Schrödinger’s quantum theory requires 3 dimensions for every electron he considers. Of course he does not believe that there are really about 1070 dimensions, but that this theory will explain the behaviour of an electron. He thinks of 6 dimensions, or 9, or whatever it may be without forming any mental picture. If you like you can say that for every new electron you introduce these new variables analogous to the coordinates of space.
This came from Eddington’s description of that other change in fundamental physical concepts, one much more mysterious than relativity. The quantum theory had done away with the billiard-ball corpuscles and the ethereal waves of the nineteenth century, and replaced both by entities which had characteristics both of particles and of waves; lumpy but nebulous.
Eddington had a lot to say, for the 1920s had been a decade of rapid advance in theoretical physics, following up the spate of discoveries at the turn of the century. In 1929 Schrödinger’s formulation of the quantum theory of matter was only three years old. The two boys also read books by Sir James Jeans, the other Cambridge astronomer, and here too there were entirely new developments. It had only just been established that some nebulae were clouds of gas and stars on the margins of the Milky Way, and that others were completely separate galaxies. The mental picture of the universe had expanded a millionfold. Alan and Christopher discussed these ideas and ‘usually didn’t agree’, wrote Alan, ‘which made things much more interesting.’ Alan kept ‘some pieces of paper with Chris’ ideas in pencil and mine in ink scrawled all over them. We even used to do this during French.’
The date 28/9/29 appeared on them, and so did the official work:
Monsieur … recevez monsieur mes salutations empresseés*
Cher monsieur … Veuillez agréer I’expression des mes sentiments distingués Cher ami … Je vous serre cordialement la main … mes affectueux souvenirs … votre affectioné
but also there were generalised noughts and crosses, a reaction involving iodine and phosphorus, and a diagram which suggested doubting Euclid’s axiom that for every line there would be exactly one parallel line passing through a given point.
Alan kept these pages, as souvenirs affectueux, although he could never express his sentiments distingués. As for serrer cordialement la main, or more – that was probably pretty firmly repressed in his mind, although soon he would write: ‘There were times when I felt his personality particularly strongly. At present I am thinking of an evening when he was waiting outside the labs, and when I came too, he grasped me with his big hand and took me out to see the stars.’
Alan’s father was delighted, if amazed, when the reports began to change their tone. His interest in mathematics was confined to the calculation of income tax, but he was proud of Alan, and so was John, who admired him for taking on the system and getting away with it. There had been a method in his madness all along. Unlike his wife, Mr Turing never claimed to have the faintest idea of what his son was doing, and this was the theme of a punning couplet that Alan once read out from his father’s letter in his study:
I don’t know what the ’ell ’e meant
But that is what ’e said ’e meant !
Alan seemed quite happy with this bluff and trusting ignorance. Mrs Turing, however, took the more accusing line of ‘I told you so,’ and made a good deal of the idea that her choice of school had been the right one. She had certainly paid a certain amount of attention to Alan, and it had not all been in the direction of moral improvement, for she liked to feel that she understood his love of science.
Alan was now in a position to think of winning a scholarship to university, a scholarship representing not only merit but a reasonable income, almost enough to live on as an undergraduate. An exhibition, awarded to second-class candidates, would mean significantly less. Christopher, now eighteen, was expected to win a Trinity College scholarship like his brother. It was ambitious of Alan to attempt the same at seventeen. In mathematics and science, Trinity held the highest reputation among the colleges of the university which was itself, after Göttingen in Germany, the scientific centre of the world.
The public schools were good at putting candidates through the daunting procedure for entrance scholarships to the ancient universities, and Sherborne also gave Alan a £30 per annum subsidy. But there was no automatic red carpet laid down. The scholarship examinations were distinguished by questions of an open-ended, imaginative kind, without a published syllabus. They gave a taste of future life. To Alan this was an excitement in itself, but there was more than this to stimulate his ambition. There was Christopher, who would so shortly be leaving Sherborne; there was some muddle over when this would be, but it would probably be at Easter 1930. To fail in the scholarship would be to lose Christopher for more than a year. Perhaps it was this uncertainty that provoked gloomy forebodings in November, when Alan had recurring thoughts that something would happen before Easter to prevent Christopher from going to Cambridge.
The Cambridge examinations opened up the prospect of a whole week in Christopher’s company, unconstrained by the house system – ‘I was looking forward as much to spending a week with Chris as to seeing Cambridge.’ On Friday 6 December, Christopher’s study-mate Victor Brookes was to be driving from London to Cambridge, and had offered to take Alan as well as Christopher. They went on the train together to London, where they stopped off to see Mrs Morcom. She took them to her studio, allowed them to play at chipping marble from a bust that she was working on, and then gave them lunch at her flat. Christopher used to tease Alan a good deal, and had a particular running joke about ‘deadly stuff’, the joke being to pretend that certain harmless substances were really poisonous. He joked about the vanadium in the special Morcom vanadium-steel cutlery being ‘absolutely deadly’.
In Cambridge they could live the lives of young gentlemen for a week, with rooms of their own and no lights-out. There was dinner in the Hall of Trinity College, in evening dress, with the portrait of Newton looking down. It was an opportunity to meet and compare themselves with candidates from other schools. Alan made one new acquaintance, Maurice Pryce, with whom he established an easy rapport through almost identical interests in mathematics and physics. Pryce was taking the examination for the second time. A year before he had sat under Newton’s portrait and had said to himself that now nothing else would suffice. And although Christopher was rather blasé about everything, that was what it was like for them all: nothing could be quite the same again.
It was, wrote Alan, ‘a very good meal’, and then they
went to play Bridge with some other Sherburnians in Trinity Hall. We were … to be back at our Colleges by 10 o’clock but at 4 minutes to 10 Chris wanted to play another hand. I wouldn’t let him, and as it was, we were only back just in time. The next day, Saturday, we played cards again ‘Rummy’ this time. After ten o’clock Chris and I went on playing other games. I remember very clearly Chris’ broad smile when we decided we didn’t want to go to bed just yet. We played till 12-15. A few days later we tried to get into the Observatory. We had been invited by an astronomer friend of Chris’ to go there if it was fine. Our idea of what was fine did not quite agree with his.
Christopher ‘loved all games and was always finding out new ones (of the more trivial kind).’ He used to ‘try to make people believe things that were credible but just not true,’ and at Cambridge persuaded Alan to advance his watch by twenty minutes. ‘He was immensely pleased when I found out.’ They also went to the cinema together, joined by Norman Heatley, who had been Christopher’s friend at a preparatory school, and was now a Cambridge undergraduate. Christopher told him how Alan had a notation of his own for the calculus, and had to translate everything into standard formulae when he did examinations. This aspect of Alan’s independence also worried Eperson, who found that ‘on paper his solutions were often unorthodox, and required the writer’s elucidation.’ He doubted whether the Cambridge examiners would perceive the mind that struggled behind the hand.
On the
way back from the cinema, Alan hung back and walked with Heatley, to test how much Christopher wanted his company. He was rewarded:
Evidently I looked rather lonely as Chris beckoned to me (mostly I think with his eyes) to walk beside him. Chris knew I think so well how I liked him, but hated me shewing it.
Alan was conscious that he was a boy in another house, and that everything was open to comment. (‘We never went on bicycle rides together. I think perhaps Chris was rather ragged about me at the house.’) But this pleased him ‘ever so much’.
After what Alan said had been the happiest week of his life, the boys went back to school on 13 December for the last few days of term. At the house supper, they sang about Alan:
The maths brain lies often awake in his bed
Doing logs to ten places and trig in his head
The results were published on 18 December in The Times, just after term ended. It was a Great Crash. Christopher had won a Trinity scholarship, and Alan had not. Writing in congratulation, Alan had a letter in return with a particularly friendly tone:
20/12/29
Dear Turing,
Thank you very much for your letter. I was as sorry you did not get a schol as I was pleased that I did. What Mr Gow says means that you would have certainly got an Exhibition if you had put it down …
… Have had two of the clearest nights I have known. I have never seen Jupiter better and I could see 5 or 6 belts and even some detail on one of the large central belts. Last night I saw no. I satellite come out from eclipse. It appeared quite suddenly (during a few seconds) at some distance from Jupiter and looked very attractive. It is the first time I have seen one. I also saw Andromeda Neb. very clearly but did not stay out long. Saw spectrum of Sirius, Pollux and Betelgeux and also bright line spectrum of Orion nebula. Am at moment making a spectrograph. Will write again later. Happy Christmas etc. Yrs ever C. C. M.
Anything like ‘making a spectrograph’ was far beyond the resources Alan enjoyed at Guildford, but he got hold of an old spherical glass lampshade, filled it with plaster of Paris, covered it with paper (which made him think about the nature of curved surfaces) and set out to mark in the constellations of fixed stars. Typically, he insisted on doing it from his own observation of the night sky, although it would more easily and accurately have been done from an atlas. He trained himself to wake at four o’clock in the morning so that he could mark in some stars not visible in the December evening sky, thus waking up his mother, who thought she had heard a burglar. This done, he wrote to Christopher about it, also asking him whether he thought it would be advisable to try for a college other than Trinity next year. If this was a test of affection, he was again rewarded, for Christopher replied:
5/1/30
Dear Turing,
… I really can’t give you any advice about exams because it is nothing to do with me and I feel it would not be quite write [sic]. John’s is a very good College, but of course I should prefer personally that you came to Trinity where I should see more of you.
I should be very interested to see your star map when it is done but I suppose it is quite impracticable to bring it to school or anything. I have often wanted to make a star globe, but have never really bothered, especially now I have got the star atlas going down to 6th mag….
Recently I have been trying to find Nebulae. We saw some quite good ones the other night, one very good planetary in Draco 7th mag. 10". Also we have been trying to find a Comet 8th mag. in Delphinus …. I wonder if you will be able to get hold of a telescope to look for it with your 1½" will be useless for such a small object. I tried to compute its orbit but failed miserably with 11 unsolved equations and 10 unknowns to be eliminated.
Have been getting on with plasticine. Rupert has been making horrid smelling soaps and fatty acids from … Rape Oil and Neal’s Boot Oil….
This letter was written from his mother’s flat in London, where he was ‘to see the dentist … and also to avoid a dance at home.’ Next day he wrote again from the Clock House:
… I found the Comet at once in its assigned position. It was much more obvious and interesting than I had expected … I should say it is nearly 7th mag. It … should be obvious in your telescope. The best way is to learn the 4th & 5th mag. stars by heart, and move slowly to the right place, never losing sight of all the known stars…. In about half an hour I shall look again if it is clear (it has just clouded) and see if I can notice its motion among the stars and also see what it looks like with the powerful eyepiece (×250). The group of 5 4th mag. stars in Delphinus come into the field of the finder in pairs. Yrs. C. C. Morcom.
But Alan had already seen the comet, though in a more haphazard manner
10/1/30
Dear Morcom,
Thank you very much for the map for finding the comet. On Sunday I think I must have seen it. I was looking at Delphinus and thinking it was Equuleus and saw something like this [a tiny sketch] rather hazy and about 3´ long. I am afraid I did not examine it very carefully. I then looked for the comet elsewhere in Vulpecula thinking it was Delphinus. I knew from the Times that there was a comet in Delphinus that day.
… The weather really is annoying for this comet. Both on Wednesday and today I have had it quite clear until sunset and then a bank of cloud comes over the region of Aquila. On Wednesday it cleared away just after the comet had set….
Yours A. M. Turing
Please don’t always thank me for my letters so religeously. I’ll let you thank me for writing them legibly (if I ever do) if you like.
Alan plotted the course of the comet, as it sped from Equuleus into Delphinus in the frosty heavens. He took the primitive star globe back to school to show to Christopher. Blamey had left at Christmas, and Alan now had to share another study, in which the inky sphere was poised. There were but few constellations marked in, but they amazed the younger boys with Alan’s erudition.
Three weeks into the term, on 6 February, some visiting singers gave a concert of sentimental part-songs. Alan and Christopher were both present, and Alan was watching his friend, trying to tell himself, ‘Well, this isn’t the last time you’ll see Morcom.’ That night he woke up in the darkness. The abbey clock struck; it was a quarter to three. He got out of bed and looked out of the dormitory window to look at the stars. He often used to take his telescope to bed with him, to gaze at other worlds. The moon was setting behind Ross’s house, and Alan thought it could be taken as a sign of ‘goodbye to Morcom’.
Christopher was taken ill in the night, at just that time. He was taken by ambulance to London, where he underwent two operations. After six days of pain, at noon on Thursday 13 February 1930, he died.
* * *
* Warrington Lodge, now the Colonnade Hotel, Warrington Crescent, London W9. His baptism was at St Saviour’s Church, immediately across the road.
* Alan’s spelling and punctuation, here and throughout, is faithfully reproduced.
* Unlike Sir Archibald Campbell.
* These were practice papers
* The series is:
It was a standard result in sixth form work, but the point was that he discovered it without the use of the elementary calculus. Perhaps the most remarkable thing was his seeing that such a series should exist at all.
* Usually called ‘the law of geodesic motion’.
* This piece of work was marked ‘Nine wrong genders. 5/25. Very poor.’
2 The Spirit of Truth
I sing the body electric,
The armies of those I love engirth me and I engirth them,
They will not let me off till I go with them, respond to them,
And discorrupt them, and charge them full with the charge of the soul.
Was it doubted that those who corrupt their own bodies conceal themselves?
And if those who defile the living are as bad as they who defile the dead?
And if the body does not do fully as much as the soul?
And if the body were not the soul, what is the soul
?
No one had told Alan that Christopher Morcom had contracted bovine tuberculosis from drinking infected cows’ milk as a small boy; it had set up a pattern of internal damage, and his life had been constantly in danger. The Morcom family had gone to Yorkshire in 1927 to observe the total eclipse of the sun on 29 June, and Christopher had been taken terribly ill in the train coming back. He had undergone an operation, and that was why Alan had been struck by his thin features when he returned to school late that autumn.
‘Poor old Turing is nearly knocked out by the shock,’ a friend wrote from Sherborne to Matthew Blamey next day. ‘They must have been awfully good friends.’ It was both less and more than that. On his side, Christopher had at last been becoming friendly, rather than polite. But on Alan’s side – he had surrendered half his mind, only to have it drop into a void. No one at Sherborne could have understood. But on the Thursday that Christopher died, ‘Ben’ Davis, the junior housemaster, did send to Alan a note telling him to prepare for the worst. Alan immediately wrote1 to his mother, asking her to send flowers to the funeral, which was held on the Saturday, at dawn. Mrs Turing wrote back at once and suggested that Alan himself write to Mrs Morcom. This he did on the Saturday.
15/2/30
Dear Mrs Morcom,
I want to say how sorry I am about Chris. During the last year I worked with him continually and I am sure I could not have found anywhere another companion so brilliant and yet so charming and unconceited. I regarded my interest in my work, and in such things as astronomy (to which he introduced me) as something to be shared with him and I think he felt a little the same about me. Although that interest is partly gone, I know I must put as much energy if not as much interest into my work as if he were alive, because that is what he would like me to do. I feel sure that you could not possibly have had a greater loss.
Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game Page 10