The Three-Body Problem

by Catherine Shaw

  ‘I really don’t know – I suppose they might have.’

  ‘What do these notes in the margin mean?’ I asked him.

  He bent over the sheets and turned them over one by one, deciphering the tiny letters.

  ‘They are odd,’ he remarked. ‘They are very odd, really – what a strange mentality Beddoes had. He must have objected to crossing things out. Look at this one here! On the page it says (A) => (B), that is, A implies B, and in the margin is a question mark. He must have written down A implies B, and then come to question the implication while rereading it.’

  ‘Could it not be that he wrote down what another person explained to him?’ I asked. ‘Then perhaps he could not understand it later, when he looked it over.’

  ‘Yes, I guess that is not impossible,’ he said consideringly. ‘Except that the writing is so extraordinarily neat – it really doesn’t seem like someone taking notes, does it? It looks like a fair copy.’

  ‘Well, he could have copied out the rough notes, I suppose.’

  ‘Sounds strange, but maybe.’ He looked up at me, his eyes brilliant with interest. ‘Yes, I guess I can imagine that. The three of them closeted secretly together, working for the grand prize. One of them – Akers or Crawford – gets up to the blackboard and begins to explain his idea. Beddoes writes it all down. Then he goes home and, being a precise sort of fellow, goes over the notes again, copying them out neatly and trying to make sure that he understands the logical process behind each and every line. Whoever was explaining the idea must have been a little careless about going into the details, because Beddoes has marked a good three or four places he doesn’t understand.’

  Something that Arthur had said during his testimony came back into my head.

  ‘Do you remember how Arthur said in court that at his dinner with Mr Beddoes, Mr Beddoes wrote down a question about some differential equations that he didn’t understand, and Arthur tried to help him with it?’

  ‘Yes!’ he answered excitedly. ‘You’re right! It must mean that Beddoes was working over this manuscript then, trying to understand every bit of it. No, but wait. Why wouldn’t he have just asked Crawford?’

  ‘Perhaps this manuscript holds notes of work by Mr Akers, and he was already dead!’ I cried. ‘But then, it would still have made more sense to discuss it with Mr Crawford, if they were working together. Oh, no! I remember now – they had quarrelled! It is true that Mr Crawford had said that he wanted to dine with Mr Beddoes, but perhaps Mr Beddoes was waiting for the invitation to speak with him about it. Yes, of course. He expected to have dinner with Crawford that very night, but since he did not come, he asked his questions to Arthur instead. He must have had the formulae in his head, for he certainly did not show this manuscript to Arthur. If he hid it so carefully, it must have been a great secret.’

  ‘Well, I should think it would be, if it is really a solution to the grand old problem,’ he said. ‘But it seems that they never had time to write it up and submit it for the prize, since they were both dead within a few days after Beddoes asked his question to Arthur.’

  ‘I don’t know,’ I said slowly, gazing into the fire. It dimmed into confusion before my eyes, and seemed filled with whirling images. Mr Akers, writing down a formula and thrusting it into his pocket. Mr Beddoes, holding a glass of wine, arguing with Mr Crawford, a manuscript on the table between them. A blow with a poker – a blow with a great rock. A gloved hand, carefully, silently pouring drops of digitalin, in a little stream, into a bottle of whisky, and Mr Crawford throwing glass after glass down his throat, exclaiming in triumph. A killer, seeking for a manuscript, perhaps even finding one – but who?

  Fear invaded my limbs once again, as I visualised the gloved figure. Faces flitted in front of its formless visage – those of all my mathematical acquaintances – Mr Withers, Mr Wentworth, Mr Young, even Mr Morrison himself. I became faint with anxiety – I felt myself to be surrounded by murderers! Then the flames took shape, and became flames once again, as I heard Mr Morrison saying,

  ‘You don’t look too well, Miss Duncan. Are you all right?’

  ‘Oh, yes,’ I said confusedly. ‘Thank you so much for your help. I should go home now.’

  ‘I will accompany you,’ he said with alacrity, rising.

  ‘No – no! Oh, no, thank you,’ I said in dismay, recalling my momentary, flickering vision.

  He looked at me intently.

  ‘It may be a little dangerous for you, to wander about the streets alone, do you not think?’

  ‘I need to be alone!’ I cried, and hastily shaking his hand, I made my way down the stairs and out of the door.

  Dora, no one can have made the road homewards longer than I did! For protection, I resolved never to be within less than a few yards from some other person, preferably of the male sex. But each time I fixed upon someone and carefully matched my pace to his, he persistently took a wrong turning, so that I arrived home only after making a remarkable number of squares and rectangles. And even at home, I hardly felt reassured. I barred the doors and windows, yet fear assailed me, and even trying to write to you did not bring me the usual feeling of calm. I got into my bed, and lay rigid, listening to every sound, but after ten minutes I could not bear it any more.

  I got up, lit a candle, and holding the candlestick and my letter, very silently, in the silent house, I made my way to my front door, opened it, and slipped outside, closing it silently behind me. Noiselessly, I climbed the stairs to Arthur’s rooms – perhaps his door was not locked, for Mrs Fitzwilliam often went in and out, to dust, and also, at various times (somewhat grumblingly and against her will) to fetch articles of his that I then transported to him in prison. I tried the door quietly. It opened, and I slipped inside – and here I am.

  I have never been in Arthur’s rooms before, or even seen them. By the light of my candle, I am looking around me. They are harmoniously bare and simple; a little monastery. An antique urn sits in a niche, mathematical papers are scattered on the desk, a worn volume of Shakespeare lies upon the table. If Mrs Fitzwilliam finds me here, she will be really very annoyed. I must rise very early, and slip down the stairs. But now … Arthur’s bed is calling me, and I shall finish this letter, which I am writing with his pen in my hand and his eiderdown pulled about me. In spite of everything, I feel swept up in an unreasonable wave of warmth and safety, and so I shall bid you goodnight.

  Your loving

  Vanessa

  Cambridge, Monday, May 28th, 1888

  Dear Dora,

  Last night, I slept deeply and beautifully, and woke up somewhat later than I had meant. I slipped downstairs with tremendous trepidation (really, I cannot understand exactly what Mrs Fitzwilliam does to provoke such fear!) and, seeing no one, reached my own door with a great sense of relief. There, I found that she had already pushed the daily post under the door, and your very own letter awaited me on the carpet. I tore it open eagerly.

  I read it again and again, struck above all by this extraordinary sentence: There appears to me to be a strange parallel between the famous three-body problem, and that which you are so desperately trying to solve. I see two satellites, Mr Akers and Mr Beddoes, orbiting around the larger-than-life figure of Mr Crawford, struggling with the laws of gravity binding them to him inexorably, and wishing, as it were, to go ‘spiralling off’ to the ‘infinity’ of independent glory. Oh, Dora, what do you mean? Can you mean what I think you mean? Can the preposterous, unbelievable idea which flooded into my mind on reading and rereading that sentence possibly be true? Is that what you are trying to tell me? – you, my twin, who sometimes knows my mind better than I know it myself!

  The more I think about it, the more I feel convinced. Yet can it be? The thoughts and images which whirled in my head yesterday seem to fall into place, and form a new picture, one I had never thought of before …

  I have written down a list of the main events and details, as I recall hearing about them, in order to study whether what I now guess (what
you guessed, Dora?) makes sense.

  Mid-February: Three people met and drank whisky in Mr Crawford’s rooms (according to Mrs Wiggins).

  February 14th: Mr Akers dined with Arthur and talked about the n-body problem, showed him a formula, mentioned a manuscript. Strange behaviour with his medicine: he began to pour it out, stopped after only a drop or two (the usual dose being ten drops) and stuffed the flask back into his pocket. He was killed upon returning home by someone waiting in his rooms. The bottle of digitalin was not found on him. His rooms may have been searched, the manuscript may have been taken; in any case it was never found. Mr Crawford spent this same evening in London.

  Mid-April: Someone visited Mr Crawford in his rooms and had a glass of wine (according to Mrs Wiggins). Also at this time (so perhaps on this occasion?) Mr Crawford and Mr Beddoes quarrelled (according to Mrs Beddoes).

  April 23rd: Mr Crawford addressed Mr Beddoes at the garden party, asking him to dine with him some day shortly. Mr Beddoes seemed surprised (as well he might) but not displeased at this gesture of reconciliation.

  April 30th: Mr Crawford organised a dinner with Arthur and Mr Beddoes together, but excused himself at the last minute because of ill-health. So Mr Beddoes dined with Arthur. He showed him a formula and tried to ask him for help with understanding it. Arthur thought it had to do with the three-body problem though Mr Beddoes did not say so. Mr Beddoes was killed upon returning home, by someone waiting for him in the garden (so someone who knew, somehow, that he would be returning in the evening).

  May 3rd: Mr Crawford dies after drinking whisky containing digitalin which may have been put there any time in the previous weeks.

  May 19th: Emily and Rose find a strange manuscript in Mr Beddoes’ handwriting, with questions and annotations in the margins, purporting to solve the three-body problem. Relation with Mr Akers’ lost manuscript …

  Dora – it all comes together! I am still not sure exactly what happened and how it happened, but in any case I am sure that what you are saying is right.

  What shall I do? What shall I do?

  Should I rush to the courtroom, that terrible courtroom, and pull Mr Haversham aside, or plead for an audience with the judge, and pour out to him all that has occurred to me? But I can imagine him only too well, wearing a patronising smile, and saying to me, ‘You have not the shadow of a proof, my dear young lady, whereas we are now all aware that you have every reason for inventing such a fairy tale.’ And then, how can I tell him what happened, when I am not completely sure yet myself?

  Proof, proof! Is everything to collapse because of proof? I must have proof. What do I have? Nothing, nearly nothing – only the manuscript, and the meaning that it holds. A manuscript which I felt immediately to be the fundamental hinge on which the whole mystery turned, and yet whose sense I did not understand until this very moment.

  No, I need more, I need evidence. Where can I find it? In Europe, on the mainland – in Belgium – in Stockholm!

  It is the only answer. I must leave at once.

  Vanessa

  Calais, Monday, May 28th, 1888

  Dear Dora,

  I am writing to you, not in a moment of leisure, but in a terrible moment of forced inactivity, late in the evening of a day so strange, that I never imagined I would live through one like it. To think that this very morning, I wrote you another letter, in another world – it seems so long ago! No sooner had I concluded my letter to you, than I leapt up, fired by the urgent desire to depart. But for someone whose greatest journey was from the countryside of Kent to the town of Cambridge, and from the town of Cambridge to the great city of London, the prospect of a European journey held something rather terrifying. I hardly knew how to begin. To calm my nerves, I bent my mind severely to a few simple thoughts.

  All that is necessary is to purchase a ticket to London, thence take a boat to Europe … and then continue to purchase tickets and take trains until my destination is reached.

  Surely many people in these foreign countries must speak English, and be kind and helpful. Miss Chisholm will fearlessly leave her country to study in an unknown land, for the love of mathematics.

  Arthur risks his life if I do not act.

  The last thought sent me scuttling out of the house to the small railway station where, quivering with dismay, I forced myself to ask for a ticket to London in a calm voice. It was not so difficult; I purchased a one-way ticket (to the great surprise of the gentleman behind the counter, and somewhat to my own surprise, but heaven alone knows where my adventure will end – I dared not make any assumptions about the date of my return).

  Then I sped home to my rooms and taking out a small valise, rather than the great trunk I had when I first arrived here, I packed only my best grey dress and as many underthings as I could fit in with it. Then I put on the dark brown travelling dress. Shortly before the departure of the train, I grasped the valise firmly, put on my small brown hat, stepped out of doors, filled with resolution, and walked perhaps twenty paces. Suddenly, I remembered something. I stopped and turned around – I thought I saw a surreptitious figure dart behind a corner, and my heart contracted momentarily with fear. But I turned back firmly, re-entered my rooms, took up a large piece of paper and wrote upon it ‘Lessons are cancelled for some days’, pinned it to my door with a severe gesture, and departed once again.

  Taking the train would not have been bad, Dora dear, if I had not been so fearful of all that was to follow. I sat down, and observed my fellow travellers, and waited, trying to control my racing thoughts and consider my next step, until the train drew up in the London station. Then I stepped forth and went to the nearest counter, to enquire as calmly as possible how I could get myself on a boat to Europe. I stood behind a British family who asked as though it were the most natural thing in the world for a boat-train to Calais, and I found myself asking for the same thing. Later, I discovered I could have travelled directly to Ostend in Belgium. But what happened was perhaps meant to be, as you will see.

  I was sent to another counter, purchased a ticket, boarded a train to Dover, stood in various lines, always clutching my valise, and after what seemed like an endless time of trains, stations, lines and waiting, I found myself upon a boat, for the first time in my life.

  The day was fine, the boat lifted and slopped gently in the water; a great many people got on it before and after me, some gabbling away in French, but many as British as you and I. I felt reassured by the presence of these friendly people, and resolved to converse with some of them, to ask if they could indicate a modest but agreeable hotel in Calais, for evening would be drawing in by the time I reached the shores of France, and I thought I should spend the night there, and begin my journey to Belgium as early as I could tomorrow morning.

  I hung over the railings on the deck, looking out over the water, and as the boat slowly pulled away from the shore, and England began to recede, I understood for the first time what is meant by ‘the white cliffs of Dover’, and my heart was torn with emotion at leaving England and all that it held for me – leaving it in danger, as it seemed to me. I felt suffocated with fear that I was making a dreadful mistake, travelling away to no purpose, abandoning Arthur. And yet, as a mere observer, a daily witness to his passive misery, I was so useless – worse than useless! I was walking about the deck, miserable and quite hungry, tormented by the inactivity of travel, when all of a sudden I received a great shock – a shock so fearfully unexpected you can hardly imagine it. Two tender arms were flung about my neck, and Emily – my dear Emily – was in my arms, clinging to me, and talking at a great speed, as though afraid to let me say a word.

  ‘Oh, Miss Duncan, dear Miss Duncan,’ she cried, ‘please help me! Oh, you must help me – no one in the world can help me except you! I have followed you here all the way from Cambridge, but I dared not allow you to see me before, I was so very frightened you would take me back!’

  ‘Emily – Emily, what are you doing here?’ I gasped. ‘Your mother – she must be
out of herself with distress. How could you, Emily – why, whatever are you thinking of? Oh, what can I do with you, oh, what shall I do, what shall I do?’

  My distress was as great as hers, for the idea of turning back from my mission, losing not only time, effort and money but also the courage and the impulse, was dreadful to me.

  ‘It is for Robert, Miss Duncan,’ she told me, her white little face looking into mine, all framed by her soft dark hair, her eyes like pools of sadness, ‘we must save him, you must, you must help me to save him!’

  ‘Robert? Your father’s little orphan? Why, what must we save him from, pray?’

  ‘From Mother!’ she cried dramatically. ‘Mother does not want him, Miss Duncan, she says she cannot bear to have him home, and she will send him to – oh, to boarding school, to boarding school – it is too horrible, and he is only six, only six years old!’

  ‘But my dear child, a great many little boys of six are sent to boarding school, and they are all the better for it,’ I began. ‘Just because your poor brother had such a very dreadful experience there does not mean …’

  But she interrupted me imploringly. ‘Oh, Miss Duncan, it was not just my brother! Every boy in the school suffered so, only Edmund is more fragile and cannot bear it. Oh, you cannot imagine all that he has told me, and some of the things he cries out in his sleep! He cannot bear to go to sleep, it was so dreadful in school; he said he began to be frightened after dinner, and it went on growing all the evening until bedtime. Don’t you understand? You can’t do that to a little boy, especially one who only just became an orphan! Miss Duncan, shall I tell you a story Edmund told me once? It was about his best friend, a boy called Watkins. Watkins was given a message: he was called to see the Headmaster. That meant he was to be punished for something. He was so afraid he cried. Edmund thought it would be worse if he didn’t go, so he went down with him, and waited outside the door, listening. He said he was very surprised to hear nothing – no screams. Then Watkins came out, and he was smiling with relief. And he said to Edmund “Thank God – I’m not to be punished!” Edmund said “Why did he call you?” And Watkins said – “He told me my mother had died.” Oh, Miss Duncan, can you imagine it? Can you? It is worse than a prison! Edmund shan’t go back if I can help it, and neither shall Robert!’