The Three-Body Problem

by Catherine Shaw

  ‘We only ask you for one small thing,’ I said to her, taking advantage of this momentary softening; ‘only a few moments. Please do let me explain.’ I placed my valise upon the floor, opened it and extracted Mr Beddoes’ manuscript, which I had flattened out neatly at the very bottom, together with Mr Morrison’s translation of the announcement of King Oscar’s Birthday Competition.

  ‘I believe that the gentleman who wrote this manuscript of mathematics stole something from your brother,’ I began carefully.

  ‘Who is he? What did he steal? And how can I know anything of it?’ she answered suspiciously.

  ‘He stole an idea,’ I began, ‘a mathematical formula.’

  ‘I know nothing of such things,’ she said again, and I saw that she clung to the idea that her brother’s murderer had been discovered, and that we were his friends, and therefore she must regard us as enemies, with mistrust.

  ‘Oh, please – do let me tell you,’ cried Emily eagerly. ‘There was a great mathematical competition – why, it’s still going on, and your brother had a wonderful idea to solve the problem that was set! Perhaps he would have won the prize. But he died, and nobody found anything he wrote down, except that he wrote down one formula for Mr – for – for a friend of his, but then he put it back in his pocket, and then he was killed, so he could never send in his manuscript to the King of Sweden. And we don’t want his solution to be lost forever! He put it in his pocket, so my uncle said it must have been sent to you when he died. Oh, that is what you are looking for – that is why you are here, isn’t it, Miss Duncan? My uncle says it is ever so important!’

  I thought that Madame Walters would be entirely taken aback and confused by this whirlwind of competitions, uncles, kings and formulae. Instead, unexpectedly, she became very pale, and sank onto the bench across, leaning heavily upon the table.

  ‘You are right, you are right,’ she gasped. ‘The competition, the King of Sweden – Geoffrey wrote to me about it! He wrote that he believed he had a chance to win the grand prize, the golden medal, and he was keeping it all the deepest secret. How could you possibly know about it?’

  ‘We found it out little by little,’ I told her. ‘And now we have found something which may allow us to rediscover your brother’s lost idea. I have here a manuscript which may possibly hold the key to it.’

  I held Mr Beddoes’ manuscript out to her, and she looked at the strange sentences and formulae in confusion.

  ‘How can we know if you are right?’ she said.

  ‘As Emily said, on the evening of his death, Mr Akers told a – another friend about his idea,’ I told her. ‘Your brother was a suspicious man, but like all men, he needed friends, he needed to talk. He was wonderfully proud of his formula, and could not resist the desire to show it to his friend, but then he quickly folded up the scrap of paper and thrust it into his breast pocket. We need to know if it is still there, Madame Walters. If the formula it contains is the same as this one—’ and I showed her the central formula of Beddoes’ manuscript, heavily underlined, ‘then we shall be practically certain that this manuscript here contains the essence of your brother’s work! And it may yet be saved, for the greater honour of his memory.’

  ‘I don’t understand,’ she told us, her face grey with distress. ‘That manuscript you are holding is not in my brother’s handwriting. Yet you say it may contain his ideas. What does it mean? Did the author of this one steal my brother’s manuscript and copy it?’

  Emily looked at me in surprise. ‘That’s a funny idea,’ she said, ‘my uncle told me that the manuscript is odd, as though Mr Beddoes wrote down things and then questioned them afterwards. Perhaps Madame Walters is right. He might have just copied Mr Akers’ manuscript directly! Maybe he thought Mr Akers’ handwriting was too messy, or else he wanted to take it home and study it there, and Mr Akers didn’t want to let his own manuscript out of his sight. It would make sense, look! When Mr Beddoes tried to read through what he had copied, he found he didn’t understand some of it, and that’s why he wrote the questions in the margin!’

  ‘I should tell you that a man already came here from England, weeks ago, near Easter. He told me much the same story as you have, about my brother’s secret work, and like you, he said that he was trying to discover it and save it from oblivion. He said he knew the police had sent me all of my brother’s personal affairs, and he needed them in order to solve the mystery. I brought them out to show him, and stood at this very table with my husband and he looked eagerly at everything, above all at the many different scraps of paper my brother had in his pockets, all full of writing such as this,’ and she indicated Mr Beddoes’ manuscript.

  ‘There was one paper which excited him particularly, as well as my brother’s pocket diary,’ she went on. ‘He tried hard to convince me to let him take them away with him, telling me they were essential for his research. My husband would have let him, but I could not do it. Oh, miss, these are my only, last memories of poor Geoffrey. I told the man to copy the papers down for himself if he wanted them; what difference could it have made to him? But he did not care to, and went away, quite angrily, I thought.’

  Emily and I glanced at each other.

  ‘That is very interesting. What was his name? What did he look like?’ I asked quickly.

  ‘He said his name was Mr Davis,’ she replied. ‘As to his looks, it is difficult to say, really; he was very ordinary. He seemed distinguished and quiet, not young, but he wore a dark overcoat and hat, so it is difficult to describe him better.’

  ‘Would you know him again?’ asked Emily breathlessly.

  ‘I believe I would.’

  ‘Who could it have been?’ Emily wondered aloud. ‘It’s funny that he should have been angry about not being allowed to take the paper. Why should he have cared? It’s just a formula! He could have copied it out.’

  ‘I didn’t like that man,’ said Madame Walters, her brow furrowed. ‘Something seemed wrong with him – I felt very suspicious. Oh God, oh God – what does it all mean? Let me show you everything.’ And she arose, and went into the inner rooms. After a moment she returned, carrying a soft cloth bag, whose contents she poured out upon the table. It contained the entire contents of Mr Akers’ pockets at his death. Just as Mr Morrison had told us, we saw keys and coins, a handkerchief, the pocket diary and quite a large number of bits and pieces of paper scribbled over with notes and computations.

  I opened Mr Beddoes’ manuscript to the page containing the central formula, and then began to take up the papers one by one, and compare their contents to that of the page before me, to see if the formulae were identical. Several were unfamiliar and unintelligible to me, but at length I came upon one which immediately appeared to me to be the right one. One side was covered with Mr Akers’ usual illegible scribbling, that he used in writing for himself, but on the other side, which had been blank, he had written out the entire central formula in a clear, bold hand, and underneath, ‘the series converges!’

  I felt absolutely certain that I was holding in my hand the very paper that Mr Akers had written in the Irish pub for Arthur, on the last evening of his life. Madame Walters and Emily compared the two formulae, laboriously, Greek symbol for mathematical symbol, and agreed with me that they were identical.

  I then took up Mr Akers’ pocket diary, and began turning the pages. I started by looking at the very date of his death, the 14th of February, and saw two brief entries: first ‘ABC 2 p.m.’, then ‘dinner W.’

  ‘This is the day on which your brother died,’ I said, showing the page to Madame Walters.

  ‘That must be Mr Weatherburn, then!’ cried Emily, and Madame Walters flinched, for she identified this name with the hated murderer of her only brother.

  ‘What is ABC?’ asked Emily.

  ‘I know!’ I answered, as this piece of information worked its way perfectly into the puzzle I had been fitting together. ‘I believe that it is the name used for a little secret society, which met to work together on
the n-body problem! A must be for Mr Akers, B for Mr Beddoes and C for Mr Crawford. Let us see if they met at other times.’

  I turned backwards through the pages, looking curiously through the brief, austere record of the poor man’s life. Certain events could be identified – ‘Morrison lecture’ I saw on October 11th – but for the most part, it was difficult to guess much from the single initials Mr Akers habitually employed. On December 13th, I located another entry ‘ABC 2 p.m.’, and again on October 18th.

  ‘They always met on a Tuesday,’ remarked Emily.

  ‘You are right! October, December, February – they met every two months, on the same day of the week, at the same time. It was probably convenient for their teaching hours. I wonder where they met?’

  ‘I wonder if they meant to meet again in April,’ mused Emily.

  ‘That is a good question. Let us look. Why, yes, they did! April 17th – ‘ABC 2 p.m.’. There is no entry for June, though.’

  ‘Perhaps, at each meeting, they fixed the date of the next one,’ said Madame Walters.

  ‘Oh, no! Surely it was because they were working for the competition. They would have to be finished by June 1st!’ cried Emily.

  ‘You may be right,’ I answered, my mind churning and full of thoughts. ‘Madame Walters, I must tell you the truth. I have come, not only to save your brother’s lost work, but also because as Emily told you before, I am convinced that the man who has been arrested for his murder is not the true murderer. Mr Akers was killed for his idea, and I believe I know who killed him, and I need this evidence to prove it. I beg you to lend me this pocket diary and this paper written by your brother. I swear on my honour, on the Bible if you prefer, that I will keep them absolutely safe and return them to you as soon as everything has been made clear.’

  ‘Is it the man who came here?’ she asked, gathering up the paper and diary with trembling hands.

  ‘I believe it is,’ I told her.

  ‘I believe it too,’ she said suddenly, and thrust the bundle into my hands. ‘I knew it, I knew it! I felt it – there was something wrong with him. He was afraid – I could feel it, and his eyes were shifty, and he wanted the papers too much. Not just to see them, but to have them. It was for that that I did not give them to him. I felt that he wanted to destroy them!’

  ‘I am sure that that is what he wanted,’ I answered.

  ‘Do you not think, if you know who he is, that I should travel to England and identify him?’

  ‘Not yet,’ I said. ‘I still do not have enough proof; his visit here alone would do nothing to prove his guilt. I myself am not returning to England immediately, for I believe that evidence of major importance, concerning your brother in the deepest possible way, lies in Stockholm, and I am travelling there with the children before returning home. Still, it may be necessary for you to come to England later, if I succeed in gathering enough evidence that the judge wishes to confirm it all.’

  ‘I do not know why, but I believe you; I believe you are honest and sincere,’ she said. ‘I thank you for what you are doing, and wish you luck and Godspeed. How are you returning to Brussels? Did you come by cab? Has he waited for you?’

  I had completely forgotten about the impetuous departure of our sour-faced cab driver. Seeing our discomfited faces, Madame Walters went outside, and in stentorian tones, called a young man who was working in a field some distance away.

  ‘He will drive you to the city in the wagon,’ she told us. ‘I pray that what you are doing is right, and that if truly the man accused of my brother’s murder is innocent, God save him.’

  And we took our leave, and trotted back to Brussels in a farm wagon drawn by an old and very solid cart horse, Robert chattering gaily with the farmer youth the entire way. What a happy little boy he seemed to be, his own miseries briefly forgotten, unaware of the clouds of fear and danger which hovered vaguely about us. He was delighted with his ride in the fresh countryside, and more delighted still, when, in order to cheat the remaining hours of the day of their frightening emptiness, I took the children shopping, and we purchased a sturdy little sailor suit for him and various other necessaries to replace the contents of his dingy canvas bag. Emily insisted we also visit a toy store.

  ‘Oh, Emily,’ I remonstrated, thinking of murderers and lawyers and ruthless, hard-faced juries. ‘It seems so frivolous in the midst of questions of life or death!’

  ‘A child’s happiness is also a question of life or death,’ she said firmly. ‘It’s like your charade, Miss Duncan – do you remember it?

  My second with ‘you’ forms a phrase of great joy

  To a child who’s offered a gaily wrapped toy.

  It was “for you” – and you called it great joy! It isn’t at all frivolous. If you don’t believe me, just imagine what Mr Weatherburn would say.’

  The little imp! In immediate reaction to her words, my imagination produced an image of Arthur, standing next to me, considering little Robert with a grave twinkle, quietly approving of the deep and simple bond of love which so instantly unites a child and a toy. Little Robert’s cheeks were all flushed with delight, as he clutched to his chest the locomotive that he and Emily picked out together. Emily insisted on paying for it with her very own money, and we left the shop a happier trio than we had entered. Now we have settled for the night in a small pension whose address was given to us by Madame Walters, and tomorrow at dawn, we arise and depart for Stockholm.

  I retire in the comforting knowledge that your loving thoughts are with me, as mine are with you,

  Vanessa

  Malmö, Thursday, May 31st, 1888

  My dearest Dora,

  Two strange days have passed since last I wrote to you – two days of travel, nothing but travel, trains, cabs, walking, dingy hotels and dingier railway stations. Wiring to Mrs Burke-Jones from Calais and Brussels was easy enough, but from Germany difficult and from Denmark and Sweden a task rendered alarming by our ignorance of the language and customs. Yesterday, early in the morning, we left Brussels by train for Germany, and by nightfall, weary, dirty and underfed, we found ourselves in the northern city of Hamburg. How grey and sordid it seemed, with its tall, dirty chimneys against the dusky sky. How difficult it was to seek for an hotel, and how depressing when the first three we tried had no rooms available. Emily’s German is far more limited than her French, since she does not converse with Annabel in that language, but merely studies the rules of grammar; she soon taught me ‘Wir möchten ein Zimmer für drei, bitte’, and in the end we found refuge in a small dark room at the very top of a twisting staircase, and were all three too afraid of the maze of streets to descend and seek for dinner. We had bought bread and fruit at the railway station, and made do with them for the evening, promising ourselves to make up for it at breakfast the next morning, when the sunlight would surely cheer us.

  It was a relief just to be in a room with a bed, and to be able to wash, and stretch, and even to laugh, for children will always laugh, and Emily caused such startling adventures to befall the little locomotive that both children’s ringing voices soon filled the room and spilt down the stairs, lightening my dark mood. Emily has sworn to help me in every way, and indeed, even if she did nothing else, her constant proximity, her steadfast strength, and her youthful light-heartedness are already better than a tonic for me. What a treasure! I hardly dare imagine the sufferings and anxiety of her poor mother, in spite of my reassuring telegram Emily and Robert well and happy, travelling northwards together. I cannot deny that I am fearful of the days ahead, and venturing as far afield as Denmark and Sweden appears to me rather like wandering in the wilderness.

  So far, thank goodness, my fears have not really been justified. Today’s trip through Denmark was long and weary, but the country is charming, the people kind, and many of them speak some words of English, so that to our surprise, our Danish day turned out oddly pleasant in spite of the fact that the greatest part of it was spent seated in various vehicles, and all the food came from
baskets. I have now discovered that, assuming Robert to be a typical specimen, little boys adore trains big and small, and that tumbling them about in a swaying, rattling conveyance, with the ever-changing landscape sailing continually past, is apparently a sufficiently delightful activity to occupy all their natural energy and playfulness for hours on end.

  With the instinct of a budding physicist, Emily set about to study the effects of the big train on the tiny one, and set it upon the floor to see how its movement would be affected. Quite naturally, it took to rolling along in the opposite direction to ours, towards the back of the carriage, and (it must be admitted) rather frequently into the feet of the people sharing our compartment. They did not really mind, as the inhabitants of third-class carriages are used to such behaviour; children and food were everywhere, and the atmosphere was one of general rumpus. In any case, I found myself quite unable to remonstrate with any real intensity, as the sound of their joyful laughter was so sweet, and I was so relieved that they were not quite simply rendered bored and peevish (as I was, rather) by the endless riding.

  We reached Copenhagen in the late afternoon, and it was not too late to sail across to the port of Malmö. Ah, these northern countries are orderly and beautiful. I felt a wave of triumph as I set foot on the ground (in spite of the peculiar manner in which it tilted beneath my feet). Sweden at last! Tomorrow – on to Stockholm, and to the final proof!

  Ever your own

  Vanessa

  Stockholm, Friday, June 1st, 1888

  My dearest Dora,

  We have spent the whole of this endless day journeying northwards, ever northwards to Stockholm. We arrived here late, worn out and (for myself) weary with the ever renewed fear of failure. The moment we reached the city, I gave way to my increasing sense of urgency, and bundled the children into a cab without giving them a moment, poor dears, to rest or look about them. Only one thought was in my mind: today is the very day of the opening of the submissions to the King’s Birthday Competition. They will be opened – perhaps have already been opened – by the director of the competition, Professor Gösta Mittag-Leffler.