2 Also by Steven Strogatz Sync: The Emerging Science of Spontaneous Order The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Maths 3 4 5 6 First published in the United States in 2012 by An Eamon Dolan Book, an imprint of Houghton Mifflin Harcourt Publishing Company, New York. Published in trade paperback in 2012 by Atlantic Books, an imprint of Atlantic Books Ltd. Published in hardback in Great Britain in 2013 by Atlantic Books, an imprint of Atlantic Books Ltd. Copyright © Steven Strogatz, 2012 The moral right of Steven Strogatz to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act of 1988. 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, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of both the copyright owner and the above publisher of this book. Every effort has been made to trace or contact all copyright holders. The publishers will be pleased to make good any omissions or rectify any mistakes brought to their attention at the earliest opportunity. Chapters 1–3, 5, 7, 8, 11, 12, 16–18, 20, 23, 26, 28, and 30 are adapted, with permission, from pieces originally published in The New York Times. 7 Grateful acknowledgment is made for permission to reprint an excerpt from the following copyrighted work: pp. 201–202, from p. 111 of The Solitude of Prime Numbers: A Novel by Paolo Giordano, translated by Shaun Whiteside, copyright © 2008 by Arnoldo Mondadori Editore S.p.A., translation copyright © 2009 by Shaun Whiteside. Used by permission of Pamela Dorman Books, an imprint of Viking Penguin, a division of Penguin Group (USA) Inc. Further credits can be found on page 307 10 9 8 7 6 5 4 3 2 1 A CIP catalogue record for this book is available from the British Library. Hardback ISBN: 978 84887 843 3 Trade paperback ISBN: 978 1 84887 844 0 Ebook ISBN: 978 0 85789 845 6 Printed in Great Britain by Atlantic Books An Imprint of Atlantic Books Ltd Ormond House 26–27 Boswell Street London WC1N 3JZ www.atlantic-books.co.uk 8 9 Contents Preface Part One NUMBERS 1. From Fish to Infinity An introduction to numbers, pointing out their upsides (they’re efficient) as well as their downsides (they’re ethereal) 2. Rock Groups Treating numbers concretely — think rocks — can make calculations less baffling. 3. The Enemy of My Enemy The disturbing concept of subtraction, and how we deal with the fact that negative numbers seem so . . . negative 4. Commuting When you buy jeans on sale, do you save more money if the clerk applies the discount after the tax, or before? 5. Division and Its Discontents 10