March 05, 2000|By Mark Ribbing | Mark Ribbing,Sun Staff

"The Advent of the Algorithm: The Idea That Rules the World," by David Berlinski. Harcourt. 368 pages. $28.

Say this much for David Berlinski: The guy's got guts. In an age of instant gratification and flea-like attention spans, Berlinski has the temerity to ask his readers to actually stretch their minds. His subject is math, and he wants to make its complex outer reaches accessible to a lay audience, much as Stephen Jay Gould has done for biology or Carl Sagan for astronomy.

Berlinski acknowledges the difficulty of his mission: "For the most part, it is true, ordinary men and women regard mathematics with energetic distaste, counting its concepts as rhapsodic as cauliflower. This is a mistake -- there is no other word. Where else can the restless human mind find means to tie the infinite in a finite bow?"

This snippet fills the reader with hope. It suggests that Berlinski understands and sympathizes with the ignorances and fears of the mathematically unsophisticated. It indicates that he is more than capable of stringing together a compelling sentence. It shows that he has a passion for his topic.

That topic is the algorithm, roughly defined as a ladderlike sequence of commands that proceed step by step to the solution to a given mathematical problem. Algorithms are crucial to the functioning of computers, a fact that inspires Berlinski to write that "it has been the algorithm that has made possible the modern world."

What a pity, then, that a book brave enough to discuss this abstruse but important topic should turn out to be such a mess. Berlinski's narrative veers from cursory, unhelpful math lessons to biographical sketches of great mathematicians to shards of memoir and fiction.

This odd combination could be wonderful if it were handled more deftly. If Berlinski were to employ his narrative elan in illustrating the basic mathematical principles underlying the algorithm, then the reader could be ushered along toward greater heights of understanding. Instead, Berlinski offers skimpy lessons on complicated mathematical matters, then swerves into scarcely relevant memories of some past lover or accounts of imagined discussions between mathematicians of centuries past.

The reader, meanwhile, is left reeling by the curbside. Or at least I was. I found myself having to go over Berlinski's math teachings again and again in an effort to divine their meaning. This, I readily concede, may be at least partly my own fault; maybe Berlinski's explanations are simply lost on a non-mathematically inclined reader like me.

However, "The Advent of the Algorithm" holds itself out as a guide for the uninitiated, not as a textbook for doctoral candidates. This come-one, come-all approach will sell more books, but it also compels the author to take into account the needs of readers whose minds are open but whose knowledge is scant. Such are the burdens of the popularizer, and Berlinski fails to shoulder them.

In addition, Berlinski's prose too often crosses the line that separates verve from pomposity: "My students look up, prepared to agree to absolutely anything, the brilliant, thrilling sunshine now occupying the whole of the classroom, encompassing my words in a burst of light."

There is one superb chapter in which Berlinski writes with lucidity and even restraint about the enormous contributions that British logician Alan Turing made to the development of the computer and the cracking of Nazi Germany's Enigma codes. Berlinski's portrait of Turing -- who was eventually driven to suicide by the military's attempts to medically rid him of his homosexuality -- is a fine example of how biography can enhance our understanding of technological progress. It is also proof of what this book could have been.

Mark Ribbing has covered the telecommunications industry for The Sun since 1997. He was previously a staff writer and attorney for the Lehman Communications chain of newspapers in Colorado.