118 of 127 people found the following review helpful:
5.0 out of 5 stars
A highly original guide to a foundational concept, March 24, 2000
By A Customer
David Berlinski has delivered another fascinating tale of an underappreciated topic. What he did for the calculus he now does for the algorithm. The text preserves all of Berlinski's extravagant, quirky and sometimes difficult style, shifting between careful analysis, historical drama, insightful explanation, and obscure fictional aside. Readers will either love it or hate it. (I love it.)
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.
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19 of 20 people found the following review helpful:
4.0 out of 5 stars
Fascinating Look at a Difficult Topic - But Eclectic, February 9, 2002
First, symbolic logic is not an easy subject and requires attention to detail. Second, Berlinski's discursive style can require the reader to be accomodating and patient. Some may abandon Berlinski in frustration. But others will discover that Berlinski has created a rather unique work.
It is easy to be disoriented by Berlinski's eclectic mix of fiction, biography, essays, and mathematics. I would hunker down for some serious math, but be sidetracked to an unfamiliar Greek fable. Just as quickly I was being introduced - with surprising clarity - to propositional calculus, truth tables, and tautologies. Another sidetrack and I was privy to the delusional thoughts of some stranger.
At this point I fortuitously observed fine print on the copyright page: "This is a work of scholarship. The author has woven stories, involving imagined people and incidents into the text, the better to enable the reader to enjoy the technical discussions. Or to endure them." I relaxed and accepted that while my road might be a bit bumpy, I now had some understanding of Berlinski's itinerary.
I particularly valued the short biographies of the mathematicians and logicians that played key roles in developing symbolic logic and its protege, the algorithm. My attitude was more mixed regarding the playful stories (pure fiction) "woven"
into the text. Although some shed light on the technical discussions from unexpected perspectives,I found other stories to be more distracting than helpful.
Notwithstanding the occasional flights of fancy, "The Advent of the Algorithm" is indeed "a work of scholarship". Clarity characterizes most technical sections, but careful reading is still necessary. The technical sections include:
categorical syllogism (pg. 9-11) and Peano's axioms for arithmetic (pg. 32-35) - 4 stars.
propositional calculus plus truth tables (pg 50-59) - 5 stars,
predicate calculus (pg. 65-68, 71-80, 94-95) - 5 stars,
Frege's "Foundations of Arithmetic" plus Russell's paradox (pg. 91-93) - 5 stars,
"Principia Mathematica" plus Hilbert's program (pg. 96-100, 105-108, 112-114) - 5 stars,
formal arithmetic (pg. 109-111) - 4 stars,
Godel's Proof and recursion (pg. 116-129, 136-141, 143-145) - 5 stars,
the calculus of lambda conversion (pg. 162-179) - 3 stars,
Turing machine (pg. 181-192) - 4 stars,
thermodynaymics (pg. 226-234, 238-248) - 3.5 stars,
and the final three chapters (13-15) on neural networks, DNA coding, and complexity - 5 stars.
I bogged down on chapter 8, a discussion of Alonzo Church's calculus of lambda conversion. Even after some study, I was still not comfortable. I began with no knowledge of lambda calculus; I ended with only a partial understanding. Fortunately, a detailed understanding is not critical to the remaining chapters.
The final three chapters are especially interesting. Berlinski's examination of the question, "Why does complexity exist within a universe characterized by simple physical laws?", was fascinating and insightful.
Should you buy this book? I think not, if you are looking for a typical book on mathematics for the layman. "The Advent of the Algorithm " requires attention to detail and persistence.
However, a persistent reader, one willing to invest time and effort to gain an understanding of symbolic logic, should give Berlinski's book a try. His interests may not always coincide with yours, but the tour will be memorable. Berlinski has created a unique book about a difficult subject. Substantial sections clearly deserve five stars. I give it four stars overall.
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