Alan Turing: The Enigma (70 page)

^*
Indeed the second Waugh, in 1945, had largely revisited the semi-platonic sentimentality of the first.

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 notes
²
, 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.