The Advent of the Algorithm: The 300-Year Journey from an Idea to the Computer

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Berlinski's argument seems to be that algorithms--step-by-step procedures for getting answers--superceded logic, and will be superceded in turn by more biological, empirical, fuzzy methods.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, Goedel, 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

Product Description

Unfortunately, some readers misunderstand Berlinski's subtlety and insight. For instance, the official trade review of the book complains that Berlinski never really defines "algorithm." This is incorrect. The introduction concludes with an offset definition: "In the logician's voice: an algorithm is a finite procedure, written in a fixed symbolic vocabulary, governed by precise instructions, moving in discrete steps, 1, 2, 3,..., whose execution requires no insight, cleverness, intuition, intelligence, or perspicuity, and that sooner or later comes to an end." It doesn't get much clearer than that. But Berlinski doesn't ponder long over what he takes to be obvious, and he doesn't always speak in the logician's voice.

The Advent of the Algorithm demonstrates that a seemingly dull concept can have unimaginably profound implications. Those implications illuminate everything from computing and information technology to the nature of life and the universe. And ultimately (not to spoil the ending) Berlinski argues that the advent of the algorithm foretells the end of scientific materialism, suggesting nothing so much as a world permeated by the marks of intelligence and design. To paraphrase, we are shocked to discover information--something we had assumed was found exclusively in the domain of human activity--flourishing on the alien shores of biology.


An intellectual and spiritual adventure   January 5, 2003
James Huddleston (Newport, DE United States)
4 out of 9 found this review helpful

Quirky and quixotic, but often illuminating, this charming monograph brings to life the great thinkers who struggled to understand what may well be the most monumental achievement of the human intellect, the algorithm.

Those expecting a detailed or formal description of what an algorithm is will be disappointed. It's not that kind of book.

Those seeking insight into the power and limitations of mathematics and logic will find much to contemplate. It is that kind of book.

Not for everyone, but a treat for those who esteem both mind and soul.


Does Mathematics Support Darwin or Intelligent Design?   June 21, 2006
Discovery Reviewer (Seattle, WA)
6 out of 12 found this review helpful

Mathematician David Berlinski explains how the "algorithm" is sure to play a major role in the future of mathematics. An algorithm, Berlinski explains, is essentially a logical, mathematical procedure by which a goal can be accomplished in a finite number of steps.

After recounting the origin of the algorithm within mathematics, Berlinski explains that it is the algorithm which has made possible the physical sciences. Turning his attention to molecular biology, and the genetic code specifically, Berlinski notes that algorithms are required to convert information from one set of symbols, the genetic code, into another set, the proteins. Berlinski believes these strings of information are far richer than analogous strings of information we find in say, a novel: "while Tolstoy's Anna Karenina can only suggest the woman, her black hair swept into a chignon, the same message, carrying the same meaning, when read by the right biochemical agencies, can bring the woman to vibrant and complaining life, reading now restored to its rightful place as a supreme act of creation" (pg. 290-291).

Berlinski concludes on a philosophical note. While materialists like Steven Weinberg believe the universe is "pointless," other thinkers in history, such as William Paley, believe that the complexity of the natural world require us to ask deeper questions. Intelligence, Berlinski believes, can be explained by algorithm. This is seen in that the intelligence which authored his book (if Berlinski would consider himself intelligent) was created via the algorithms which convert DNA-information to living, breathing assemblies of proteins.

From whence did this algorithm come? Berlinski analogizes from the reasoning of Kurt Goedel, who saw that law and chance alone would not be expected to produce an increase in complexity. Darwin's theory using blind natural selection acting upon chance mutations cannot account for the complexity of life as it has developed over time. Berlinski thinks that the rapid origin of biological complexity might require a process of "careful coordination and intelligent design" (pg. 321). Thus, science would be best to use the explanatory tools of law, chance, and the algorithm, which he calls "an intelligent artifact" (pg. 325). Applying Goedel's logic, complexity cannot be derived entirely from something simple. Complexity can be shifted, transferred, but the complexity in the universe can never provide a complete explanation for its own origin.


I adore Berlinski   February 9, 2008
Sunny Wallace (NC)
1 out of 2 found this review helpful

Not for the faint-hearted, this is my most favorite math read of all times. It should be, since it's been a difficult companion for more than five years. Nevertheless, the whipsmart Berlinski has an uncanny knack at making math make sexy sense for the nonsensical fraction-challenged. He invites passage into the deeper language that only a few really understand. I adore Berlinski and his book; await the simplicity that's certain to be hiding in the challenge.


mystery revealed   March 23, 2000
1 out of 11 found this review helpful

brilliant and exciting book which offers an extraordinary look at the world of calculus, A most for serious readers and the general public.