The Three-Body Problem Read online

  Professor Cayley: Undoubtedly.

  Mr Haversham: Now, as to the publication of an article drawn from research done as part of a doctoral dissertation under your guidance. Would you say that that is normal procedure?

  Professor Cayley: Certainly.

  Mr Haversham: All students do it?

  Professor Cayley: All those who succeed in writing a doctoral dissertation containing material original enough to warrant publication.

  Mr Haversham: So that it cannot be used to conclude that Mr Weatherburn is not an independent mathematician, or makes abusive use of the help of others to advance in his profession?

  Professor Cayley: Absolutely not.

  Mr Haversham: Thank you very much, Professor Cayley. I have no more questions.

  The judge invited Professor Cayley to stand down, with flowery expressions of respect, and the bailiff appeared to usher him politely to the exit. He was not required to waste a single moment of his precious time more than was necessary for the taking of his deposition.

  I considered Professor Cayley’s testimony to be highly positive for Arthur. But the stolid and impassive faces of the members of the jury did not seem to reflect such feelings. Perhaps it should be considered a draw.

  Following Professor Cayley, Mr Morrison was called to the stand.

  Direct examination of Mr Morrison, by Mr Bexheath

  The witness was sworn in.

  Mr Bexheath: Please state your name, age and occupation for the benefit of the jury, sir.

  Mr Morrison: My name is Charles Morrison, I am twenty-seven years old, and I hold a Fellowship in Pure Mathematics at the University of Cambridge.

  Mr Bexheath: When, where, and under whose direction did you write your doctoral thesis?

  Mr Morrison: I completed it three years ago, here in Cambridge, under the direction of Professor Arthur Cayley.

  Mr Bexheath: How many articles have you published in professional journals since that time?

  Mr Morrison: Six, some under my name alone, others in collaboration.

  Mr Bexheath: How many of these articles were written in collaboration with the prisoner?

  Mr Morrison: One.

  Mr Bexheath: How many articles has the prisoner published?

  Mr Morrison: Two, but it doesn’t mean anything!

  Mr Bexheath: Mr Morrison, please confine yourself to strictly answering my questions. Your opinions are not required here. Now, let us turn to the article you published jointly with the prisoner. I would like to ask you some questions concerning your contributions to that article, as compared with those of the prisoner. I wish to discuss the procedure of writing an article jointly. How is it possible for a mathematical idea to germinate in more than one mind?

  Mr Morrison: Well, what usually happens is that conversation with another person, possibly more of an expert than oneself in some aspect of the material under discussion, stimulates the idea.

  Mr Bexheath: That is a very interesting answer. So, before writing this article together, you and the prisoner had mathematical discussions?

  Mr Morrison: Oh, yes.

  Mr Bexheath: Frequently?

  Mr Morrison: Oh, yes, quite frequently.

  Mr Bexheath: And one day, these discussions caused a new idea to germinate?

  Mr Morrison: Yes.

  Mr Bexheath: Mr Morrison, how would you say that the ideas contained in those articles which you published alone germinated?

  Mr Morrison: Well, you think about something by yourself, looking at it, turning it over from all angles, trying to figure out what it looks like and how it works, until suddenly you see the light.

  Mr Bexheath: So mathematical ideas can be stimulated either by conversation or through deep and tenacious personal reflection?

  Mr Morrison: Yes.

  Mr Bexheath: Now, let us take the situation you have described; two mathematicians are talking about some problem in mathematics, and all of a sudden, some remark made by one of them, whom we can imagine to be a well-educated mathematician who has recently completed brilliant studies, causes the other one, whom we can imagine to be an imaginative and fertile mathematician with several original publications to his credit, to ‘see the light’, as you put it; to perceive, say, a solution to some problem. What would the procedure of publication be in a case like that? Would the two mathematicians publish jointly, or only the one who actually came to the solution?

  Mr Morrison: It all depends on how big, how necessary the help given by the other one was, and what kind of relations they had with each other.

  Mr Bexheath: If they are close friends and peers, for example.

  Mr Morrison: Well, there is no rule.

  Mr Bexheath: But it is quite likely that they would publish together?

  Mr Morrison: It certainly could happen. But my collaboration with Arthur Weatherburn wasn’t at all like that.

  Mr Bexheath: Mr Morrison! You will confine yourself to answering the questions.

  Mr Morrison: That whole story of motive you invented was just arrant nonsense, Mr Bexheath!

  Mr Bexheath: Mr Morrison!

  Mr Justice Penrose: Mr Morrison, you will please cease these extraneous remarks. That last one will be struck off the record.

  Mr Morrison: Strike it off, but it doesn’t make it any the less true. Arthur is a first-class mathematician!

  Mr Justice Penrose: Mr Morrison! Desist immediately. That last remark will also be struck off the record.

  Mr Morrison: This is all wrong!

  Mr Bexheath: My examination of this unruly witness is terminated.

  Mr Morrison: I still have a lot of things to say.

  Mr Justice Penrose: Mr Morrison! You are not in court to express your personal opinions! Please be quiet at once. You will now be cross-examined, and I pray that you CONFINE YOURSELF TO ANSWERING COUNSEL’S QUESTIONS, otherwise you will be held for contempt of court.

  Cross-examination of Mr Morrison, by Mr Haversham

  Mr Haversham: Mr Morrison, I would like to ask about the joint article published by yourself together with the prisoner.

  Mr Morrison: Yes, and I should greatly like to answer.

  Mr Justice Penrose: Mr Morrison!

  Mr Haversham: Would you say that that article contains a valuable mathematical idea?

  Mr Morrison: Frankly, it contains what I believe to be more than just an idea; the beginnings of a fascinating new theory.

  Mr Haversham: In a joint article, it must often be extremely difficult, if not meaningless, to try to discern which author is responsible for what concept. Would you say that this is the case for the article in question?

  Mr Morrison: No, actually.

  Mr Haversham: No?

  Mr Morrison: Well, no. In the case of our article, it is actually quite clear.

  Mr Haversham: Would it be possible for you to give some description of the nature of your collaboration with the prisoner, and of your respective contributions to the joint article?

  Mr Morrison: Yes. Arthur has a theoretical mind which grapples with vast concepts, whereas I like to solve problems using techniques, often adapted from those developed by Professor Cayley, in interesting ways. I was showing Arthur how I solved some technical problem or other, writing on the blackboard, and he was listening. All of a sudden, he said to me something like ‘What you’re doing is just the tip of the iceberg!’ He realised what I hadn’t realised; that I was just working on a special case of a grand theory which could be applied to solve a great many different problems by a coherent, general expression of my technique. I thought his idea was fantastic.

  Mr Haversham: So you do not agree with my learned friend’s evaluation of the process of the collaboration between you.

  Mr Morrison: It’s plain ridiculous! Arthur’s just talking mathematics all the time with people, because they always want to talk to him, seeing that he knows so much about practically every subject. As for trying to imply that having published more articles or less articles is a reflection of one’s mathematical c
reativity, it’s all rot. One deep article can be worth a bushel of little ones.

  Mr Justice Penrose: Mr Morrison, you will immediately cease to employ insulting terms. This is a court of justice. Behave yourself accordingly!

  Mr Morrison: Yes, my Lord. Let me express myself better. (Pinchedly) The arguments submitted by the counsel for the Crown, tending to indicate that the value of a mathematician’s depths, originality and creative power can be measured by a yardstick as crude as the positive integer denoting the quantity of published articles is a mistaken point of view, which bears the risk of misleading the members of the jury, who are unfamiliar with the nature of mathematical research, into unfortunate errors of judgement.

  Mr Haversham: (hastily) My cross-examination is finished, my Lord.

  Mr Justice Penrose: In that case, this wearisome witness would do well to stand down immediately. Court is adjourned.

  Oh, Dora – even the jury smiled sometimes during this deposition! When Mr Morrison came back to the witnesses’ bench, I could have kissed him! I found it inside me, for the first time, to forgive him for having been convinced of Arthur’s guilt in the first days. If only things continue this way, then Mr Bexheath’s horrible arguments will all fall apart. Oh, if only it could happen so!

  Your very own, somewhat more optimistic

  Vanessa

  Cambridge, Saturday, May 19th, 1888

  My dearest Dora,

  Some days ago, I met poor Mrs Beddoes in a shop, and she stopped to speak to me. She seemed pleased to see me, if one can use the word pleased of someone who seems inexorably separated from the outer world by a barrier of inner mourning. We spoke for a moment, and she asked after Rose and Emily, and invited me to bring them to tea; she told me that the silence of her lonely house was full of sorrow, and I felt that she would like to chase it away, however briefly, with the voices of children.

  Today, I had no lessons, and felt reluctant to remain alone, and I do not know exactly what faint feelings drew me towards her; I felt the need to talk to her, because she was placed so near the centre of my troubles. I went to see her, therefore, this morning, and she welcomed me with pleasure – no; again, the word is not applicable, but she said that it would give her great pleasure to have Emily and Rose for tea, and spend a moment in the company of their adorable pink cheeks and gaiety. I then called on the girls’ mothers and obtained their permission, and at four o’clock this afternoon, the three of us made our way together through the garden gate and up the pretty path, half-smothered in flowers, where poor Mr Beddoes met his death less than two weeks ago.

  When Mrs Beddoes perceived our approach, her sad and rather tired face lit up with a kind smile. She (or her cook) had prepared sundry scones, sandwiches and cakes, of which we partook with a distressing lack of moderation. The little girls then went to romp outside in the garden back of the house, which runs long, rich and green down to the fence behind. They soon discovered the tiny wooden shed which Mr Beddoes had built at the end of it to lodge his cats, as Mrs Beddoes could not bear them in the house. She smiled as she saw the girls, through the glass door, chasing and playing with the animals, of which I made out at least six.

  ‘The little kittens have grown now, they dearly love a romp,’ she said. ‘We meant to give them away; my husband had already written out a list with their descriptions.’ She showed me the neatly printed little list, in which each kitten was identified by a fanciful name, together with its colour and description.

  ‘Now I feel that I should keep each and every one of them,’ she went on, ‘they may have been the last thing which gave my husband joy before his death. I cannot really abide them, but they do not need much care; I simply put food out for them. Mr Beddoes used to visit those kittens several times a day, when they were tiny things still in their basket.’

  She wanted to talk a great deal about Mr Beddoes, and I wanted nothing else, hoping against hope to learn something, anything at all that could help some new understanding develop in my mind. The house was so fresh and pretty, the garden so blooming, and she herself so kind and welcoming – yet, behind the scene lay the pale echoes of other images; a dark night, a creeping, hiding person, a dead man lying across the path, a widow weeping alone.

  ‘Everyone perceived my husband as a gentle and accommodating man,’ she told me. ‘And indeed, he was; he did not like disputes of any kind. Yet his feelings and opinions were strong, although he was very private about them. I believe no one really knew how much he thought about most things, to hear how casually he mentioned them. And although he was friendly with everyone, he did not have many real friends.’

  ‘Who were his closest friends?’ I asked.

  ‘Oh, he talked most often about Mr Crawford,’ she smiled. ‘They were really a pair, those two – so very different from each other! You saw Mr Crawford – he was so very loud and strong-minded! Their friendship was all full of ups and downs on account of it. Philip always avoided quarrels – he used to say that they were no way to solve any problem of any kind. But as Mr Crawford did not avoid them, they did occasionally happen; Mr Crawford would shout, and Philip would come home most annoyed. It happened just a month or two ago. He visited Mr Crawford, and something must have come up between them, for he came home and told me they’d had a most disappointing discussion, and Crawford was furious on account of it. Philip was not pleased himself, by any means, but it was not his way to quarrel. He would ruminate alone, and see how to obtain what he wanted by his own means.’

  ‘Did they make up their quarrel afterwards?’

  ‘Oh yes, they did. We saw Mr Crawford at the garden party after Professor Cayley’s lecture, do you remember? And he behaved as though nothing was amiss. Philip was happy enough to let it go at that. They always did make up their quarrels sooner or later.’

  ‘Yes, I remember,’ I said. ‘Mr Crawford suddenly greeted Mr Beddoes, and even said that he wanted to dine with him soon, and Mr Beddoes seemed quite surprised.’

  ‘Yes, he was, for Mr Crawford had quite a temper. I never could take to him really. Yet he and Philip had something in common, I know, though we rarely spoke of it. Their profession is a difficult one, my dear. You cannot imagine what it is to live for so many years among mathematicians. It seems as though the striving and disappointment and frustration which must naturally accompany any kind of scientific research must constantly struggle within them, against the joy and elation of discovery. Mr Crawford was a bitter man, really. He was truly brilliant, I believe; at least Philip often said so, but because he made one or two serious errors in the last decades, publishing results which turned out to be flawed, he lost some of the consideration of his colleagues, and he felt that his true worth was unjustly unrecognised. It seemed to me sometimes that he blamed the whole world for it, he was so very aggressive. My husband was also bitter at moments, though not for the same reason. He admired the ideas of others, but his estimation of his own work was a permanent disappointment to him; he often felt that something great had come nearly within his grasp, and he had let it escape. I believe this perpetual resentment and bitterness is the curse of many mathematicians; certainly Philip worked and sought and studied as hard as any.’

  Her eyes filled with tears as the memory of her loss arose in her, and she changed the subject suddenly. ‘Let us go out in the garden,’ she said. ‘My husband always used to walk about in it while he was working. And he had been working so very hard these last months, upstairs in his little office; there were days when he seemed absolutely delighted, and others which were rather terrible. All of the mathematical papers he left upstairs have been sorted and studied by his colleagues and students; several of them came here, and they looked at everything so carefully, and did a lovely job. It can’t have been very difficult; Philip’s handwriting was as clear as print.’

  We went out, and joined the girls, who were playing with the kittens, and dancing about with twinkling eyes.

  ‘We cleaned out the kitties’ house!’ they told us proudl
y. I bent my head to peer inside the little wooden structure, which Mr Beddoes had built with his own hands for his beloved cats, and admired how the girls had swept it out with a branch and shaken out and plumped up the colourful quilted morsels which cosily lined each basket.

  ‘Thank you so much, my dears,’ Mrs Beddoes told them. ‘I should do it myself now and then, but the cats do so make my eyes water! Perhaps you will come again some day and do it for me.’

  She bid us goodbye kindly, and we went on our way, the girls discussing cats and giggling violently over some shared secret, and I walking along absently, my mind on the quarrel between Mr Beddoes and Mr Crawford, which had taken place ‘some days’ before the garden party of the 23rd of April. What could it have been about, I wonder? I am sure it is a clue.

  I must ponder it all in solitude,

  Your loving Vanessa

  Cambridge, Monday, May 21st, 1888

  Dear Dora,

  The third day of the trial has begun. It appears less favourable than yesterday, and yet I still find that Mr Bexheath is not succeeding in providing anything like a proof of his case that eliminates the Mr Crawford theory, in spite of all his leading questions and the answers he elicits. On the other hand, although Mr Haversham makes some progress in spoiling the coherent impression that Mr Bexheath would like to give, he makes very little in eliciting any useful positive information in support of the alternative theory … and nothing at all which could help us to determine whether or not it is true. Yet it must be true. For what else, what else is possible?

  The first witness called this morning by the prosecution was Mrs Wiggins.

  Direct examination of Mrs Wiggins, by Mr Bexheath

  The witness was sworn in by the court clerk.

  Mr Bexheath: Please give your name, age and occupation.

  Mrs Wiggins: Alice Wiggins, fifty-one, charlady of St John’s College.

  Mr Bexheath: Were you responsible, until his death, for cleaning the rooms in college of Mr Geoffrey Akers?