Chances Are: Adventures in Probability

by Michael Kaplan and Ellen Kaplan

Quick Summary

A wide-ranging intellectual history of probability theory and its applications across human endeavor, from gambling and insurance to medicine, law, warfare, and philosophy. The Kaplans trace how humanity gradually developed the mathematical tools to reason about uncertainty, exploring how probability shapes decision-making in fields as diverse as epidemiology, courtroom evidence, weather prediction, military strategy, and the fundamental nature of physical reality in quantum mechanics.

Detailed Summary

Michael Kaplan and Ellen Kaplan's "Chances Are: Adventures in Probability" is a literary exploration of probability that combines historical narrative, philosophical reflection, and mathematical exposition. Rather than a textbook treatment, the book traces the intellectual development of probabilistic thinking through its applications across diverse fields, arguing that probability is the essential framework through which humans navigate an inherently uncertain world.

The opening chapter, "Thinking," establishes the central tension between humanity's craving for certainty and the irreducible uncertainty of existence. The authors invoke Gibbon's reflection on his own mortality as an example of how even in the 18th century, educated people were beginning to think in probabilistic terms about their own futures.

"Discovering" traces the origins of formal probability theory from the correspondence between Pascal and Fermat in 1654 about the problem of dividing stakes in an interrupted game of chance, through the contributions of Huygens, Bernoulli, and Laplace. The authors show how the development of probability was intertwined with the rise of mercantile capitalism and the need to quantify commercial risk.

"Gambling" explores the mathematical foundations through games of chance, examining the law of large numbers, expected value calculations, and the crucial distinction between probability (a mathematical abstraction) and frequency (an empirical observation). The chapter on "Securing" traces the birth and development of insurance, from Lloyd's of London to modern actuarial science, showing how the quantification of risk transformed the relationship between individuals and uncertainty.

"Figuring" examines the development of statistical methods, including Bayesian reasoning, regression to the mean (discovered by Francis Galton), and the normal distribution (the bell curve). "Healing" applies probabilistic thinking to medicine, covering the development of clinical trials, the base rate fallacy in diagnostic testing (where a positive test result for a rare disease is more likely to be a false positive than a true positive), and the placebo effect.

"Judging" explores probability in the legal system, including the prosecutor's fallacy (confusing the probability of the evidence given innocence with the probability of innocence given the evidence), DNA evidence, and the fundamental tension between the law's demand for binary verdicts and probability's inherent graduation of certainty.

"Predicting" covers weather forecasting, economic prediction, and the limits of predictability in complex systems, connecting to chaos theory and the sensitivity to initial conditions discovered by Lorenz. "Fighting" examines probability in military contexts, from game theory and the RAND Corporation's work on nuclear strategy to the statistical methods used in code-breaking during World War II.

The final chapter, "Being," enters the realm of quantum mechanics, where probability is not merely a reflection of human ignorance but appears to be woven into the fundamental fabric of reality. The book concludes with the philosophical implications of a universe that is, at its deepest level, probabilistic rather than deterministic.