Rating: 
Summary: Does not quite compute, yet...
Review: 'The Advent of the Algorithm' contains useful data but one must wade through torrents of purple prose to find the nuggets. My impression is that Dr. Berlinski wanted us to feel the romance of the idea, but wasn't quite sure how to present that idea. The book seems to have been written in haste and by no means matches the excellence of his 'Tour of the Calculus.' Nevertheless, a novice, such as me, can benefit from Berlinski's discussion of the Turing and Post machines, Goedel's theorems, and Church's lamda calculus. The work of these logicians made precise the concept of 'algorithm,' says Berlinski. I think I know what he means, but he is a bit vague -- though admittedly he has the difficult task of trying to present a rarefied subject to a lay readership. We learn, for example, that if a problem is Turing computable, then an algorithm exists for its solution. So that means, I suppose, that, in this case, an algorithm is the set of instructions given that computes an answer on a Turing machine. To me, this does not quite get at the nitty gritty of what an algorithm is .... I realize that, in writing this book, Berlinski was balancing his poetic instinct against his mathematical streak. He doesn't quite succeed in the balancing act. Yet the discussion of the work of the four logicians makes the book useful. Perhaps Berlinski would have done a bit better had he, before writing his book, designed an algorithm to outline what he wanted to say. I recommend that he write another, more serious book focused specifically on the life and work of the logicians he cites.
Rating: 
Summary: Excellent ideas, buried under bad prose
Review: Berlinski gathered the right set of ideas for this subject, and he explains them in thorough detail. In particular, I found the level of detail for Godel's, Church's, and Turing's work to be very informative, e.g. this was the first time I saw Godel's encoding scheme explained well enough for me to see just how it works.
However, the prose in this book was so bad that I just couldn't finish it. While it was good that he stayed away from a dry textbook style, the style he ended up with was better suited for a romance novel than a technical history. In addition to the prose style itself, the book is littered with fictional asides that are meant to illustrate subtle points but end up being a distraction. It seems that the author was trying to create both a good technical history and a work of art, but in the end he failed at both.
Rating:
Summary: Excellent ideas, buried under bad prose
Review: Berlinski gathered the right set of ideas for this subject, and he explains them in thorough detail. In particular, I found the level of detail for Godel's, Church's, and Turing's work to be very informative, e.g. this was the first time I saw Godel's encoding scheme explained well enough for me to see just how it works.
However, the prose in this book was so bad that I just couldn't finish it. While it was good that he stayed away from a dry textbook style, the style he ended up with was better suited for a romance novel than a technical history. In addition to the prose style itself, the book is littered with fictional asides that are meant to illustrate subtle points but end up being a distraction. It seems that the author was trying to create both a good technical history and a work of art, but in the end he failed at both.
Rating:
Summary: interesting topics marred by typos and changes in notation
Review: Berlinski is entertaining but too erudite for an illiterate slob such as I. Big words notwithstanding, it was educational and entertaining to see the breadth of mathematical topics covered in this way. He is very creative and has tied many topics together neatly. Tolerance for ambiguity (and a willingness to fix the problems yourself) is required if you want to follow the math, because of numerous typos and changes in notation & conventions. I suspect that he corrected these in a draft but that the publisher somehow failed to incorporate said corrections in the edition that went to press. In other words, this would be intolerable as a textbook. That said, if you don't want to follow the math in depth but just want a survey level coverage of some very important ideas in mathematics, then at today's price on amazon.com it's truly a bargain. It's not just algorithms he's talking here but a broad range of topics: set theory, propositional and predicate calculus, the incompleteness theorem.... The book is a lot of fun (I majored in math so my idea of fun may not match yours) but, well, those typos.... Some of the typos (like p134's 999,000 or p174's mismatched parens) don't hurt anything, but the changes in notation on pp 25 and 165 impede understanding, and the incorrect grouping on p134 is extremely annoying. Here are a few (by far not a complete list): page 25, are the a-sub-n values the terms or the running sums? In the top half of the page, they're the terms, but in the bottom half they are the partial sums of the infinite series. Page 74, line 2, insert "and B is otherwise the exact same formula as A" just before the ']' -- otherwise how could it be an axiom? pp 87,92: maybe notation has changed since I went to school (but Berlinski is older than I) but the empty set was written as {} or as "O with a slash through it" (looks like phi sorta), so every expression on these two pages with {braces} has IMO one pair too many. On page 134, you have to take (1+sqrt(5)) and divide the whole thing by 2, not 1 + (sqrt(5)/2) like that; try it and you'll see. In the middle of the page, x=999,999 and 999,998 -- NOT 999,000 and 998,000 :^(. He changes notation between pages 164 and 165 :^( which may have been the factor that prevented a previous reviewer from feeling comfortable with the lambda-calculus. Page 174, mismatched parentheses; delete a ')' from the first set of "f"s and add a '(' between 'ff' in the 2nd expression.
Rating:
Summary: Affected prose and poor explaination
Review: David Berlinkski has done for algorithms what he had previously done for the caluculus; that is, he has taken a bare minimum of technical explaination and buried it in thick, affected, barely readable prose. And as with his calculus book, he is wading into waters where far more skilled writers have gone before. Like the calculus book, this will appeal to readers who don't really want to be troubled by detail, and who like the idea of reading about science without actually having to deal with the difficult notions. It may also appeal to those who don't mind the confusing narrative and who will appreciate the scattershot style and pointless asides. I have to admit I couldn't finish this book. After numerous attempts I just put it aside. Life's too short to waste on some things.
Rating: 
Summary: The Advent of the Algorithm
Review: David Berlinski has written two popular books on mathematics, the first entitled, A tour of the Calculus, and second, The Advent of the Algorithm. The theme of this duo of books is that mathematicians have produced two great ideas of 'the great scientific culture of the West.' Neither book requires the reader to have more than a high school level of mathematical knowledge. He does present proofs in appendices that a lay-person might find difficult or beyond their ability to follow; however, these are not required in order to understand the major ideas of the books.
The author's thesis, as stated at the beginning and end of both books, is that the analytical thought of Calculus has gone through it's cycle of growth and is now, for the most part, come to a stand-still, while the sort of mathematical logic embodied in the computer's use of the algorithm, has emerged as the succeeding great idea 'of the great scientific culture of the West.' Yet, the content of both books is not so much an argument in support of this thesis but a guided tour of the essential ideas of both mathematical methods. Mr Berlinski is an emancipated professor of college mathematics and clearly knows his subject. He also is a sophisticated writer, presenting the reader with plenty of rhetorical devices in an attempt to make the terse matter of mathematical concepts easier to digest. These devices include imaginary reconstructions of plausible scenes and dialog he might have had with the great pioneering mathematicians, past professors and students. He also frequently meanders into metaphysical interpretations of the mathematical ideas, particularly between sections of the book bearing proofs. His choice of vocabulary can be challenging; I recommend having a pocket dictionary on hand. Mr. Berlinski's second book, "The Advent of the Algorithm," describes the evolution of the second great mathematical idea: the algorithm. It begins with a portrait of the acknowledged founder of modern logic, Gottfried Leibnitz, who envisions a universal logic where all facts about the world can be organized and analyzed systematically and so avoid human corruption. Next, the reader encounters an attempt to achieve Leibnitz' vision within the field of mathematics. The first step towards the development of the algorithm are the attempts of 16th century mathematicians, such as Fourier and Leonhard Euler, to define irrational and transcendental numbers through the sums of numeric sequences. Advances in these sorts of studies led to critical ideas about how to define the limits of infinite sequences and the need for a logically cogent and encompassing numbering system. Logicians such as Peano, Georg Cantor and Gottlobe Frege set forth their answers in the form of well-constructed axioms that define limits, real numbers, and arithmetical systems. The dawn of the 20th century saw David Hilbert propose his famous 20 mathematical problems, in the hope of establishing all mathematics upon a few irreducible axioms and rules for working them. Just when the ponderous tomb, Prinicipia Mathematica of Bertrand Russell and Alfred Whitehead appeared to fulfill the holy quest, the Swiss, Kurt Godel published his famous Incompleteness Theorems that demonstrated the impossibility of such a system. The silver lining of Godel's work was his discovery of a remarkably succinct method for representing mathematical functions, by use of recursive algorithms. Something of the idea seemed to be stirring in the mid-twentieth century, for variations of these recursive algorithms were simultaneously discovered by Alonzo Church and Allan Turing. While Alonzo Church achieved his project through the design of a clever form of symbolic notation, Allan Turing conceived of a simple mechanical machine--a computer--that could carry out any computation that was logically possible. Curiously, while the Turing machine corroborated Godel's famous theorem, implying the impossibility of a set of axioms to account for all mathematical possibilities, he nevertheless felt certain that his machine represented the essential workings of human thought and that it was only a matter of time before a computer's output could be mistaken for the range and depth of human thought. In the final pages of this book, the author describes the onset of the biological sciences, with its discovery of genetic coding in DNA. The discovery is timely, for western science had just begun to experience man-made algorithms in working with computers. The author suggests that DNA is a sort of natural algorithm where enumerable variables are coordinated to produce living things. This brings us to the present state-of-the-art where biologists are attempting to make sense of the human gnome with the aide of the computer.
Rating:
Summary: In case you don't know HOW bad the prose is...
Review: 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.
Rating:
Summary: A Frequently Unhelpful Attempt To Be Helpful
Review: From the book's introduction: "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." Everyday examples include computer programs and the functioning of our genetic systems to produce aspects of life. Dr. Berlinski works from the conceptual questions and quests in philosophy (especially logic) and mathematics that led to the development of the mental concept of the algorithm that we know and think about consciously today. The path is an interesting one, and full of randomness and false leads. Like most progress, it is two steps forward and one step back. Today, use of algorithms is at the base of our most powerful forms of progress. For example, some classes of problems are all but impossible to solve and we use algorithms to create simulations that allow us to approximate the answers. Mathematicians can now solve vastly more classes of problems using computers than they ever could before, rapidly expanding our knowledge. The speed up in progress in many scientific areas is also related to the use of algorithms to ask and answer questions. For example, the human genome decoding was greatly accelerated by using computer-based decoding algorithms to locate the likely sections of meaningful DNA information. With so much intellectual richness and potential to work with, how did Dr. Berlinski end up with a 3 star instead of a 5 star rating from me? First of all, he has one of the most irritating writing styles I have ever had the displeasure to persist through. Most annoying were the long fictional diversions he uses to faintly illuminate minor aspects of the point that he is making. These are denoted by four shadowed boxes before and after them. My advice is, SKIP THESE SECTIONS! As your faithful reviewer, I read almost all of them. I found little to reward me in these sections, and much to annoy. I also resented the space that could have gone to better use. The second annoying characteristic was the overuse of symbolic logic and mathematical expressions. Long after the point was made, he was still wandering around filling in little nuances that added almost nothing to one's understanding of the development of algorithms and their development. The reason for deducting the second star was that he spent far too little time speculating on the future implications of algorithms. Dr. Berlinski is actually quite good in this area, and his writing on this aspect of the book is spare and effective. He also seems to have good ideas. Clearly, as new users of algorithms in the last few decades, we are only beginning to understand their implications. What a wonderful opportunity to inform our next quest! But alas, it was a too short trip in this book. I was tempted to grade the book down one more star for unnecessarily complicated explanations of symbolic logic conventions and of mathematical functions. I studied these areas in college, and the explanations I received then were much simpler, shorter, and clearer. Many people who are unfamiliar with these subjects will find the material here unnecessarily confusing. But then I realized that writing a book about algorithms is a brilliant concept, deserving of a star for itself. This negative and this positive canceled one another out, leaving me at 3 stars. Now your understand the algorithm I used to rate the book. The stories of Liebniz, Godel, and Turing were especially interesting for me. These were quite well told. If you cannot bear the whole book, be sure to look at these. You can use the index to find them. I hope someone with a better sense of what the reader would like to examine and how to communicate will follow this book with a better one on this subject. If you decide to read this book, despite its drawbacks, please use the experience to think about how you can simplify important communications in your life so they will be better understand and acted upon.
Rating:
Summary: A Hard Slog Surrounded by Silly Writing
Review: I have very mixed feelings about this book. On the one hand, Berlinski writes very well. He has a knack for the off-the-wall simile that reminds me a lot of Douglas Adams. On the other hand, the guts of the book are several chapters dealing with formal systems of logic, and I my brain just bounced off a lot of the hard parts.
It's not as if I didn't know a little bit about this going in. I have a fairly good background in mathematics and programming. I was at least aware of Leibnitz, Hilbert, Godel, Church, Turing, Russell, Morgenstern, and the other major characters. Even so, I was floundering in the middle of the technical chapters and had to take the conclusions more or less on faith. Berlinski peppers the book with little interludes that don't seem to be related to the main story at all. They start out as historical portraits of the participants and the times in which they live, but by the end they are little fictional vignettes told in the first person. One gets the feeling that they are intended to be related to history of the algorithm in some symbolic way. If so, I wasn't smart enough to see that. I almost suspect that they are just little breaks to wake up the reader between bouts of technical analysis. Although the book seems to be a history, it doesn't provide much a sense of development. One can see the problems that the great mathematicians were working on, but why they were needed to develop the idea of an algorithm is not made clear. At the end, after Turing, the chapters just kind of splutter around, dealing with a variety of topics. Again, I get the impression that the author means for them to be a complete whole, but I'm afraid I missed his point.
Rating:
Summary: Not quite as good as A Tour of the Calculus
Review: Purple prose aside, this book is not as illuminating as his Calculus book. But then again the subject itself is not as well developed as the Calculus, and the author's mastery of this area is not as sure. The fact is modern logic has never recovered from Russell's paradox and Godel's theorem is more often quoted then understood, or for that matter explained. The author is also a bit chauvinistic in attributing the idea of algorithm to European root when the word algorithm itself came from the name of an Arabic mathematician who taught the world algebra, a fact never mentioned in the book. Also the assertion that calculus and algorithm are the only two great ideas in modern science is wildly exaggerated. Darwin's evolution theory may yet prove to be the greatest one of all. All in all not as bad a book as many of the other reviews seem to imply. Definitely not a book for the impatient however...
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