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Cosmology has undergone a revolution in recent years. The exciting interplay between astronomy and fundamental physics has led to dramatic revelations, including the existence of the dark matter and the dark energy that appear to dominate our cosmos. But these discoveries only reveal themselves through small effects in noisy experimental data. Dealing with such observations requires the careful application of probability and statistics. But it is not only in the arcane world of fundamental physics that probability theory plays such an important role. It has an impact in many aspects of our everyday life, from the law courts to the lottery. Why then do so few people understand probability? And why do so few people understand why it is so important for science? Why do so many people think that science is about absolute certainty when, at its core, it is actually dominated by uncertainty? This book attempts to explain the basics of probability theory, and illustrate their application across the entire spectrum of science.
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FROM COSMOS TO CHAOS This page intentionally left blank FROM COSMOS TO CHAOS The Science of Unpredictability Peter Coles AC AC Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York # Oxford University Press 2006 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2006 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 permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Coles, Peter. From cosmos to chaos : the science of unpredictability / Peter Coles. p. cm. ISBN-13: 978–0–19–856762–2 (alk. paper) ISBN-10: 0–19–856762–6 (alk. paper) 1. Science—Methodology. 2. Science—Forecasting. 3. Probabilities. I. Title. Q175.C6155 2006 501 0 .5192—dc22 2006003279 Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain on acid-free paper by Biddles Ltd. www.Biddles.co.uk ISBN 0–19–856762–6 978–0–19–856762–2 1 3 5 7 9 10 8 6 4 2 ‘The Essence of Cosmology is Statistics’ George Mcvittie Acknowledgements I am very grateful to Anthony Garrett for introducing me to Bayesian probability and its deeper ramifications. I also thank him for permission to use material from a paper we wrote together in 1992. Various astronomers have commented variously on the various ideas contained in this book. I am particularly grateful to Bernard Carr and John Barrow for helping me come to terms with the Anthropic Principle and related matters. I also wish to thank the publisher for the patience ove