May 6, 2019
Stewart (Significant Figures), an emeritus mathematics professor at Warwick University, delves into the mysteries of probability and statistics in this fascinating look at chaos theory and the uncertainties of the quantum universe. He begins with the surprisingly complex probabilities that arise from dice throwing and coin tossing, but finds his most intriguing material when considering his subject’s application to real-life problems. For example, he describes how the egregious misuse of statistics resulted in the murder conviction, later overturned, of a woman who lost two children to sudden infant death syndrome. Elsewhere, he explains how statistics failed to identify the dangers of the morning sickness drug Thalidomide. Stewart’s discussion of weather as a “nonlinear system,” in which small changes in initial conditions can create large changes in resulting conditions, is effectively conveyed with a detailed explanation of the famous butterfly effect. His discussion of climate also includes concise and convincing ripostes to the common tropes of climate change skeptics. Readers interested in whether Schrödinger’s famous cat is actually dead or alive, or how uncertain Heisenberg’s uncertainty principle really is, will find in Stewart’s survey a challenging but rewarding trip through a quantum world of uncertainties.
June 15, 2019
A definitely-not-dumbed-down exploration of predicting outcomes, whether of an election, card game, medical test, or weather front. Stewart (Emeritus, Mathematics/Univ. of Warwick; Significant Figures: The Lives and Work of Great Mathematicians, 2017), the prolific popular author of books on his specialty, points out that "an aspect of the human condition that arguably singles out our species from most other animals is time-binding. We're conscious that there will be a future, and we plan our current behavior in the context of our expectations of that future." Predicting odds is straightforward (though not always easy), and predicting the future turns out to be surprisingly possible, but both require calculations--in other words, mathematics. Popular writers on difficult topics involving math and science often assure readers that they will limit the equations, but Stewart has no patience with this tradition, so readers who do not remember high school algebra will have a difficult time. The author interweaves his account with a lively history that, few readers will be surprised to learn, began in the Renaissance, largely with gamblers who wrote long monographs that teased out the unnerving peculiarities of dice and cards. Stewart states bluntly that "the human intuition for probability is hopeless." Evolution has trained us to make quick decisions, which are essential in the struggle for existence but a bad idea when faced with even simple abstractions such as estimating odds. He illustrates with plenty of squirm-inducing paradoxes. Example: A couple has two children; at least one is a girl. What is the chance that they have two girls? Almost everyone answers 1 in 2, but it's 1 in 3. Now suppose that the elder child is a girl. What is the chance that they have two girls? This time 1 in 2 is correct. The innumerate will struggle, but every reader will encounter gems and jolts in this expert analysis of probability.
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