A fascinating account of the breakthrough ideas that transformed probability and statistics
In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.
Persi Diaconis and Brian Skyrms begin with Gerolamo Cardano, a sixteenth-century physician, mathematician, and professional gambler who helped develop the idea that chance actually can be measured. They describe how later thinkers showed how the judgment of chance also can be measured, how frequency is related to chance, and how chance, judgment, and frequency could be unified. Diaconis and Skyrms explain how Thomas Bayes laid the foundation of modern statistics, and they explore David Hume’s problem of induction, Andrey Kolmogorov’s general mathematical framework for probability, the application of computability to chance, and why chance is essential to modern physics. A final idea—that we are psychologically predisposed to error when judging chance—is taken up through the work of Daniel Kahneman and Amos Tversky.
Complete with a brief probability refresher, Ten Great Ideas about Chance is certain to be a hit with anyone who wants to understand the secrets of probability and how they were discovered.
Persi Diaconis is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University and the coauthor of Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks (Princeton). Brian Skyrms is Distinguished Professor in the Department of Logic and Philosophy at the University of California, Irvine, and Professor of Philosophy at Stanford University. His books include From Zeno to Arbitrage.
"In this attractively written book, which is rigorous yet informal, Persi Diaconis and Brian Skyrms dispel the confusion about chance and randomness. They range from coin tosses to particle physics and show how chance and probability baffled the best minds for centuries. I cannot imagine a more accessible account of these deep and difficult ideas."--Jon Elster, Columbia University and Collège de France
"There is something fundamentally paradoxical about probability theory, as a mathematical language for saying precisely what we do not know. In this book, an eminent philosopher and mathematician guide us through the resolution of these paradoxes, to offer a deeper understanding of how we can analyze problems of uncertainty in the world."--Roger Myerson, University of Chicago
"One should add an eleventh great idea to Ten Great Ideas about Chance: namely, for probabilist, statistician, and magician Persi Diaconis and philosopher of science Brian Skyrms to write a book about the subject! This fascinating book mingles the foundations of probability with history and philosophy, covering topics that include the uncertain and elusive notion of inference, and bringing forth a broad and powerful vision of concepts that should appeal to both specialists and general science readers."--Christian P. Robert, Université Paris-Dauphine and University of Warwick
"This wonderful book looks at both the nature of probability and the history of thinking on the subject, following a path that goes from coin-flipping machines to quantum physics via psychology and behavioral economics. It will fascinate general readers and stimulate constructive reflection in scientists who use probability. Outstanding!"--Stephen Schaefer, London Business School
Table of Contents:
1 Measurement 1
2 Judgment 22
3 Psychology 48
4 Frequency 62
5 Mathematics 79
6 Inverse Inference 100
7 Unification 122
8 Algorithmic Randomness 145
9 Physical Chance 165
10 Induction 190
Appendix: Probability Tutorial 209
Annotated Select Bibliography 239
Image Credits 247
Another Princeton book authored or coauthored by Persi Diaconis: