Read The Three-Body Problem Online
Authors: Catherine Shaw
The Three-Body Problem (31 page)
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 say 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
The mathematical framework of the three-body problem is absolutely historical. The Birthday Competition
1
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/
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C
ATHERINE
S
HAW
is a professional mathematician and academic living in France.
The Three-Body Problem
is her first mystery novel.
The Three-Body Problem
Flowers Stained with Moonlight
The Library Paradox
The Riddle of the River
Fatal Inheritance
Allison & Busby Limited
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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 C
ATHERINE
S
HAW
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
