The Advent of the Algorithm: The Idea That Rules the World [Anglais] [Relié]

Francis Sullivan of the Institute for Defense Analysis said "Great algorithms are the poetry of computation"; David Berlinski calls the algorithm "the idea that rules the world." The Advent of the Algorithm is not so much a history of algorithms as a historical fantasia. Berlinski spins freely between semifictional accounts of historical figures, personal reminiscence, and mathematical proofs--without ever really defining an algorithm in so many words.

This is not the book for those who were maddened by Berlinski's A Tour of the Calculus; his style remains quirky, digressive, self-referential, and dense:

And then, by some inscrutable incandescent insight, Leibniz came to see that what is crucial in what he had written is the alternation between God and Nothingness. And for this, the numbers 0 and 1 suffice.

Twinkies and Diet Coke in hand, computer programmers can now be observed pausing thoughtfully at their consoles.

Berlinski's argument seems to be that algorithms--step-by-step procedures for getting answers--superceded logic, and will be superceded in turn by more biological, empirical, fuzzy methods. The structure of the book reflects this argument--sketches of people like Leibniz, Hilbert, Gödel, and Turing are interwoven with proofs and with characters of Berlinski's own invention. Berlinski's voice, closer to Hofstadter than to Knuth, remains unique. --Mary Ellen Curtin

Berlinski's successful A Tour of the Calculus displayed his spectacular talent for explaining math and its various real-world consequences. This hefty follow-up explores what Berlinski considers "the second great scientific idea of the West. There is no third." Calculus gave us modern physics, but the algorithm gave us--is still giving us--the computer (or, more precisely, the computer program). In short, densely intertwined, lyrically constructed chapters, Berlinski describes the discoveries of major algorithmic thinkers. We hear of Gottfried von Leibniz, one of the founders of formal logic; of Gottlob Frege, David Hilbert and Bertrand Russell, who set out to draw up formal, mathematical criteria for truth; of Kurt G?del, who proved that it couldn't be done; of computer pioneer, code breaker and gay martyr Alan Turing; of programs, undecidability, DNA and entropy. We see equations and graphs, but we also hear tales from Isaac Bashevis Singer and bizarre anecdotes of Berlinski's own travels. A novelist (The Body Shop) as well as a mathematician, Berlinski has composed energetic, intertwined tales that make it nearly impossible for readers, once drawn in, to lose interest or to get lost among flying abstractions. (He may well attract the same readers who gravitated, 20 years ago, to Douglas Hofstadter's G?del, Escher, Bach, though the books' personalities and prose styles have little in common.) Although not perfect--the book can be hyperbolic or too aphoristic and digressive for those who just want to learn about math (or the philosophy of computing)--this captivating volume is nevertheless an uncommon achievement of both style and substance. Agent, Susan Ginsburg; author tour. (Mar.)
Copyright 2000 Reed Business Information, Inc.

In his newest work, which complements his A Tour of the Calculus (Pantheon, 1996), professional writer and sometime mathematician Berlinski traces some of the highlights in the development of modern mathematical logic and shows how they have converged on the algorithm--which may be defined as a prescription for carrying through a computation in a finite series of steps. Berlinski compares and contrasts the triumph of the algorithm with the earlier successful career of calculus. His writing style is vivid and dynamic--almost too much so. However, he succeeds in carrying his readers through the basic notation of mathematical logic in a fashion that should work well even for lay readers. Thumbnail biographical sketches of several major logicians and several fragments of fiction further enliven this zesty and unusual book. Recommended for public and academic libraries.
-Jack W. Weigel, formerly with Univ. of Michigan Lib., Ann Arbor
Copyright 2000 Reed Business Information, Inc.

David Berlinski is a brave man. His last book, A Tour of the Calculus, explored in laymen's terms (as much as that's possible), the subject that caused most laymen great pain during their student years. Now he has returned to explain "the second great scientific idea of the West. There is no third."

An algorithm is a procedure, written in a symbolic vocabulary, that gets something done step-by-step without the need for any intelligent assistance. Even if the word rings some dusty bells, it comes as a surprise to most of us that it is a revolutionary concept. But without it, the amazingly powerful, and equally dumb, machine that sits on our desktops - the digital computer - would be completely useless.

Rest assured, you no more need to master the technical details of this book to run your computer than you need to know the ignition temperature of unleaded gasoline to run your car. But if you master the details, there are satisfactions aplenty.

The algorithm is one of the astounding intellectual achievements of modern times. Until the late 19th century, the rules of logic were much the same as they had been in ancient Greece. Aristotle invented the syllogism, which comprises a major premise (for example, "All Microsoft products are overpriced"), a minor premise ("Word is a Microsoft product") and a conclusion ("therefore, Word is overpriced").

The scope of logic was pushed several thousand years ahead by one remarkable man, Gottlob Frege, whose aim, along with the handful who comprehended his work, was to find a logic within mathematics. Mathematics (and eventually the world, which runs according to the mathematical laws discovered by Isaac Newton and others) would then be subject to proofs, which determine truth or falsehood beyond the possibility of doubt.

Several generations later, in one of the mighty intellectual thunderbolts of all time, Kurt Godel proved that the procedure Frege had sought would not be found - because it could not exist. No matter how the truth-seeking algorithm is devised, there will always be truths that elude it.

This was a devastating conclusion: From then on something less than certainty would be the best that logicians, mathematicians and scientists could ever hope to find. Berlinski walks us through this remarkable "incompleteness" theorem, and this is where he is at his best, illuminating complex concepts with clarity.

In the course of his proof, Godel demonstrated how complex reasoning can be reduced to a series of mechanical steps. Alan Turing, another tortured genius (as most of these logicians were), invented an imaginary "machine" that could use such mechanical steps to solve virtually any intellectual problem. This became the basis of the digital computer, long before any such device existed. A few years later Turing would help crack the Enigma machine, the Nazis' cryptographic code during World War II. Fifty years later, it was largely his insight that yielded the information revolution.

The algorithm extends beyond even the furthest reaches of computing. Berlinski sees DNA as an algorithm: The molecule of life replicates exactly by automatic biochemical command, sending information not only throughout an organism, but also forward from generation to generation. Will human thought itself be reduced to an algorithm?

Now the bad news. Berlinski intersperses informative sections of his book with short stories of elusive significance, imaginary conversations with historical personalities, and even accounts of cute meetings among himself, his agent and his editor. Berlinski's writing often gets so mannered that you can imagine him typing with one hand and patting himself on the back with the other.

The workings of Turing's machine had only two commands: what to write and what to erase. This fascinating book would have been far better if Berlinski had devised such a machine for it.

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Daniel Evan Weiss is the author of Honk If You Love Aphrodite, and other novels.

Put precisely, an algorithm "is an effective procedure, a way of getting something done in a finite number of discrete steps." One can also say that "an algorithm, speaking loosely, is a set of rules, a recipe, a prescription for action, a guide, a linked and controlled injunction, an adjuration, a code, an effort made to throw a complex verbal shawl over life's chattering chaos." Thus Berlinski, who has taught mathematical logic but now devotes himself to writing, introduces his deep and instructive account of the algorithm's development and its role in modern life. He does not shirk the mathematics of his subject. Although he strives to put its points clearly, the nonmathematical reader will still have to lean into them. But the same reader will find much rewarding information about mathematics, famous and not so famous mathematicians, and philosophy.

EDITORS OF SCIENTIFIC AMERICAN

Praise for David Berlinski's previous book, A Tour of The Calculus "A playful, witty, highly literate effort to guide the mathematically uninitiated through the mysteries of the calculus. . . A wonderful and enlightening book."

The algorithm is just code, but it makes things happen. It's the set of abstract, detailed instructions that makes computers run. Any programmer can invent a new algorithm-and many have become millionaires doing just that. Computers, the Internet, virtual reality-our world is being transformed before our eyes, all because some quirky logicians and mathematicians followed the dream of ultimate abstraction and invented the algorithm. Beginning with Leibniz and culminating in the middle of this century with the work of little-known geniuses and eccentrics like Gödel and Turing, David Berlinski tells this epic tale with clarity and imaginative brilliance. You don't have to be a programmer or a math buff to enjoy his book. All you have to do is be fascinated by the greatest innovation of the twentieth century.

The algorithm--the greatest mathematical discovery of the 20th century; a recipe that runs the computer and gives DNA its instructions. In this book, the author of "The Tour of Calculus" tells how it all happened, taking readers on a breathtaking voyage of invention, genius, and human frailty.

David Berlinski is the author of three novels and four works of nonfiction, most recently the bestselling A Tour of the Calculus. Berlinski received his Ph.D. from Princeton University and is a regular contributor to Commentary; his essays on Darwinism and the Big Bang have become famous; he also writes for Forbes ASAP. He lives in San Francisco.