus scroll’.

As for the other most important aspect of the machine, this was the ‘Logical Control’. It corresponded to the ‘scanner’ of the Universal Turing Machine. The principle was simple: ‘The universal machine has only to keep looking at this description’ – that is, at the instructions on its tape – ‘to find out what it should do at each stage.’ So the Logical Control was a piece of electronic hardware which would contain two pieces of information: where it was on the ‘tape’, and what instruction it had read there. The instruction would take up thirty-two ‘squares’ or pulses in a delay line store, and might be of two kinds, in the design that he proposed. It might simply cause the ‘scanner’ to go on to another point of the ‘tape’ for its next instruction. Alternatively, it might prescribe an operation of adding, multiplying, shifting or copying, of numbers stored elsewhere on the ‘tape’. In the latter case, the ‘scanner’ was to move to the next point on the ‘tape’ for its next instruction. None of this involved anything but the reading, writing, erasing, changing of state, and moving to left and right, that was to be done by the theoretical Universal Turing Machine working on the description numbers on its tape – except that there were special facilities added so that addition and multiplication could be achieved in only a few steps, rather than with thousands of more elementary operations.

Of course, there was to be no physical motion when the ‘scanner’ went to fetch an instruction, or operate upon numbers stored on the ‘tape’; no motion but that of electrons. Instead, the control of the ACE would work by a process rather like that of dialling a telephone number, to reach the right place. Most of the complexity of the electronic circuits arose from the demands of this ‘tree’ system. There was also a complexity in the way that thirty-two half-way houses, ‘temporary storage’ locations consisting of special short delay lines, were provided for the shunting around of pulses. This was quite different from the EDVAC conception, in which all the arithmetic would be done by shunting numbers in and out of a central ‘accumulator’. In the ACE design the arithmetical operations were ‘distributed’ around the thirty-two ‘temporary storage’ delay lines in an ingenious way.

The point of this complexity was that it increased the speed of operation. Speed took a slightly higher priority than simplicity. This was reflected also in the fact that Alan planned the pulse rate of the ACE to be a million a second, straining electronic technology to the full.* His emphasis on speed was natural enough, granted his Bletchley experience, in which speed was of the very essence, a few hours marking the difference between usefulness and pointlessness. It was also related to the universality of the electronic computer. In 1942 they had tried to get faster Bombes to cope with the fourth rotor; they had been saved by the German slip-up with the weather reporting signal system, but without this stroke of fortune they would have had to wait over a year for the machinery to match the problem. One virtue of a universal machine would lie in its ability to take on any new problem immediately – but this meant that it must be as fast as possible from the start. It would hardly be desirable to re-engineer a universal machine, for the sake of a special problem. The whole point was to get the engineering out of the way once and for all, so that all the work thereafter could go into the devising of instruction tables.

Although the ACE was based upon the idea of the Universal Turing Machine, in one way it departed from it. The departure lay in the feature, at first sight an extraordinary one, that it had no facility for conditional branching. In this respect it might seem to lack the crucial idea that Babbage had introduced a hundred years earlier. For the ‘scanner’, or Logical Control, of the ACE could only hold one ‘address’, or position on the tape, at a time. It had no way of holding more than one, and then of selecting a next destination according to some criterion.

The omission, however, was only on the surface. The reason for it was that it was a case where the hardware could be simplified, at the cost of more stored instructions. Alan set out a way in which conditional branching could be done without needing the logical control to hold more than one ‘address’ at a time. It was not the best technical solution, but it had the ment of a brutal simplicity. Suppose that it were wished to execute instruction 50 if some digit D were 1, and to execute instruction 33 if it were 0. His idea was to ‘pretend that the instructions were really numbers and calculate D × (Instruction 50) + (1-D) × (Instruction 33).’ The result of this calculation would be a instruction which would have the effect that was required. The ‘IF’ was effected not by hardware, but by extra programming. It was a device which had led him to mix up data (the digit D) with instructions. This in itself was of great significance, for he had allowed himself to modify the stored program. But this was only the beginning.

Von Neumann had also seen that it was possible to interfere with the stored instructions, but had done so in only one very particular way. If a stored instruction had the effect of ‘taking the number at address 786’, then he had noticed that it would be convenient to be able to add 1 into the 786, so that it gave the effect of ‘taking the number at address 787’. This was just what was needed for working along a long list of numbers, stored in locations 786, 787, 788, 789 and so forth, as would so frequently occur in large calculations. He had programmed the idea of going to the ‘next’ address, so that it did not have to be spelt out in explicit form. But von Neumann went no further than this. In fact, he actually proposed a way of ensuring that instructions could not be modified in any other way than this.

The Turing approach was very different. Commenting on this feature of modifying instructions, he wrote in the report: ‘This gives the machine the possiblity of constructing its own orders. …This can be very powerful.’ In 1945 both he and the ENIAC team had hit upon the idea of storing the instructions inside the machine. But this in itself said nothing about the next step, that of exploiting the fact that the instructions could now themselves be changed in the course of running the machine. This was what he now went on to explain.

It was an idea that had arrived somewhat by chance. On the American side, they had thought of storing instructions internally because it was the only way of supplying instructions quickly enough. On the Turing side, he had simply taken over the single tape of the old Universal Turing Machine. But neither of these reasons for adopting stored instructions said anything about the possibility of interfering with the instructions in the course of a computation. On the American side, it was not pointed out as a feature of the new design until 1947.4 Equally, the Universal Turing Machine, in its paper operation, was not designed to change the ‘description number’ that it worked upon. It was designed to read, decode, and execute the instruction table stored upon its tape. It would never change these instructions. The Universal Turing Machine of 1936 was like the Babbage machine in the way that it would operate with a fixed stock of instructions. (It differed in that that stock was stored in exactly the same medium as the working and the input and output.) And so Alan Turing’s own ‘universality’ argument showed that a Babbage-like machine was enough. In principle there was nothing that could be achieved through modifying the instructions in the course of an operation that could not be achieved by a universal machine without this facility. The faculty of program modification could only economise on instructions, and would not enlarge upon the theoretical scope of operations. But that economy could, as Alan said, be ’Very powerful’.

This original perception flowed from the very universality of the machine, which might be used for any kind of ‘definite method’, not necessarily arithmetical. That being so, the pulses ‘1101’ stored in a delay line, might well not refer in any way to the number ‘thirteen’, but might represent a chess move or a piece of cipher. Or, even if the machine were engaged upon arithmetic, the ‘1101’ might be representing not ‘thirteen’, but indicating perhaps a possible error of thirteen units, or a thirteen in the floating-point representation * of numbers, or something else altogether, at the choice of the user of the machine. As he saw it from the start, there would be far more to adding and multiplying than putting pulses through the hardware adder and multiplier. The pulses would have to be organised, interpreted, chopped up, and put together again, according to the particular way in which they were being used. He dwelt in particular upon the question of doing arithmetic in floating-point form, and showed how the mere addition of two floating-point numbers required a whole instruction table. He wrote some tables of this kind. MULTIP, for instance, would have the effect of multiplying two numbers which had been encoded and stored in floating-point form, encoding and storing the result. His tables made use of the ‘very powerful’ feature of the machine, for he had it assemble bits of the necessary instructions for itself, and then execute them.

But if a simple operation like multiplying floating-point numbers would require a set of instructions, then a procedure of any useful scale would involve putting many such sets of instructions together. He envisaged this not as a stringing together of tables, but as a hierarchy, in which subsidiary tables like MULTIP would serve a ‘master’ table. He gave a specific example of a master table called CALPOL which was to calculate the value of a fifteenth-order poly nominal in floating-point. Every time a multiplication or addition was required, it had to call upon the services of a subsidiary table. The business of doing this calling up and sending back of subsidiary tables was something which itself required instructions, as he saw:

When we wish to start on a subsidiary operation we need only make a note of where we left off the major operation and then apply the first instruction of the subsidiary. When the subsidiary is over we look up the note and continue with the major operation. Each subsidiary operation can end with instructions for the recovery of the note. How is the burying and disinterring of the note to be done? There are of course many ways. One is to keep a list of these notes in one or more standard size delay lines …with the most recent last. The position of the most recent of these will be kept in a fixed TS [short delay line] and this reference will be modified every time a subsidiary is started or finished. The burying and disinterring processes are fairly elaborate, but there is fortunately no need to repeat the instructions involved each time, the burying being done through a standard instruction table BURY, and the disinterring by the table UNBURY.

Perhaps he drew the imagery of burying and unburying from the silver bar story.* This was an entirely new idea. Von Neumann had thought only in terms of working through a sequence of instructions.

The concept of a hierarchy of tables brought in further applications of program modification. Thus he imagined ‘keeping the instruction tables in an abbreviated form, and expanding each table whenever we want it’ – the work being done by the machine itself, using a table called EXPAND. The further he progressed with this idea, the more he saw that the ACE could be used to prepare, collate, and organise its own programs. He wrote:

Instruction tables will have to be made up by mathematicians with computing experience and perhaps a certain puzzle-solving ability. There will probably be a good deal of work of this kind to be done, for every known process has got to be translated into instruction table form at some stage. This work will go on whilst the machine is being built, in order to avoid some of the delay between the delivery of the machine and the production of results. Delay there must be, due to the virtually inevitable snags, for up to a point it is better to let the snags be there than to spend such time in design that there are none (how many decades would this course take?) This process of constructing instruction tables should be very fascinating. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself.

It is not surprising that he looked forward to the process of writing instruction tables as ‘very fascinating’. For he had created something quite original, and something all of his own. He had invented the art of computer programming.^† It was a complete break with the old-style calculators – of which, in any case, he knew little. They assembled adding and multiplying mechanisms, and then had the job of feeding in a paper tape to make them work in the right order. They were machines to do arithmetic, in which the logical organisation was a rather tiresome burden. The ACE was quite different. It was to be a machine to play out programs ‘for every known process’. The emphasis was placed on the logical organisation of the work, and the hardware arithmetic added only to short-cut the more frequently used constituent operations.

On desk calculators, the figures 0 to 9 would appear visibly in the registers and the keyboard, and the operator would be led to feel that in some way the calculator had the numbers themselves stored within it. In reality, it had nothing but wheels and levers, but the illusion would be strong. The illusion carried over to the big relay calculators, the Aiken and Stibitz machines, and to the ENIAC. Even the EDVAC proposals carried the feeling that the pulses in the delay lines would somehow actually be numbers. But the Turing conception was rather different, and took a more abstract view. In the ACE, one might regard pulses as representing numbers, or as representing instructions. But it was really all in the mind of the beholder. The machine acted, as he put it, ‘without understanding’, and in fact operated not on numbers nor on instructions, but on electronic pulses. One could ‘pretend that the instruction was really a number’, because the machine itself knew nothing about either. Accordingly, he was free in his mind to think about mixing data and instructions, about operating on instructions, about tables of instructions being inserted by other instructions of ‘higher authority’.

There was a reason for his facility to take this liberated approach. Ever since he first thought about mathematical logic, he was aware of mathematics as a game played with marks on paper, to be manipulated by chess-like rules, regardless of their ‘meaning’. This was the outlook that the Hilbert approach encouraged. Gödel’s theorem had cheerfully mixed up ‘numbers’ and ‘theorems’, and Computable Numbers had represented instruction tables as ‘description numbers’. His proof of the existence of unsolvable problems depended upon this mixing up of numbers and instructions, by treating them all alike as abstract symbols.* It was therefore a small step to regard instructions, and instruction tables, as grist to the ACE’s own mill. Indeed, since so much of his war work had depended upon indicator systems, in which instructions were deliberately disguised as data, there was no step for him to make at all. He saw as obvious what to others was a jump into confusion and illegality.

This vision of the ACE’s function was also tied in with the imitation argument. The ACE would never really be ‘doing arithmetic’, in the way that a human being would. It would only be imitating arithmetic, in the sense that an input representing ‘67 + 45’ could be made to guarantee an output representing ‘112’. But there were no ‘numbers’ inside the machine, only pulses. When it came to floating-point numbers, this was an insight of practical significance. The whole point of his development was that the operator of the ACE would be able to use a ‘subsidiary table’ like MULTIP, as if it were a single instruction to ‘multiply’. In actual fact, it would have the effect of much shunting and assembling of pulses inside the machine. But that would not matter to the user, who could work as if the machine worked directly on ‘floating-point numbers’. As he wrote, ‘We have only to think how this is to be done once, and then forget how it is done.’ The same would apply if the machine were programmed to play chess: it would be used as if it were playing chess. At any stage it would only be outwardly imitating the effect of the brain. But then, who knew how the brain did it? The only fair use of language, in Alan’s view, was to apply the same standards, the standards of outward appearance, to the machine as to the brain. In practice, people said quite nonchalantly that it was ‘doing arithmetic’; they should also say it was playing chess, learning, or thinking, if it could likewise imitate the function of the brain, quite regardless of what was ‘really’ happening inside. Even in his technical proposals, therefore, there lay a philosophical vision which was utterly beyond the ambition of building a machine to do large and difficult sums. This did not help him to communicate with other people.

Although he had shifted the emphasis from the building of a machine, to the construction of programs, there was nothing nebulous about his engineering plans for the ACE. The delay lines, he wrote,

have been developed for RDF purposes to a degree considerably beyond our requirements in many respects. Designs are available to us, and one such is well suited to mass production. An estimate of £20 per delay line would seem quite high enough.

He did in fact make a visit to the Admiralty Signals Establishment to see T. Gold, who was working there on delay lines. His plan was for two hundred mercury delay lines, each with a capacity of 1024 digits. But the figures, dimensions, costs, and the choice of mercury as the medium, were not taken off the radar engineers’ shelf. He worked out the physics himself. On the basis of his calculation, mercury was only marginally to be preferred to a mixture of water and alcohol, which he observed would have the same strength as gin. He rather hankered after using gin, which would come cheaper than mercury. However, he did not propose doing the development work himself. He wanted this to be done by the Colossus engineers, at the Post Office Research Station. Flowers was already familiar with delay lines, having been shown Eckert’s model in October 1945.

As for the engineering of the logical control and arithmetical circuits (‘LC and CA’), he wrote:

Work on valve element design might occupy four months or more. In view of the fact that some more work needs to be done on schematic circuits such a delay will be tolerable, but it would be as well to start at the earliest possible moment. …

In view of the comparatively small number of valves involved the actual production of LC and CA would not take long; six months would be a generous estimate.

A great many of the ‘schematic circuits’ were already planned out in the report. He included a detailed design of the arithmetical circuits, making use of (and extending) von Neumann’s notation. Perhaps he had the pleasure of drawing upon his experience in designing a binary multiplier before the war. There was also another feature of the design which might well have harked back to an earlier experience. There was to be a facility for plugging in special circuits, if these were required, for operations over and above the arithmetical and Boolean functions that were permanently incorporated in the machine. This idea was rather at variance with the principle of putting as much as possible into the instructions, but it might be appropriate if some exceedingly efficient special-purpose circuit were at hand. This had been the case, for instance, with the Bombes. Here the steps which depended upon relay clicks were slow by electronic standards. But the steps which depended upon electricity flowing through the internal Enigma wirings were effectively instantaneous. These would have taken longer to achieve by means of an instruction table played out on an electronic computer. Alan’s design allowed for such short-cuts to be taken, if desired. But no one could possibly have guessed that he was writing on the basis of such experience with mechanical methods.

Nor was it planned out only at the logical level of circuit diagrams. There were many pages also on the specific electronic equipment required. One section owed a direct debt to the Delilah, another unknown aspect of his expertise:

Unit delay. The essential part of the unit delay is a network, designed to work out of a low impedance and into a high one. The response at the output to a pulse at the input should preferably be of the form indicated in Fig. 50,* i.e. there should be maximum response at time 1 μβ after the initiating pulse, and the response should be zero by a time 2μs after it, and should remain there. It is particularly important that the response should be near to zero at the integral multiples of 1 μs after the initiating pulse (other than 1 μs after it).

A simple circuit to obtain this effect is shown on Fig. 51a. …It differs from the ideal mainly in having its maximum too early. It can be improved at the expense of a less good zero at 2 μs by using less damping, i.e. reducing the 500 ohm resistor. It is also possible to obtain altogether better curves with more elaborate circuits.

He also considered the practical requirements of the project as a whole:

It is difficult to make suggestions about buildings owing to the great likelihood of the whole scheme expanding greatly in scope. There have been many possibilities that could helpfully have been incorporated, but which have been omitted owing to the necessity of drawing a line somewhere. In a few years time however, when the machine has proved its worth, we shall certainly want to expand and include these other facilities, or more probably to include better ideas which will have been suggested in the working of the first model. This suggests that whatever size of building is decided on we should leave room for building-on to it.

He had learnt from the mushrooming of Bletchley. He proposed a total of 1400 square feet for the machine and its accessory equipment, and estimated the total capital cost of a machine with two hundred delay lines at £11,200. Changes would have to be made as they went along, but his plans allowed for that: the main thing was to get started.

His February 1947 talk would expand on how the machine would ‘prove its worth’, by giving

a picture of the operation of the machine. Let us begin with some problem which has been brought in by a customer. It will first go to the problems preparation section where it is examined to see whether it is in a suitable form and self-consistent, and a very rough computing procedure made out.

He gave a specific example of a problem, namely the numerical solution of a differential equation involving Bessel functions. (This would be a very typical problem arising in applied mathematics and engineering.) He explained how the instruction table for the Bessel function would be already ‘on the shelf’, and so would one for the general procedure for solving a differential equation. So

The instructions for the job would therefore consist of a considerable number taken off the shelf together with a few made up specially for the job in question. The instruction cards for the standard processes would have already been punched, but the new ones would have to be done separately. When these had all been assembled and checked they would be taken to the input mechanism, which is simply a Hollerith card feed. They would be put into the card hopper and a button pressed to start the cards moving through. It must be remembered that initially there are no instructions in the machine, and one’s normal facilities are therefore not available. The first few cards that pass in have therefore to be carefully thought out to deal with this situation. They are the initial input cards and are always the same. When they have passed in a few rather fundamental instruction tables will have been set up in the machine, including sufficient to enable the machine to read the special pack of cards that has been prepared for the job we are doing. When this has been done there are various possibilities as to what happens next, depending on the way the job has been programmed. The machine might have been made to go straight on through, and carry out the job, punching or printing all the answers required, and stopping when all of this has been done. But more probably it will have been arranged that the machine stops as soon as the instruction tables have been put in. This allows for the possibility of checking that the content of the memories is correct, and for a number of variations of procedure. It is clearly a suitable moment for a break. We might also make a number of other breaks. For instance, we might be interested in certain particular values of the parameter a, which were experimentally obtained figures, and it would then be convenient to pause after each parameter value, and feed the next parameter value in from another card. Or one might prefer to have the cards all ready in the hopper and let the ace take them in as it wanted them. One can do as one wishes, but one must make up one’s mind.

These proposals were eminently practical, and indeed prophetic, foreseeing the need for flexible interaction between operator and machine. But of course he had already seen the future, in the use of the Colossus. Another passage brought in the possibility of using remote terminals:

…the ace will do the work of about 10,000 [human] computers. It is to be expected therefore that large scale hand-computing will die out. [Human] computers will still be employed on small calculations, such as the substitution of values in formulae, but whenever a single calculation may be expected to take a [human] computer days of work, it will presumably be done by an electronic computer instead. This will not necessitate everyone interested in such work having an electronic computer. It would be quite possible to arrange to control a distant computer by means of a telephone line. Special input and output machinery would be developed for use at these out-stations, and would cost a few hundred pounds at most.

He also perceived the demand for computer programmers:

The main bulk of the work done by these computers will however consist of problems which could not have been tackled by hand computing because of the scale of the undertaking. In order to supply the machine with these problems we shall need a great number of mathematicians of ability. These mathematicians will be needed in order to do the preliminary research on the problems, putting them into a form for computation. …

And indeed he could foresee a new field of industry and employment:

It will be seen that the possibilities as to what one may do are immense. One of our difficulties will be the maintenance of an appropriate discipline, so that we do not lose track of what we are doing. We shall need a number of efficient librarian types to keep us in order.

Twenty years ahead of his time, in his conception of the organisation of a computer installation, he had drawn his picture from his experience at Bletchley. There they had likewise employed ten thousand human operators, and had worked as a system, involving remote out-stations, telephone communications, an élite who transformed the problems into programs, and plenty of ‘librarian types’. But he could never say anything directly about it, and no one could picture what had never officially existed, so his analysis came as news from nowhere.

The ACE report was also the first account of the uses to which a universal computer could be put. The ACE was to solve ‘those problems which can be solved by human clerical labour, working to fixed rules, and without understanding’, restricted by the size of the machine to cases where ‘the amount of written material which need be kept at any one stage is limited to …50 sheets of paper’ and where ‘the instructions to the operator’ could be described in ‘ordinary language within the space of an ordinary novel’. It would be able to do so in one hundred thousandth of the time taken by ‘the human operator, doing his arithmetic without mechanical aid.’

The implication was that the ACE could have taken over all the routine mental work of the British war effort. Here he made what was for him an unusually good ‘political’ point: in a list of possible applications, ‘Construction of range tables’ came first. This was the job for which the ENIAC had been specifically designed. There followed four further examples of calculations of practical importance, which currently required months or years of work on desk machines. But another four were non-numerical, reflecting his much wider view of the nature of the computer, and indeed being much closer to his experience.

The first would have the computer interpreting a special language for describing electrical problems:

Given a complicated electrical circuit and the characteristics of its components, the response to given input signals could be calculated. A standard code for the description of the components could easily be devised for this purpose, and also a code for describing connections.

It would mean the automatic solution of circuit problems such as he had spent weeks over at Hanslope. The second was a more mundane example of the world’s work:

To count the number of butchers due to be demobilised in June 1946 from cards prepared from the army records.

The machine, he wrote, ‘would be quite capable of doing this, but it would not be a suitable job for it. The speed at which it could be done would be limited by the rate at which cards can be read, and the high speed and other valuable characteristics of the calculator would never be brought into play. Such a job can and should be done with standard Hollerith equipment.’ The third non-numerical problem * was described thus:

A jig-saw puzzle is made up by cutting up a halma-board into pieces each – consisting of a number of whole squares. The calculator could be made to find a solution of the jig-saw, and, if they were not too numerous, to list all solutions.

This was the nearest he came to a mention of cryptanalysis, although it was latent in a number of his ideas, such as including the logical operations of AND and OR from the start, and regarding them as on an equal footing with arithmetical operations. Alan wrote that this particular problem was ‘of no great importance, but it is typical of a very large class of non-numerical problems that can be treated by the calculator. Some of these have great military importance, and others are of immense interest to mathematicians.’ But at the end came the suggestion that he was most interested in himself, although he could hardly expect it to motivate the government:

Given a position in chess the machine could be made to list all the ‘winning combinations’ to a depth of about three moves on either side. This is not unlike the previous problem, but raises the question, ‘Can the machine play chess?’ It could fairly easily be made to play a rather bad game. It would be bad because chess requires intelligence. We stated at the beginning of this section that the machine should be treated as entirely without intelligence. There are indications however that it is possible to make the machine display intelligence at the risk of its making occasional serious mistakes. By following up this aspect the machine could probably be made to play very good chess.

This was not so much a report, as a plan of campaign in which tactical and strategic were jostling as close on paper as they did in his own mind. The promise of an electronic ‘brain’ was as fanciful as space travel, and this report was like explaining the advantages of colonising Mars, while in next breath describing the design of a fuel pump. The naive, colloquial style was not calculated to appeal to the authorities, and its detailed considerations went far beyond their absorptive capacities. No one was going to work through the example programs or the circuit diagrams, nor resolve the baldly stated paradox of a machine ‘entirely without intelligence’ nevertheless ‘displaying intelligence’. Even Hartree found it very hard going.

Although undated, the ACE report was completed by the end of 1945,5representing an amazing burst of energy. It then went to Womersley, who wrote both a memorandum⁶ for Darwin and an introductory report⁷ for the Executive Committee meeting of 19 February 1946. Womersley was quick to perceive the opportunities offered by a universal machine, and whatever the intellectual limitations noted by Alan and the other mathematicians, he certainly wrote an able defence of what he claimed as ‘one of the best bargains the DSIR^* has ever made.’ ‘The possibilities inherent in this equipment are so tremendous that it is difficult to state a practical case …without it sounding completely fantastic …’ Optics, hydraulics, and aerodynamics could be ‘revolutionised’; the plastics industry could be ‘advanced in a way that is impossible with present computing resources.’ Besides the range table problem already noted by Alan, a problem expected to require three years of work by the existing Mathematics Division, Womersley claimed that ‘The machine will also grapple successfully with problems of heat-flow in non-uniform substances, or substances in which heat is being continuously generated’ – of explosives old and new, in fact. Womersley also claimed that ‘the promised support of Commander Sir Edward Travis, ^† of the Foreign Office, will be invaluable.’

On the more theoretical side, Womersley stressed that ‘this device is not a calculating machine in the ordinary sense of the word. One does not need to limit its functions to arithmetic. It is just as much at home in algebra And on the more political side he drew attention to the large sums already expended in America on machines whose capacities would be far outstripped by the ACE. More subtly, Womersley pointed to the advantage to be gained from having such a machine installed in the NPL:

…we in this country, and particularly in this Division, have a unique contribution to make to world progress. I can say quite definitely that in the use of such equipment we shall be far more resourceful and cunning than the Americans. …All the USA machines are in Electrical Engineering Departments. In this Division the machine will be in the hands of the user, rather than the producer …

Discussion of this visionary cooperation of British brain and hand was postponed until the meeting of the Executive Committee on 19 March. This time Alan was invited to attend, and after being dauntingly introduced by Womersley as ‘an expert in the field of mathematical logic’, he did his best to explain the ACE as simply as possible. It was a particularly clear account, in which he began by saying

that if a high overall computing speed was to be obtained it was necessary to do all operations automatically. It was not sufficient to do the arithmetical operations at electronic speeds: provision must also be made for the transfer of data (numbers, etc.) from place to place. This led to two further requirements – ‘storage’ or ‘memory’ for the numbers not immediately in use, and means for instructing the machine to do the right operations in the right order. There were then four problems, two of which were engineering problems and two mathematical or combinatory.

Problem (1) (Engineering) To provide a suitable storage system.

Problem (2) (Engineering) To provide high speed electronic switching units.

Problem (3) (Mathematical) To design circuits for the ace, building these circuits up from the storage and switching units described under Problems 1 and 2.

Problem (4) (Mathematical) To break down the computing jobs which are to be done on the ace into the elementary processes which the ace is designed to carry out. …To devise tables of instructions which translate the jobs into a form which is understood by the machine.

Taking these four problems in order, Dr Turing said that a storage system must be both economical and accessible. Teleprinter tape provided an example of a highly economical but inaccessible system. It was possible to store about ten million binary digits at a cost of £1, but one might spend minutes in unrolling tape to find a single figure. Trigger circuits incorporating radio valves on the other hand provided an example of a highly accessible but highly uneconomical form of storage; the value of any desired figure could be obtained within a microsecond or less, but only one or two digits could be stored for £1. A compromise was required; one suitable system was the ‘acoustic delay line’ which provided storage for 1000 binary digits at a cost of a few pounds, and any required information could be made available within a millisecond.

But explaining excitedly to the committee how the delay line was to work, he rapidly became too technical and was cut off before even touching upon the question of devising ‘tables of instructions’. Darwin was therefore sceptical, reasonably enough.

The Director asked what would happen, in cases where the machine was instructed to solve an equation with several roots. Dr Turing replied that the controller would have to take all the possibilities into account, so that the construction of instruction tabies might be a somewhat ‘finicky’ business.

Hartree came to the rescue with an argument which appealed less to science than to post-war patriotism:

…It requires only 2000 valves as against 18000 in the eniac, and gives a ‘memory’ capacity of 6000 numbers compared with the 20 numbers of the eniac …if the ace is not developed in this country the USA will sweep the field. …this country has shown much greater flexibility than the Americans in the use of mathematical hardware. He urged that the machine should have every priority over the existing proposal for the construction of a large differential analyser.

This was a genuinely far-sighted and generous recommendation, coming as it did from a person who had spent much of his own time and energy on the differential analyser. It was a remarkably smooth victory for the digital over the analogue approach. Hartree had, of course, seen the ENIAC when near to completion, and might also have seen the Colossus after the war had ended. He was also a particularly cooperative and helpful person.

Darwin was still not convinced and

enquired whether the machine could be used for other purposes if it did not fulfil completely Dr Turing’s hopes. Dr Turing replied that this would depend largely on what part of the machine failed to operate, but that in general he felt that many purposes could be served by it.

He was probably gritting his teeth at Darwin’s failure to grasp the principle of universality. Now Womersley infiltrated a new concept into the discussion, one which had played no role in the Turing report. It was that of a pilot machine.

There was next some discussion as to the possible cost of the machine and Mr Womersley said that a pilot set-up could possibly be built for approximately £10000, and it was generally agreed that no close estimate of the overall cost of the full machine could be made at this stage.

Not much notice was taken of Alan’s estimate of capital cost. Womersley had said it should be multiplied by a factor of four or five. In fact they were probably annoyed that he had trespassed across the demarcation line into the administrative province; the more so as he wrote as though he could shop around for the equipment himself. Recommendations were passed on, notably that of the Ministry of Supply which handled all military contracts.*

Then the

Committee resolved unanimously to support with enthusiasm the proposal that Mathematics Division should undertake the development and construction of an automatic computing engine of the type proposed by Dr A.M. Turing, and Director agreed to discuss the financial and other aspects of the matter with Headquarters.

Alan Turing held a great and burning dislike for committee meetings such as this, resenting the fact that the decisions were made not because of a clear understanding of his ideas, but for political and administrative reasons. The report he had submitted was, in fact, largely irrelevant, and played the role of pleasing Humpty Dumpty by having something down on paper, no matter what it was. But Sir Charles Darwin did take swift action. Indeed already, on 22 February, he had written 8 to the Post Office about this ‘electronic mathematical machine of a novel type, which should be immensely superior in every way to anything hitherto constructed anywhere’.

Very broadly it works using principles developed by your staff during the war for a certain Foreign Office project, and we want to be able to take advantage of this, enlisting the help …in particular of Mr Flowers who has had much experience in working out the electronic side of it.

The initial response from the Post Office was encouraging, and on 17 April Darwin was able to present to the Advisory Council of the DSIR a cogent plan of action, which showed that he had by this time marshalled the essential ideas:

…The possibility of the new machine started from a paper by Dr A.M. Turing some years ago, when he showed what a wide range of mathematical problems could be solved, in idea at any rate, by laying down the rules and leaving a machine to do the rest. Dr Turing is now on the staff of the NPL and is responsible for the theoretical side of the present project, and also for the design of many of the more practical details.

It gave three examples of large calculations that it would be able to perform, and explained:

The complete machine will naturally be costly; it is estimated that it may call for over £50,000, but probably not twice as much. A smaller one, containing the essential characteristics, could be constructed first, perhaps for a cost of £10,000, but its chief function would be to reveal some of the details of design that cannot be planned without trial, and its scope would be too limited to be worth constructing for its own sake. This would involve development work on delay lines and trigger circuits, and this part of the work would be undertaken by the Post Office, where facilities and specially trained staff exist, with the collaboration of Dr Turing and his assistants. …

The small machine would not be a miniature substitute for the large machine but would later constitute a part of the full scale machine in due course. It is hoped that the complete machine can be constructed in three years. …It is proposed to proceed immediately, and with high priority, in the design and construction of this preliminary machine, but in doing so it is important to know that if it fulfils its promise there will be full backing for the greater sums required for the real operating machine. In view of its rapidity of action, and of the ease with which it can be switched over from one type of problem to another it is very possible that the one machine would suffice to solve all the problems that are demanded of it from the whole country …

Darwin requested up to £10,000 to be allocated to the ‘small machine’ in the current financial year. On 8 May 1946 the DSIR agreed to support his application, and also that if the ‘small machine’ fulfilled expectations then they would recommend the expenditure of up to £100,000 on a full-scale machine. On 15 August the Treasury sanctioned the £10,000, although according to standard procedure refused further commitment. Meanwhile by 18 June the NPL had committed itself by sending a letter to the Post Office asking for development work on delay lines. The ACE was under way. It might now be couched in terms more like those of a Five Year Plan than those getting on with it in a hut, but it still promised a machine that would solve all the problems demanded of it from the whole country. The legacy of a total war, and of the capture of a total communication system, could now be turned to the construction of a total machine.

After submitting the report, Alan continued to improve the design and to write ‘instruction tables’ for the paper machine. In this he gained some assistance, Darwin having decided that ‘high priority’ meant the allocation of two Scientific Officers to the project. First came J.H. Wilkinson, one of the pure-mathematical Part III class of 1939, by now experienced through six years of work in the numerical analysis of explosives problems. It was Charles Goodwin who had sought to bring him to the NPL, to work in numerical analysis; but when Wilkinson made a visit he found himself being told by Alan about the exciting ACE plans.⁹ It was the ACE that made him decide to remain in government service, rather than to return to Cambridge mathematics. It was agreed that he should work half-time for Goodwin on desk machines and half-time on the ACE. It was a position fraught with possible inter-departmental frictions, but fortunately Jim Wilkinson was the most equable and diplomatic person. He joined on 1 May 1946. A second assistant joined a little later: this was the young Mike Woodger, son of the theoretical biologist and philosopher of science J.H. Woodger. He was immediately attracted by the Turing vision of a universal machine. Unfortunately, after training on desk machines in June, he caught glandular fever and was away until September.

Mike Woodger was there when Alan’s official honour was announced in June. For his war service he was appointed to the Order of the British Empire — standard for civil servants of the rank that he had officially held. The letters OBE were added to his office door, which made him furious, perhaps because he did not want to be asked what it was for, perhaps at the absurdity of advertising a token recognition. The King was ill, so the OBE medal, bearing the inscription Tor God and the Empire’, arrived by post. It was lodged in his tool-box.

Already by May, when Jim Wilkinson joined in work on the ACE design, it had reached a Version V. One difference was that this incorporated a hardware facility for conditional branching. It was quickly replaced by a transitional Version VI and then a Version VII. By this time Alan was devoting more attention to speed of operation than he had done in the original report, at the cost of more hardware. In Version VII enough equipment was added to make it possible for an instruction to have the effect of a complete arithmetical operation, taking two numbers from store, adding them, and putting the result back into store. Again in the interest of speed, it was necessary to program the instructions so that as far as possible each instruction would be leaving its delay line just as the previous one had been executed. Since different operations would take different lengths of time to complete, this made the construction of tables into a crossword-puzzle operation. It also led to a decision that every instruction should specify which instruction the ‘head’ was to take next, abandoning the idea of a natural stream of consecutive orders, flowing with only occasional interruptions. It also increased the length of the instruction words from thirty-two to forty pulses, again requiring more equipment. In Version VII each such operation would take forty microseconds, but it would then take another forty microseconds to assemble the next instruction in the control circuits. Again in the interest of speed, Alan wished to eliminate this period by duplicating part of the equipment so that each instruction could be assembled while the last was being performed.

It was entirely in line with his original report that as experience was gained with writing instruction tables, he should modify aspects of the hardware design. It was consistent, too, that he should sacrifice a certain amount of simplicity for the sake of greater speed. All the same, the assembling of actual components could not begin too soon for him; the paper ‘tables’ were intended for a real machine, not as theoretical exercises.

In this respect, however, development was very far from speedy. There was an overwhelming problem with the ACE project. This was that although the ν PL had a Radio Division, it did not have a single electronic engineer capable of appreciating, let alone implementing, Alan’s ideas. Back in December 1944, Womersley had told the Executive Committee that plans for new machines ‘could be put into effect only by cooperation between the Division and certain industrial organisations – possibly along the lines of extra-mural development contracts.’ But no progress had been made towards making this cooperation possible. There was one solid medium-term possibility, that of having English Electric, a firm with which Darwin had connections, manufacture a machine to commercial standards. Its director, Sir George Nelson, had attended the March meeting. But it was not at all clear who was to do the immediate development work. This was no small impediment to the confident hope expressed in Alan’s report of being able to produce the equipment for the logical control within six months.

A further problem lay in the internal structure of the NPL. At Hanslope, Alan had worked happily with Don Bayley, putting their different kinds of skill together. In this respect the Delilah project had been practice for the ACE, for he would have liked to work in much the same way again, if on a larger scale. (He had vaguely suggested that Don himself should come to the NPL, but Don was not due for release until February 1947, and he also felt he was rather more than the ‘amplifier king’ that Alan said he would need.)

But the National Physical Laboratory did not encourage any such ad hoc, informal collaboration. Its division of labour drew a firm line between brain and hand. Alan was cast firmly in the role of the theoretical designer, and was not expected to know anything about practical engineering. The bureaucratic outlook of the NPL also showed in the form-filling and permission-seeking necessary for the requisition of equipment, Meanwhile, to make matters worse, the post-war chaos, presenting something akin to a black market in war surplus materials, called for the skills of the spiv in locating hardware of any kind. For these reasons, there was no immediate prospect of having engineers qualified to build the circuits, and there was no facility for Alan to conduct practical experiments himself.

There was a more general difficulty facing the ACE project. It was one analogous to the arrival of the Enigma information in 1940. Alan had poured out a decade’s worth of ideas into the lap of an organisation which had not been noted for innovation. In 1940 the cryptanalysts had naively expected that the government could take the deciphered messages and put them to good effect. In fact it had needed two years of painful adjustment before this could be done, even with all the pressure of war. Now again the cornucopian abundance of the ACE design would require a change in attitudes. But there was no precedent for it, and although the administrators talked knowingly about what was needed, they had no clear idea of how to proceed. There was no tradition of major innovation at the NPL, and the ACE project brought out the conservative and negative character of the institution. Just as in 1941, Alan was impatient and uncomprehending of the organisational inertia.

Nor, perhaps, did he appreciate that the very high priorities enjoyed by Bletchley, and the willingness of other organisations to sacrifice their independence, could no longer be expected in 1946. Thus at Dollis Hill, while there was no question about the competence of the Colossus engineers, their director, Radley, did not attach great importance to the work being done on delay lines for the ν PL. The Post Office had manifold tasks of its own in connection with the wartime backlog, and there was now no higher authority, no national policy, to coordinate the priorities of the various state enterprises. Alan and Womersley made an official visit to Dollis Hill on 3 April 1946, and thereafter work began – but in a desultory way, with the effect of creating an unforeseen delay, and a sense of uncertainty as to direction.

Alan had written in his report about the possibility of using cathode ray tubes as a quite different kind of storage system, and it was probably at his prompting that on 8 May 1946 Womersley wrote to TRE with an enquiry about the state of research at the radar establishment into the use of such tubes for storage, explaining that it might ‘form a suitable alternative to, or possibly even an improvement on, the mercury delay line which we are at present intending to use in our automatic computing engine .. V The response was not unhelpful, and on 13 August Darwin was able to write to Sir Edward Appleton at the DSIR:10

…As I told you Womersley was down at TRE to see whether they could do any work about the ACE machine. He tells me that it looks a most promising chance, and I think we should go ahead on it. Their lay-out for the job looks good, and I gather it appealed strongly to F.C. Williams as a job he would like to do, so that it should get a good chance. I am kicking myself for not having thought of it months ago as a possibility.

As to what comes next Womersley has got to use some tact in exploring how we stand with the Post Office who have started to give us help, which would be very good but that they are not in a position to plunge very deep. It will also be necessary to square TRE officially over priorities, and on this I should like to bring high power to bear if necessary, because we have got a splendid chance of jumping in ahead of America.

F.C. Williams was one of the top electronic experts at TRE, and he was enthusiastic not because he was interested in computing, which he was not, but because he was anxious to find peacetime applications for the electronic skills developed in wartime radar. In finding such applications he had a mind of his own, and had an option open to him that did not accord with Darwin’s ‘high power’. It derived from Manchester.

Newman had left Bletchley to become Professor of Pure Mathematics at Manchester University, taking Jack Good and David Rees with him as junior lecturers. (Rees was another of the 1939 Part III class, who had joined Welchman’s hut in December 1939, and later joined the Newmanry.) In moving from a Cambridge lectureship to a Manchester University chair, he was following Blackett, then Professor of Physics. Together they constituted a formidable team, and one which did not see why Darwin should monopolise electronic computers. As the first reader of Computable Numbers and the co-author of the Colossus, Newman appreciated the potential of computers as well as anyone, and if he lacked Alan’s emotional thrust towards ‘building a brain’, and the experience of assembling components himself, he compensated with a greater skill in the art of the possible.

Writing to von Neumann 11 on 8 February 1946, Newman had explained that he was

hoping to embark on a computing machine section here, having got very interested in electronic devices of this kind during the last two or three years. By about 18 months ago I had decided to try my hand at starting up a machine unit when I got out. It was indeed one of my reasons for coming to Manchester that the set-up here is favourable in several ways. This was before I knew anything of the American work, or of the scheme for a unit at the National Physical Laboratory. Later I heard of the various American machines, existing and projected, from Hartree and Flowers.

Once the NPL project was started it became questionable whether a further unit was wanted. My view was that in this, as in other branches of technology, basic research is wanted, which can go on without worrying about getting into production …

Newman’s intention was that

mathematical problems of an entirely different kind from those so far tackled by machines might be tried, e.g. testing out (say) the 4-colour theorem or various theorems on lattices, groups, etc. …

He explained that

Anyhow, I have put in an application to the Royal Society for a grant of enough to make a start. I am of course in close touch with Turing. After discussion with him, and hearing Hartree and Flowers, it seemed to me that if we start on ‘mathematical’ problems here, in the above sense, we ought to be able to manage with considerably less storage, though I have asked to the Royal Society to be prepared for something fairly substantial.

Newman’s application was for a grant to cover the capital cost and five years of salaries for an electronic computer.¹² The Royal Society set up a committee to investigate the application for a grant, consisting of Blackett, Darwin, Hartree, and two pure mathematicians, Hodge from Cambridge and Whitehead from Oxford. Darwin opposed it on the grounds that the ACE was to serve the needs of the country. Womersley had expressed the particular fear that Newman would steal Flowers away from the ACE. But he was outvoted, for it was approved that there should be ‘a different type of machine’ for Newman’s project. On 29 May the Treasury allocated £35,000 to Newman. The rationale was that as ‘fundamental science’, his proposal fell into the orbit of the Royal Society, and did not conflict with the DSIR. It meant that a rather surprising breath of mathematical innocence was felt again, with a computer development not required for weaponry.

It so happened that Blackett knew F.C. Williams from before the war, when they had collaborated on an automatic curve-tracer for the differential analyser. Both Darwin and Newman, therefore, were looking to Williams to help them ‘jump in ahead of America’, and Darwin’s plan for a single national computer installation had already been undermined. The question of who was going to build the ACE remained unresolved while Williams decided between these suitors.

This incipient rivalry was further complicated by the fact that a third British electronic computer project was initiated in mid-1946. This was the brainchild of M.V. Wilkes, Alan’s fellow ‘B-star’ of 1934 who in 1945 had left wartime work at TRE to resume his position at the Mathematical Laboratory in Cambridge, of which he now became director. He was in touch with Womersley at once, but the ENIAC and EDVAC plans were secret until the spring of 1946, and only then could Hartree tell him about what he had seen in 1945. Hartree then also arranged for him to attend a course of lectures arranged by the ENIAC team at Philadelphia in July and August 1946.

This course at the Moore School, together with the reports issued by von Neumann’s group at the IAS, enjoyed very considerable influence upon the future development of computers. For one thing, it brought about the first federal funding for a machine on the lines of the EDVAC. A certain James T. Pendergrass represented the Navy’s CS AW, and reported back 13 upon the virtue of a universal machine, as opposed to the special purpose equipment which had ‘often proved to be expensive and time-consuming.’ (Presumably Travis had been given the same analysis a year earlier.) For another, it inspired Wilkes with great enthusiasm for putting his wartime electronic experience to work in building a British version of the EDVAC.

Alan, in contrast, remained unaffected by the American developments, and they by him. In growth as in conception they were independent. There was a little indirect contact between the ν PL and the American group. Hartree had made a visit to the ENIAC in the summer of 1946, being allowed to use it himself, and took with him a copy of the ACE report and a ‘third version’ of the ACE design.¹⁴ But its programming ideas made no obvious impression upon the Americans.

As a theoretician of computers, von Neumann had been joined by Norbert Wiener, the American mathematician of a slightly earlier generation, whom the war had likewise taken from group theory to machinery, although in his case the servo-mechanisms of anti-aircraft artillery had been the formative influence. Thus von Neumann and Wiener corresponded in connection with the potential of the planned EDVAC, but mostly in terms of the faculty of conditional branching corresponding to ‘feedback’. They did not discuss hierarchies of programs, nor the computer reorganising and creating its own instructions. They remained most impressed with the McCulloch and Pitts ideas, which suggested that the logical functions of electronic valves bore some similarity to the structure of neurons in the human nervous system. In a letter 15 of 29 November 1946, von Neumann wrote to Wiener of the ‘extremely bold efforts’ of Pitts and McCulloch, with which he ‘would like to put on one par the very un-neurological thesis of R. [sic] Turing.’

In the other direction, likewise, there was limited communication. The Draft Report on the EDVAC was there at the NPL, and Alan continued to make use of its notation for logical networks. David Rees, who attended the Moore School lectures on behalf of the Manchester interest, reported back to Alan and Jim Wilkinson for ten days or so. But the American plans had no particular influence on the ACE project, Alan being notably sceptical about the prospects for the Iconoscope, the storage medium on which the Americans were pinning their hopes. They did not think of the American development as a rival; it was simply another project. The ACE was Alan Turing’s own thing, like naval Enigma, like the Delilah. It was not, however, developing in quite the same way.

Although the wartime spirit lived on amongst the huts and bombsites of 1946, the ACE section did not flower with the camaraderie of Hut 8, or the quite remarkable rapport that Alan had established with Don Bayley. Mike Woodger came back from sick leave in September and found a note on his desk asking him to program BURY and UNBURY. The relationship continued in this master-and-servant way. Alan liked the earnest, rather nervous Mike Woodger, and tried to be kind, but hid it under what appeared as an abrupt, rather frightening manner. He probably did not realise the awe with which he was regarded by young people like Mike Woodger, just starting on a career. Always casting himself as the Young Turk embattled against officialdom, he still found it hard to see himself as the official in others’ eyes. He was impatient of slowness, and could not use his imagination to make communication more effective.

Jim Wilkinson was older and more experienced than Mike Woodger, but he too found many days when it was better to keep out of the way of the now somewhat isolated ‘creative anarchy’ that was Alan Turing. ‘Likeable, almost lovable …but some days depressed’, he appeared; his mercurial temperament and his emotional attitude to his work showing clearly. It was at about this time that Alan got the long-promised promotion to Senior Principal Scientific Officer, and he took Jim Wilkinson and Leslie Fox from Goodwin’s department out to a celebration dinner in London. The train journey was spoilt by a sultry row over some mathematics, and then, as they arrived at Waterloo, the clouds cleared and he was buoyant again.

This particular argument arose because Alan had become involved in a problem of numerical analysis, the work done in Goodwin’s section. In 1943 the statistician H. Hotelling 16 had analysed the procedure for solving simultaneous equations (or, roughly equivalently, for inverting a matrix) and his result made it appear that errors would grow very rapidly as successive equations were eliminated. If this were so it would undermine the practical usefulness of the ACE. Goodwin’s section, being directly concerned with the problem, had attacked it heuristically in 1946 by solving a set of eighteen equations that had come up in an aerodynamic calculation, and Alan had joined in (notably the least competent at the detailed work), on the desk machine exercise. To their surprise, they found the final errors to be remarkably small. Alan had undertaken a theoretical analysis of why this should be. It was a typical Turing problem, needing a fresh attack, and with a concrete application. He tackled it much as he had developed a theory of probability for use at Bletchley.

This work of course, did not lie far in the past, and he set Mike Woodger some probability problems, including the one about the ‘barrels of gunpowder’. There was also professional contact arising out of wartime work. Jack Good and Newman had made a visit to the ν PL – Newman, of course, being interested in setting up his Manchester computer project – and Jack had managed to disprove Alan’s assertion that no one could write an instruction table that was free from error at the first attempt. Jack Good had also written a short book¹⁷ on Probability and the Weighing of Evidence, effectively setting out the theory they had employed at Bletchley, though not its more advanced applications. The ‘sequential analysis’ method was, as it happened, soon published in America by the statistician A. Wald,¹⁸ who had developed it independently for the testing of industrial components. Alan, in contrast, published nothing that came of his Bletchley work, except in the less direct sense that almost everything he was doing was flowing from his wartime experience added to his pre-war theory of machines.

Rather than forming new ties of friendship at the ν PL, he retained those of the war. Donald Michie, now an undergraduate at Oxford, was one of these friends, and a footnote on Alan’s October 1946 letter to Jack Good, with comments on the draft of his book, noted cryptically that ‘Donald has agreed to help and I have now got the necessary gadgets for the treasure.’ This was a reference to a proposed expedition to recover the silver bars. (David Champernowne had meanwhile realised a healthy profit in his ingots, which had remained safely in his bank.) There had been a previous attempt with Donald Michie, who was offered the choice of either a one-third share of the total proceeds or a payment of £5 per expedition. This was itself a nice example of the Turing theory of probability, which appealed to the odds that a perfectly rational person would be prepared to bet on an event. As a perfectly rational man, Donald Michie opted for the latter choice. The first real-life treasure hunt had been a failure, since when they went to the wood near Shenley where one bar was buried, Alan found that the landmarks had changed since 1940, and he could not locate the spot. The point of the ‘gadget’ was that it was a metal detector which Alan had designed and built himself. On the second trip, it functioned, though only to a depth of a few inches. It successfully located a great many pieces of metal under the surface of the wood, but not the silver bar. As for the second bar, he knew where that was, but they found that they were unable to apply the UNBURY routine when standing in the bed of the stream.

Such failures he would easily laugh off. This was not his only visit back to Buckinghamshire, for he spent a weekend, probably in December 1946, discussing D. Gabor’s new theory of communication 19 with Don Bayley. This time he distinguished himself by fainting when he grazed himself shaving. He had told Don long before about this reaction to blood, but this was the first time Don had seen it happen. There had also been an occasion in October 1945, when he, Don Bayley, Robin Gandy and ‘Jumbo’ Lee met up to go to a lecture on wartime radio work at the Institute of Electrical Engineers. Afterwards they had gone to Bernard Walsh’s oyster restaurant and rather hoped to be fed on the house – in which they had been disappointed. Alan had cycled into London from Teddington and had parked his bicycle outside the Soho restaurant, from which it was duly stolen.

For him to cycle the fifteen miles was not entirely characteristic, since he would quite happily take in such distances on foot. His success in the Hanslope races had been followed up. On arrival at Teddington he had joined the local Walton Athletics Club, and had taken up running as a serious amateur. He was a long-distance runner, rather than a sprinter; it was his stamina that gave him the edge in races over three miles in length. During this period he would spend two or three hours every day on training, and would run for the club on Saturday afternoons. Thus in October 1946 he wrote to his mother:

My running was quite successful in August. I won the 1 mile and 1/2 mile at the NPL sports, also the 3 miles club championship and a 3-mile handicap at Motspur Park. That was the meeting^* at which all the stars were trying to break records, but in fact were pulling muscles instead. Being a very humble athlete myself I was able to get away without pulling a muscle. …The track season is over now, but of course the cross country season will be beginning almost at once. I think that will suit me rather better, though the dark evenings will mean that my weekday runs will be in the dark.

He was lengthening his distance, and working up to marathon running. If possible he would make official visits double as training runs. In particular, he would run the ten miles across west London to Dollis Hill in connection with the plodding development of the ACE delay lines. Every few months, he would run the rather longer distance of eighteen miles to Guildford, to put Mrs Turing’s social imperatives to some constructive use. It amazed everyone, but he did not care about that. It also, as Mrs Turing put it, gave him contact with men ‘in all walks of life.’

He even managed to combine running and chess. He saw something of David Champernowne from time to time, either at Oxford, where he now had a position, or at his parents’ house at Dorking. They would play ping-pong, and talk about probability theory, but they also devised a form of chess in which each player had to make his move while the other ran round the garden. Fast running would tend to prevent good thinking, so the problem was to choose the right balance. Alan was also interviewed by the Sunday Empire News on training hints. He might have remembered the discussion of ‘second wind’ in Natural Wonders, which explained how it depended upon ‘teaching’ the brain not to ‘raise such a row’ when it smelt a little carbon dioxide in the blood.

One of the difficulties of his position was that there was a good deal of carbon dioxide in the blood supplying the British brain. For all the talk of planning for the future, there was a terrible exhaustion after the war, and little eagerness to upset the apple-cart any further. In one way this became clear at once. At Hanslope, Don Bayley had continued to improve and test the Delilah. Later in 1945 he had taken it to Dollis Hill for evaluation where – hardly surprisingly – they failed to find any cryptographic weakness. In early 1946 he had taken it to the Cypher Policy Board, which was a coordinating organisation established in February 1944. He set it up in the basement of their London offices, and left it with one of their officers. They were more interested than the Post Office, and suggested to Gambier-Parry that his man might join them to continue work. But Gambier-Parry turned this down, and this refusal closed the story. The Delilah’s two neat packages of equipment, providing speech security with no more than thirty valve-envelopes, were completely forgotten. As a contribution to British technology it had been a complete waste of time.*

But Delilah had been part of the preparations for the ACE, and this, Alan Turing’s logical Overlord, was what mattered. The plans were all ready, and only needed the signal to start. And they did at least gain a sort of second wind on 31 October 1946, when Mountbatten, as president of the Institution of Radio Engineers, gave a speech 20 that conveyed – however inaccurately – the excitement of what had happened in the new technology of communication and control. It was as far beyond the old days of the Glorious y as they had been ahead of the papyrus scroll:

The war not only taught us a great deal about techniques, but it proved the occasion for new departures in application, particularly in electronics, which had enormously augmented our present human senses. Apart from radar, which aided to a remarkable degree the sense of sight, we might in future be able, by pooling and transforming the potentialities of other forms of radiation, such as light, heat, sound, X-rays, gamma-rays and cosmic rays, to receive the counterpart of radar screen pictures from inside our bodies, or even from individual body cells. Or perhaps we might receive them from the interior of the earth, or from the stars and galaxies.…there was reason to believe that facilities for impressing information and knowledge on the human brain …may be extended by the direct application of electrical currents to the human body or brain. …

The stage was now set for ‘the most Wellsian development of all’. It was considered possible to evolve an electronic brain, which would perform functions analogous to those at present undertaken by the semi-automatic portions of the human brain. It would be done by radio valves, activating each other in the way that brain cells do; one such machine was the electronic numeral [sic] integrator and computer (ENIAC), employing 18,000 valves …

Machines were now in use which could exercise a degree of memory, while some were being designed to employ those hitherto human prerogatives of choice and judgment. One of them could even be made to play a rather mediocre game of chess! …

Now that the memory machine and the electronic brain were upon us, it seemed that we were really facing a new revolution; not an industrial one, but a revolution of the mind, and the responsibilities facing the scientists to-day were formidable and serious. ‘Let us see to it,’ he concluded, ‘that we not only insist on being allowed to shoulder it; but that when we have established our right, we can also prove our fitness.’

In 1946 people still believed that the great war surplus of scientific and technical advance could be turned to good use, although Mountbatten’s comments on ‘responsibilities’ reflected the fact that few had any idea of how this was going to be achieved.

The ENIAC had been released from military secrecy months before, and Hartree had written about it in the scientific journal Nature,²¹ but it needed Mountbatten to make it ‘news’. He had taken his information from the NPL, and the inaccurate reference to chess-playing machines would suggest that he heard an excited Alan Turing talking about the future possibilities of the ACE. (There was, of course, no machine in existence that could play chess.) Darwin and Hartree were embarrassed not only by Mountbatten getting the wrong ends of the technical sticks, but also by his perfectly correct assertion that the ACE would exercise ‘hitherto human prerogatives of choice and judgment’. They did not like to criticise Mountbatten, but wrote 22 to The Times complaining that its headline ELECTRONIC BRAIN had given a false impression.^*

The official NPL press release,²³ on 6 November, was very different in tone. It presented the building of the ACE as a somewhat distant possibility, rather than being just round the corner. Correctly it set the origin of the ACE in Alan’s ‘severely mathematical paper’ of 1936, and explained how electronic switching provided the speed to make such a machine practical. It explained the superiority of the ACE over the ENIAC, through its large memory store, and referred to the work already done on programming instruction tables. But the cost had now risen to a figure ‘in the region of £100,000 to £125,000’ and it was stated that ‘It will be two or three years before the completion of this machine can be hoped for, since its construction presents formidable problems, both mathematical and technical.’

Now that this stirring if remote prospect had at last been entrusted to the British public, the Daily Telegraph showed itself the most eager to spread the good tidings, which it imbued with a suitably patriotic flavour. The headline BRITAIN TO MAKE A RADIO BRAIN/‘Ace’ Superior to US Model/ BIGGER MEMORY STORE appeared on 7 November, followed up next day with an account by its own reporter, who had interviewed Hartree, Womersley, and Alan at the NPL:

‘ACE’ WILL SPEED JET FLYING

…Revolutionary developments in aerodynamics, which will enable jet-planes to fly at speeds vastly in excess of that of sound, are expected to follow the British invention of ‘Ace’, which has been commonly labelled the electronic ‘brain’.

…Professor Hartree said: ‘The implications of the machine are so vast that we cannot conceive how they will affect our civilisation. Here you have something which is making one field of human activity 1,000 times faster.

In the field of transport, the equivalent of Ace would be the ability to travel from London to Cambridge …in five seconds as a regular thing. It is almost unimaginable.

…Dr Turing, who conceived the idea of Ace, said that he foresaw the time, possibly in 30 years, when it would be as easy to ask the machine a question as to ask a man.

Dr Hartree, however, thought that the machine would always require a great deal of thought on the part of the operator. He deprecated, he said, any notion that Ace could ever be a complete substitute for the human brain, adding:

’The fashion which has sprung up in the last 20 years to decry human reason is a path which leads straight to Nazism.’

The Germans, like the computer, had only been obeying orders, but this allusion did not deter Alan when next day a reporter from the local newpaper came to investigate the ‘New NPL Wonder’. He only lengthened the time-span of his prophecy. They published the interview 24 of the ‘34-year-old mathematics expert’ under the headline ELECTRIC BRAIN TO BE MADE AT TEDDINGTON:

Dr Turing, speaking about the ‘memory’ of the new brain …said it would be able to retain for a week or more about as much as an actor has to learn in an average play. Asked about Lord Louis Mountbatten s statement that it would be able to play an average game of chess, Dr Turing said that was looking far into the future. …The point was then put to him that chess and similar activities required judgment as well as memory, and Dr Turing agreed that that was a matter for the philosopher rather than the scientist. ‘But,’ he added, ‘that is a question we may be able to settle experimentally in about 100 years time.’

This was the most exciting if embarrassing thing to happen at the NPL for a long while, and Darwin was sufficiently encouraged to make a radio broadcast²⁵, in which he outlined the ‘idealised machine’ of Computable Numbers, and explained that ‘Turing, who is now on our staff, is showing us how to make his idea come true.’ But as the newsreel music faded away, the awkward fact remained that it was now nearly a year since Alan had shown in detail how to ‘make his idea come true’, and Darwin still did not know how the NPL was to give effect to his proposals.

On 22 October, when Hartree enquired about progress on the ACE, Darwin had to confess that ‘Post Office assistance had not been as great as was expected.’ On the TRE side, there had been more technical progress, since F.C. Williams had begun in about June to investigate the behaviour of spots on cathode ray tubes with a view to creating a storage system. During the war he had seen attempts at the Massachusetts Institute of Technology radar research laboratory to employ ordinary cathode ray tubes for echo cancellation, attempts which failed because of the transience of the spots, which faded in a second or so. But during the autumn of 1946, he had the idea, independently of Alan’s proposal in the ACE report, of refreshing the spots periodically to overcome this problem.²⁶ He had also seen a way to do it. On the other hand, from an administrative point of view there had been a setback to NPL’s plans, since Williams had accepted the chair of electrical engineering at Manchester University – an appointment which he believed he owed to Blackett. Darwin explained to the Executive Committee that

He had also hoped that considerable assistance could be obtained from Dr F.C. Williams of TRE, but that he now understood that Dr Williams had accepted a University appointment. He said that he would explore the possibility of Dr Williams working on this project at his University – perhaps with the help of NPL or TRE staff …

The possibility, thin as it was, was indeed duly explored. On 22 November 1946, Williams, together with two other top TRE men R. A. Smith and A. Uttley, made a visit to the NPL ‘to discuss with Mr Womersley and Dr Turing in what way help could be given to the ACE project.’ The official minutes 27 were a masterpiece of discretion, Darwin being furious that Williams had been seduced into the Manchester orbit. Speaking alone with Smith, he banged on the negotiating table:

The Director emphasised the extreme importance which he attached to the development of ace, and put it as having the highest priority in his opinion of any work that was being done for DSIR at TRE. He was most anxious that some effort should be set aside for work done on this project.

Smith explained that this was very difficult. ‘Apart from the small number of staff now working for Dr F.C. Williams most of the able circuit technicians had been transferred to the Department of Atomic Energy’ – a statement reflecting another post-war story. So ‘the only way in which TRE could continue to contribute would be to second a small number of staff …to work under Dr Williams’ direction at Manchester University.’ This was not at all what Sir Charles Darwin wanted to hear, but he did not give up. The meeting was enlarged to include Williams and Uttley from TRE, and Womersley for the ν PL, while Alan was allowed in as well. In the discussion of the ACE

…It appeared that although an elaborate paper design had been laid down, the fundamental problem of storage of information had not been solved and that, as had been suspected, the experimental work of Dr Williams’ at TRE on storing information on a cathode ray tube was considerably in advance of the work which the Post Office were doing on the use of delay lines for storage purposes. …

Williams had, in fact, already succeeded in storing a spot on a cathode ray tube for an indefinite period. A compromise formula was agreed, according to which Williams’ work ‘should continue with as little disruption as possible’. The NPL drafted a contract for Williams to sign, according to which he would develop both electronic storage and components for the arithmetical hardware.

There was, however, a triple misunderstanding. For one thing, there was still the strong possibility of Manchester funding allowing Williams to develop his storage independently of NPL requirements. For another, the ACE design and programming had been done for a delay line store, and would have to be completely reworked if policy changed to the use of cathode ray tubes. Very probably Darwin and Womersley did not appreciate that the storage medium effectively dictated many aspects of the design of the machine and its programming. Alan might not have minded rewriting everything if it meant that progress could be achieved, but there was a deeper difficulty. While Darwin spoke as though he had had a ‘mathematician’ to lay down a design, and now was finding a practical man to build it, Williams’ attitude was that he was negotiating for funds wherewith to construct his computer. They were talking at cross-purposes. Success would depend upon bridging that gap, so closely tied in with social class, between ‘mathematics’ and ‘engineering’. But the crossing of demarcation lines was very difficult now. No longer was Germany enforcing cooperation upon its enemy.

Hartree, wanting to see more cooperation, took the next step. On 19 November he explained to Darwin that ‘Mr Wilkes was prepared to give as much help as he could on the ACE as he had facilities at Cambridge; he had experience of making up [delay] lines and would exchange information with Dr Turing.’ Next day Wilkes wrote²⁸ to Womersley:

I believe Professor Hartree has told you that I am beginning to do a little work on electronic calculating machines and that I am anxious to co-operate with you. As you know I recently paid a visit to the United States and saw what they are doing over there. Professor Hartree said he had discussed the matter with you and thought perhaps we might be able to make some mutually advantageous arrangement.

Wilkes visited the NPL a week later, on 27 November, to discuss his plans. On 2 December he wrote again:

I have been thinking over in more detail the subject we were discussing last Wednesday and what I have now in mind is that I should build up a group here containing about eight people of varying grades in addition to the mechanic and boy who are at present in the workshop. This would involve an annual wage bill of something like £2,500. In addition there will be cost of materials and getting things made outside.

I am quite convinced that the construction of a pilot model of some sort is an essential step in designing ACE.* I do not see how else one can test out such things as control circuits. I am attaching a note I have written on the design of the pilot model and I think it would be a good thing if you decide to place a contract with us to call for this specifically. It does not follow that no part of ace may be ordered until the pilot model is finished but there will be many matters which it will be hard to settle, without experience at least of trying to get a pilot model working.

But the attached note outlined the specification of a computer on the EDVAC model, and thus entirely different from the ACE. Not only did it employ a central accumulator, but it ran counter to the Turing philosophy of keeping the hardware as simple as possible, and putting the work into the programming. Instead, it made the programming as easy as possible, at the cost of requiring electronic circuits to do the work of recognising and executing the various arithmetical instructions. Wilkes wrote apparently in ignorance of the fact that at the NPL they already had Version VII of a detailed design, for which six months’ hard work had been put into writing programs. Even to contemplate Wilkes’ proposal, as Womersley apparently did, was to undermine his own division’s work. On 10 December he passed the proposal to Alan, whose reaction was understandably brusque:

Mr Womersley:

I have read Wilkes’ proposals for a pilot machine, and agree with him as regards the desirability of some such machine somewhere. I also agree with him as regards the suitability of the number of delay lines he suggests. The ‘code’ which he suggests is however very contrary to the line of development here, and much more in the American tradition of solving one’s difficulties by means of much equipment rather than by thought. I should imagine that to put his code (which is advertised as ‘reduced to the simplest possible form’ ) into effect would require a very much more complex control circuit than is proposed in our full-size machine. Furthermore certain operations which we regard as more fundamental than addition and multiplication have been omitted.

It might be argued that if one is to have so little memory then it is necessary to have a complex control to make up. In so far as this is true I would say that it is an argument for either having no pilot model, or for not using it for serious problems. It is clearly rank folly to develop a complex control merely for the sake of the pilot model. I favour a model with a control of negligible size which can later be expanded if desired. Only test problems would be worked on the minimal machine.

But Womersley wrote back to Wilkes on 19 December:

Thanks for your suggestions regarding the pilot model for the ACE. They don’t quite agree with Turing’s ideas of what a minimal machine should be. In his opinion the control part of it is too elaborate though he agrees about the amount of memory. I have therefore asked him to prepare a note giving his ideas of what the minimal machine should contain, and this I propose to send to you (without commitment on either side) so that we can meet and discuss further the question of a formal contract.

Meanwhile the publicity given to the ACE had engendered a couple of enquiries from British industry regarding the potential of the new machine. On 7 November the editor of the Industrial Chemist had requested an article from Alan, who replied that while the ACE ‘would be well adapted to deal with heat transfer problems, at any rate in solids or in fluids without turbulent motion,’ he thought that an article would be appropriate only ‘when a few similar problems have actually been solved with the ACE and more practical details can be given.’ On 11 November, Alan had been invited to give a paper to the Institution of Radio Engineers, to which Mountbatten had vouchsafed his revelations a few days earlier. In this case, however, Alan had to write:29

I am sorry that I cannot give such a paper without permission from our Director.
I suggest you write to him about it.

The administrators, by this time, were concerned to reduce to a minimum the exposure of Alan Turing to the outside world. There had already been enough embarrassment in the newspapers. Thus Womersley suggested to Darwin that ‘Dr Turing, rather than explaining his machine to a number of isolated people on many different occasions, should conserve his time by giving a course of lectures intended primarily for those who will be concerned with the technical development of the machine. Such a course was indeed arranged to take place on Thursday afternoons during December and January at the Adelphi, headquarters of the Ministry of Supply.30 The invitations, less than twenty-five in all, went to the relevant electronic engineers, component manufacturers, military departments, and to a few others already in the know. The scene was set for a British equivalent of the Moore School lectures, although the setting was subtly different. According to an NPL memorandum, there was to be ample time after Alan’s exposition for ‘Discussion – in particular, criticism of Dr Turing’s technical proposals.’ They did not trust him to know what he was talking about. Criticism was, in any case, inevitable; for by this time several of those who attended had ideas of their own, and no inclination to be fitted into the Turing plans. Wilkes wrote³¹later that he

found Turing very opinionated and considered that his ideas were widely at variance with what the main stream of computer development was going to be. I may have gone to his second lecture but I certainly went to no more. Hartree continued to go and insisted on giving me his notes, but I found them of little interest.

On the other hand, lectures on elementary electronics did not go down well with those from TRE, who could also see for themselves how the ACE design was built round the delay line storage. It had been intended that ‘from these discussions would emerge more clearly what contribution TRE should make’ to the ACE. This was indeed to happen, but not in the way that Darwin had hoped.

As it happened, the scheme of lectures was suddenly disrupted, thanks to the arrival of a letter from America. On 13 December Womersley found himself invited to a grand Symposium on Large Scale Digital Calculating Machinery to be held at Harvard from 7 to 10 January, in connection with the inauguration of Aiken’s Mark II relay calculator. But Darwin quickly decided that it would be better for Alan to drink at the fount of American wisdom, making arrangements for him to attend the conference, and then to visit the ENIAC and the von Neumann group. Jim Wilkinson took over the Adelphi lectures. Alan spent Christmas at David Champernowne’s parents’ house at Dorking, and in a Boxing Day athletics meeting lost the three-mile race by one foot,³² with a time of 15 minutes, 51 seconds. The sports reporter of the Evening News obtained a unique statement from him regarding the authorship of the digital computer:

‘electronic’ athlete

Antithesis of the popular notion of a scientist is tall, modest, 34-year-old bachelor Alan M. Turing, scratch man in the Walton Athletics Club’s three-mile open event on Boxing Day.

Turing is the club’s star distance runner, although this is his first season in competitive events. At the National Physical Laboratory, at Molesey [sic], he is known as Dr Turing, [and] is also credited with the original idea for the Automatic Computing Engine, popularly known as the Electronic Brain.

He is diffident about his prowess in science and athletics, gives credit for the donkey work on the ace to Americans, says he runs only to keep fit, but admits he rowed in his college eight at Cambridge.

After trying and failing to find a post office so that he could mail his sweater and pullover to his mother, who took in his non-shrink washing, he boarded the Queen Elizabeth that evening. This visit to the land of Oz was a very pale reflection of the liaison of just four years before. But taking the laundry parcel with him, to be ‘lugged round America’ in a characteristically awkward Turing style, he went to see the donkey workers.

The conference had brought together almost every conceivable interested American party,* but Alan was the only British participant. He played a large part in the discussions. For example, he discussed the cathode ray tube storage proposals made by J.W. Forrester and J.A. Rajchman, the latter being responsible for development of the Iconoscope at RCA. His discussion³³ was in characteristic style, taking an engineering problem and locating a point of abstract principle that lay behind it:

Dr Turing: I do not know whether I should really ask my question of Dr Rajchman or Dr Forrester, because this difficulty arises in both papers. Dr Forrester mentioned that there was a possibility of reconstituting the charge by use of low velocity electrons and said that Dr Rajchman would explain it in his paper. I understand from Dr Forrester that the method should be applicable to his type of storage. But there seems to me to be a fundamental difficulty which in principle amounts to this: unless the storage medium has some kind of association with the granular structure, such a method cannot be applicable because if any one such pattern is stable, then by a symmetry argument, by a slight shift one way or the other, as it were, a slightly different configuration is also stable. Thus you do not get a finite number of stable configurations, but an infinite number.

He also identified the guiding principle which distinguished his plans for the ACE from those of the von Neumann group and of Wilkes:

We are trying to make greater use of the facilities available in the machine to do all kinds of different things simply by programming rather than by the addition of extra apparatus. …

This is an application of the general principle that any particular operation of physical apparatus can be reproduced within the EDVAC-type machine.^* Thus, we eliminate additional apparatus simply by putting in more programming.

The conference brought Alan into contact with Claude Shannon and Andrew Gleason again. He also took the opportunity to brush up and submit to Alonzo Church’s journal some wartime work on type theory.³⁴

Afterwards, Alan spent about two weeks at Princeton. The Americans were no further ahead in constructing an electronic computer than was the NPL, and had run into parallel problems. The line between ‘mathematics’ and ‘engineering’ was one of these, Eckert and Mauchly having split off to found their own company, and a patent suit over aspects of the EDVAC design being in progress. Von Neumann and Goldstine had been thinking, like Alan, about the problem to do with the numerical analysis of matrix inversion, and also about the physics of mercury delay lines.35 Goldstine got the false impression that Alan thought delay lines could not work. This might have been because Alan talked about some of the more subtle difficulties. He had, for instance, already devised a grid³⁶ (later patented) to be inserted in the short ‘temporary storage’ lines to prevent reflected pulses from travelling backwards.

He did not bring anything back from America which changed his ideas about the ACE. This was the one kind of liaison which at the present time he did not need at all, and it had been irrelevant to his plans. But he brought back some presents – some nylons and dried fruit for his mother, and a food parcel for Robin Gandy which included a much-valued tin of cream. Britain was now even more severely rationed than during the war, the balance of payments proving a sterner constraint than the U-boats. And as he returned across the Atlantic, the bitter winter of early 1947 had set in.

The talk of cooperation was still going on, but it was only talk. On 21 January E.S. Hiscocks, the NPL Secretary, had reported that ‘the Post Office had succeeded in keeping a number circulating for half an hour through their delay line set-up. This news was very encouraging. Professor F.C. Williams’s work on electronic storage will, of course, continue.’ But two days later Williams had declined the NPL contract and the illusion that he was doing work for the ACE finally crumbled away. Wilkes had written to Womersley on 2 January, expecting a contract, the incompatibility in design notwithstanding. (‘I shall be glad to hear of Turing’s ideas on the subject of a pilot model.’) This letter remained embarrassingly in Womersley’s in-tray. Another of Hartree’s ideas had proved to be more realistic. He had invited H.D. Huskey, one of the ENIAC team, to spend 1947 as a sabbatical year at the NPL, and he was already installed when Alan arrived back in a shivering Britain to give the last of the talks at the Ministry of Supply. The rationale 37 was that he would bring with him American expertise especially on ‘the apparatus side’. But otherwise, the twelve months of 1946, a period within which the Colossus had been designed and built from scratch, had passed and nothing had happened. Alan took advantage of his American tour to summarise the state of affairs at the NPL:

My visit to the USA has not brought any very important new technical information to light, largely, I think, because the Americans have kept us so well informed during the last year. I was able, however, to get a useful impression of the values of the various projects, and the scale of their organisation. The number of different computing projects is now so great that it is no longer possible to have a complete list. I think this is a mistake, and that they are dissipating their energies over too wide a range. We ought to be able to do much better if we concentrate all our effort on the one machine, thereby providing a greater drive than they can afford on any single one. At the present, however, our effort is puny compared with any one of the larger American projects. To give an idea of the numbers of people involved in this work in the USA I may mention that there were between 200 and 300 present at the Symposium at Harvard, and that about 40 technical lectures were given. We are quite unable to match this.

One point concerning the form of organisation struck me very strongly. The engineering work was in every case being done in the same building with the more mathematical work. I am convinced that this is the right approach. It is not possible for the two parts of the organisation to keep in sufficiently close touch otherwise. They are too deeply interdependent. We are frequently finding that we are held up due to ignorance of some point which could be cleared up by the engineers, and the Post Office find similar difficulty; a telephone conversation is seldom effective because we cannot use diagrams. Probably more important are the points which are misunderstood, but which would be cleared up if closer contact were maintained, because they would come to light in casual discussion. It is clear that we must have an engineering section at the ace site eventually, the sooner the better, I would say.

Looking on the bright side my visit confirmed that our work so far has been on the right lines. It is probable that the Princeton machine, based on the Selectron, will have some advantage over the ace in speed, but our proposed machine has some compensating advantages, and I think that, other things being equal, it is better that the two different types should both be tried. The Princeton group seem to me much the most clear headed and far sighted of these American organisations, and I shall try to keep in touch with them.

We shall eventually obtain a word-for-word account of the conference. All the information given was ‘unclassified’.

If, like the Second Front, the plans had been delayed again and again, no loss of confidence was betrayed when Alan gave a talk on 20 February to the London Mathematical Society. This was when he elaborated in detail^* on the imagined operation of the ACE, and spoke as if its realisation was almost a formality: before long the terminals would be humming with activity, and the programmers would be busy with the work of converting the nation’s problems into logical instructions.

His talk, however, dwelt rather more upon the dream that lay behind the practicalities of an installation, bringing out in a public form the ideas that he had long been developing in Bletchley conversations. In fact his discussion opened with the picture of ‘masters’ and ‘servants’ who would attend the ACE, very much as the high-level cryptanalysts and the ‘girls’ had worked to decipher naval Enigma. The masters would attend to its logical programming, and the servants to its physical operation. But, he said, ‘as time goes on the calculator itself will take over the functions both of masters and of servants. The servants will be replaced by mechanical and electrical limbs and sense organs. One might for instance provide curve followers to enable data to be taken direct from curves instead of having girls read off values and punch them on cards.’ This was not a new idea, for F.C. Williams had built just such a thing for the old Manchester differential analyser. But the novelty lay in suggesting that:

The masters are liable to get replaced because as soon as any technique becomes at all stereotyped it becomes possible to devise a system of instruction tables which will enable the electronic computer to do it for itself. It may happen however that the masters will refuse to do this. They may be unwilling to let their jobs be stolen from them in this way. In that case they would surround the whole of their work with mystery and make excuses, couched in well chosen gibberish, whenever any dangerous suggestions were made. I think that a reaction of this kind is a very real danger. This topic naturally leads to the question as to how far it is in principle possible for a computing machine to simulate human activities.

This was a more controversial claim. Hartree, for instance, writing to The Times in November, had repeated his statement in Nature that ‘use of the machine is no substitute for the thought of organising the computations, only for the labour of carrying them out.’ Darwin had written more expansively that

In popular language the word ‘brain’ is associated with the higher realms of the intellect, but in fact a very great part of the brain is an unconscious automatic machine producing precise and sometimes very complicated reactions to stimuli. This is the only part of the brain we may aspire to imitate. The new machines will in no way replace thought, but rather they will increase the need for it …

To describe such careful and responsible statements as ‘gibberish’ was not the most tactful policy.

Darwin and Hartree were, in fact, echoing the comment by Ada, Countess of Lovelace, who wrote an account 38 of Babbage’s planned Analytical Engine in 1842, and claimed that ‘The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform.’ At one level, this assertion certainly had to be urged against the very naive view that a machine doing long and elaborate sums could be called clever for so doing. As the first writer of programs for a universal machine, Lady Lovelace knew that the cleverness lay in her own head. Alan Turing would not have disputed this point, as far as it went. The manager who took all decisions from the rule book would hardly be ‘intelligent’, or really taking a decision. It would be the writer of the rule book who was determining what happened. But he held that there was no reason in principle why the machine should not take over the work of the ‘master’ who programmed it, to a point where, according to the imitation principle, it could be called intelligent or original.

What he had in mind went much further than the development of languages which would take over the detailed work of the ‘masters’ in compiling instruction tables. He mentioned this future development, which in the ACE report he had already explored a little, quite briefly:

Actually one could communicate with these machines in any language provided it was an exact language, i.e. in principle one should be able to communicate in any symbolic logic, provided that the machines were given instruction tables which would enable it to interpret that logical system. This should mean that there will be much more practical scope for logical systems than there has been in the past. Some attempts will probably be made to get the machines to do actual manipulations of mathematical formulae. To do so will require the development of a special logical system for the purpose. This system should resemble normal mathematical procedure closely, but at the same time should be as unambiguous as possible.

Rather, in speaking of a computer ‘simulating human activities’, he had in mind the simulation of learning, in such a way that after a point the machine would not merely be doing ‘whatever we know how to order it to perform,’ as Lady Lovelace had claimed, for no one would know how it was working:

It has been said that computing machines can only carry out the purposes that they are instructed to do. This is certainly true in the sense that if they do something other than what they were instructed then they have just made some mistake. It is also true that the intention in constructing these machines in the first instance is to treat them as slaves, giving them only jobs which have been thought out in detail, jobs such that the user of the machine fully understands in principle what is going on all the time. Up till the present machines have only been used in this way. But is it necessary that they should always be used in such a manner? Let us suppose we have set up a machine with certain initial instruction tables, so constructed that these tables might on occasion, if good reason arose, modify those tables. One can imagine that after the machine had been operating for some time, the instructions would have altered out of recognition, but nevertheless still be such that one would have to admit that the machine was still doing very worthwhile calculations.

It was in this passage that he drew first attention to the richness inherent in a stored-program universal machine. He was well aware that strictly speaking, exploitation of the ability to modify the instructions could not enlarge the scope of the machine, later writing:39

How can the rules of a machine change? They should describe completely how the machine will react whatever its history might be, whatever changes it might undergo. The rules are thus quite time-invariant. …The explanation of the paradox is that the rules which get changed in the learning process are of a rather less pretentious kind, claiming only an ephemeral validity. The reader may draw a parallel with the Constitution of the United States.

But with that strictly logical reservation, he held the process of changing instructions to be significantly close to that of human learning, and deserving of emphasis. He imagined the progress of the machine altering its own instructions, as like that of a ‘pupil’ learning from a ‘master’. (It was a typically quick shift to the ‘states of mind’ idea of the machine from the ‘instruction note’ view.) A learning machine, he went on to explain:

might still be getting results of the type desired when the machine was first set up, but in a much more efficient manner. In such a case one would have to admit that the progress of the machine had not been foreseen when its original instructions were put in. It would be like a pupil who had learnt much from his master, but had added much more by his own work. When this happens I feel that one is obliged to regard the machine as showing intelligence. As soon as one can provide a reasonably large memory capacity it should be possible to begin to experiment on these lines. The memory capacity of the human brain is of the order of ten thousand million binary digits. But most of this is probably used in remembering visual impressions, and other comparatively wasteful ways. One might reasonably hope to be able to make some real progress with a few million digits, especially if one confined one’s investigation to some rather limited field such as the game of chess.

The ACE, as planned, would have at most 200,000 digits in store, so to speak of a ‘few million’ was looking well into the future. He described the storage planned for the ACE as ‘comparable with the memory capacity of a minnow’. But even so, he perceived the development of ‘learning’ programs as something that would be feasible within a short period: not merely a hypothetical possibility, but affecting current research in a practical way. On 20 November 1946 he had replied to an enquiry from W. Ross Ashby, a neurologist eager to make progress with mechanical models of cerebral function, in the following terms:⁴⁰

The ace will be used, as you suggest, in the first instance in an entirely disciplined manner, similar to the action of the lower centres, although the reflexes will be extremely complicated. The disciplined action carries with it the disagreeable feature, which you mentioned, that it will be entirely uncritical when anything goes wrong. It will also be necessarily devoid of anything that could be called originality. There is, however, no reason why the machine should always be used in such a manner: there is nothing in its construction which obliges us to do so. It would be quite possible for the machine to try out variations of behaviour and accept or reject them in the manner you describe and I have been hoping to make the machine do this. This is possible because, without altering the design of the machine itself, it can, in theory at any rate, be used as a model of any other machine, by making it remember a suitable set of instructions. The ace is in fact, analogous to the ‘universal machine’ described in my paper on computable numbers. This theoretical possibility is attainable in practice, in all reasonable cases, at worst at the expense of operating slightly slower than a machine specially designed for the purpose in question. Thus, although the brain may in fact operate by changing its neuron circuits by the growth of axons and dendrites, we could nevertheless make a model, within the ace, in which this possibility was allowed for, but in which the actual construction of the ace did not alter, but only the remembered data, describing the mode of behaviour applicable at any time. I feel that you would be well advised to take advantage of this principle, and do your experiments on the ace, instead of building a special machine.

Enlarging in his talk upon the favourite example of chess-playing, Alan claimed that

It would probably be quite easy to find instruction tables which would enable the ace to win against an average player. Indeed Shannon of Bell Telephone Laboratories tells me that he has won games playing by rule of thumb; the skill of his opponents is not stated.

This was probably a misunderstanding. Shannon had been thinking about mechanising chess-playing, since about 1945, by a minimax strategy requiring the ‘backing up’ of search trees – the same basic idea as Alan and Jack Good had formalised in 1941. But he had not claimed to have produced a winning program. In any case, however, Alan

would not consider such a victory very significant. What we want is a machine that can learn from experience. The possibility of letting the machine alter its own instructions provides the mechanism for this, but this of course does not get us very far.

Alan next turned a little aside from this central idea in order to consider the objection to the idea of machine ‘intelligence’ that was raised by the existence of problems insoluble by a mechanical process – by the discovery of Computable Numbers, in fact. In the ‘ordinal logics’ he had invested the business of seeing the truth of an unprovable assertion, with the psychological significance of ‘intuition’. But this was not the view that he put forward now. Indeed, his comments verged on saying that such problems were irrelevant to the question of ‘intelligence’. He did not probe far into the significance of Gödel’s theorem and his own result, but instead cut the Gordian knot:

I would say that fair play must be given to the machine. Instead of it sometimes giving no answer we could arrange that it gives occasional wrong answers. But the human mathematician would likewise make blunders when trying out new techniques. It is easy for us to regard these blunders as not counting and give him another chance, but the machine would probably be allowed no mercy. In other words then, if a machine is expected to be infallible, it cannot also be intelligent. There are several theorems which say almost exactly that. But these theorems say nothing about how much intelligence may be displayed if a machine makes no pretence at infallibility.

This was very true. Gödel’s theorem and his own result were concerned with the machine as a sort of papal authority, infallible rather than intelligent. But his real point lay in the imitation principle, couched in traditional British terms of ‘fair play for machines’, when it came to ‘testing their IQ’, a point which brought him back to the idea of mechanical learning by experience:

A human mathematician has always undergone an extensive training. This training may be regarded as not unlike putting instruction tables into a machine. One must therefore not expect a machine to do a very great deal of building up of instruction tables on its own. No man adds very much to the body of knowledge. Why should we expect more of a machine? Putting the same point differently, the machine must be allowed to have contact with human beings in order that it may adapt itself to their standards. The game of chess may perhaps be rather suitable for this purpose, as the moves of the opponent will automatically provide this contact.

At the end of this talk there was a moment of stunned incredulity, during which his audience looked round with disbelief. This was probably much to Alan’s delight. He knew perfectly well that he was upsetting the conventional armistice between science and religion, and it was all the more grist to his mill. He had thought it all out since reading Eddington while in the sixth form, and he was not now going to toe this official line that separated the ‘unconscious automatic machine’ from the ‘higher realms of the intellect’. There was no such line – that was his thesis.

At heart it was the same problem of mind and matter that Eddington had tried to rescue for the side of the angels by invoking the Heisenberg Uncertainty Principle. But there was a difference. Eddington had addressed himself to the determinism of physical law, in order to deal with the kind of Victorian scientific world-picture that Samuel Butler had parodied in Erewhon:

If it be urged that the action of the potato is chemical and mechanical only, and that it is due to the chemical and mechanical effects of light and heat, the answer would seem to lie in an enquiry whether every sensation is not chemical and mechanical in its operation? …Whether there be not a molecular action of thought, whence a dynamical theory of the passions shall be deducible? Whether strictly speaking we should not ask what kinds of levers a man is made of rather than what is his temperament? How are they balanced? How much of such and such will it take to weigh them down so as to make him do so and so?

It was a picture drawn from nineteenth century physics, chemistry and biology. But the Turing challenge was on a different level of deterministic description, that of the abstract logical machine, as he had defined it. There was another difference. Victorians like Butler, Shaw and Carpenter had concerned themselves with identifying a soul, a spirit or life force. Alan Turing was talking about ‘intelligence’.

Alan did not define what he meant by this word, but the chess-playing paradigm, to which he constantly returned, would make it the faculty of working out how to achieve some goal, and the reference to IQ tests would indicate some measurable kind of performance of this skill. Coming from Bletchley, this kind of ‘intelligence’ was of burning and obvious significance. Intelligence had won the war. They had solved countless chess problems, and had beaten the Germans at the game. And more broadly, for his scientific generation, life had been a battle for ‘intelligence’, fought against stupid out-of-date schools, a stupid economic system, and stupid Blimps from ‘a profession for fools’ during the war – not to mention the Nazis, who had elevated stupidity into a religion. There was the influence of a Webbsian vision of socialism, in which society was going to be administered by intelligent functionaries of the state, as in the near future of Back to Methuselah, and in 1947 there was much talk about IQ tests, since the British youth was supposedly being newly divided into scientifically defined categories according to ‘intelligence’ rather than by class. Oscar Wilde had written of The Soul of Man under Socialism, but under the socialism of Attlee and Bevin words like ‘soul’ – supernatural or ‘soupy’ words as Bertrand Russell called them – could be left to bishops and pep talks about team spirit.

While many people might have reservations about the wisdom and beneficence of scientists, they were at last basking in the favour of government. The war had converted government to an interest in science, and a view once visionary, then progressive, was becoming orthodox. The scientists had emerged from the miserly corners in which they had done their despised ‘stinks’ before, and it seemed that their swords could be turned into ploughshares, or more precisely, that they would supply governments with scientific solutions to their problems. On one level Alan Turing belonged to this climate of opinion, and certainly rejected the idea that scientists, rather than generals and politicians, were to blame for the world’s current imperfections. Mermagen from Sherborne days, now a master at Radley, another public school, wrote to Alan at this time for advice about the place of mathematics and science in the post-war world, and Alan replied:41

On the subject of careers for mathematicians I am strongly inclined to think that the effect of ACE, guided projectiles, etc, etc, will be towards a considerably greater demand for mathematicians from a certain level upwards. For instance I am in need of a number who will be required to convert problems into a form which can be understood by the machine. The critical level may be described roughly as the degree of intelligence shown by the machine. We obviously do not want people who can take no responsibility at all. We just make the machine do the work which might have been given to them.· At present of course this critical level is very low and I am sure you need not be afraid of encouraging boys that are keen and want to take up a mathematical career. The worst danger is probably an anti-scientific reaction (Scientists instead of goats at Bikini etc) but this is a digression.*

But what was the intelligence for? – that was the unasked question. What was the goal towards which the technicians and managers were now working? There was a vacuum at the centre in 1947, as the convictions of the 1930s and the enforced unity of the war, evaporated away. The great opponent in the chess game had been beaten, and no one had yet taken his place.

By speaking of the mind in terms of puzzle-solving intelligence, of finding efficient means for undiscussed ends, Alan Turing superficially epitomised the technocratic outlook of 1947 social management. But it was only on the surface. For he had no interest in applying computers or related ‘Wellsian developments’ to the problems of society. He had wisely put examples of the usefulness of the computer into his report, to get it paid for. But his picture of the imagined installation simply copied what he had seen in operation at Bletchley. He knew it could be done, but had little interest in it nor indeed the ability to organise this side of it himself. The ACE would need a Travis to keep it going. Even in this letter, superficially about the usefulness of mathematics, his interest lay in comparing the intelligence of the planned computer with that of boys – a favourite comparison, in fact. His whole enterprise was still motivated by a fascination with knowledge itself, in this case with an understanding of the magic of the human mind. He was not a Babbage, with an interest in the more efficient division of labour. His interest in the ACE had little to do with the ‘mechanization, rationalization, modernization’ that Orwell foresaw, although the computer might be funded for this purpose. It was much closer to an undiminished wonder at ‘the glory and beauty of Nature’, and an almost erotic longing to encompass it. Indeed his letter to W.R. Ashby had stated baldly that

In working on the ACE I am more interested in the possibility of producing models of the action of the brain than in the practical applications to computing.

If, furthermore, he had left something out by confining his account of mind to a discussion of puzzle-solving, an omission that reflected the temper of the times, this was not because he thought that this kind of ‘intelligence’ was one of vast superiority to other human characteristics. In fact it was almost the reverse.

Perhaps this was the most surprising thing about Alan Turing. Despite all he had done in the war, and all the struggles with stupidity, he still did not think of intellectuals or scientists as forming a superior class. The intelligent machine, taking over the role of the ‘masters’, would be a development which would cut the intellectual expert down to size. As Victorian technology had mechanised the work of the artisans, the computer of the future would automate the trade of intelligent thinking. The craft jealousy displayed by human experts only delighted him. In this way he was an anti-technocrat, subversively diminishing the authority of the new priests and magicians of the world. He wanted to make intellectuals into ordinary people. This was not at all calculated to please Sir Charles Darwin.

Alan’s talk was, as it happened, given on the same day that the British government announced its rapid withdrawal from India. The lessons of the war were at last sinking in, accentuated by the fuel crisis which the new management of the National Coal Board were powerless to control. Britain was no longer one of the ‘Big Three’, her role in the Mediterranean being quickly taken by the United States. It was a moment of truth, in which Britain appeared as a giant desert island. Germany had forced the truly Big Two out of an artificial isolation, and neither of them had fought to preserve British interests or markets. If there was a silver lining in the clouds, it was the fond belief that Britain could do better than ‘the American tradition of solving one’s difficulties by means of much equipment rather than by thought,’ in Alan’s words.

The British government was well-disposed to finding scientific solutions to its problems, and had announced on 5 February a grand plan to plant its East African colonies with groundnuts. The ACE, likewise, though it represented only a fraction of the investment in the groundout scheme, was still in 1947 a highly progressive project. It was just what the left-wing pressure groups had called for in the 1930s, with the state taking over the development of new science and technology instead of leaving it to the caprice of commerce. Blackett, as president of the Association of Scientific Workers, was at the vanguard of this movement. In 1947 he wrote an introduction to the ASW book Science and the Nation, which promised such modern wonders as ‘the scientific organisation of bureaucracy’. Yet the application in peacetime of such scientific policies was liable to go in unforeseen directions. Blackett himself, by enticing F.C. Williams to work on a pure-mathematical computer at Manchester, had not exactly helped the national plan. And although a left-wing advocate of planning, he had shown considerable personal dash and enterprise. Darwin’s position was more paradoxical still. Whether for hereditary or other reasons, he held the right-wing views of a Social Darwinist, taking a dim view of the welfare state.42(’The policy of paying most attention to the inferior types is the most inefficient way possible of achieving the perfectibility of the human race.’) His recipe for progress, or rather for a check to what he considered to be European racial suicide, was that men who had been ‘promoted’ should endeavour to have more children than others. Yet the dispensations of the NPL resembled less the jungle of cut-and-thrust competition than the ham-fisted management of the Soviet Union. They did not create an environment in which variety and initiative could long survive.

In the spring of 1947, while Darwin applied the higher realms of his thought to solving the problem of Alan Turing, incoherent initiatives were taken by more impatient people on the lower rungs of the promotion scale. One of these was Harry Huskey, who was very eager to see a start made on building a computer before his year was out. He admired the general form of the ACE design, but believed that the best plan would be to construct a small delay line machine ‘on a plan which is a compromise between the NPL and the Moore School plans.’ Relations between Alan and Huskey had been cool from the start, but they deteriorated when one day in the spring, Alan went into Mike Woodger’s room to find him engaged upon writing a program headed ‘Version H’. This was in fact an adaptation by Huskey of the Version V of the ACE, trimmed to include only the barest minimum of apparatus required to do a useful job, which was defined as the solution of eight simultaneous equations.^* Though generally consistent with the ACE design philosophy, such a departure necessarily subverted Alan’s control of the project. He had tolerated the ‘pilot’ policy on the understanding that the pilot would not detract from the full machine, but would become an integral part of it. If Huskey’s project failed, it would be a waste of time, and if it succeeded, it would lead to a marked change of plan. Naturally, Alan boycotted the development. Somehow Harry Huskey managed to scrape together enough equipment to make a start. His official role was ‘on the apparatus side’, and he was better at the form-filling; furthermore he did not need to think in terms of building the grand ACE installation, but only in terms of an experimental set-up. Jim Wilkinson and Mike Woodger joined in. Life in the Mathematics Division became very complicated, but they did learn something about electronics for the first time.

At the same time, Alan managed to make a few experiments of his own in the cellar of Teddington Hall, the Mathematics Division building, and explained some electronics to Mike Woodger. He had devised circuits to transmit and receive pulses along a delay line, and a system to probe the circuit so as to examine the shape of the pulse on an oscilloscope. The NPL had nothing in the way of a machine to do this elementary engineering task, so, as at Hanslope, he had made one for himself. The whole thing 43involved mounting four or five valves on a breadboard, and no more. He had no delay line to work with. A little later, coming back from lunch, he spotted a drainpipe lying in the long grass, and had someone help carry it back for him to try out as an air delay line. Don Bayley and ‘Jumbo’ Lee came and saw this ‘dog’s breakfast’ of an outfit in March or April 1947. Alan took Don for a walk round the grounds and complained bitterly of how he had been thwarted. Alister Watson, philosopher now turned radar expert, visited the NPL on business and heard Alan complain that ‘they say I don’t understand magnetism!’ Francis Price from Princeton days, whose family lived at Teddington, heard out his acrid comments on how the administration denied him the most standard pieces of equipment for experiment.^*

But these anarchic developments were overtaken by Darwin’s decision. He had become reconciled to the fact it would not be possible now, as it might have been during the war, to farm out the ACE to other organisations. Hitherto he had resisted setting up an electronics section within the NPL. But now it had become clear that there would be no single national computer, as had been expected in 1946, but various installations of which the NPL, if it was lucky, would have just one. His new plan was for a prototype to be constructed at the NPL, whereupon it would go to English Electric.

This was a sound policy. The tenuous link with Wilkes was formally snapped on 10 April, and the Post Office contract cancelled. Instead, during the summer of 1947, a new Electronics section of the Radio Division was set up, under a certain H.A. Thomas.

But these were two drawbacks to the new policy. The first was that Thomas’s interest lay in the industrial application of electronics, and not in computers. The second was that he had little knowledge of the use of electronics for pulse or digital techniques. It was not that he refused to make any concession at all to the ACE project, for indeed he very quickly produced a report (with which Womersley was ‘in full agreement’) on how a computer should be built. But this made little reference to the Turing scheme. Then Thomas imported some enormous cathode ray tubes from Germany. He intended them for use as digital display tubes. The staff from the ACE section dutifully went and stared at these, but with some amazement, for they seemed completely irrelevant to the plans for the computer.

It was a curious sequence of events, in which the NPL administration had done everything possible to avoid ‘building a brain’. They had chased after Williams, although it would mean a complete redesign to use the kind of storage he was developing. They contemplated handing the construction to Wilkes, when he had only ‘a mechanic and a boy’ and incompatible design principles. They paid for Huskey to come over from America because of his experience ‘on the apparatus side’, and then failed to use it. Finally they had appointed, as the head of an electronics section, a man without motivation or experience for the job in hand. The one person whom they had not trusted was Alan Turing. The one policy they had not adopted was that of finding or training engineers to effect the proposals to which they had agreed in 1946. It was certainly not easy to find such expertise, but ultimately, they had not really tried.*

After this happened, Alan withdrew. The programming work continued, and they went a long way with subroutines for floating-point arithmetic, including matrices and the numerical solution of differential equations. But Alan had lost interest in this work, although he spent time on what he called ‘abbreviated code instructions’. These took up the ideas announced in his original report, of having the computer expand its own programs. They made, in effect, a high level language for the computer, long before such things were developed elsewhere. But he was thinking more about the even higher level that he had announced in February, that of making a computer show intelligence. In this respect there was nothing to be gained by working at the NPL. Darwin and Womersley concurred in this opinion, and on 23 July Darwin wrote to the DSIR that since the ace had now reached the stage of ‘ironmongery’, it would be best if its designer were to ‘go off for a spell’. The separation of brain from hand could not have been made more explicit. It was agreed that Alan should spend a year at King’s to develop his theoretical ideas. It was too early in his Civil Service career for this to be a normal ‘sabbatical year’, but the DSIR and the Treasury were persuaded to treat him as a special case.

Monday 18 August 1947 was declared to be the official start to the building of the ACE. Darwin presided over a special morning meeting carefully calculated to impress upon the lowly engineers the privilege they enjoyed in working for Womersley’s project. There was much brave talk of taking on the Americans, and then Thomas ‘indicated the way in which he was about to approach the project in its initial stages’. Alan attended, but said nothing.

Womersley, reporting to Darwin that the ACE should be complete by early 1950, was satisfied. In theory the ACE was still a venture of immense national importance, and Hiscocks had called this its ‘D-Day’. The truth, however, was that the NPL had now almost succeeded in cutting the ACE down to its own bureaucratic size. Only Alan Turing prevented the triumph being complete, awkwardly remaining to voice the original vision. On 30 August he wrote to Darwin that 44

A letter has come from Ministry of Supply …asking us to do their programming for them. This is work that we ought to be able to undertake, but it will not be possible with our present very small programming staff. This staff is quite inadequate for our own needs; it will have to be at least three times greater than it has been up to now, if we are to make a success of the ace project. The arrival of Mr D.W. Davies …will, of course, be of some help, but we need in addition another two or three bright [Scientific Officers] …immediately.

It is essential to recruit the ace planning staff now, because it must be trained and in full production long before the machine itself is available for use. A large body of programming must be completed beforehand, if any serious work is to be done on the machine when it is made.

In 1941 a direct appeal had worked wonders, but by 1947 the war might as well have never been. And talk of ‘planning staff’ for the universal machine was almost as unreal as it would have been in 1936. As it happened, the new recruit, Donald Davies, who came from atomic research, had been studying the abstract universal machine of Computable Numbers, rather annoying Alan by finding mistakes of detail in its construction. Alan had also given a talk on the ACE at the NPL which Rupert Morcom attended. The unhappy fact was that after eleven years there was still nothing but paper plans, a paper machine and paper programs, abstruse and insubstantial as the ‘satisfactory numbers’ he had tried to explain at the Clock House in 1936. He had given his all, and had nothing to show for it but paper. He would give them another chance to create the right conditions. But the wheels of 1939, that once had seemed to be turning in his direction, were now revolving backwards.

In the summer of 1946 Alan had made contact again with James Atkins, who came to visit at Teddington. He had had a very different war, for standing fast as a conscientious objector he had spent four months in prison and then worked in the Friends Ambulance Unit. He asked Alan what he had done, and Alan replied ‘Can’t you guess?’ But James could only guess that it was to do with the atomic bomb. After the passage of nine years, they found that there was nothing that they could truly say or do. When James went, he left something behind, and returning after a few minutes caught Alan sitting in his bed-sitter with a particularly acute look of misery.

Alan had mentioned The Cloven Pine to James, and in early 1947 Fred Clayton himself got in touch again. Alan replied on 30 May

I was very glad to hear from you again, and should very much enjoy teaming up with you again for another sailing holiday.

The best dates for me would be either the beginning of September or the beginning of July. The last year or two I have taken to running rather a lot. This is a form of compensation for not having been good at games at school. The application at present is that I have a Marathon race on August 23 and do not want to upset my training by sailing in August or late July.

In the spring Alan had tried himself out against much stronger competition than that of the local suburban clubs. In the Southern Counties ten-mile championship of 22 February he had done ‘very badly’, but two weeks later at the National ten-mile event had come in sixty-second place out of three hundred runners. The Marathon race to which he referred brought out his endurance training to better advantage, and in fact he would come in fifth place.45 With a time of 2 hours, 46 minutes, 3 seconds he was only thirteen minutes behind the winner. Behind the off-hand words about ‘running rather a lot’, he had taken it very seriously. His letter to Fred continued with an equally off-hand reference to the war:

I heard rumours at B.P. from time to time that you were coming there, and was disappointed that nothing came of it. You didn’t really miss anything.

Alan went to Bosham at the end of June and fixed up a September holiday.

Meanwhile on 3 August Alan’s father died at the age of seventy-three. He had been in poor health for several years. He left £400 more to Alan than to his brother, in compensation for the sum spent on John’s articled clerkship twenty years before. But Alan handed it over to his brother, not thinking this fair.^* He also received his grandfather John Robert Turing’s gold watch. As it happened, Mr Turing died just twelve days before the passing of the British Raj ended that exile world to which he belonged. After his death Mrs Turing spoke little of him, and kept few reminders of his existence. Her own life was far from declining, and a new independence was reflected in the adoption of her second name Sara in preference to Ethel. She had also taken more interest in Alan’s doings, pleased that he was busy on something useful at last. She had sensed the high hopes of 1945, and sympathised with his complaints on how he had been thwarted.

When Mountbatten relinquished British rule to the new Dominions of India and Pakistan, it was a belated victory of the new men. Another case of where the war had obliged the reforms long urged in the 1930s, it also represented the renovation of an independent British role in world affairs. But these were still uncomfortable days, in which the new world order was rapidly becoming apparent. The American loan, negotiated by Keynes before his death in 1946, and supposed to repair the British economy, had largely evaporated thanks to American insistence on making sterling convertible again. After a financial crisis, Dr Dalton withdrew convertibility on 20 August, pepping up the sagging team spirit on the radio: ‘God bless you all and your families. Get all you can of happiness and health and strength out of the sea air and then go all out in a great effort to help your country.’

As usual the servants were being called upon to make up for the crimes and follies of the masters. Alan had probably had enough of this by now. But he and Fred Clayton took the advice regarding sea and fresh air, and had a holiday which recaptured something of the days of August 1939. Alan tended to be rather impatient with his friend’s handling of the boat, trying to explain feedback to him, and swearing mildly. But one day Fred took the helm over to the Isle of Wight, helped by a favourable wind, and all went well except that on the way back they bumped into a buoy and Alan said, without thinking, ‘I really ought to be a bit more careful with buoys.’ Then they both saw the joke and laughed.

But it was no laughing matter. They exchanged their observations on the black market of unofficial truth, Fred contributing comments on the customs prevailing in India, where he had done low-level Japanese code-breaking, and Alan speaking of the war as a sexual desert (‘You didn’t miss anything’) except for the incident while in America. It then transpired that Alan had expected this holiday to hold something for him in that direction, which came as a shock to Fred, who explained that he was going to get married.

Picking up the German threads after the war, Fred had entered into a warm correspondence with the sister of the two boys on whom The Cloven Pine was mainly based. It was she whom Fred intended to marry. It was an odd coincidence that one day, out on the water, Alan caught sight of a passing boat and said Oh, that’s rather awkward, it’s Martin Clarke’s sister, we were engaged.’ Joan recognised Alan, and waved and smiled. (She had seen him a few months before at the LMS lecture.) But they did not meet. Alan told Fred of the broken engagement. Fred was left confused by his rejection of Alan whom, however, he did not find at all attractive. He and Alan talked about their respective decisions, ‘freedom and consistency of mind’ was not so easy for his friend, but Alan was now quite clear as to where he stood.

On 30 September 1947 Alan resumed his King’s fellowship,* after a break of just under eight years from 2 October 1939. Because of the 1944 renewal, it was set to run until 13 March 1952. He was thirty-five, but could have, for not wearing a gown after dark. He had been taken for an undergraduate, and his youthfulness surely accentuated what was something of a return to the life of the past. In certain ways, of course, Cambridge had changed. Most students were in their mid-twenties, and had arrived after some years of service life rather than with the artificial immaturity of public schools. It was a more personally ambitious, less politically conscious Cambridge than that of the 1930s. But no one spoke of the war, which was fading like a dream, and it would take more than the war to change the special character of Kings.

One friend immediately stood out from the rest. Robin Gandy had taken Part III of the Mathematical Tripos that summer, and was now working in theoretical physics towards a fellowship. Soon after term began, Robin called on Alan and asked if he could borrow his copy of Eisenhart’s book on continuous groups. Alan took it off the shelf, and out fluttered a newspaper picture of a rank of pageboys at Princess Elizabeth’s wedding. There was someone else in the room, probably Robin’s physicist friend Keith Roberts, and Alan only said darkly ‘You’ll find nice pages like that in my books.’ But next morning, Alan said to him, ‘We know each other quite well now …I might as well tell you that I am a homosexual.’ Robin’s own personality was different, but he was someone who like Alan cared that (as Carpenter had put it)46

men shall learn to accept one another simply and without complaint …honour the free immeasurable gift of their own personality, delight in it and bask in it without false shames and affectations.

and he was pleased that Alan had chosen to tell him. It was very different from the sticky moment with Don Bayley. Robin was rather surprised that Alan was so forthright, for if obliged to give an opinion at Hanslope, he would have said that Alan did seem to be more drawn towards men, but that he was probably too shy and inhibited to do anything about it. The truth made Alan less austere and more fun. Alan in turn was very pleased that Robin should understand him so well, and with that out of the way, there was nothing (except Bletchley Park) that they could not talk about, whether of science or gossip.

He was altogether more confident with people than he had been before the war, and was elected to George Rylands’ play-reading Ten Club, which he would have found frighteningly precious and pretentious then. He was not elected to the Apostles. Robin was an Apostle, and would have proposed him, except that at that point they were choosing only rather younger candidates. He did, however, become rather better connected with the King’s social network, and Robin was particularly helpful in opening up his life to more communication, compensating for some of the fraught years of silent, frustrated desire. ‘When I recall some past epoch,’ Alan said in reply to some question about the past from Norman Routledge, a new acquaintance of this year, ‘I think of whoever I was in love with at the time.’

The winter was spent on various topics, none with all-absorbing attention. The numerical analysis paper 47 – the only published evidence of his ACE work – was finished in November. Most of all he wanted to understand more about ‘thinking’. Somehow the brain did it – but how? Contemporary physiologists had only the faintest ideas about neural stimuli and responses. He went to R.H. Adrian’s lectures, but was disappointed. Chemistry and physics were at last pushing their way into biology, but his whole thesis lay in a different kind of description, the logical description of the nervous system, for which chemistry and physics were only the medium. He conveyed his disappointment to Peter Matthews, a very sharp undergraduate, one of the few who had come to Cambridge at eighteen, with whom he went to the physiology lectures. They would talk long over lunch and over mugs of cocoa in the evenings, since they lived on the same staircase.

Jim Wilkinson would visit Cambridge from time to time, and kept Alan informed as to the developments, or lack of them, back at Teddington. The news was that of cuts, crises, and an ever-narrowing vision. At a meeting in November, they had abandoned many of the advanced ideas for the ACE, including the ‘abbreviated code instructions’. An edict from Darwin had stopped Huskey’s Test Assembly, because of complaints from Thomas. The ACE section was reduced to the writing of a report⁴⁸ on their numerical analysis and programming work.

In the new year of 1948, an alternative possibility came into being for Alan’s future. For if the NPL project had ground to a sticky halt, the Manchester development had bounded along with great speed. By the end of 1947 Williams had stored 2048 digits on an ordinary cathode ray tube screen, which was at least the equivalent of having a cheap, working delay line available. Newman still had his Royal Society grant virtually intact, and mooted the idea that Alan should take an appointment at Manchester to direct the computer construction there instead. Alan did not decide immediately, but in March Newman asked his university⁴⁹ to create a new position, with a salary paid from the computer fund, but with the status of Reader.^*

The prospect of getting his hands on a computer after all was very attractive. But so was life at Cambridge, the nearest he had to a home. He joined the Moral Science Club again, and gave them a talk⁵⁰ on ‘Problems of Robots’ on 22 January. (That Czech word ‘robot’ had a topical flavour.) He joined the Hare and Hounds Club, and continued his training, often running to Ely and back in the afternoon. He tried some von Neumann game theory, and rather laboriously worked out a strategy for a simplified version of poker, slightly improving upon the account given by von Neumann,51 and also for the Princeton game of Psychology. Robin was moving away from theoretical physics and into the philosophy of physics, and there were many discussions with him and his friend Keith Roberts. Once they had tried to set up a purely operational definition of Special Relativity, and when one of them objected that there was no such thing as a rigid body in relativity, Alan said, ‘Well, let’s call them squeegees’ It was that pleasant, unpompous way of being serious without being solemn that in 1948 was far from widespread in academic life, and was associated with the legacy of the Apostles and the King’s milieu – though it came naturally to Alan. There was another nice occasion when Don Bayley came for the weekend to see Alan and Robin, to be greeted with a toy steam engine that Alan had bought at Woolworths. ‘I always lusted after things like this as a boy,’ he said ruefully, ‘but didn’t have enough pocket money for them. Now I have got enough money, I might as well have it.’ They played with it for the afternoon.

Alan had told Robin that ‘Sometimes you’re sitting talking to someone and you know that in three quarters of an hour you will either be having a marvellous night or you will be kicked out of the room.’ It was not always like that, for the innocent Peter Matthews’ cocoa sessions did not involve this stark dichotomy. Nor was Alan accomplished in the necessary social game of words and eye-contact; he was too shy and brusque and lacking in confidence in his looks. Cambridge did inspire him with greater interest in his appearance, and sometimes he would show Robin a photograph of himself at sixteen and say how handsome he looked then. He was certainly not attractive in the Aryan-Brylcreem style of the 1940s. To the fastidious, his open-necked, shabby, breathless immediacy came as messy and coarse, though there were redeeming features; he could put on a roguish charm which reminded people of his Irish ancestry, and besides his piercing blue eyes he had thick, luxuriant eyelashes and a soft-contoured nose. But whatever his doubts and disadvantages he would pace round the courts of King’s and invite young men in for tea. Sometimes he struck lucky. In April 1948 he struck very lucky indeed, for Neville Johnson stayed for tea, and stayed many times.

Neville was a third-year mathematics student, then twenty-four, but mathematics was not a cement but an embarrassment in their relationship, for although Neville had won a scholarship, this was ‘a flash in the pan’. It made Neville feel inferior that they were in this respect on quite different planes. Once Alan said, ‘When you know what the Entscheidungs problem is, you will know what a great mathematician I am,’ with a sad twinkle, but Neville never did find out. Neville thought he was very ordinary compared with the more glamorous side of King’s, and that he was just ‘the best that Alan could get’.

But for Alan, it was probably an attraction that Neville, a Geordie from Sunderland Grammar School and the Army, was someone down to earth and rather tough. His problem lay far more in having to remove the anaesthetising shell with which he had protected himself for so long. Perhaps it was too late. To Neville, it seemed that Alan had enjoyed ill luck with people, and that it was not surprising that he was keen on machines to replace them. Once he said to Neville, lying on his bed, ‘I have more contact with this bed, than with other people.’ He also unburied a little of the past. Christopher still prodded him, if only because he would faint at the mention of blood or dissections in the physiology lectures; but in 1948 he was ‘A very upper-class boy, from where they dressed for dinner.’ Of Bletchley he revealed that the Poles had brought something crucial – but that he must not say more. Once he pointed out a professor of Greek in the street and said he had done something marvellous there.

They were often together, and sometimes with Alan’s friends, although Neville then felt rather out of place. Neville joined in the game of poker that they determinedly played in order to test out Alan’s minimax strategy. (It was not very exciting, as the strategy was largely the obvious one anyway.) It was another ordinary affair, at last, as it had been with James Atkins in the pre-war days.

This solved one problem. In other ways, Alan was back to the difficulties of 1939. For his mind still straddled mathematics, engineering and philosophy in a way that the academic structure could not accommodate. Temporarily the war had resolved his frustration, giving him something to do that was intellectually satisfying, yet which actually worked. But that was over now, and instead of being drawn in, he was being pushed out.

How was he to continue, having won the war, and lost the peace? If he did not return to the NPL then the Entscheidungs problem lay between Cambridge and Manchester. He could stay at King’s, and a lectureship ought to come his way. He could return to the world of Hilbert and Hardy, as though the last nine years had never been. Yet no more than in 1939, was that the way his spirit moved. He did not want to go backwards, and he still wanted to grasp the computer that he had invented. At Cambridge, the computer was firmly in the grasp of M. V. Wilkes, and Alan was far, far too proud to go cap in hand to use it. If he wanted a computer, it meant going to Manchester.

Darwin, meanwhile, expected him back at the NPL at the end of the Cambridge term. On 20 April 1948 he reported to the Executive Committee on ‘Future Plans for Dr Turing’:

Dr Turing, who is on a year’s leave of absence at Cambridge University, will shortly be due to return to the laboratory and Director is proposing to discuss with him what type of work he should then undertake. Director felt that from the point of view of Dr Turing’s career, it would be an advantage if he started to write some papers rather than continue with the fundamental physiological studies into which his researches are carrying him. Dr Turing will no doubt join a University staff in due course, but Director felt that intervening period should be spent at NPL.

Kind though it was of Darwin to think of his career, the fact was that the year’s wait had achieved nothing. Womersley reported to the same meeting that

The present position on this project gives no cause for complacency and we were probably as far advanced 18 months ago. …There are several competitors to the ace machine, and of these, that under construction at Cambridge University, under Professor [sic] Wilkes, will probably be the first in operation.

Coordination and cooperation had long since been replaced by competition. A few days later Womersley reported 52 to Darwin with proposals for the building of the machine, which he held to be ‘of supreme importance …in the fields of scientific research, administration, and national defence’. The proposals included ‘using as much of Wilkes’ development work as is consistent with our own programming system’, and making an approach to F.C. Williams to request a copy of the machine being built at Manchester. In this radical modification, or rather abandonment, of the ACE programme, no attention was paid to the ideas of its originator. The administrators appeared to regard him as an abstract, almost anonymous entity.

Alan was not perhaps entirely free from responsibility for this absence of communication. It was, for instance, rude of him to postpone for a long time a visit to Wilkes at the Mathematical Laboratory in Cambridge – a short walk from King’s across Market Square, but not an easy one. As the time for decision approached, Alan said, ‘I really must go and see Wilkes’, and then put it off, and put it off again until the last minute in late May. By that time the construction of what was to be the EDSAC was in full swing. They were using mercury delay lines, and by good fortune, Gold had moved to Cambridge as a research student and supplied Wilkes with the designs. Instead of trying to work it all out by himself, Wilkes kept ‘religiously’ to Gold’s specifications and got on with building them. He had obtained money from the DSIR, the University Grants Committee, and from J. Lyons and Co. Ltd., reflecting a very early interest on the part of private enterprise. He was in full control, without a Womersley or a Darwin to get in the way, and working much as Alan would have liked to. The barricade between mathematics and engineering never arose. It was enough to show the folly of NPL policy, and jealousy would have been a very natural reaction. Afterwards he meanly said, ‘I couldn’t listen to a word he said. I was just thinking, how exactly like a beetle he looked.’ But duty was done.

A few days later, on 28 May, Alan called in at the NPL. It was the sports day. He conferred with Jim Wilkinson, who explained the whole dismal story. Darwin might well have liked a series of papers going out under the NPL imprimatur, but Jim Wilkinson agreed that there was nothing in it for Alan. He also thought Alan should stay at Cambridge and return to pure mathematics. He foresaw problems at Manchester.

Manchester University had indeed agreed to create a position for him, and on 21 May the Royal Society agreed that the salary could be paid out of their grant to Newman. A letter of 26 May, which Alan presumably received just before his NPL visit, informed him of this. It was on 28 May that he wrote accepting the appointment, and resigned from the NPL. It was against the ‘gentleman’s agreement’ of the sabbatical, according to which he was supposed to stay for another two years. He had broken an engagement for a second time. Darwin was extremely annoyed with Blackett and Newman. Humpty Dumpty had had a great fall.

Everyone had been slow to adjust to the realities of the post-war period. In expecting the Post Office to cooperate on the delay lines, Alan had been as unrealistic as any of the administrators. And yet it was still extraordinary that as late as May 1948 there was no sign of any start being made on the construction of the control circuits. This failure could not be laid at Alan’s door: to see that plans were implemented was the job, and indeed the only raison d’être, of the administrators. But perhaps Darwin never really wanted a computer, just as the Admiralty had not really wanted to know where German ships were. The ‘support’ of Travis and the Ministry of Supply had not in fact made any difference to the bureaucratic inertia. Darwin and Womersley had played at being commissars while Alan remained the humbler worker and peasant.

If he had been given his head, the project might well have gone adrift. He probably underestimated the technical difficulty of running pulses at the rate of a million a second, and overestimated his own engineering knowledge. He would have interfered in too much detail, annoying people who would not like being lectured on their own jobs. He would have had no idea of how to pull off a deal for the right equipment, how to flatter someone into doing the job the way he wanted, or how to play off one expert against another. He had no management skills. But he was not given a chance to make a mess of it for himself, as was his right as the creative worker. And basically his approach was on the right lines, for in the end every successful computer project had to solve the problem of integrating ‘mathematical’ and ‘engineering’ skills, which was exactly what he longed to do.

The war had given him a false sense of what was possible. For him, breaking the Enigma was much easier than the problem of dealing with other people, especially with those holding power. During the war his own kind of work had been amplified into something enormously real, but only because other people had done all the work of organising coordination, and because he had Churchill’s personal backing. Now there was nobody to do this for him, the NPL administrators not really having tried. A different person could more easily have compromised, and more effectively have fought on for the success of the project. But with him, it was all or nothing. Like his father, he had resigned from the Civil Service when the system did not work for him. Unlike his father, however, he did not moan afterwards. Indeed, he very rarely referred to his time at the NPL. It became another great blank, to add to all the others.

Despite his resignation, and all the embarrassment that surrounded it, he completed a report 53 for the NPL in July and August 1948. Its almost conversational style reflected the discussions he had pursued, many at Bletchley, in advancing the idea of Intelligent Machinery. Although nominally the work of his sabbatical year, and written for a hard-line technical establishment, it was really a description of the dream of Bletchley Park, and reviewed in an almost nostalgic way the course of his own life rather than contributing to any practical proposals that the NPL might adopt.

Expanding upon the ideas he had publicly announced in February 1947, this time he identified some of the reasons why the concept of ‘intelligent machinery’ might be perceived by such as Darwin as a contradiction in terms:

(a) An unwillingness to admit the possibility that mankind can have any rivals in intellectual power. This occurs as much amongst intellectual people as amongst others: they have more to lose. Those who admit the possibility all agree that its realisation would be very disagreeable. The same situation arises in connection with the possibility of our being superseded by some other animal species. This is almost as disagreeable and its theoretical possibility is indisputable.

(b) A religious belief that any attempt to construct such machine is a sort of Promethean irreverence.

These objections, he wrote, ‘being purely emotional, do not really need to be refuted.’ They were like Bernard Shaw’s complaint against the first Charles Darwin, that his doctrines were ‘discouraging’. The point, however, was not to find comfort, but truth.

He next moved to what he considered a less ‘emotional’, but still erroneous objection:

(c) The very limited character of the machinery which has been used until recent times (e.g. up to 1940). This encouraged the belief that machinery was necessarily limited to extremely straightforward, possibly even to repetitive, jobs. This attitude is very well expressed by Dorothy Sayers (The Mind of the Maker, p. 46) .. which imagines that God, having created his Universe, has now screwed the cap on His pen, put His feet on the mantelpiece and left the work to get on with itself.’

This, to Dorothy Sayers, made a reductio ad absurdum of determinism. How could Lord Peter Wimsey have been laid up for all time in the motions of the particles at the Creation? To Alan all it showed was that there was no word that expressed the ‘mechanical’ operations of machines with more than trivial logical structure. Dorothy Sayers did not know in 1941 that even the little Enigma machine was sufficiently unpredictable to keep hundreds of people in employment. He was certainly fascinated by the fact that a machine like the Delilah key generator could be perfectly deterministic at one level, while producing something apparently ‘random’ at another. It gave him a model for reconciling determination and free-will. But this did not go very far. It was the capacity of machines to learn that he saw as the crux of the argument. A learning machine would part company altogether with the ‘mere machine’ of common parlance.

The objection from Gödel’s theorem he answered in the same way as he had in 1947, by separating ‘intelligence’ from ‘infallibility’. This time he gave an example of how the intelligent approach could be wrong, and the accurate one stupid:

It is related that the infant Gauss was asked at school to do the addition 15 + 18 + 21 + …+ 54 (or something of the kind) and that he immediately wrote down 483, presumably having calculated it as (15 + 54) (54 – 12)/2.3 …One can …imagine a situation where the children were given a number of additions to do, of which the first 5 were all arithmetic progressions, but the 6th was say 23 + 34 + 45 …+ 100 +112+ 122 …+ 199. Gauss might have given the answer to this as if it were an arithmetic progression, not having noticed that the 9th term was 112 instead of 111. This would be a definite mistake, which the less intelligent children would not have been likely to make.

More pertinent, perhaps, would have been the unmentionable fact that although careless about detail in the cryptanalytic work, he had still been regarded as the brain behind it. Implicitly, this argument appealed to the imitation principle of ‘fair play for machines’. This also lay behind his answer to a fifth objection, that

(e) In so far as a machine can show intelligence this is to be regarded as nothing but a reflection of the intelligence of its creator.

This he described as

similar to the view that the credit for the discoveries of a pupil should be given to his teacher. In such a case the teacher would be pleased with the success of his methods of education, but would not claim the results themselves unless he had actually communicated them to his pupil. He would certainly have envisaged in very broad outline the sort of thing his pupil might be expected to do, but would not expect to foresee any sort of detail. It is already possible to produce machines where this sort of situation arises in a small degree. One can produce ‘paper machines’ for playing chess. Playing against such a machine gives a definite feeling that one is pitting one’s wits against something alive.

This idea of teaching a machine to improve its behaviour into ‘intelligence’ was the key to most of the positive proposals of this essay. This time he would be putting the imitation principle to a constructive use. The real point of this paper was that he was beginning to think seriously about the nature of human intelligence, and how it resembled, or differed, from that of a computer. More and more clearly as time went on, the computer became the medium for his thought, not about mathematics, but about himself and other people.

He could see two possible lines of development. There was the ‘instruction note’ view, according to which better and better programs would be written, allowing the machine to take more and more over for itself. He thought this should be done. But his dominant interest now lay in the ‘states of mind’ approach to ‘building a brain’. His guiding idea was that ‘the brain must do it somehow’, and that it had not become capable of thought by virtue of some higher being writing programs for it. There must be a way in which a machine could learn for itself, according to this line of argument, just as the brain did. He explained his view that ‘intelligence’ had not been wired into the brain at birth, in a passage showing the influence of his recent research into physiology and psychology:

Many parts of a man’s brain are definite nerve circuits required for quite definite purposes. Examples of these are the ‘centres’ which control respiration, sneezing, following moving objects with the eyes, etc: all the reflexes proper (not ‘conditioned’) are due to the activities of these definite structures in the brain. Likewise the apparatus for the more elementary analysis of shapes and sounds probably comes into this category. But the more intellectual activities of the brain are too varied to be managed on this basis. The difference between the languages spoken on the two sides of the Channel is not due to differences in development of the French-speaking and English-speaking parts of the brain. It is due to the linguistic parts having been subjected to different training. We believe then that there are large parts of the brain, chiefly in the cortex, whose function is largely indeterminate. In the infant these parts do not have much effect: the effect they have is uncoordinated. In the adult they have great and purposive effect: the form of this effect depends on the training in childhood. A large remnant of the random behaviour of infancy remains in the adult.

All this suggests that the cortex of the infant is an unorganised machine, which can be organised by suitable interfering training. The organising might result in the modification of the machine into a universal machine or something like it.

Although expressed in more modern terms, reflecting the great debate between the protagonists of nature and nurture, this was little more than could have come from Natural Wonders, with its little homilies on the virtues of training the brain in childhood, and how languages and other skills could be best incorporated in the ‘remembering place’ while the brain was still receptive.

According to this view, therefore, it would be possible to start with an ‘unorganised’ machine, which he thought of as made up in a rather random way from neuron-like components, and then ‘teach’ it how to behave:

…by applying appropriate interference, mimicking education, we should hope to modify the machine until it could be relied on to produce definite reactions to certain commands.

The education that he had in mind was of the public school variety, by the carrot and stick that the Conservative party was currently accusing Attlee of taking away from the British donkey worker:

…The training of the human child depends largely on a system of rewards and punishments, and this suggests that it ought to be possible to carry through the organising with only two interfering inputs, one for ‘pleasure’ or ‘reward’ (R) and the other for ‘pain’ or ‘punishment’ (P). One can devise a large number of such ‘pleasure-pain’ systems. …Pleasure interference has a tendency to fix the character, i.e. towards preventing it changing, whereas pain stimuli tend to disrupt the character, causing features which had become fixed to change, or to become again subject to random variation. …It is intended that pain stimuli occur when the machine’s behaviour is wrong, pleasure stimuli when it is particularly right. With appropriate stimuli on these lines, judiciously operated by the ‘teacher’, one may hope that the ‘character’ will converge towards the one desired, i.e. that wrong behaviour will tend to become rare.

If the object were simply to produce a universal machine, it would be better to design and build it directly. The point, however, was that the machine thus educated would not only acquire the capacity to carry out complicated instructions, which Alan described as like a person who ‘would have no common sense, and would obey the most ridiculous orders unflinchingly’. It would not only be able to do its duty, but would have that elusive ‘initiative’ that characterised intelligence. Nowell Smith, worrying about the development of independence of character within a system of mere routine, could not better have formulated the problem:

If the untrained infant’s mind is to become an intelligent one, it must acquire both discipline and initiative. So far we have been considering only discipline. To convert a brain or machine into a universal machine is the extremest form of discipline. Without something of this kind one cannot set up proper communication. But discipline is certainly not enough in itself to produce intelligence. That which is required in addition we call initiative. This statement will have to serve as a definition. Our task is to discover the nature of this residue as it occurs in man, and to try and copy it in machines.

Alan would have liked the idea of training a boy machine to take the initiative. He did work out an example of modifying a ‘paper machine’ into a universal machine by these means, but decided it was a ‘cheat’, because his method amounted to working out the exact internal structure, the ‘character’ of the machine, and then correcting it – more like codebreaking than teaching.

It was all very laborious on paper, and he was eager to take the next step:

I feel that more should be done on these lines. I would like to investigate other types of unorganised machine, and also to try out organising methods that would be more nearly analogous to our ‘methods of education’. I made a start on the latter but found the work altogether too laborious at present. When some electronic machines are in actual operation I hope that they will make this more feasible. It should be easy to make a model of any particular machine that one wishes to work on within such a [computer]* instead of having to work with a paper machine as at present. If also one decided on quite definite ‘teaching policies’ these could also be programmed into the machine. One would then allow the whole system to run for an appreciable period, and then break in as a kind of ‘inspector of schools’ and see what progress had been made.

It was a happy thought that, like a public school, the machine could grind its way along quite deterministically, but without anyone knowing what was going on inside. They would see only the end products. There was a distinctly behaviourist flavour to all this talk of pain and pleasure buttons, but his wry use of the word ‘training’, ‘discipline’, ‘character’ and ‘initiative’ showed how this was the behaviourism of Sherborne School.

More precisely, it was the official description of the school process, albeit presented as rather a joke. It bore little relationship to his own mental growth. No one had pressed any pleasure buttons to reward his initiative; precious few pleasure buttons at all, while the pain had been dispensed freely in order to enforce patterns of behaviour that had nothing to do with intellectual advance. The only hint of contact with his own experience was the remark that discipline was necessary for the sake of communication, for certainly he had to be pushed into conventional communication in order to advance. Yet even there, it had not been jabs of pain and pleasure that had stimulated his willingness to communicate, but the aura – was it pain? was it pleasure? – that surrounded the figure of Christopher Morcom. As Victor Beuttell had often said to him, it was a mystery from where his ‘intelligence’ derived, for no one had been able to teach him mathematics.

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 Bulldozer	Continuous Active
A Telephone	Continuous Controlling
A Brunsviga	Discrete Controlling
A Brain is probably	Continuous Controlling, but is very similar to much discrete machinery
The ENIAC, ace, etc.	Discrete Controlling
A Differential Analyser	Continuous Controlling

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 10¹⁰steps, 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:

Brunsviga	90
ENIAC without cards and with fixed programme	600
ENIAC with cards	∞^*
ACE as proposed	60,000
Manchester machine as actually working (8/7/48)	1,100

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 routine⁵⁵ 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.

The US Air Force had begun its temporary stay on British soil, and Americans were overtaking plucky British losers in the Empire Stadium, where a scraggy, rationed Britain was hosting the Olympic Games.^† Alan went with Anderson, an acquaintance from the Hare and Hounds Club, and they saw the Czech athlete Zatopek win the 10,000 metre race on 30 July. The Marathon was won for Argentina but in a time still only seventeen minutes better than Alan’s. He replied to Jack:

Dear Jack,

I have repeatedly looked in books on neurology for the very important number ν you asked about, and never found any figure offered. My own estimate is 3.10⁸<N<3.10⁹. It is based on the diagram p. 207 of latest Starling which refers to a mouse together with w[eigh]t of average brain (3 lb). …I have asked many phsyiologists myself and got anwers from 10⁷ to 10¹¹.

I’ve had something wrong with my leg for some months, so wasn’t able to run in any Marathons this season.

Yours Prof

An injury to his hip had put paid to his chances for the Olympic marathon team, for which otherwise he might have qualified, and to his regret, prevented any further development in serious long-distance running.

Alan sent off another routine, for factorising numbers, to Manchester on 2 August. Then he went on holiday with Neville in Switzerland. It was the first escape from austerity England, and they could hardly believe the fresh country foods. The trip was made on the travel allowance of £25, in the form of five crisp five-pound notes. They did it by cycling and staying in youth hostels: they trod glaciers and scaled mountains and had the usual smouldering arguments of people on holiday together, as when Alan let his bicycle break down through inattention, or was keen on another young man in the hostel. It was not quite E.M. Forster’s greenwood, but as near as he had ever approached it.

The summer continued with a week in the Lake District at Pigou’s cottage, with Peter Matthews. Pigou was very keen on mountaineering, and even more, with a pre-Carpenter innocence, on Wilfrid Noyce the young mountaineer.* Alan took care to practise rock-climbing on the King’s College gate with Peter Matthews before they went. It was like some 1890s Cambridge reading party, with old Pigou clocking up the times and the victors at chess. He had a collection of First World War medals which, though a pacifist, he had been awarded for ambulance service, and used to award them after a farewell dinner to whoever had done best on the slopes. Alan did some easy climbing, but mostly trotted round Buttermere in short shorts. From Jack Good:

16 Sep 48

Dear Prof,

Pardon the use of the typewriter: I have come to prefer discrete machines to continuous ones.

When I was in Cambridge recently I hunted unsuccessfully …for an estimate …of N, the number of neurons in the human brain. Soon after this Donald succeeded in finding a reference. He tells me that…ν = 10000000000 roughly.

I visited Oxford last week-end. Donald showed me a ‘chess machine’ invented by Shaun [Wylie] and himself. It suffers from the very serious disadvantage that it does not analyse more than one move ahead. I am convinced that such a machine would play a very poor game, however accurately it scored the position with respect to matter and space. In fact it could easily be beaten by playing ‘psychologically’ i.e. by taking into account the main weakness of the machine. …

When in Oxford I succeeded in hypnotising Donald. …Would you agree that a very typical property of the brain is the ability to think in analogies? This means taking only a part of the evidence into account. …Do you know of any reference to Russian electronic computers? …

Donald Michie was now studying physiology at Oxford. He had followed up their Bletchley speculations by teaming up with Shaun Wylie to devise a chess program they called the Machiavelli. Meanwhile Alan and David Champernowne had worked out one they called the Turochamp.56 It followed the minimax system, and the important idea of pursuing chains of captures until no more could be made. It had a scoring system in which pawn mobility, castling, and getting a rook on to the seventh rank were included as well as captures. None of this went much beyond what Alan had discussed back in 1941 with Jack Good, or indeed with Champ in 1944. Going for a walk, probably at Christmas that year, they had made a bet on whether a machine could beat Champ himself at chess by 1957. The odds were put at 13 to 10 in favour of the machine succeeding. The Turochamp certainly did not reach this standard, although it beat his wife, a beginner at chess. It was not taken at all seriously, or written out in detail. But it would have been a system of this kind which gave Alan ‘a sense of pitting one’s wits against something’, as he wrote in Intelligent Machinery. Champ also took on the system for poker that Alan had more carefully worked out, and had the pleasure of beating it by sheer good luck. Alan replied to Jack:

Sept 18 48

Dear Jack,

I am glad to hear my estimate of no. of neurons is not too essentially wrong.

The chess machine designed by Champ and myself is rather on your lines. Unfortunately we made no definite record of what it was, but I am going to write one down definitely in the next few days with a view to playing the Shaun-Michie machine.

To a large extent I agree with you about ‘thinking in analogies’, but I do not think of the brain as ‘searching for analogies’ so much as having analogies forced upon it by its own limitations …

The report was handed in. Mike Woodger was very excited by the prospects it opened up, and gladly drew the diagrams neatly for the typed version. Darwin was less impressed, probably highly embarrassed by the references to Dorothy Sayers, God, and robots taking country walks. At the Executive Committee meeting on 28 September he explained sniffily that ‘Dr Turing had now produced a report which, although not suitable for publication, demonstrated that during his stay there he had been engaged in rather fundamental studies.’ The unsuitable paper disappeared into the NPL files. Ironically, it was on 20 September 1948 that von Neumann gave a first published lecture⁵⁷ on the ‘theory of automata’ – in effect, the theory of discrete controlling machines – in which he drew attention, after eleven years, to the fundamental importance of the Universal Turing Machine.

Robin had rented Blackett’s holiday home in Wales on occasion, and did so again this year. By inviting Alan, he made possible a third holiday before the summer was out. Another of the party was Nicholas Furbank, the friend of E.M. Forster, who had lately been writing a book on Samuel Butler. This too was rather like an old-style Cambridge reading party – they were amused by the resemblance – with organised walks, and funny nicknames, and reading Thomas Love Peacock’s gothic Melincourt aloud.

Alan seemed very happy. They played rationalist Twenty Questions as they filed along the hill paths and old railway tunnels. Alan developed a theory of how to choose the next question so as to maximise the expected weight of evidence of the answer. He also recounted quaint tales of the Pigou regime, whose antiquated brand of hearty male misogyny left him bemused. ‘The standard at the Pigou cottage is very high,’ he said, ‘I ran all round Buttermere faster than Noel-Baker in ‘28, and I only got a bronze.’ One day they took a taxi and a bus at dawn for an expedition to the real mountain slopes of the Snowdon horseshoe, where Nick Furbank was suitably terrified and went on all fours along the narrow ridge of Cribgoch, but Alan strode on in dogged Turing fashion, as twenty years before, but with friends at last.

Down from the mountain tops, it was time to pack up. The suitcase with the parts for the zeta-function machine was still in his room, along with the star globe and Christopher’s picture. He kept as souvenirs some of the gear wheels that had been cut, but gave the rest to Peter Matthews to sell for scrap. Alan was rather disappointed with the price they fetched.

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 293.

^† A typical circumlocution necessary for ‘the computer’.

^* The work done at RCA on the ‘Iconoscope’ 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.’

^* 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 275..

^* 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, and indeed no machine called edvac was ever actually built.

^* 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.