Alan Turing: The Enigma (69 page)

Orwell escaped from the dichotomy by appealing to an England of ‘ordinary, decent’ people. Alan Turing might have liked to do the same, but he was now hopelessly saddled with a mind full of extraordinary, indecent contradictions. It contained the greatest development of ‘mechanization, rationalization, modernization’ of the war, and another which was the greatest ever conceived, while still longing for ‘the commonest in nature’, and while still being precisely what Orwell meant by a ‘sex maniac’. He could not avoid these things, and having surrendered half of his mind to the government, was not free to try. He had done something, in a way that Orwell had not, and had passed the point of no return.

The paradox was not his alone, although his life took it to a peculiar
intensity. The war had dealt a sharp blow to ‘fixed moral codes’, with social changes accelerated, old authorities questioned and new talents employed. Everyone had been made conscious of the defects of the old system, and more insidiously, of the fact that systems could be changed when survival made it necessary. To the dismay of conservative forces, British society had undergone a second and more thorough shaking up, this time with knowledge and ideas communicated to those excluded from participation in peace – ordinary men, the young, and even women. Bletchley Park had seen this happen as much as anywhere else. It had not been all a story of ‘men of the Professor type’; there had been boys of eighteen, ‘female mathematicians’, and Post Office engineers who had risen from the bottom of the ladder, all playing crucial parts.

In other ways, too, the consciousness of being a community, sharing a very limited common wealth, had brought people closer to the ‘least waste of energy’ of Alan Turing, spartan but not joyless. Even at a place such as Hanslope, enmeshed in the technical machinations of the secret service, the pleasures of Mess Nights, mountain-walking holidays, mushroom-cooking, games and self-education had taken on that enhanced value that Carpenter had rather laboriously tried to explain as ‘the Simplification of Life’.

There was a new spirit, and yet it was a spirit within a machine. A much enlarged state apparatus, and the more centralised economy, were the legacy of the great battle for intelligence and coordination. This time it would not be undone. And it was the machine, rather than glimpses of workers’ control, that inspired Ernest Bevin:
³⁴
‘Calculation of profits and all the other things that have cluttered up progress in the past has to go and the great genius of our managers and technicians is being given full play. …’ It was true. Unhindered by wasteful competition and by the false economies of public parsimony, the Government Code and Cypher School and the Post Office had proved capable of managing fantastic feats. Now the development of the electronic computer was being taken over by the National Physical Laboratory for the public good. It deserved two cheers, as Forster would say, two cheers for managerial socialism. But management and techniques had not been the whole story, important as they might be. There had been something else, something now fading away while they waited for the other war to finish.

With Hitler out of the way, the games of Red and White could resume. Attlee replaced Churchill at the Potsdam conference when the results of the British election were known. Alan Turing went to Germany at the same time, in a party made up of five British and six American experts to report on German progress in communications. Flowers was one of the other British members. They left on 15 July, and arrived in Paris on a fine hot day. Here they were to meet the Americans, but the military headquarters had no idea who they were, so they took the day off. Late in the afternoon the telegrams from London came through, and they were assigned to the
military transit camp, a hotel near the Madeleine. The same thing happened next day at Frankfurt when they reported to the American army headquarters in the I.G. Farben building. It was Patton’s area, and they were warned not to continue into Bavaria without permission from his staff, or they would be arrested by the military police. After another day they set off in a jeep along the pot-holed roads, going ‘hell for leather’ over 200 miles to make their destination before nightfall. They were stopped thirty-seven times by the MP’s because, being civilians, they had no tin hats.

So Alan Turing re-entered the ruined land of Gauss and Hilbert under watchful American eyes and in a military jeep. The party stayed at a communications laboratory at Ebermannstadt, near Bayreuth, which they had to reach by trudging up a thousand feet of mountain. It had been a hospital, and still bore a red cross on its roof, so they simply slept in the hospital beds. Women from the village came and did their washing, in return for a fragment of soap. Only he and Flowers had any cryptological interest, and the other members of the party did not (as far as they knew) know that they had. One of the captured German scientists proudly produced a machine of the Fish type, and explained how many billions of steps it would go through without repeating the key. Alan and Flowers just blinked and said, ‘Really!’ when he went on to tell them that none the less their mathematicians had reckoned it impregnable only for two years, and that then there would be a chance of it being broken.

While
they were there, the mushroom cloud fulfilled the wilder prophecies of 1939. The quantum mechanics that Hardy had so recently pronounced gloriously useless, had come of age. It was the outward sign of the new men’s work. Maurice Pryce had played an early part in the British research, and the final touch had been added by von Neumann, calculating the height at which it should explode to effect the maximum destruction. The clouds rolled over the second enemy, that would-be latecomer to old-fashioned empire, and warned a potential new one. The Americans had solved the final problem of the war. Yet without the sequence of events that had kept the Enigma on the Allied side in 1943, the war of 1945 might have been very different, with the first atomic weapons reserved for the concrete pens of raiding U-boats.

The great secret was out – or rather, it was known that there
was
a secret, which made it so very different from the other one. American soldiers came up to the Ebermannstadt station with the news, which did not surprise Alan. He had known of the possibility before the war, and was good at picking up straws in the wind. After his return from America, he had posed both to Jack Good and to Shaun Wylie a question about a chain reaction, expressed in terms of barrels of gunpowder. He had also spoken of a possible ‘U-bomb’ at Hanslope lunchtimes. He gave a talk on the basic physical principle to the others at Ebermannstadt.

He remained in Germany until about the middle of August, and then
returned to write his report on the visit. After six years, the war was officially finished. He had given his help in breaking the slave states, and in giving victory to the Yankees. Perhaps, less directly, his work had played a part in deciding the new boundaries of Animal Farm. But in 1945 few were dwelling upon the state of the eastern menagerie, although at Bletchley Park the new men had left the means with which to resume the politics of the 1920s.

No longer responsible for the world, they could get things right at home. In this respect Alan Turing was as fortunate as anyone. Even if his work had often been wasted, he had made the most of the war for himself, and emerged ready to contribute to the peace. The British had avoided defeat, and owed America for that. The ending of Lend-Lease was only the beginning of new problems. The power of British capital had shrunk, and its empire was to melt away. Yet arising in the mind were seeds of other kinds of growth.

^*
Wynn-Williams did make some progress, but this machine was probably the work of Keen and BTM.

^*
There was more than one kind of Robinson: a ‘Peter Robinson’ and a ‘Robinson and Cleaver’ after London department stores, and a ‘Heath Robinson’ after the famous cartoonist specialising in elaborate machines to perform absurdly simple tasks.

^*
It was from 16 to 22 November 1943.

^*
Hence the name Rockex, coined by Travis and inspired by that better-known feature of the Rockefeller Center, the Rockettes.

^*
Technically, of course, there was more to it than this. The speech would first be filtered to remove frequencies above 2000 Hz, and to restrict it to a specific range in amplitude so that it could be described at any point by a number between 0 and 1. Then in fact the encipherment was done by adding a continuous key signal first, and then taking the sample by making the resulting speech-plus-key signal modulate a pulse train. The ‘remaindering’ process would then be performed, chopping down a ‘spike’ by one unit if it exceeded one unit in amplitude.

^*
The output of the ‘orthogonal’ circuit would have the characteristics of random noise in the frequency range up to 2000 Hz. It would be deciphered by performing the sampling process (in strict synchrony, of course, with the sender), and a modular subtraction of the identical key. This would yield the samples of the original speech signal, and it was then a standard procedure, requiring only a low-frequency filter, to recover the speech itself.

^†
As Alan would stress in explaining the system, this depended crucially upon the use of
modular
addition. If ordinary unremaindered addition were used, then there would be a correlation between the speech amplitudes and the speech-plus-key amplitudes, and this the cryptanalyst could exploit. Indeed, this is precisely what the ear does in sorting out speech from background noise.

^*
Fourier theory very naturally involved the use of the ‘complex numbers’, and so did other aspects of the analysis of electronic circuits. the mathematics that he needed was at the undergraduate level – nothing as advances as the work on the Riemann zeta-function before the war. as with statistical theory he developed at bletchley, this was a very good eample of how quite elemetary nineteenth-century mathematics had applications to the techology of the 1940s that no one had seen, or had tried to seee.

^*
He once expressed himself as shocked by the indiscreet talk at a college dinner of a certain eminent wartime scientist.

^*
The signal-to-noise ratio was only l0dB, meaning that the speech had only ten times the power of the noise.

^*
That is, he had arrived at the automatic electronic digital computer with internal program storage. In what follows, the word ‘computer’ will be reserved for machines satisfying all these conditions. But in 1945 the word ‘computer’ meant what it had meant in 1935: either a person who did computations, or any type of machine (in anti-aircraft artillery, for instance) which mechanised that computation. It was not for about ten years that ‘computer’, or even ‘digital computer’, took on the new meaning. Meanwhile a variety of more cumbersome terms were used, and correspondingly the concept was less clear at the time than it later became, particularly regarding the internally stored program. Alan Turing had not invented a thing, but had brought together a powerful collection of ideas; since the ideas condensed into exactly what became ‘the computer’ it does not do too grave an injury to history to employ the word anachronistically. In fact the anachronism reflects quite well the difficulty that he faced in communicating to the 1940s a picture that belonged to the 1960s.

^*
Certainly Ada, Countess of Lovelace, writing her interpretation
²¹
of Babbage’s ideas in 1842, expressed this idea in a passage of prophetic insight:

The bounds of
arithmetic
were, however, outstepped the moment the idea of applying the cards had occurred; and the Analytical Engine does not occupy common ground with mere ‘calculating machines’. It holds a position wholly its own; and the considerations it suggests are most interesting in their nature. In enabling mechanism to combine together
general
symbols, in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the
most abstract
branch of mathematical science. A new, a vast and a powerful language is developed for the future use of analysis, in which to wield its truths so that these may become of more speedy and accurate practical application for the purposes of mankind than the means hitherto in our possession have rendered possible. Thus not only the mental and the material, but the theoretical and the practical in the mathematical world, are brought into more intimate and effective connexion with each other. We are not aware of its being on record that anything partaking of the nature of what is so well designated the
Analytical
Engine has been hitherto proposed, or even thought of, as a practical possibility, any more than the idea of a thinking or of a reasoning machine.

^*
But neither was the first in this respect. At Iowa State University, J.V. Atanasoff had been using electronics for mechanising arithmetical operations since 1939.

^*
Indeed its first serious use, in late 1945, would be on a trial calculation for the hydrogen bomb.

^*
Here one must assume that the secrecy surrounding Bletchley operations had been breached sufficiently for Womersley (through Darwin and Hartree, perhaps also through Blackett), to learn of the existence of the electronic Colossus and also of Alan’s general whereabouts.