Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  Mrs Morcom had already put into effect a similar idea. She had commissioned a stained-glass window of St Christopher – not however for Sherborne, but for their parish church at Catshill. Nor was it the ‘humble service’ of Mrs Turing that it was to express, but the life that went on. Back at school, Alan wrote to Mrs Morcom:

  3/5/30

  … I am hoping to do as well as Chris in the Higher Certificate this term. I often think about how like I am to Chris in a few ways through which we became real friends, and wonder if I am left to do something that he has been called away from.

  Mrs Morcom had also called upon Alan to help choose books for the school prizes that Christopher was posthumously to receive:

  I think Chris would almost certainly have got The Nature of the Physical World (Eddington) and The Universe around us (Jeans) for the Digby prize and possibly one of The Internal Constitution of the Stars (Eddington), Astronomy and Cosmogony (Jeans). I think you would like The Nature of the Physical World.

  The Morcom family endowed a new prize at Sherborne, a science prize to be awarded for work which included an element of originality. Alan had plodded on with the iodate experiment, and now he undertook to write it up for the prize. Christopher it was, even from the grave, who induced him to communicate and to compete. He wrote to his mother:

  18 May 1930

  … I have just written to a Mellor the author of a Chemistry book to see if he can give me a reference about the experiment I was doing in the summer last year. Rupert said he would look it up in Zurich if I could get him a reference. It’s annoying I couldn’t get hold of anything before.

  Alan was also interested in perspective drawing:

  This week’s efforts in drawing are not on any better paper … I don’t think much really of Miss Gillet’s efforts. I remember she did once or twice say something in a vague sort of way about parallel lines being drawn concurrent, but she usually had the slogan ‘vertical lines remain vertical’ on the tip of her tongue. I wonder how she managed drawing things below her. I have not been doing much by way of drawing bluebells and things like that but mostly perspective.

  Mrs Turing wrote to Mrs Morcom:

  May 21 1930

  … Alan has taken up drawing which I was anxious for him to do long ago: I think this is quite likely an inspiration from you. He is quite devoted to you and I think he was just wishing for an excuse to pay you a call when he went up to Town the day after saying ‘Goodbye’ to you! You were all most awfully good to him, and in many ways opened up a new world to him.… Whenever we were alone he wanted to talk just of Chris and you and Col. Morcom and Rupert.

  Alan hoped this summer to gain an improved mark in the Higher Certificate. His name was put down for Pembroke College, Cambridge, which awarded a number of scholarships on Higher Certificate marks alone, although he half-hoped to fail, so that he would have a chance of trying for Trinity. He did fail for he found the mathematics paper much more difficult than in the previous year, and his marks showed no improvement. But Eperson reported:

  … I think he has succeeded in improving his style of written work, which is more convincing and less sketchy than last year…

  and Gervis:

  He is doing much better work than this time last year partly because he knows more but chiefly because he is getting a more mature style.

  Andrews was presented with Alan’s submission for the new Morcom science prize, and later said:2

  I first realised what an unusual brain Alan had when he presented me with a paper on the reaction between iodic acid and sulphur dioxide. I had used the experiment as a ‘pretty’ demonstration – but he had worked out the mathematics of it in a way that astonished me …

  The iodates won him the prize. ‘Mrs Morcom is extraordinarily nice and the whole family is extremely interesting,’ Alan wrote to Blamey, ‘They have founded a prize in Chris’ memory which I very appropriately won this year.’ He also wrote:

  I have started learning German. It is possible that I may be made to go to Germany sometime during next year but I don’t much want to. I am afraid I would much rather stay and hibernate in Sherborne. The worst of it is that most of the people left in Group III nauseate me rather. The only respectable person in it since February has been Mermagen and he doesn’t do Physics seriously or Chemistry at all.

  The master who taught him German wrote: ‘He does not seem to have any aptitude for languages.’ It was not what he wanted to think about in his hibernation.

  One Sunday that summer, the boys of Westcott House arrived back from their afternoon walks to find Alan, who was by now accorded a certain awed respect, engaged upon an experiment. He had set up a long pendulum in the stairwell, and was checking that, as the day went on, the plane of its motion would remain fixed while the Earth rotated beneath it. It was only the elementary Foucault pendulum experiment, such as he might have seen in the Science Museum in London. But it caused great astonishment at Sherborne, and made an impression second only to his arrival by bicycle in 1926. Alan also told Peter Hogg that it had to do with the theory of relativity, which ultimately it did: one problem that concerned Einstein was how the pendulum kept its place fixed relative to the distant stars. How did the pendulum know about the stars? Why should there be an absolute standard of rotation, and why should it agree with the disposition of the heavens?

  But if the stars still exerted their attraction, Alan also had to work out his thoughts about Christopher. Mrs Morcom had asked him in April to write his recollections of her son for an anthology. Alan found this task very hard to fulfil:

  My impressions of Chris that I have been writing for you seem to have become more a description of our friendship than anything else so I thought I would write it as such for you and write something less to do with me that you could print with the others.

  In the end he would make three attempts but every one of them strayed from manly detachment, too honest to disguise his feelings. The first pages were sent off on 18 June, and explained:

  My most vivid recollections of Chris are almost entirely of the kind things he said to me sometimes. Of course I simply worshipped the ground he trod on – a thing which I did not make much attempt to disguise, I am sorry to say.

  Mrs Morcom asked for more, and Alan promised to try again when he was on holiday:

  20/6/30

  … I think I know what you mean about those little points of which you want a record. I shall have a lot of quiet time in Ireland to think them out for you. I couldn’t do it before that because there is not much longer this term and camp is not a very suitable atmosphere. A lot of the things I cut out were things which were to me typical of Chris but when I read them through later I realized that to anyone who did not know both Chris and myself a little bit at least, they would not mean much. I tried to get over that just to shew a little bit what Chris was to me. Of course you know.…

  The OTC camp, in the first week of the summer holiday, also obstructed the invitation to stay at the Clock House which Mrs Morcom had extended to both Alan and his mother. Fortunately there was an outbreak of infectious illness at Sherborne and camp was cancelled.

  Alan arrived at the Clock House on Monday 4 August. Mrs Morcom recorded ‘… Have just been along to tuck him up. He has my room but is sleeping in sleeping pack where Chris slept last autumn…’ Next day Mrs Turing joined them. Colonel Morcom gave Alan permission to work in the laboratory on an experiment that he and Chris together had begun. There was a day out to the county show and a visit to Christopher’s grave. On the Sunday evening, Mrs Morcom wrote:

  … I went with Mrs Turing and Alan in Lanchester. They were leaving soon after 7 pm for Ireland. Stayed until 7 talking to them … Alan came in to talk to me this morning and said how he loves being here. He says he feels Chris’ blessing here.

  The Turings crossed over to Ireland and holidayed in Donegal. Alan fished with John and his father, climbed the hills with his mother, and kept his thoughts to himself.

  At the en
d of the summer term O’Hanlon had conferred the accolade: ‘A good term. With some obvious minor failings, he has character.’ Alan had become more prepared to go along with the system. It was not that he had ever rebelled, for he had only withdrawn; nor was it now a reconciliation, for he was still withdrawn. But he would take the ‘obvious duties’ as conventions rather than impositions, as long as they interfered with nothing important. In the autumn term of 1930 his contemporary Peter Hogg became head of house and, as the other third year sixth former, Alan was made a prefect. O’Hanlon wrote to Mrs Turing: ‘That he will be loyal I am well assured: and he has brains: also a sense of humour. These should carry him through…’ He did his share of disciplining the younger boys of the house. One new boy was David Harris, brother of the Arthur Harris who had been head of house four years before. As duty prefect, Alan caught him having left his football clothes off the peg for the second time. Alan said, ‘I’m afraid I shall have to beat you,’ and so he did, rendering Harris a hero among his peers for being the first of the new boys thus to suffer. Harris held on to the gas ring and Alan launched the strokes. However, without the right shoes on he slid all over the shiny washroom floor and the strokes landed at random, one on Harris’s spine, one on his leg. It was not the way to win respect. Alan Turing was a kindly but ‘weak’ prefect, one whom the younger boys could chafe, blowing out his candle in the dormitory or putting sodium bicarbonate in his chamberpot. (There were no lavatories attached to the house dormitories.) Old Turog, he was called, after the Turog loaf, and was always good for having his leg pulled. A similar incident, which took place in ‘Hall’ was witnessed3 by Knoop, one of the older boys who saw Alan as ‘brain where I was brawn’:

  During this period of 11/2 hours punishment was normally carried out by pupils. Our studies at Westcott House were down a long corridor with studies on either side shared by from 2 to 4 boys. On this particular evening during this silent period, we heard footsteps come up the corridor, a knock on a door, a mumble of voices and then two lots of footsteps come up the corridor to the locker/washroom, then we heard the swish of a cane, a crash of crockery and a loaf as cane connected with bottom, this was stroke one, exactly the same happened on the second stroke, by that time me and my companions were splitting our sides with laughter. What happened was Turing on his back stroke had knocked down some tea making crockery belonging to prefects, he did this on two consecutive strokes and from the noise we could all tell what was going on in the washroom, the third and final stroke did not connect with crockery as by that time it was lying shattered on the floor.

  Much more upsetting, his diary,4 which he kept under lock, was taken and damaged by another boy. There was, however, a limit to what Alan would take:5

  Turing … was quite a lovable creature but rather sloppy in appearance. He was a year or more older than me, but we were quite good friends.

  One day I saw him shaving in the washroom, with his sleeves loose and his general apearance rather execrable. I said, in a friendly way, ‘Turing, you look a disgusting sight.’ He seemed to take it not amiss, but I tactlessly said it a second time. He took offence and told me to stay there and wait for him. I was a bit surprised, but (as the house washroom was the place for beatings) I knew what to expect. He duly re-appeared with a cane, told me to bend over and gave me four. After that he put the cane back and resumed his shaving. Nothing more was said; but I realised that it was my fault and we remained good friends. That subject was never mentioned again.

  But apart from the important matters of ‘Discipline, self-control, the sense of duty and responsibility’, there was Cambridge to think about:

  2/11/30

  Dear Mrs Morcom,

  I have been waiting to hear from Pembroke to write to you. I heard indirectly a few days ago that they will not be able to give me a scholarship. I was rather afraid so; my marks were spread too evenly amongst the three subjects.… I am full of hope for the December exam. I like the papers they give us there so much better than the Higher Certificate ones. I don’t seem though to be looking forward to it like I was last year. If only Chris were there and we were to be up there for another week together.

  Two of my books for the ‘Christopher Morcom’ prize have come. I had great fun yesterday evening learning some of the string figures out of ‘Mathematical Recreations’ … I have been made a school prefect this term, to my great surprise as I wasn’t even a house-prefect last term. Last term they started having at least two in each house which rather accounts for it.

  I have just joined a Society here called the Duffers. We go (if we feel inclined) every other Sunday to the house of some master or other and after tea someone reads a paper he has written on some subject. They are always very interesting. I have agreed to read a paper on ‘Other Worlds’. It is now about half written. It is great fun. I don’t know why Chris never joined.

  Mother has been out to Oberammergau. I think she enjoyed it very much but she has not told me much about it yet…

  Yours affectionately, A.M. Turing

  Alan’s elevation to School Prefect was a great comfort to his mother. But much more significant was a new friendship in his life.

  There was a boy three years younger than Alan in the house, Victor Beuttell, who was also one who neither conformed, nor rebelled, but dodged the system. He also, like Alan, was labouring under a grief that no one knew about, for his mother was dying of bovine tuberculosis. Alan saw her when she came to visit Victor, himself in great peril with double pneumonia, and asked what was wrong. It struck a terrible chord. Alan also learnt something else that few knew, which was that Victor had been caned so severely by a prefect in another house that his spine had been damaged. This turned him against the beating system, and he never caned Victor (who was frequently in trouble), but passed him on to another prefect. The link between them was one of compassion, but it developed into friendship. Though at odds with the axioms of the public school, which normally would forbid boys of different ages from spending time together, a special dispensation from O’Hanlon, who kept a card index on the boys’ activities and watched closely over them, allowed it to continue.

  They spent a good deal of time playing with codes and ciphers. One source of ideas might have been the Mathematical Recreations and Essays,6 which Alan had chosen as Christopher Morcom Prize, and which indeed had served a generation of school prize-winners since it appeared in 1892. The last chapter dealt with simple forms of cryptography. The scheme that Alan liked was not a very mathematical one. He would punch holes in a strip of paper, and supply Victor with a book. Poor Victor had to plod through the pages until he found one where through the holes in the strip appeared letters that spelt out a message such as HAS ORION GOT A BELT. By this time, Alan had passed on his enthusiasm for astronomy to Victor, and had explained the constellations to him. Alan also showed him a way to construct Magic Squares (also from Mathematical Recreations), and they played a lot of chess.

  As it happened, Victor’s family was also linked with the Swan electric light industry, for his father, Alfred Beuttell, had made a small fortune by inventing and patenting the Linolite electric strip reflector lamp in 1901. The lamp was manufactured by Swan and Edison, while Mr Beuttell, who had broken away from his own father’s business in carpet wholesaling, acquired further experience as an electrical engineer. He had also enjoyed a fine life until the First World War, flying, motor racing, sailing, and gambling successfully at Monte Carlo.7

  A very tall, patriarchal figure, Alfred Beuttell dominated his two sons, of whom Victor was the elder. In his character Victor took more after his mother, who in 1926 had published a curious pacifist, spiritualist book. He combined her bright-eyed, rather magical charm, with his father’s strong good looks. In the 1920s Alfred Beuttell had gone back into research into lighting, and in 1927 had taken out patents on a new invention, the ‘K-ray Lighting System’. It was designed to allow uniform illumination of pictures or posters. The idea was to frame a poster in a glass box, whose front
surface would be curved in such a way that it reflected light from a strip light at the top exactly evenly over the poster. (Without such a reflection, the poster would be much brighter at the top than at the bottom.) The problem was to find the right formula for the curvature of the glass. Alan was introduced to the problem by Victor, and suddenly produced the formula, without being able to explain it, which agreed with Alfred Beuttell’s calculation. But Alan went further, and pointed out the complication which arose through the thickness of the glass, which would cause a second reflection at the front surface. This made necessary a change in the curve of the K-ray System, which was soon put into application for exterior hanging signs, the first contract being with J. Lyons and Co. Ltd., the catering chain.

  It was characteristic. As with the iodate and sulphite calculation, it always delighted Alan that a mathematical formula could actually work in the physical world. He had always liked practical demonstrations, even though he was not good at them, and although pushed into the corner as the intellectual ‘maths brain’, did not make the error of considering thought as sullied or lowered by having a concrete manifestation.

  There was a parallel development, in that he did not permit the Sherborne ‘games’ religion to instil in him a contempt for the body. He would have liked to have been as successful with corpus as with mens, and found the same difficulties with both: a lack of coordination and ease of expression. But he had discovered by now that he could run rather well. He would come in first place on the house runs, when rainy weather obliged the cancellation of all important Footer. Victor would go out with him for runs, but after two miles or so would say ‘It’s no good, Turing, I shall have to go back’, only to find Alan overtaking him on the return from a much longer course.