The Three-Body Problem Read online

  THE THREE-BODY PROBLEM

  CATHERINE SHAW

  Contents

  Title Page

  THE THREE-BODY PROBLEM

  MATHEMATICAL HISTORY IN THE THREE-BODY PROBLEM

  About the Author

  By Catherine Shaw

  Copyright

  THE THREE-BODY PROBLEM

  Cambridge, Wednesday, February 8th, 1888

  My dearest sister,

  This morning, for the first time, I felt a breath of springtime in the air. I opened the window and the soft breeze pushed the curtain inwards and brushed my cheek, carrying a hint, a suggestion of warmth within its coolness, instead of the chilly sting I’ve become used to over these winter weeks. I do like the dark evenings, the flickering firelight, the tea and crumpets and books, but I do so detest the cold, bleak mornings, and not being able to walk about outside without being bundled like a traveller to the Poles, and crimped to the bones against the cold even so. If the warm breeze has reached you before me, as is probable, you might even be seeing the first crocuses and daffodils poke up their green shoots, joining the carpet of white snowdrops and blue scilla under the great chestnut tree. If I close my eyes, I can see it exactly as though we still shared our little bedroom and peeped out of the diamond-shaped windowpanes early on the winter mornings, hoping for snow. I know, darling, that you will write to me when you have the strength, and in the meantime, the endless memories speak to me with your voice.

  Beautiful memories, darling Dora – it seems strange, sometimes, even to me, that with so much happiness and delight, I so longed to leave it all. I felt like the baby robins in the nest (have the robins come back to the beech tree this year?); they used to be so delightful and delighted, and yet the day inevitably came when some unseen force drove them to spread their fluttering wings. I felt the nameless call very early, and dreamt in confused silence, until the day when Mrs Squires so suddenly seemed to understand, and offered me to become her assistant in her little school here in Cambridge. On that day, only on that day, I understood the source of my dissatisfaction. Now I know that finally you understand me, and why I need to be far away from home, although I love you all so dearly.

  The little girls will be here in one hour; soon I shall leave off writing in order to get some work ready for them. I have come so far in just a year and a half! Why, I can still remember when the only thing I was fit for was teaching the smallest ones to read – and even then, I had to struggle to find the patience! Mrs Squires made me read dozens of books, instructed me endlessly in Latin and arithmetic, and questioned and scolded me for months before she allowed me to teach anything else. How frightened I would have been if I had known that at the end of just one year, she would be so lucky as to inherit an unexpected windfall, and give it all up, leaving her school to me alone! But it has turned out wonderfully. Not a single family has removed their daughter since September, and two more little girls have even joined the school. The schoolroom is quite overcrowded with the twelve of them now; perhaps I should suggest that after the age of thirteen they be sent elsewhere for a higher level of instruction. And yet, poor things, there is nowhere for them to go, and not many families care to hire governesses or tutors for their daughters. And they do so enjoy themselves here, and are getting on so well. Indeed, the oldest ones are my especial pets and I would be heartbroken to bid them farewell, though I myself am having to study ever harder in order to find things to teach them and keep them interested. I shall just have to find another idea. Sometimes I imagine you could be here with me, darling, taking care of the littlest ones. But I do not believe you would desire it, would you, even if it were possible? Cambridge is not a big town – you can walk from one end to the other with ease, and then out into the fields and countryside – yet it does not really feel spacious, and then living in rooms is so different from living in a house. I am dearly proud of my rooms – a room of my own, and a small sitting room, and the schoolroom, all mine! Not really mine, of course, since the things belong to my landlady, and Mrs Squires arranged them, but they are lovely – and they do contain my very own few things, my drawing of you, and most of all the freedom to do what I like within them. I am never bored for a single moment, between studying and preparing lessons for the girls, and writing letters, within doors, and walking and shopping and exploring, out of doors, being greeted kindly by the members of the different families who live nearby. I am so glad I was not able to accept Mrs Fitzwilliam’s offer to do for me and provide meals, as she does for the lodgers who reside on the upper floors, but the small fee I receive from the little girls really would not have sufficed – and now I find myself joyful and busy in making my modest purchases, preparing tea things on a spirit lamp, and even in the dusting and mending which I learnt so well and disliked so deeply at home. I do believe that people looked askance at me, when Mrs Squires first took her departure, and I chose to remain here, alone and independent, but the wary looks have since disappeared, to be happily replaced by friendly smiles.

  There, I really must close this letter – I have prepared a most wonderful lesson this afternoon, about magnets. I have obtained quite a strong magnet, and with it we sweep metal dust this way and that upon the table into feathery shapes. And then the needle – it is so remarkable! If you have a magnet by you, dear, try this magical experience: take an ordinary threaded needle, and while holding the end of the thread firmly in the fingers of one hand, bring the magnet to the needle so that it holds, then draw it slowly, slowly upwards. The needle will rise with the magnet, until the thread is taut, and then continue to rise until it is standing erect, touching the magnet only with its very point. And then – this is the miracle – if you draw the magnet, ever so slowly, ever so gently, the tiniest distance in the world away from the needle, the needle will not fall, but remain erect and quivering in the air, straining upwards as though with human desire. Let the magnet abandon the needle by a single hair’s breadth further, and needle and thread will collapse in despair.

  Yours tenderly, until my next letter

  Vanessa

  Cambridge, Tuesday, February 14th, 1888

  My dearest twin,

  I am sitting at my little writing table, looking out of the front window onto the street, and observing the most interesting scene. Several gentlemen are collected in a tightly knit group, and one of them has just rushed into this very house, apparently to summon someone. They are clearly gentlemen from the university, clad in their black gowns; it is quite rare to see them grouped so upon the streets. One of them is knocking at the landlady’s rooms, across the hall from mine; yes, she is sending him upstairs, dear me I cannot resist opening the window a crack wider. Here is the gentleman back down again together with a gentleman from upstairs, yes indeed, it is one whom I have had occasion to lay eyes on very briefly once or twice, just passing through the entrance hall. I did not know he was from the university as well. Naturally, how should I have known? Indeed, I know very little about any of the people who live upstairs; Mrs Fitzwilliam keeps a close watch on all comings and goings, so that it is inconceivable to hold even the slightest conversation in the hallway. I know only that the lodger just above me often paces over my head in the night time. I mentioned it to Mrs Fitzwilliam laughingly once, but did not ask her to mention it to the pacer, as in the end I found myself becoming oddly used to the regular, gently creaking sound. I also hear occasional clinks and bumps, but have never yet heard the sound of a voice until – why, until just now! Yes, I do believe our visitor cannot have gone higher than the first floor, he was so quick. Perhaps my nocturnal pacer is this very gentleman who just went out. Heavens, they are telling him the news, whatever it may be – and how excited and distressed they appear to be! and what exc
lamations of ‘shocking – impossible!’ they pour forth! Off they go, in a body, black gowns floating, like a group of crows.

  Well, I shall probably never learn the meaning of all the commotion, any more than I shall penetrate within the mysterious walls where these gentlemen scholars spend so much of their time. What can be hidden there? I know that it can be no more than rooms within and gardens without – some of the gardens can easily be glimpsed even from the street, through the stone gateways of the colleges. Yet in my imagination, they seem so filled with mystery and magic. How strange it must be to go to university, so that one not only studies but actually resides, completely and wholly, in a world of constant thought and contemplation. Why, all the usual activities of walking, eating and laughing must be imbued with the philosophical and scientific ideas, and the words of the ancient languages must be mingled daily with the modern. If only we had a brother who could share some of its secrets with us! I do long sometimes to study better, differently; to be guided by a teacher as well as by books, and to share my difficulties with other students who know the same ones, just as the little girls in my class do, when they bend their curly heads over their desks together, sharing the same book. Oh, well, I suppose I should not even bother to indulge in such idle thoughts.

  The girls are gone for today; I shall make tea, and save the anecdotes and mishaps of these last few days for my next letter.

  Yours tenderly, until next time

  Vanessa

  Cambridge, Monday, February 20th, 1888

  My dearest Dora,

  Thank you so much, darling, for the few words you added to Mamma’s letter. I was so sorry to read about how tired you have been. Mamma says it is not really any particular illness, but merely fatigue. I do so hope that the springtime will bring you health and happiness. If you are having a warm spell as we are, you should sit in the garden at least a little bit each day. I feel in haste to return home for a visit, but it will not be possible before the Easter holidays. I do hope, I do expect to find you entirely recovered by then. In the meantime, until you feel well enough to write me a true, long letter, I do not suppose I shall hear a single word about the interesting Mr Edwards, as Mamma would not mention his existence for the world. Dear Dora, if you have even so much as glimpsed him lately, do please just put an exclamation mark in next time you send me a word – then I feel I shall understand more. And if you read some bits of this letter aloud later on, please leave out that last sentence!

  I hesitated a moment about putting in this newspaper clipping from the Cambridge Evening News, a newspaper only recently established here. It dates from the 15th, and it does seem a bit unsuitable for an invalid, but then – I know you want to know what happened, just as much as I want to tell it to you. You couldn’t possibly guess it! I do believe I have found out the mystery concerning my upstairs neighbour, whose name I now know to be Mr Weatherburn. The very day after I wrote to you, I saw this alarming headline right on the front page of the evening newspaper, announcing the shocking discovery which you may read for yourself.

  MATHEMATICIAN MYSTERIOUSLY SLAIN

  Dr Geoffrey Akers, a Fellow in Pure Mathematics of St John’s College, aged 37, was found dead in his rooms today, struck down by a violent blow to the head with the poker taken from his own fireplace. Still clad in his overcoat and scarf, his hat hung upon a nail near the door, he appeared to have barely stepped into the rooms when the fatal blow fell. The body was discovered this afternoon by a student, Mr Rayburn, who, having waited in vain for his tutor to appear at their scheduled meeting, walked to his rooms in the college to check if he had forgotten about the appointment. ‘He frequently forgot meetings or lost track of the time,’ Mr Rayburn said. The unfortunate young man, having arrived at his destination and knocked in vain, tried the door as a mere gesture before turning away, and found that it opened at once.

  Thereupon he saw the body of his tutor stretched lifeless upon the floor, and after taking only the briefest moment to ascertain the situation, he dashed off immediately to call for a doctor and a policeman.

  The doctor, being the first to arrive upon the scene, examined the body and was immediately able to absolve the student from all blame, as the Fellow had been deceased for between twelve and sixteen hours, which is to say that the fatal blow was struck between nine o’clock last night and one o’clock this morning. Having alerted the police, Mr Rayburn then hastened to let his colleagues know of the dreadful event, and it soon emerged that the unfortunate victim had dined last night with another mathematician, Mr Weatherburn, a Fellow at Trinity College, who must have been the last person to see him alive.

  The question of whether Mr Akers had any particular enemies who might have wished him ill elicited a peculiar reaction from the tightly knit group of his erstwhile colleagues. After an awkward silence, a voice spoke up: ‘There’s not many that Akers hadn’t offended or quarrelled with, when you think of it.’ ‘Yes indeed, Weatherburn’s one of the few that would still talk to him,’ added another. ‘If they want to find out who did it,’ put in a third voice in calm and level-headed tones, ‘it doesn’t seem that motive is going to be a very useful angle of attack.’

  Mrs Wiggins, the bedder who did the deceased’s rooms, could not but agree. ‘A very nasty gentleman, ’e was,’ she informed us after due negotiations had been concluded. ‘I shan’t miss ’im. And ’is rooms, very dirty they was sometimes, at least not so much dirty as dusty and messy, and ’im grumbling whenever anything was moved. ’Ow one could do one’s job properly is beyond me, when a man’s that way.’

  Fortunately, our police force have experience and intelligence behind them, and we feel certain that the mystery will soon be entirely cleared up.

  Dora dear, the newspaper doesn’t say so, but isn’t it dreadful to think that someone really did strike down that poor man, no matter how horrid he might have been, and that very person is hiding it inside himself right this very minute, and smiling and talking and probably even telling people how he never disliked poor Mr Akers so very much, though everyone else did. Perhaps they really do ought to be looking for the only person who didn’t hate him. Oh no – that would bring them to my poor neighbour, Mr Weatherburn, then, wouldn’t it? Oh, he did look so upset the evening of the article, when he came home. He was brought back to the house by policemen; I didn’t notice it myself, as I was making toast (I really should not live quite so much on toast), but I heard Mrs Fitzwilliam’s voice in the hall, and she talked ever so much more than usual, and she sounded Most Displeased, and the words Police and My House were very frequently to be heard. I felt sure she must be scolding poor Mr Weatherburn for something which really was not his fault, and already he paces at night, the poor man, and I so wanted to come to his aid, but I couldn’t think of any reason, so I just suddenly opened my door and said ‘Mrs Fitzwilliam, I am so very sorry to disturb you, but I – I—’ and I was just feeling quite foolish when the toasting fork, which I had balanced with care, fell over and crashed into the fire, sending up a shower of sparks and a fearful smell of burnt toast. Mrs Fitzwilliam said ‘The carpet!’ and rushed into the room, and Mr Weatherburn looked at me and then turned away quietly up the stairs. Mrs Fitzwilliam swept up the ashes, a little angrily, but then she said ‘such goings on!’ and I saw that she wanted more to talk about it than she wanted to be cross with me. But as she never gossips, in fact almost never speaks, she could only say ‘such goings on, and a respectable house!’ I tutted and sympathised, for she is immensely proud of her stately home on the Chesterton Road, although she does have to let nearly all of it. I told her that surely nothing so very dreadful could be associated with her house, and she asked what it was I had wanted of her, and I said it had quite gone out of my head, and she said how were the girls doing and I said lovely. I could see a great struggle in her, because she truly believes that respectability has a great deal to do with not telling anything, in which she is perhaps not entirely mistaken, but dismay and indignation, perhaps even some excitemen
t were boiling up in her too. In the end, though, she simply bid me good evening – it was a great triumph of discretion over curiosity! Hmph, if I have another opportunity to do so, I shall offer her of cup a tea, and try to break the ice. I do think it is all so interesting – at least, well, not interesting, not about poor Mr Akers … but, well, a little of the rudeness of real life has irrupted into this quiet household. Whatever will come of it, I wonder?

  Your very loving sister

  Vanessa

  Cambridge, Tuesday, February 28th, 1888

  Dearest Dora,

  Oh dear. No exclamation mark. Do you know – tiredness and sadness are not so different as one might think. One feeling might be so easily mistaken for the other. It’s strange how little one knows about one’s own feelings really. Do you know that I felt quite a new one, the day before yesterday? Here I was, all alone in the evening as usual, quietly making – no, not toast, for once, but soup over the spirit lamp, and I felt quite an odd feeling inside me. At first I thought I might be hungry, but then I had such a very incongruous thought – I thought of stepping across the hall and visiting Mrs Fitzwilliam! – and it suddenly came to me that I felt lonely. I looked at my books and did not feel like taking any of them up. It would be nice to have a companion, someone sharing the rooms, as I used to with Mrs Squires. We did have such nice conversations, often. But then, I love to be alone, and no hint of loneliness ever crept into my life at all, until today. It is beautiful to meet someone’s gaze, sometimes, with understanding, however briefly, but it can also unsettle sweet habits. At least, I know that you and I understand each other and always will – with or without words, as only twins can – about this and everything else.