Inventors and engineers have invested centuries of effort trying to build a perpetual-motion machine. They have never succeeded, but without their valiant attempts, a particularly piquant chapter would be missing from this new book on scientific impossibilities. Science-writer Dewdney teases illuminating logic and formulas from the despair of physicists who wish to predict how electrons will dance, from the frustration of computer programmers who want to resolve certain types of yes-no questions, and from the embarrassment of meteorologists who would like to predict next week's weather. Rigorous enough to challenge intelligent readers but not so daunting as to overwhelm the nonspecialist, the investigation of each impossibility clarifies the barriers that forbid further progress along certain theoretical paths, limning the conceptual boundaries of science and even reflecting the limitations inherent in the structure of human rationality. Still, Dewdney concedes a catalogue of scientific impossibilities may just provoke some maverick to do what the greatest scientists have always done: enlarge the limits of the possible.

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