Perplexing paradoxes Unraveling enigmas in the world around us

In this lackluster outing, Swiss mathematician Szpiro (Numbers Rule) investigates 60 paradoxes from economics, philosophy, politics, and other disciplines. He notes the contradictory nature of Socrates's apocryphal pronouncement, "I know that I know nothing," and elucidates the statistical reasoning behind why contestants on Let's Make a Deal, when given the option to pick which of three doors holds a prize inside, should always change their guess after the host eliminates one of the incorrect options. Other "paradoxes" might more reasonably be described as unintuitive facts, as when Szpiro explains that the perception that one's friends are more popular than oneself is often accurate because "people with lots of friends are more likely to be among your circle of friends." The economic paradoxes are particularly contrived, such as when Szpiro unconvincingly contends that the incentives felt by competing companies to undercut each other's prices somehow contain a contradiction. Elsewhere, math-heavy paradox explanations are likely to elude the general reader; for instance, a particularly arcane discussion draws on "the theory of combinatorics" and Bayes's theorem to explain why mathematicians disagree over whether slight differences in the proportion of newborn girls and boys constitutes a 50-50 split. The real enigma is how such a promising book idea came up so short. (Feb.)