The Three-Body Problem

by Catherine Shaw

  Upon her remark, everyone looked at each other, and there was a moment’s silence. Nobody appeared to know the answer to this very interesting question.

  ‘Yes, it’s worth finding out about that, isn’t it,’ said Mr Weatherburn slowly.

  Then dinner was announced, and we all went in, arm in arm; Mr Cayley took in Mrs Beddoes and Mr Beddoes took in Mrs Cayley. Mr Morrison took in his sister, and Mr Wentworth took in Miss Forsyth, who is Emily’s governess, and was asked by Mrs Burke-Jones to join the dinner in order to even out the numbers. She teaches Emily all the things I know nothing of (alas): music, embroidery, French and German. Mr Young took in Miss Chisholm, and you can see for yourself who was left.

  The dinner was delightful, in a lovely room, not very large but spacious and attractive. Mrs Burke-Jones’s house must be very nearly as large as Mrs Fitzwilliam’s, and it is all for herself and her family, and her servants! Her brother, Mr Morrison, lives there too, as I learnt afterwards. During dinner we talked about all kinds of things; that is, the others talked, and I listened a great deal, and exchanged only a very few words with my left-hand neighbour, as I did not seem to be able to do more without blushing uncomfortably. Things were somewhat easier with my right-hand neighbour, Mr Beddoes, who became quite agreeable as the dishes succeeded each other, and barked out kind remarks in my direction, such as ‘So you teach, do you?’ and ‘Whereabouts are you from, my dear?’ before becoming reabsorbed in his plate and glass. The others spoke of general things, politics, India, Queen Victoria, and various other topics, to all of which I listened eagerly, feeling sadly ignorant because of my sheltered life. Dear me, to think that I dare to teach anyone anything, when I know so little! Between the stammering awkwardness on my left and the sharpness on right, and my own feelings of ignorance, I was a little nervous the whole time and unable to appreciate the details of the meal itself, although it did seem very different from either toast or soup.

  After dinner, the six ladies retired to the drawing room, actually only five of us, because Miss Forsyth returned upstairs to the children. The conversation was most interesting – Mrs Burke-Jones appears to have lost her husband some years ago – at least she did not say so, but seemed sad for a moment, and said that six years ago she had asked her brother to occupy the upstairs apartments, as she felt uncomfortable alone with children and servants in such a large house. He, naturally, was only too happy to oblige, and be spoilt and pampered. (She really did say this, with nothing like the respect due to a promising young research fellow of the university!) I believe he is her younger brother. She told me that Emily also has a younger brother, Edmund, who is to Emily just as Mr Morrison is to her. Edmund is sent to a very good boarding school, which strains the family fortunes rather, I gathered, though Mrs Burke-Jones only sighed and said it was not always easy. She added that Edmund is very fragile, and that she feels she must have him home occasionally on weekends, although the school does not approve. He did make a brief appearance later with his sister, and it was like seeing a frail white rose next to a blooming pink one. Mrs Cayley asked him if he enjoyed his school and was looking forward to going back next day. I think it was a mistake. Already pale, he became paler and cast his eyes about, until Emily stepped forward and relieved the situation by stating categorically, ‘Naturally he likes home better.’

  The most amazing thing I learnt, however, in the course of our postprandial conversation, was that Miss Chisholm is a student at the university! She studies mathematics at Girton College, of those two colleges I learnt about from Mrs Burke-Jones, where ladies may enrol. Mr Young is her tutor there. She says that in England, ladies may only study for the degree called the Tripos, but they may not attempt to write doctoral dissertations. It is, however, possible although rare for a lady to write one in Germany, and she would like to travel there after having passed her examinations here. When she talks about it, she sounds like the way I felt when I first thought of coming here: eager, but almost frightened. I do hope I will have a chance to meet her again.

  I digested all these facts and allowed my mind to dream and roam, this afternoon, during a lengthy ramble, taking advantage of the lovely weather on the one day that I am not required to spend all the afternoon indoors. Although most often, I love to wander out of the town into the fields, or take the direction of Grantchester, today my legs carried me straight towards the university: down the Chesterton Road past Jesus Green, left on Magdalene Street and then into St John’s Street; why, it is almost as good as reading one’s Bible! I could not resist taking a particularly good look at St John’s, where poor Mr Akers was a Fellow. I remained there for a moment, gazing upon the imposing red facade, above whose main gateway, flanked by octagonal towers decorated with white brickwork upon the red, a set of ancient arched windows is topped by medieval crenellations over which one half expects to see the tip of an arrow pointing, ready to shoot.

  I passed the less imposing although similarly styled gateway leading to Trinity College, somewhat distracted by recalling that it was not only the college whose walls once were home to Isaac Newton, but that they also constituted the daily place of work of my neighbour Mr Weatherburn. Turning into Trinity Lane, I passed the more modest colleges there as in a dream, and turned to walk along the Cam, between the green fields dotted with daffodils and crocuses, upon which gave the back parts of Trinity and St John’s with their tempting and mysterious ramparts and bridges with nostalgic names. Cambridge is a beautiful place, Dora, not least because its fields and buildings are all steeped and burnished with meaning from the past. No, decidedly, I have no regrets about coming here.

  My very best love until next time,

  Vanessa

  Cambridge, Monday, March 12th, 1888

  My dearest sister,

  I have made great friends with Emily since the dinner party. She would like to see a new Knot every day, but I am restricting her to a single Knot each week; they require successively more and more reflection, and she has promised on her honour not to seek help from her uncle. I am to go to tea at her house at least once a week, from now on, she says! I must say that such outings hold great pleasure for me, as a change from my own rooms, and Emily is a delightful girl, not in the least bit infantile, and possessed of a sharp, enquiring mind.

  Today was our very first tea date; we had it in the nursery together with Miss Forsyth, whose first name is Annabel, though I must not use it because Emily may not. We took it in turns to tell Emily about our early childhood, and asked her a great many questions about hers, for Miss Forsyth has been with her only six years. Before Miss Forsyth, she had a French governess, who cared for both herself and her brother, and she told us how happy the family had been all together, and talked at length about her father. There was something sweet and strange about the way she spoke of him, almost as though she did not know, or feel, that he was dead, but thought of him as being somewhere far away, but thinking and caring about her and waiting to see her again some day.

  We asked her how it had happened that her governess had left, but she answered rather oddly, that she really did not know what had become of her, with a curious indefinable tone in her voice. It seems as though she is holding back some secret, or perhaps has simply heard tell of things she could not understand, and keeps them in her little heart, waiting for the future to bring wisdom. She told us that the decision had been taken at that time to find a school for her brother, and that he cried terribly and begged not to leave home. Although poor Emily was only seven years old at the time, she understood that after the changes that had been so suddenly wrought within the family, little Edmund would scarcely be able to endure an even greater one, whereas their mother seemed to think that a fatherless life at home would be unbearable for him. The children were compelled to submit, naturally, but Emily’s mutinous little face told us how right she still believed herself to be. After what seemed a great effort to remain discreet and ladylike, under the gentle pressure of my questions, she suddenly burst out in a passion a
nd told me how her brother hated school with all his heart, and longed only to return home, that he was vexed and tormented there day and night by the other boys, all of whom undergo brutal treatment by the masters. ‘Oh, Edmund says they beat them horribly,’ she cried heart-rendingly, ‘he says they have to go into the headmaster’s office, all white and trembling and then those outside hear the most awful screams. Edmund says it’s near as bad or worse when it’s somebody else as when it’s himself. I’m so happy, so happy I don’t have to go to boarding school! If only he could just stay at home with us, and go to your school, Miss Duncan!’

  Could such awful things really be true, Dora? I so often envied boys their luck, free to travel, to leave home, to go to school and later explore the whole world. But perhaps – in fact quite probably, I am learning, having had no brothers, I understood nothing of the masculine realities, and keep only an ideal image within me. Poor Edmund! I would be only too happy to include one pale little boy in my group of blooming girls, if only it could be allowed, but I expect it is perfectly unthinkable. I tried greatly to cheer up Emily in all kinds of ways, and distracted her so well with foolish stories that in a few moments she was shouting with laughter instead of near tears.

  And who should come into the nursery just at that very moment, as we were finishing our tea, but Mr Morrison! He sat down on a low stool, stretching his legs out in front of him, and said we seemed to be having a far better time than the grown-ups at proper tea down below, and that he’d be dashed if he didn’t prefer to stay with us. Emily played the fool, teasing him in all kinds of ways and saying he would do nothing of the kind, until he laid a bet with her that he would not only come along next time she had a tea party, but bring his friends. Dear me – I do hope he was merely joking.

  ‘I would be so grateful,’ I asked him, ‘if you would tell me something about the Birthday Competition I heard mentioned the other evening. Was it not a celebration of some king’s birthday? What king could possibly wish to celebrate his birthday with mathematics?’

  ‘Why, by all means,’ he answered eagerly. ‘Our benefactor is King Oscar II of Sweden, of the Bernadotte family. He studied mathematics in depth while at the University of Uppsala, and has a great fondness for the subject, as well as a close friendship with Sweden’s leading mathematician, Gösta Mittag-Leffler. The Birthday Competition was his own suggestion, and I believe that rather than using mathematics to celebrate his own anniversary, he entertains the hope that the illustrious date, surely to be accompanied by pomp and festivities of all sorts, may shed some glory onto at least one member of the horde of unknown but devoted researchers scattered all about Europe, and illuminate the one and only Swedish mathematical journal. Furthermore, in posing a specific problem as the subject of the competition papers, he hopes to motivate such work as may possibly produce a solution.’

  ‘And is it possible to tell me what the subject of the competition is?’

  ‘Why, I have a couple of volumes of Acta Mathematica in my room below,’ he said, ‘the announcement of the competition appeared there some two or three years ago, and I may well have it.’ And ignoring my remonstrances and expostulations that he not disturb himself, he sped away to investigate, and soon came back with the volume in hand, to show me a page so unintelligible to me, that he might not have taken the trouble! To begin with, not only the announcement of the competition, but the entire volume, is written partly in French and partly in German, without a single English word between its two covers. The volume begins with the announcement of the competition, written in columns with the left-hand one German and the right-hand one in French – it looks rather as though French were a briefer language than German, with great gaps between the French paragraphs, so as to make them begin at the same levels as the corresponding German ones. I could not understand much of it, although many of the French words such as ‘anniversaire’ and ‘mathématiques’ certainly do appear familiar. But Mr Morrison sat himself at Emily’s school desk, and taking her quill in hand and drawing a bit of paper towards him, began to translate it for me, transferring his gaze from the page to his writing to my face, and interspersing his translation with all manner of interesting remarks and explanations, so that I could not be bored for a single moment, although the text is not only quite long but almost impossible to comprehend without the aid of friendly explanations!

  HIS MAJESTY Oscar II, desirous of giving a fresh proof of the interest SHE – no, I mean he, but in French it is always ‘she’, as for some peculiar reason His Majesty becomes Her Majesty – Mr Morrison explains that Majesty is feminine – and that the possessive agrees with the object rather than the subject in French – oh dear – feels in the advancement of the mathematical sciences, an interest SHE – I mean HE, these capital letters make it seem rather Biblical somehow, but they are really that way in the original – has already shown by encouraging the publication of the journal Acta Mathematica, which lies under HIS august protection, has resolved, upon the 21st of January 1889, the sixtieth anniversary of HIS birth, to offer a prize for an important discovery in the domain of higher analytical mathematics. This prize will consist of a golden medal, carrying the image of HIS MAJESTY and having a value of one thousand francs, as well as a sum of two thousand five hundred golden Crowns (1 crown = about 1 franc and 40 centimes).

  ‘Must all mathematicians, then,’ I enquired, ‘necessarily be familiar with the French and German languages?’ Emily had crept near us and was listening with interest as her uncle translated.

  ‘Oh,’ he responded with a slight blush, ‘not to speak, so to speak. We merely need to read the languages, and even then, only to read mathematics in the languages. It is far easier than trying to read a novel; why, at worst, we need only look as far as the next formula, which is written in a kind of international language, equally intelligible to everybody.’ And he showed me a formula on the first page of the article following the announcement of the competition, which said something to the effect that x dx + y dy = 0 has for general integral y = My goodness.

  HIS MAJESTY has deigned to confer the care of realising HIS intentions to a commission of three members: Mr CARL WEIERSTRASS in Berlin, Mr CHARLES HERMITE in Paris, and the Chief Editor of this Journal, Mr GÖSTA MITTAG-LEFFLER in Stockholm.

  ‘Weierstrass is really the most venerable and famous of German mathematicians of today,’ Mr Morrison told us, ‘the father of them all, in some way, something like Professor Cayley here in Cambridge, who should have been on the commission, they say, had an Englishman been included at all. Do you know, Miss Duncan, that Mr Weierstrass is quite famous for having produced not only mathematical ‘sons’, but also a ‘daughter’? Yes, the famous Sonya Kovalevskaya was his student, she who two years ago won the Bordin Prize from the French Academy of Sciences with a paper so impressive that they doubled the prize money to recompense it as it deserved. She now holds an extraordinary professorship in Stockholm, is an editor of the very journal I am holding in my hands, and advises Mittag-Leffler, I believe, on the organisation of the Birthday Competition.’

  I was amazed. Germany and Sweden appear to be countries with wonderful ideas about ladies who wish to study, and England appears to lag far behind (particularly if one judges by the ideas expressed in The Monthly Packet, which greatly stress the value of obedience and docility). I wonder if I shall ever have the good fortune to visit such a country.

  The work of the commissioners was the object of a report considered by HIS MAJESTY, and here are their conclusions, of which SHE – I mean HE – has approved:

  Taking into consideration the questions which, for different reasons, both occupy analysts and whose solutions would be of the greatest interest for the progress of science, the commission respectfully proposes to HIS MAJESTY to attribute the prize to the best memoir on one of the following subjects.

  1. Given a system of an arbitrary number of material points which mutually attract each other according to NEWTON’s laws, we propose, under the hypothesis that no two
points ever collide, to represent the coordinates of each point in the form of a series in a variable expressed in known functions of time, and which converge uniformly for every real value of the variable.

  ‘What on earth does all that mean?’ asked Emily curiously.

  ‘Well, let me show you,’ said her uncle, warming to his task of explanation. He cast about her schoolroom, and moving to the shelves where various toys were gathered, took up a ball and a box of marbles and sat with them upon the floor.

  ‘Now,’ he told her, ‘you know what gravity is, don’t you? You know that objects fall to the floor because they are attracted by the gravitational force of the Earth, which is very large compared to themselves.’

  ‘Well,’ she observed guardedly, ‘I know that an apple fell upon Newton’s head.’

  He shouted with laughter. ‘Indeed, nobody can grow up in Cambridge without knowing that! And there is truth to it, you know, and to the notion that that event sparked the whole theory of gravity in his brilliant mind. Ah, he was our great genius, unequalled in the last hundred and fifty years. He understood that if you have a giant body, like the sun, for instance,’ and he set the ball upon the floor, ‘and a smaller body moving near it,’ he suited the action to the word with a marble, ‘it will enter the sphere of the sun’s gravity and begin to orbit around and around, unable to escape the power of the sun.’

  ‘Why does it not fall to the sun, just as a marble falls to the earth?’ asked Emily in surprise. ‘A marble does not orbit – how queer that would be, to see it flying around and around.’