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.

19 of 20 found the following review helpful:

Fascinating Look at a Difficult Topic - But Eclectic  Feb 09, 2002
By Michael Wischmeyer
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.

16 of 18 found the following review helpful:

I understand the mixed reviews...  May 09, 2000
By P MARTIN
I understand the mixed reviews this book has received on Amazon.com. The style is definitely not that of the standard popularizing text of mathematical or scientific concepts that we are so used to seeing today. And I think it's a lot better for that! Even readers who do not have the time, energy or (dare I say it?) mental capacity to understand this book in its entirety (I'm in the latter camp)should find this a pleasurable read. There's much in here of great historical and biographical interest and Berlinski's prose style is original, often unexpected, usually fun and just occasionally very moving. And the concepts are well developed, if complex in nature.

I'm going to buy his book on calculus because I enjoyed this book.

16 of 19 found the following review helpful:

In case you don't know HOW bad the prose is...  Dec 17, 2004
By James Brust "Batgeek"
First of all, I somewhat liked A Tour of the Calculus, and found it much easier reading than Advent of the Algorithm. Especially considering that the prose here is so annoyingly affected, that I couldn't get farther than a couple of chapters. I have tried in good faith to finish the book, but I really could not, and I do have to apologize for any incompleteness of my review as a result.

Also, I consider some of the earlier digressions--in the part of the book I was able to get through--to be okay, as far as content goes. However, these and everything else in the book seem to just be marred by the crippling excesses of this guy's prose.

So many people have said enough about this guy's writing that it would seem to speak for itself, so at first I wasn't going to weigh in. However, there have been a few people writing to claim that Berlinski's writing style is refreshing, and more approachable than the dry, prosaic style of a textbook. I MUST set the record straight here, for those who have not tried this book out.

I can understand the frustration some people have when "popular" books on science or mathematics might not be as interesting as we'd like to hope. But Berlinski's style is NOT poetic, and it is NOT refreshing. It is NOT like some chap at a pub explaining something to you, because most likely the "some chap" is not going out of his way to speak in an artificial, over-poetic (to the point that it is NOT poetic) way, often using unnecessarily obscure words. Other reviewers have cited examples--though some examples are more telling than others.

Have you ever known somebody who speaks or writes in an unnecessarily affected way, in order to appear smarter than he really is? Berlinski writes like that. I am sure that he is an intelligent and learned person, but his writing reeks with pretentousness. He uses too many overblown metaphors that seem like they are attempting to hide the awkwardness of a given sentence, or (more likely) to dress up a really basic, unimpressive idea, to make it seem unfathomably profound. Often his devices are so unnatural, they make the writing even more awkward than if they had not been there at all. This writing is not artful, it is artificial. A truly good artist might be playful, but knows when it is better just to keep things simple and straightforward.

It is a shame that I cannot really give much of a review on the content, because that is the effect of bad writing. It is so distracting that one cannot tell whether the author is saying anything valid or not.

Hemingway is supposed to have said that every good writer has a built-in s**t detector. The Advent of the Algorithm suggests strongly that Berlinski--and some of his fans--lack that detector. The prose in this book is literally an insult to anybody who actually knows what good writing looks like. Even the normal kind of bad writing is preferable to this, because it is sincere and not nearly so annoying.

The ONLY reason this book is getting two stars from me is because it does look like there is some real potential in this book. Sadly, I cannot force myself to see it.

12 of 14 found the following review helpful:

The Advent of My Ego  Jan 05, 2003
By Nicholas C Georgalis
The only good thing about this book is that it cost [$] and even at that it is too expensive. The book is more about the author's sexual prowess than about the idea of an Algorithm. Between somewhat cogent biographies of the major 19th and 20th century contributors to the subject of numerical analysis and information theory, the author included short vignettes about either some personal or fictional experience that had nothing to do with the subject at hand. This was most annoying and wasteful of the reader's time. The author failed to communicate that he really had any real understanding of the subject matter. The only idea that I found somewhat developed and interesting was that the algorithm is a creation of the mind, that it has no substance. It is a process and a process only exists because there is a mind to comprehend it. This is the only jewel in the book and one that the author fails to develop more fully. Even in his discussion of numerical analysis and information theory the author leaves the reader yearning for more but there is no more to be had. I was particularly disappointed by his cursory survey of Shannon and his contribution to information theory and the relationship of information theory to entropy and probability.

One of the vignettes in the book describes a breakfast meeting with the author's agent and his publicist. In the meeting they complain about the manuscript's incomprehensibility and urge the author to be more understanding of his readers. It is advice that he failed to take and should have.

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