The Three-Body Problem Read online

  Automatically, counsel for the defence arose, and his speech was even shorter than the prosecutor’s.

  ‘Members of the jury, I explained to you before how the accused could be perfectly innocent of the horrendous crimes imputed to him, and guilty of nothing more than being in the wrong place at the wrong time on two separate occasions. The additional information brought to you by this new witness completes my presentation of the case. I have nothing more to add.’

  Mr Justice Penrose bowed his head apologetically towards the jury. ‘Members of the jury, please deliberate once again, and return when your verdict is ready.’

  No trial can ever have closed more speedily. The jury returned in less than two minutes. They sat down, and the judge asked them: ‘Members of the jury, have you reached a conclusion?’

  ‘Yes, my Lord.’

  ‘What is your verdict?’

  ‘We have changed from our previous conclusion, my Lord. We now unanimously believe that the prisoner is not guilty. We wish to say that we feel we have very narrowly escaped being led into grave injustice.’

  The courtroom erupted in cries of all kinds and the judge banged his gavel again.

  ‘The prisoner is hereby acquitted and released without a stain on his character!’ he shouted over the noise in stentorian tones.

  All of a sudden I could not bear the noise and the crowd and the hundreds of eyes for a single second longer. I rushed from the courtroom and stepped into the quiet darkness of the streets, where I wandered about for a long time before returning home. It has been too much and too long and too hard, and I feel too numb to triumph tonight.

  Tomorrow, however, I shall begin a new adventure!

  Vanessa

  Cambridge, Sunday, June 11th, 1888

  My dearest sister,

  The whole of this past week has been full of sunshine and roses, outdoors, indoors, and within my very heart. Each morning, I awake, and recall afresh that Arthur’s trial is over, and with it the very trial of my soul; my entire life feels renewed and joyful. And each day has brought its own unexpected, delightful surprise.

  The first one came the very day after the end of the trial. Naturally, the unexpected and dramatic ending was reported in our local newspaper. I was so tired after my performance in the witness box, that I tumbled into bed and slept like the dead until astonishingly late the next morning, and was awoken by Mrs Fitzwilliam entering with a tea tray in her hands, upon which lay a newspaper.

  ‘Well, my dear,’ she said to me, as she drew the curtains kindly and let in a wave of brilliant sunshine, ‘you must be tired enough to sleep so long! I know you’ve had a hard time of it all, and I thought I’d bring your breakfast in this morning, so you may have some much-deserved relaxation. And do have a look at this, dear – you’re on the very front page of the newspaper! Just think!’

  Oh dear, it was perfectly true. There was a picture of me, taken as I left the courthouse, framed within the doorway, almost a silhouette against the lighted background. It was followed by a very foolish article. I did not like to read it at all; it presented things in a very silly way, not at all properly. No one, reading it, would imagine that I was simply driven to search for the truth and avert a dreadful injustice – they all seemed to foolishly impute some deeper reason for it all! Such motivations as mine must lie below the visual field of ordinary journalists.

  The very next afternoon, I received visits from the mothers of nearly all the little girls in my class. With amazing speed and efficiency, Mrs Burke-Jones had been to call on each and every one of them, and had presented her proposition of widening the class to contain boys as well as girls, and welcoming it, if necessary, in her home.

  My class contains several pairs of sisters (and even one collection of three), so that in fact, my twelve little students possess only seven mothers between them; Mrs Burke-Jones aside, I was called upon by the other six. Rose’s mother was the first to call. She praised me with enthusiasm for my role at the trial, and told me that she would have been delighted to send any brothers of Rose to join my class, if only she had had any, but alas, Rose was an only child. To cut a long story of discussions and negotiations short, three mothers, one of whom has two daughters, said that they could not agree to continue to send their daughters to a class as daring and scandalous as what I, or rather, Mrs Burke-Jones, was proposing. I had been afraid of this reaction, and had half made up my mind to say that I had not taken any decision on the subject yet. But that is not how it went, for I found myself stubbornly upholding the project, and in the end found my little class to be reduced from twelve to eight.

  And yet, it is at the same time most interestingly increased, for not only are Emily’s two brothers to attend, but – good heavens – I had no idea, but the mother of the three little girls followed them up directly by a series of three little boys, none of whom have begun lessons yet. I am to take the oldest one immediately, and the following two in subsequent years. And two other little brothers are to join us, making a total of five boys in all, beginning immediately. They are all very little boys, with the exception of Edmund, as all the older ones are in school already. It will be most awfully sweet!

  The calls and visits were followed by a lengthy discussion with Emily, her mother, and Miss Forsyth. I am to continue residing in Mrs Fitzwilliam’s rooms, but the schoolroom will now be located in Mrs Burke-Jones’s large nursery, and Miss Forsyth will be my assistant for part of the afternoon; she will teach French, and help me with the smallest children if they become overexcited, as seems more than likely. There is to be a break in the middle of the afternoon, during which the children may run about in Mrs Burke-Jones’s lovely garden. She is overjoyed at the whole idea, and appears to have recovered a purpose for her life in it; I quite believe that she sees herself as a kind of honorary headmistress, and who knows, perhaps she will end up as the headmistress of an excellent and reputable and very modern school!

  The next morning, I received your letter. Oh, Dora, how exciting! All the changes in my life, which seemed so great to me, and the varied experiences I have had during these last weeks, pale before those which await you now that you have accepted Mr Edwards’ proposal. How beautifully he expresses the feeling that at such a distance, one’s true needs and desires become clear and sharply outlined, whereas in the confusion of daily presence, they become blurred and confused. Poor Mr Edwards – so many people would burn to confront the long and mysterious journey to vast, hot and unfamiliar regions, filled with natives and strange illnesses, which awaits him, and he yearns only to return home to the English countryside and live amongst the fresh green fields. Still, Dora, in your quiet way, you have always been more stubborn than I; simply reserving yourself for the great moment. I know you; now that you know what you are waiting for, you will be able to reserve yourself as long as necessary, with an infinity of obstinate patience, while Mr Edwards works until the government permits him to return. Surely it cannot be more than a small number of years! And after all, we are only twenty, you and I.

  By the same post, I also received a letter from Professor Mittag-Leffler. He had heard all about the final results of my efforts, and wrote to congratulate me and once again encourage me to return to visit him in Stockholm. One paragraph of his letter has left a profound and striking impression upon me.

  Because of the amazing nature of its contents, the manuscript number seven was immediately and intensively studied by myself and my associate Dr Phragmén. I regret to say that quite soon, we came to realise that the computations, although brilliantly virtuoso in style, contain a deep flaw in one particular place. It seems to me that I remember, in the partial manuscript you showed me written in very legible handwriting, that the author had written a question in the margin next to this very point. He may have believed himself simply unable to understand it, but he was more perspicacious than he thought, and the author of the manuscript submitted to the competition desired success too keenly to exercise his critical judgement. I am sorry to s
ay that the entire conclusion of the manuscript is invalidated by this error. In any case, the paper submitted by M. Henri Poincaré has shown that such a classical solution to the three-body problem (and in fact to the n-body problem in general) is in fact an impossibility, and that the problem must be approached in an entirely different way. He begins this radically new study in his article, which is a work of genius that will unquestionably mark the whole of the century to come.

  So it turns out that all three of them murdered and were murdered for nothing. This fact leaves me with a most remarkable impression of the inanity of the things of this world.

  I longed to share this letter, and all of my experiences, with Arthur, but I had not seen him since the end of the trial; nobody appeared to know where he had gone. I tried to occupy myself with a thousand things, but my thoughts were always upon him, and I jumped at every sound, every knock on the door. He appeared, finally, towards the end of the afternoon.

  I heard his step in the hallway, and his gentle knock, and opened the door at once. We stood in the doorway for a moment; he took my two hands in his, looking down at me. I looked up at him, and we remained there in silence – silence will ever be our most intense mode of communication, I think. I felt his touch, and found no words. He seemed to wish to speak and change his mind a dozen times. Time stopped; I would have waited forever. Finally, he said, ‘Will you marry me?’

  I said yes. There was another silence.

  ‘I’m afraid it won’t be easy for you,’ he said slowly. ‘You know, I have never been very strong on the business of living, and though I have tried in these last days to forget and recover, something, somewhere inside me, feels broken forever. I could not find any interest in anything at all – except the thought of you.’

  ‘I’ll mend it – I can mend anything!’ I said stoutly.

  He took me in his arms.

  Fellows of the university are not allowed to marry, and a fellowship lasts for several years. But what of it! We are young, and the future is long, and my class needs me, and the days stretch before me filled with loveliness, and poetry and wild flowers growing in the hedgerows. Beyond that, it grows misty, and I prefer it that way.

  How wonderful to think that I will be home so soon. I can hardly wait to see our darling old house. I have been away for so long – I have become used to town houses, all square and stone and straight. How I miss the crooked rafters and low ceilings, and tiny diamond-paned windows half-covered with leafy vines. To think I will see it all again in just a few days, and the cats, and our solid little ponies – and you! I long to ramble in the fields for hours with you, Dora, as only twins can. Just walking, and talking – about all the things which cannot be fitted into, or even between, the lines of letters.

  Your loving sister

  Vanessa

  MATHEMATICAL HISTORY IN

  THE THREE-BODY PROBLEM

  The mathematical framework of the three-body problem is absolutely historical. The Birthday Competition1 occurred exactly as described, down to the unsigned manuscripts identified by epigraphs; several of the authors, in fact, have never been identified even to this day. The manuscript concerned in this story has borrowed its title from one of those.

  The competition was organised by Gösta Mittag-Leffler (1846–1927)2 under the auspices of King Oscar II of Sweden; Mittag-Leffler’s villa still exists and is now a famous mathematical institute. The announcement of the competition in the mathematical journal Acta Mathematica is accurately reproduced, and the end result of the competition was historically just as described in the book. There was in fact a further development; Poincaré discovered that his prize-winning paper contained an error, which he rectified after all the copies of Acta Mathematica had already been printed; he insisted on paying himself for them all to be reprinted, which cost him all of his prize money. The events concerning the supposed solution of Lejeune-Dirichlet (1805–1859) to the n-body problem and his deathbed confidences to Leopold Kronecker (1823–1891) also occurred as told.

  Arthur Cayley (1821-1895) and Grace Chisholm (1868–1944) were really members of the Cambridge Mathematics Department during the period described; Cayley’s defence of teaching Euclid and Chisholm’s departure to Germany in order to write a thesis are factual. Karl Weierstrass (1815–1897) and his famous student Sonya Kovalevskaya (1850–1891) were real people, and Kovalevskaya was, as described, the first woman professor of mathematics in Europe. Henri Poincaré (1854–1912) was of course one of the greatest mathematicians of his time. The n-body problem was a burning subject of research in the 1880s, and Poincaré’s work on it was seminal; it is still a most popular research subject today. As Poincaré showed, there can be no general solution in closed form; however, many astonishing special solutions have been found in recent years.3

  The Victorian girls’ magazine The Monthly Packet really existed; it contained many mathematical tales and problems by Lewis Carroll (1832–1898), including the Tangled Tale reproduced in the book. For that matter, Oscar Wilde really did undertake to edit the magazine Woman’s World, and evinced a great interest in women’s clothing, being strongly against corsets and all other fashionable constrictions: ‘It is from the shoulders, and from the shoulders only,’ he wrote, ‘that all garments should be hung’.

  A final remark: the answers to the tea-party charades are Vanes-sa (as in ‘weathervanes’ and ‘sa majesté’) Dun-can, Weather-burn, Miss-For-Scythe.

  1 The book Poincaré and the Discovery of Chaos by June Barrow-Green contains a great deal of interesting scientific information as well as a historical chapter.

  2 A website containing brief biographies of a great number of mathematicians can be found at http://www-gap.dcs.st-and.ac.uk/~history/BiogIndex.html

  3 Moving versions of some of these special solutions can be charmingly visualised on the internet at http://www.cse.ucsc.edu/~charlie/3body/

  We hope you enjoyed this book.

  Do you want to know about our other great reads, download free extracts and enter competitions?

  If so, visit our website www.allisonandbusby.com.

  Click to sign up to our monthly newsletter for exclusive content and offers, news of our brand new releases, upcoming events with your favourite authors and much more.

  And why not click to follow us on Facebook and Twitter?

  We’d love to hear from you!

  About the Author

  CATHERINE SHAW is a professional mathematician and academic living in France. The Three-Body Problem is her first mystery novel.

  By Catherine Shaw

  The Three-Body Problem

  Flowers Stained with Moonlight

  The Library Paradox

  The Riddle of the River

  Fatal Inheritance

  Copyright

  Allison & Busby Limited

  12 Fitzroy Mews

  London W1T 6DW

  www.allisonandbusby.com

  First published in Great Britain by Allison & Busby in 2004.

  This ebook edition published by Allison & Busby in 2013.

  Copyright © 2004 by CATHERINE SHAW

  The moral right of the author is hereby asserted in accordance with the Copyright, Designs and Patents Act 1988.

  All characters and events in this publication other than those clearly in the public domain are fictitious and any resemblance to actual persons, living or dead, is purely coincidental.

  All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means without the prior written permission of the publisher, nor be otherwise circulated in any form of binding or cover other than that in which it is published and without a similar condition being imposed on the subsequent buyer.

  A CIP catalogue record for this book is available from the British Library.

  ISBN 978–0–7490–1444–5

 
>