Computers rely on such things as semiconductors, memory chips, and electricity. But they also rely on a hard-won body of scientific knowledge that has enabled the now-ubiquitous devices to perform complex calculations, multitask, and even play a game of solitaire. Martin Davis, a fluent interpreter of mathematics and philosophy, locates the source of this knowledge in the work of the remarkable German thinker G. W. Leibniz, who, among other accomplishments, was a distinguished jurist, mining engineer, and diplomat but found time to invent a contraption called the "Leibniz wheel," a sort of calculator that could carry out the four basic operations of arithmetic. Leibniz subsequently developed a method of calculation called the calculus raciocinator, an innovation his successor George Boole extended by, in Davis's words, "turning logic into algebra." (Boole emerges as a deeply sympathetic character in Davis's pages, rather than as the dry-as-dust figure of other histories. He explained, Davis reports, that he had turned to mathematics because he had so little money as a student to buy books, and mathematics books provided more value for the money because they took so long to work through.) Davis traces the development of this logic, essential to the advent of "thinking machines," through the workshops and studies of such thinkers as Georg Cantor, Kurt Gödel, and Alan Turing, each of whom puzzled out just a little bit more of the workings of the world--and who, in the bargain, made the present possible. --Gregory McNamee
From Scientific American
"As computers have evolved from the room-filling behemoths that were the computers of the 1950s to the small powerful machines of today that perform a bewildering variety of tasks, their underlying logic has remained the same," Davis says. "These logical concepts have developed out of the work of a number of gifted thinkers over a period of centuries. In this book I tell the story of the lives of these people and explain some of their thought." Davis, professor emeritus of mathematics at New York University, has devoted his career to "this relationship between the abstract logical concepts underlying modern computers and their physical realization." His tale encompasses seven mathematicians who contributed to that relationship: Gottfried Leibniz, George Boole, Gottlob Frege, Georg Cantor, David Hilbert, Kurt Gödel and Alan Turing. Leibniz, one reads, dreamed of "machines capable of carrying out calculations." Boole put forward an algebra of logic. And on to Turing, who envisioned a "universal machine" that could play games like chess, be induced to learn much as a child does and ultimately "could be made to exhibit behavior one would be led to call intelligent." Davis believes that the story he tells "underscores the power of ideas and the futility of predicting where they will lead." EDITORS OF SCIENTIFIC AMERICAN
Review
Anyone who works with computers today, who seeks to look into the electronic future, can profit greatly from reading [this]. -- John McCarthy, Stanford University
Delightfully entertaining and most instructive! -- Raymond Smullyan, author of The Riddle of Scheherazade and First-Order Logic
Erudite, gripping and humane, Martin Davis shows the extraordinary individuals through whom the groundwork of the computer came into being. -- Andrew Hodges, author of Alan Turing: The Enigma
Martin Davis speaks about logic with the love and touch of a sculptor speaking about stone. -- Dennis Shasha, New York University
[A]n elegant history of the search for the boundaries of logic and the machines that live within them. -- Wired, Peter Wayner, December 2000
About the Author
Martin Davis's other books include Computability and Unsolvability. A professor emeritus at New York University, he is currently a visiting scholar at the University of California-Berkeley.
