Summary of Ten Great Ideas about Chance

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Probability features in the history of philosophy and mathematics, and the study of chance dates to the ancient Greeks. But only in the 16th and 17th centuries did anyone measure chance precisely. Gambling fueled coherent ideas about probabilities; people want to predict likely outcomes, whether when rolling dice or betting on financial markets. Persi Diaconis and Brian Skyrms illustrate in 10 illuminating chapters how the complex theory of chance encompasses concepts in decision-making psychology and reasoning that form the foundations of science. All thinkers, no matter how mathematical, will be curious to find out if the future will be like the past.

About the Authors

Persi Diaconis is a professor of statistics and mathematics at Stanford University. Brian Skyrms is a distinguished professor of logic and philosophy of science and economics at the University of California, Irvine and a professor of philosophy at Stanford University.

 

Summary

Chance can be precisely measured.

Ancient cultures considered chance. People played games of chance with dice and the Greeks had a goddess of chance. Despite this concern with chance and its vagaries in life and the world, the ancients didn’t develop a rigorous, mathematical theory of chance. It wasn’t until the 16th and 17th centuries that thinkers figured out how to measure chance.

People measure things by assigning them standardized parts – as with, for example, length. In order to measure chance or probability, you must find or create equally probable instances – and add them. A given X’s probability is the sum of the instances in which X occurs over the total number of instances. This strategy can adapt to increasingly complex problems, such as the likelihood that two people in a group have the same birthday.

Personal judgments provide probabilities.

As with chance, you can measure judgments and thus assign probabilities to “coherent judgments.” Judgments exhibit degrees of belief, which show a mathematical form that resembles equally probable gambling results. In these cases, the probabilities...


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