Like Princeton it was a place of exile, but without the compensations of American largesse. Manchester University also resembled the American milieu in that it represented a bastion of respectability, its Nonconformist northern middle class being less accommodating to human diversity than was (in private) the more privileged Cambridge establishment. But Manchester had a spark of generosity in its city life, rather than the parochial attitudes of the small town. It had the liberal Manchester Guardian which, along with The Observer, was Alan’s newspaper. And perhaps he found something satisfying about working in ordinary industrial England, without the affectations and traditional rituals that went with Cambridge life.
If Alan had really objected to being left out on a limb, he could have resigned and returned to King’s, of which he remained a Fellow.* At some point there was talk of him taking a position at Nancy in France (perhaps through Wiener’s connections with its premier school of mathematics), but this came to nothing except the obvious joke with Norman Routledge of finding Nancy boys. He could always have found an American position – but that would have gone quite against his grain. Instead, he made the best of what had been his own decision. To many at Manchester, Alan Turing was something of an embarrassment, foisted upon them, but they would have to put up with him.
In March 1949 he wrote to Fred Clayton:
I am getting used to this part of the world, but still find Manchester rather mucky. I avoid going there more than I can avoid.
Instead, he worked or pottered around at home. Most of the university staff lived in the suburb of Victoria Park, but Alan lived further out in a large lodging house in Nursery Avenue, Hale. (‘Only one large bed – but I think you will find it quite safe,’ he described it to Fred, inviting him to stay.) It was on the very edge of the built-up area so that he could go running in the Cheshire countryside, far from the dark satanic mills and from the tensions of the university. He retained his connection with the Walton Athletic Club, and sometimes ran for them, as in the London to Brighton relay race on 1 April 1950.† His competitive days were, however, coming to a close and he ran more as a solitary exercise. Sometimes he ran into Manchester, though more often he cycled through the scrubby suburbs to work, cutting a comic figure in a yellow oilskin and hat when it rained. Later he added a small motor to his bicycle, but he never acquired a car: ‘I might suddenly go mad and crash,’ he told Don Bayley rather dramatically. He had not done too well at Princeton with the car, and probably tended to daydream with mathematical thoughts in a dangerous way. He preferred in any case to use his own steam.
He cared little for the Victoria University, as it was officially called, taking what he found relevant and ignoring the rest. For him there were those who were serious, in his own sense, and those who were not, and he wasted no time on the latter. This had little to do with formal positions. In September 1947, just as Alan effectively left the NPL, they had appointed a young engineer, E. A. Newman, who did have knowledge of pulse electronics from his experience of the H2S airborne radar system. Ted Newman, also a strong runner, used to go to Manchester to see Alan every month or so. Beside training together, they would argue for hours about the idea of intelligent machinery. In contrast, Alan would repulse abruptly any kind of ingratiating shop talk from those who might well be more academically qualified.
People did not have a second chance. If they tuned into a Turing wavelength, they would receive hours of attention at full blast, with an almost embarrassing intensity. But with a wobble of frequency, a hint of being judged by conventional or secondhand standards, the light went out, the door banged. It was all or nothing, like the pulses of the computer. He would walk away without a word of apology, when bored. And in his hatred of pretence and pretentiousness he must have thrown away many sincerely meant, but too tentative, approaches. In 1936 he had felt rebuffed by Hardy, but now it was he who obliged others to meet him on his own terms alone.
‘Boyish’ or ‘schoolboyish’ was the word that still came to many lips to describe the immediacy of his presence, his shaggy, dog-eared, larger-than-life appearance, and his ability to see that the Emperor had no clothes. His role at Manchester, indeed, was sometimes seen as that of Newman’s enfant terrible. He had little social life at Manchester; it would have required too much compromise. Apart from a few visits to Bob and his wife, now living in the Cheshire suburbs, it was the Newman home, a piece of Cambridge in the North, that gave him a welcome. They came to be on first-name terms, something unusual for Max Newman, who cut a distinctly magisterial figure in his department. His wife was the writer Lyn Irvine, who first came across Alan when he stayed with them at Criccieth for Easter 1949, amazing them with long runs round Cardigan Bay. She was struck by Alan,6 with ‘his off-hand manners and his long silences – silences finally torn up by his shrill stammer and the crowing laugh which told upon the nerves even of his friends’; there was his ‘strange way of not meeting the eye’ and of ‘sidling out of the door with a brusque and offhand word of thanks.’
Nor did he compromise with Manchester society by associating with the small homosexual set centred on the university, the BBC and the Manchester Guardian. In this respect life centred still on Cambridge. The exile in Manchester meant in particular a separation from Neville, whom over the next two years he would visit at Cambridge every few weeks. Neville was taking a two-year postgraduate course in statistics. At Easter 1949 they had another short holiday together in France, cycling and visiting the Lascaux Caves. (The prehistoric paintings rather suited Alan, who always wanted to draw nature from scratch himself.) Alan also spent the August of each year back for the long vacation in King’s, rather as he had in 1937.
So King’s retained its protective role, and Robin in particular was the White Knight in the forest, as the most helpful character in the story. In other ways, Robin was not the White Knight at all, being rather dashing and energetic. Later he acquired a powerful motor-cycle and a full set of black leathers, and sometimes took Alan for rides in the Peak District. Alan told his friends about the Princeton treasure hunts, and he, with Robin, Nick Furbank and Keith Roberts, organised several of them over the next few years. Alan would run round in search of the clues, while the others would cycle. Once Noel Annan joined in, and made a great hit by producing a bottle of champagne to match a clue which involved an Old French text with the word champaigne. Keith Roberts had many discussions with Alan about science and computers, but was innocent of other matters which Alan shared with his friends. He never deciphered the coded messages that passed between the others. Nick Furbank, on the other hand, did not have the scientific background, but he was very interested in rationalism and game theory and the imitation principle.
Alan and Robin and Nick devised a new game called Presents. The idea was that one person went out of the room and the others made up a list of imaginary presents that they believed he would like to have. Then he came back and could ask questions about the presents before choosing them, and here the game of bluff and double bluff came in, for one of the presents would secretly be designated ‘Tommy’ and once Tommy was chosen, the turn was finished. The imaginary presents moved after a while into a more probing realm. Alan tentatively dropped ‘Tea in Knightsbridge Barracks’ into the game at one point, perhaps reflecting fantasies of twenty years before. The Manchester computer had, in its unexpected and back-handed way, realised one of the products of his imagination. There still remained other dreams; no less hard to fulfil; no less liable to go awry.
The arrangement at Manchester was that the university engineers were to build a prototype machine, which Ferranti would use as ‘the instructions of Professor F. C. Williams’. So throughout 1949 the engineers, who were now able to recruit more staff, were adding to the original ‘baby machine’. By April it had been fitted with three more cathode ray tubes for fast store, multiplier and ‘B-tube’, and by that time a small magnetic drum was being tested. Another change was that each line on the cathode ray tube store now held forty spots, an instruc
tion taking up twenty of them. These were conveniently thought of as grouped in fives, and a sequence of five binary digits as forming a single digit in the base of 32.
Meanwhile Newman made an ingenious choice of problem with which to demonstrate the machine as it stood with only a tiny store but with a multiplier. It was something that had been discussed at Bletchley – finding large prime numbers. In 1644 the French mathematician Mersenne had conjectured that 217–1, 219–1, 231–1, 267–1, 2127–1, 2257–1 were all prime, and that these were the only primes of that form within the range. In the eighteenth century, Euler laboriously established that 231–1=2,146,319,807 was indeed prime, but the list would not have progressed further without a fresh theory. In 1876 the French mathematician E. Lucas proved that there was a way to decide whether 2p–1 was prime by a process of p operations of squaring and taking of remainders. He announced that 2127–1 was prime. In 1937, the American D. H. Lehmer attacked 2257–1 on a desk calculator and after a couple of years of work showed that Mersenne had been mistaken. In 1949 Lucas’s number was still the largest known prime.
Lucas’s method was tailor-made for a computer using binary numbers. They had only to chop up the huge numbers being squared into 40-digit sections and to program all the carrying. Newman explained the problem to Tootill and Kilburn and in June 1949 they managed to pack a program into the four cathode ray tubes and still leave enough space for working up to p=353. En route they checked all that Euler and Lucas and Lehmer had done, but did not discover any more primes.*
This was part of an uneasy treaty of alliance, according to which the zones of ‘engineers’ and ‘mathematicians’ were agreed. Newman took little further interest in the machine, and Alan took on the role of ‘the mathematician’. It was for him to specify the range of operations that should be performed by the machine, although his list was in fact cut back by the engineers. He had no part in the internal logical design, which was done by Geoff Tootill, but had control over the input and output mechanism, which lay more in the province of the user.
At the NPL he had chosen punched cards for input since they already had a punched card section; here he preferred to generate a teleprinter tape which could later be run off on a printer. He was, of course, very familiar with the teleprinter system from Bletchley and Hanslope, and people knew it was from ‘a place you mustn’t talk about’ that he obtained a paper tape punch, which ran off a dry battery, and ‘had a tendency to replace 1 by 0’. After it had been attached, those 32 different combinations of 0s and 1s in five-row teleprinter tape became the language of the Manchester machine, haunting the days and dreams alike of its users.
It was Alan’s job to make the Manchester machine convenient to use, but his ideas of convenience were not always shared by others. He had, of course, attacked the principle on which Wilkes was working according to which the hardware of the machine would be designed to make the instructions easy for a human user to follow – so that in the EDSAC design, the letter ‘A’ was used as the symbol for the instruction to add. In contrast, Alan held that human convenience should be catered for by programming techniques, not by electronics. In his 1947 talk he had referred to such matters of convenience as ‘fussy little details’, and had stressed how they could be taken care of by ‘pure paperwork’. Now at Manchester, he had the opportunity, in principle, to put this into practice – for the machine hardware had not been designed to pander to the programmer. However, by 1949 he had lost interest in doing this kind of work. The ‘fussy little detail’ of binary to decimal conversion, for instance, he now found not worth bothering about. He himself found it simple to work directly in the base-32 arithmetic in which the machine could be regarded as working, and expected other people to do the same.
To use base-32 arithmetic it was necessary to find 32 symbols for the 32 different ‘digits’. Here he took over the system already used by the engineers, in which they labelled the five-bit combinations according to the Baudot teleprinter code. Thus the ‘twenty-two’ digit, corresponding to the sequence 10110 of binary digits, would be written as ‘P’, the letter that the sequence 10110 encoded for an ordinary teleprinter. To work in this system meant memorising the Baudot code and the multiplication table as expressed in it – something he, but few others, found easy.
The ostensible reason for sticking to this hideously primitive form of coding, which entailed so much work for the user, was that the cathode ray tube storage made it possible – indeed necessary – to check the contents of the store by ‘peeping’, as Alan called it, at a monitor tube. He insisted that what one saw as spots on the tube had to correspond digit by digit to the program that had been written out. To maintain this principle of correspondence it was actually necessary to write out the base-32 numbers backwards, with the least significant digit first. This was for technical electronic engineering reasons, the same as those which obliged cathode ray tubes always to scan from left to right. Another awkwardness arose on account of the five-bit combinations which did not correspond to a letter of the alphabet on the Baudot code. (It was the same problem that the Rockex system overcame.) Geoff Tootill had already introduced extra symbols for these, the zero of the base-32 notation being represented by a stroke ‘/’. The result was that pages of programs were covered with strokes – an effect which at Cambridge was said to reflect the Manchester rain lashing at the windows.
By October 1949 the machine was ready, bar some details, for Ferranti to manufacture. The prototype remained in place while this was done, and the idea was to use the time to write an operations manual and basic programs ready to use on the computer (the Mark I, it would be called), when it arrived.
This was Alan’s next job, and he must have spent a great deal of time in checking the operation of every single function on the prototype, arguing over their efficiency with the engineers. By October he had written out an input routine: that is, a means to persuade the machine when first switched on and empty of instructions, to read in new instructions from a tape, to store them in the right place, and to begin executing them.
But this was low-level work; and on this level the Programmers’ Handbook7 that he wrote, though full of helpful and practical advice, involved few new ideas. Indeed, it had nothing as sophisticated as the routines he had devised at the NPL for floating-point numbers. Nor did he do anything inspired in connection with the organisation of sub-routines. This, in the Manchester development, was dominated by the existence of two kinds of storage: on the Ferranti-built machine this would amount to eight cathode ray tubes each with their 1280 digits, and the magnetic drum promising no fewer than 655360 digits, arranged in 256 tracks of 2560 digits each.* Programming revolved around the process of ‘bringing down’ data and instructions from the drum to the tubes, and sending them back again, and the hardware more or less obliged each sub-routine to be stored on a new track of the drum, to be transferred in toto as required. The Turing scheme coped with this, but he did not bother with a system for sub-routines nested to any depth. He referred to this possibility in a rather flippant passage of the Handbook:
The sub-routines of any routine may themselves have sub-routines. This is like the case of the bigger and lesser fleas. I am not sure of the exact meaning the poet attached to the phrase ‘and so ad infinitum’, but am inclined to think that he meant there was no limit that one could assign to the length of a parasitic chain of fleas, rather than that he believed in infinitely long chains. This certainly is the case with sub-routines. One always eventually comes down to a routine without sub-routines
but he left this for the user to organise. His own ‘Scheme A’ only allowed for one level of sub-routine calling.
The Handbook brought out many of the problems of communication that he faced at Manchester. To Williams and the other engineers, a mathematician was someone who knew how to do calculations; in particular they saw binary notation as something new introduced to them by ‘mathematics’. To Alan Turing, however, all their schemes with base-32 arithmetic and the rest
were merely simple illustrations of the deeper fact that mathematicians were free to employ symbolism in any way they chose. To him it was obvious that a symbol had no intrinsic connection with the entity that it symbolised, and so a long paragraph at the beginning of the Handbook explained how it was that there existed a convention according to which sequences of pulses could be interpreted as numbers. While this was a far more accurate and also more creative idea than the usual statement that the machine ‘stored the numbers’, it was not immediately helpful to the person who had never before known that numbers could be expressed other than in the scale of ten. It was not that Alan despised doing routine, detailed work within a symbolism such as the Manchester machine demanded: but as in Computable Numbers and the ACE report he tended to veer from the abstract to the detailed in a way that made sense to him, but not to others. The development that could have absorbed both his liberated understanding of symbolism, and his willingness to do the donkey work when necessary, was that of designing programming languages, the development he described as ‘obvious’ in 1947. But this was precisely what he did not do; and thus he failed to exploit the advantage that a grasp of abstract mathematics gave him.*
In writing the standard routines for square roots and so forth, he had two assistants after October 1949. One was Audrey Bates, a postgraduate student. The other was Cicely Popplewell, whom he had interviewed for the advertised post in summer 1949. She was a Cambridge mathematics graduate with experience of punched cards used in housing statistics. They both shared his office in that Victorian fortress, the university Main Building, pending the construction of the new Computing Laboratory to house the Ferranti machine. It was not a happy arrangement, for he never really acknowledged their right to exist. On Cicely’s first day he said ‘Lunch!’ and marched out of the room without telling Cicely where the Refectory was. He would talk away himself to anyone who visited, but would be very annoyed if either of them did. Sometimes the shell would crack; they persuaded him to play tennis once, and they were amazed the first time they saw him arrive apparently wearing a raincoat and nothing else, which caused some laughs. Once there was some business of him borrowing a ten-shilling note to pin on his shorts when he went home. But usually they were glad when, as often happened, he did not come in. He made no allowance for the amount they had to learn, and did nothing to mitigate what Cicely felt as ‘an acute inferiority complex’ in terms of speed of brain. Cicely also had the job of smoothing things over with the engineers, when interdepartmental tension was running high.
Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game Page 63
