Chance The life of games and the game of life
With its many easy-to-follow mathematical examples, this book takes the reader on an almost chronological trip through the fascinating and amazing laws of chance, omnipresent in the natural world and in our daily lives. Along the route many fascinating to
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Joaquim P. Marques de Sá
CHANCE The Life of Games & the Game of Life
With 105 Figures and 10 Tables
123
Prof. Dr. Joaquim P. Marques de Sá
Original Portuguese edition © Gravida 2006
ISBN 978-3-540-74416-0
e-ISBN 978-3-540-74417-7
DOI 10.1007/978-3-540-74417-7 Library of Congress Control Number: 2007941508 © Springer-Verlag Berlin Heidelberg 2008 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig, Germany Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig, Germany Cover design: eStudio Calamar S.L., F. Steinen-Broo, Girona, Spain Cartoons by: Luís Gonçalves and Chris Madden Printed on acid-free paper 987654321 springer.com
Preface
Our lives are immersed in a sea of chance. Everyone’s existence is a meeting point of a multitude of accidents. The origin of the word ‘chance’ is usually traced back to the vulgar Latin word ‘cadentia’, meaning a befalling by fortuitous circumstances, with no knowable or determinable causes. The Roman philosopher Cicero clearly expressed the idea of ‘chance’ in his work De Divinatione: For we do not apply the words ‘chance’, ‘luck’, ‘accident’ or ‘casualty’ except to an event which has so occurred or happened that it either might not have occurred at all, or might have occurred in any other way. 2.VI.15. For if a thing that is going to happen, may happen in one way or another, indifferently, chance is predominant; but things that happen by chance cannot be certain. 2.IX.24. In a certain sense chance is the spice of life. If there were no phenomena with unforeseeable outcomes, phenomena with an element of chance, all temporal cause–effect sequences would be completely deterministic. In this way, with sufficient information, the events of our daily lives would be totally predictable, whether it be the time of arrival of the train tomorrow or the precise nature of what one will be doing at 5.30 pm on 1 April three years from now. All games of chance, such as dicethrowing games for example, would no longer be worth playing! Every player would be able to control beforehand, deterministically, how many points to obtain at each throw. Playing the stock markets would no longer be hazardous. Instead, it would be a mere contractual operatio
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