BOOK
Long before people wondered whether computers could think, a group of mathematicians pondered if there was a limit to the power of raw logical thought. Martin Davis' The Universal Computer: The Road from Leibniz to Turing is an elegant history of the search for the boundaries of logic and the machines that live within them. Blending mathematical details with biographical tidbits, Davis explains how we've come to understand what we do about the limits of computers and logical thought.
The classic treatment of this topic is Douglas R. Hofstadter's Gödel, Escher, Bach, a sometimes humorous excursion that includes many mathematical riffs on Kurt Gödel's discovery that logic can't solve every problem.
Davis has written a more straightforward and serious book that begins in the late 1600s with the life of G. W. Leibniz and ends with the construction of the first universal computers at the end of World War II. These devices, the first not hardwired for a specific task, sparked a heated debate over exactly what machine intelligence can do. Davis examines the papers and mathematical proofs offered by giants like Gödel, George Boole, David Hilbert, and Alan Turing. He pokes into their mathematical discoveries - and doesn't scrimp on details about the logical steps they took.
While the book is very much a history of mathematical ideas, it's also filled with personal details and tidbits from lives that seemed to end in tragedy. Gödel broke down in the tumult brought by the ascent of the Nazi Party. Leibniz was pulled away from his quest for a perfect logical calculus because his patron sent him off to do genealogical research. The English government prosecuted Turing because he was a homosexual.
Through it all, these mathematicians still managed to develop a clear sense of where logic could fail. But Davis is careful to note that Gödel's famous flaw may not be enough to answer our questions about whether machines can think, stating that it's all still a mystery. But he notes - with some pleasure - that the flaw is only present in perfect logical systems: Because mathematicians are far from perfect, they may yet be able to outthink their machines.
Though Davis generously sprinkles his book with equations and other mathematical constructions, they are easy to either ignore or dive into. Mathphobes can skip over them, while those who are intrigued will gain a much better understanding of what's going on.
I've always felt that books like James Gleick's Chaos teased me by offering metaphors that danced around the mathematical ideas but never actually touched them. Davis' book is a full-contact tour through an important branch of math and logic.
The Universal Computer: The Road from Leibniz to Turing by Martin Davis: $25.95. W. W. Norton: www.wwnorton.com.
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