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The Advent of the Algorithm: The 300-Year Journey from an Idea to the Computer
Francis Sullivan of the Institute for Defense Analysis said "Great algorithms are the poetry of computation"; David Berlinski calls the algorithm "the idea that rules the world." The Advent of the Algorithm is not so much a history of algorithms as a historical fantasia. Berlinski spins freely between semifictional accounts of historical figures, personal reminiscence, and mathematical proofs--without ever really defining an algorithm in so many words.
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Berlinski's argument seems to be that algorithms--step-by-step procedures for getting answers--superceded logic, and will be superceded in turn by more biological, empirical, fuzzy methods.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, Gödel, 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
Listening Length: 10 hours and 42 minutes
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First published January 1, 2000
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About the author
David Berlinski
32 books264 followersDavid Berlinski is a senior fellow in the Discovery Institute’s Center for Science and Culture.
Recent articles by Berlinski have been prominently featured in Commentary, Forbes ASAP, and the Boston Review. Two of his articles, “On the Origins of the Mind” (November 2004) and “What Brings a World into Being” (March 2001), have been anthologized in The Best American Science Writing 2005, edited by Alan Lightman (Harper Perennial), and The Best American Science Writing 2002, edited by Jesse Cohen, respectively.
Berlinski received his Ph.D. in philosophy from Princeton University and was later a postdoctoral fellow in mathematics and molecular biology at Columbia University. He has authored works on systems analysis, differential topology, theoretical biology, analytic philosophy, and the philosophy of mathematics, as well as three novels. He has also taught philosophy, mathematics and English at Stanford, Rutgers, the City University of New York and the Université de Paris. In addition, he has held research fellowships at the International Institute for Applied Systems Analysis in Austria and the Institut des Hautes Études Scientifiques. He lives in Paris.
Recent articles by Berlinski have been prominently featured in Commentary, Forbes ASAP, and the Boston Review. Two of his articles, “On the Origins of the Mind” (November 2004) and “What Brings a World into Being” (March 2001), have been anthologized in The Best American Science Writing 2005, edited by Alan Lightman (Harper Perennial), and The Best American Science Writing 2002, edited by Jesse Cohen, respectively.
Berlinski received his Ph.D. in philosophy from Princeton University and was later a postdoctoral fellow in mathematics and molecular biology at Columbia University. He has authored works on systems analysis, differential topology, theoretical biology, analytic philosophy, and the philosophy of mathematics, as well as three novels. He has also taught philosophy, mathematics and English at Stanford, Rutgers, the City University of New York and the Université de Paris. In addition, he has held research fellowships at the International Institute for Applied Systems Analysis in Austria and the Institut des Hautes Études Scientifiques. He lives in Paris.
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Displaying 1 - 30 of 32 reviews
February 13, 2011
Many people who know me would think that reading David Berlinski, for me, would be an act of studying the enemy. Yet I am an agnostic with a healthy respect for the philosophical argument of ID, and my belief in the fallibility of humankind is matched only by my belief in our indomitability. Therefore, while I am currently a supporter of the theory of evolution, I do not see Berlinski and I as sitting on the opposite sides of a fence.
It is impossible, when reading works like this to deny the man's genius or to ignore the charm of his singular mind. The book is a ramble of science, fictionalizations, and personal asides. It is more like having a cafe discussion on science and theology with a very eclectic but brilliant lunch-mate. If he had been born two hundred years ago, it would be easy to see berlinski develop into some sort of Jewish William Blake. Very interesting read.
It is impossible, when reading works like this to deny the man's genius or to ignore the charm of his singular mind. The book is a ramble of science, fictionalizations, and personal asides. It is more like having a cafe discussion on science and theology with a very eclectic but brilliant lunch-mate. If he had been born two hundred years ago, it would be easy to see berlinski develop into some sort of Jewish William Blake. Very interesting read.
January 12, 2021
" The algorithm is …the second great scientific idea of the West. There is no third."
This sentence at the very beginning of the book should warn us that this is not going to be science writing in the Asimov vein. Dr. Berlinski once boasted that he can be accused of many things, but shrinking from controversy is not one of them. A professor of mathematics, a novelist, something of a poet and the successful author of “a tour of the calculus”, Dr. Berlinski is also famous for his very public insistence that Darwinian evolution does not add up; that something is missing from the story and the high priests are engaged in a cover-up. In “the advent of the algorithm” he sets out to tell us about the algorithm: "a procedure, written in a symbolic vocabulary, that gets something done step-by-step without the need for any intelligent assistance”. But he ends by questioning the ability of science to explain the mind: the intelligence that fashions and uses these algorithms and infuses them with meaning.
The book begins and ends with Gottfried Leibniz. Between inventing the calculus, imagining the monads and carrying out his diplomatic duties, Gottfried Liebniz also laid the foundations of mathematical logic and the science of computing. He is followed by Guiseppe Peano, Gottlieb Frege, George Cantor and others, till we get to the great David Hilbert and his challenge to mathematicians to show that mathematics is consistent, complete and decidable (in principle, if not in practice). Within a few years, Kurt Godel was able to show that this is not possible. After an explanation of Godel’s revolutionary result, Alonzo Church, Alan Turing, Emil Post, Claude Shannon and others are introduced and the reader learns about the developments in logic and mathematics that form the foundations of our modern digital world.
Berlinski’s explanations of these developments are lucid, even brilliant, and someone with little mathematical knowledge beyond high school should still be able to understand what he is saying. But he does not want to stop at the bare bones of the theories. He is determined to give his readers a hint of the larger import of these matters, and he presses into service a number of stories, asides and literary flourishes. Sometimes the prose is so purple, it throbs and begs to be deflated, but the overall effect is not unpleasant. Here is a typical fragment about Liebniz:
“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.”
And here are the last days of Hilbert in Nazi Germany:
“Hilbert closed his remarks with words that were later inscribed on his tombstone: we must know. We will know.
We realize now that that was the last time those words could have been uttered without irony…the mathematicians who had heard his voice and fallen under his command had scattered, some going to the US or South America or even China, others, for all their sophisticated and intellectual cunning, finding themselves packed in freight cars, grinding their way to some place in the east.”
This powerful and humane sense of history and tragedy is accompanied by an almost wicked sense of humor and an absolute unwillingness to submit to fashionable opinion. The stories and asides are generally delightful, though the author could easily have spared us his own amorous adventures and multiple marriages without any loss to the book. The math is challenging, but not overwhelming and worth the effort to understand it. In the last chapters, he takes on the issue of whether the mind is simply an algorithm, albeit a very sophisticated one? The question is not if the mind uses algorithms or if many of its functions can be reduced to algorithms (it does, and they can). The 300-pound gorilla in the room is consciousness: an algorithm is merely symbols, manipulated according to rules (themselves strings of symbols) but an intelligence creates those symbols and assigns them meaning. When the mind sees, something is seen by someone. Who is this someone who sees? Berlinski knows that even the scientists do not know the answer to that. The attack on scientific monotheism in the last chapters may upset those who suspect that such “attacks from within” will provide ammunition to those who wish to bludgeon us into more extreme monotheisms of their own. But Berlinski believes that doubt has brought us this far, it is too late in the day to stop. All the emperors are naked, why should the emperor of science get special treatment? And so he ends with Heracleitus:
”you could not discover the limits of the soul, not even if you traveled down every road. Such is the depth of its form”
This sentence at the very beginning of the book should warn us that this is not going to be science writing in the Asimov vein. Dr. Berlinski once boasted that he can be accused of many things, but shrinking from controversy is not one of them. A professor of mathematics, a novelist, something of a poet and the successful author of “a tour of the calculus”, Dr. Berlinski is also famous for his very public insistence that Darwinian evolution does not add up; that something is missing from the story and the high priests are engaged in a cover-up. In “the advent of the algorithm” he sets out to tell us about the algorithm: "a procedure, written in a symbolic vocabulary, that gets something done step-by-step without the need for any intelligent assistance”. But he ends by questioning the ability of science to explain the mind: the intelligence that fashions and uses these algorithms and infuses them with meaning.
The book begins and ends with Gottfried Leibniz. Between inventing the calculus, imagining the monads and carrying out his diplomatic duties, Gottfried Liebniz also laid the foundations of mathematical logic and the science of computing. He is followed by Guiseppe Peano, Gottlieb Frege, George Cantor and others, till we get to the great David Hilbert and his challenge to mathematicians to show that mathematics is consistent, complete and decidable (in principle, if not in practice). Within a few years, Kurt Godel was able to show that this is not possible. After an explanation of Godel’s revolutionary result, Alonzo Church, Alan Turing, Emil Post, Claude Shannon and others are introduced and the reader learns about the developments in logic and mathematics that form the foundations of our modern digital world.
Berlinski’s explanations of these developments are lucid, even brilliant, and someone with little mathematical knowledge beyond high school should still be able to understand what he is saying. But he does not want to stop at the bare bones of the theories. He is determined to give his readers a hint of the larger import of these matters, and he presses into service a number of stories, asides and literary flourishes. Sometimes the prose is so purple, it throbs and begs to be deflated, but the overall effect is not unpleasant. Here is a typical fragment about Liebniz:
“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.”
And here are the last days of Hilbert in Nazi Germany:
“Hilbert closed his remarks with words that were later inscribed on his tombstone: we must know. We will know.
We realize now that that was the last time those words could have been uttered without irony…the mathematicians who had heard his voice and fallen under his command had scattered, some going to the US or South America or even China, others, for all their sophisticated and intellectual cunning, finding themselves packed in freight cars, grinding their way to some place in the east.”
This powerful and humane sense of history and tragedy is accompanied by an almost wicked sense of humor and an absolute unwillingness to submit to fashionable opinion. The stories and asides are generally delightful, though the author could easily have spared us his own amorous adventures and multiple marriages without any loss to the book. The math is challenging, but not overwhelming and worth the effort to understand it. In the last chapters, he takes on the issue of whether the mind is simply an algorithm, albeit a very sophisticated one? The question is not if the mind uses algorithms or if many of its functions can be reduced to algorithms (it does, and they can). The 300-pound gorilla in the room is consciousness: an algorithm is merely symbols, manipulated according to rules (themselves strings of symbols) but an intelligence creates those symbols and assigns them meaning. When the mind sees, something is seen by someone. Who is this someone who sees? Berlinski knows that even the scientists do not know the answer to that. The attack on scientific monotheism in the last chapters may upset those who suspect that such “attacks from within” will provide ammunition to those who wish to bludgeon us into more extreme monotheisms of their own. But Berlinski believes that doubt has brought us this far, it is too late in the day to stop. All the emperors are naked, why should the emperor of science get special treatment? And so he ends with Heracleitus:
”you could not discover the limits of the soul, not even if you traveled down every road. Such is the depth of its form”
August 6, 2017
I've read many books about computation: historical perspectives, flights of fancy, technical papers; the works. This was without a doubt the least interesting one I've read on the topic, and in general, a book that seems to drift along on the author's whimsy - ironic for a book describing a thing that is comprised of concrete and (usually) necessary steps. If you're interested in computation/algorithms from a historical perspective, try out Bernhardt's "Turing's Vision", or Dyson's "Turing's Cathedral" for a bit more of the engineering history as well. If you're looking for something about what makes algorithms practically useful, give Fortnow's "The Golden Ticket" a go. Anything but this.
Nothing in the book struck me as grossly technically inaccurate, so at least this book doesn't seek to misinform, but I can't see an audience who would find it informative either. Berlinski manages to weave a convoluted tale about the modern origination of the algorithm as the result of a few great insights from mathematicians you might have heard of. The insights don't really get tied up clearly, and he spends a great deal of time imagining himself to be friends of these mathematicians or otherwise daydreaming about their personality quirks. These fictional interactions are still preferable to Berlinski's more personal musings. He clearly fancies himself as quite the lady's man and thinks that personality defect should get center stage in a book about something far more interesting and important.
I just got the feeling that the few algorithms that were actually described in the text were ways to pat himself on the back - like he was proving to himself that he knew someone who could string together some simple code. Instead of writing as an authority on the subject, he mingled opinion, speculation, and facts around in a way that eroded his credibility to the point that I think he has no actual experience developing or inspecting algorithms. I have no idea what his actual experience is, but that's the way his writing on the subject came across. He wrapped up the book with an incoherent comparison to biology and physics which was particularly devoid of substance. There are so many interesting avenues to draw from in biological computation, but he managed to avoid them all. Similarly for physics, he went on some discussion about simulations that was a shadow of what it could have been, meanwhile, a lot of interesting applications of algorithms arise in particle physics to say nothing of the role nuclear physics played in driving early computation.
Don't read this book. You might come away less informed than when you went in.
Nothing in the book struck me as grossly technically inaccurate, so at least this book doesn't seek to misinform, but I can't see an audience who would find it informative either. Berlinski manages to weave a convoluted tale about the modern origination of the algorithm as the result of a few great insights from mathematicians you might have heard of. The insights don't really get tied up clearly, and he spends a great deal of time imagining himself to be friends of these mathematicians or otherwise daydreaming about their personality quirks. These fictional interactions are still preferable to Berlinski's more personal musings. He clearly fancies himself as quite the lady's man and thinks that personality defect should get center stage in a book about something far more interesting and important.
I just got the feeling that the few algorithms that were actually described in the text were ways to pat himself on the back - like he was proving to himself that he knew someone who could string together some simple code. Instead of writing as an authority on the subject, he mingled opinion, speculation, and facts around in a way that eroded his credibility to the point that I think he has no actual experience developing or inspecting algorithms. I have no idea what his actual experience is, but that's the way his writing on the subject came across. He wrapped up the book with an incoherent comparison to biology and physics which was particularly devoid of substance. There are so many interesting avenues to draw from in biological computation, but he managed to avoid them all. Similarly for physics, he went on some discussion about simulations that was a shadow of what it could have been, meanwhile, a lot of interesting applications of algorithms arise in particle physics to say nothing of the role nuclear physics played in driving early computation.
Don't read this book. You might come away less informed than when you went in.
September 27, 2019
Te moeilijk 😢
September 27, 2015
Subtitle: The 300-Year Journey from an Idea to the Computer. Berlinski's prose occupies a hazy territory between fiction and not. The subject matter is fairly arcane and technical (I am guessing that 2/3 of the general populace doesn't even know what an algorithm is, much less care to read a book about its history). His idea of how to tell its story is to fill it with imaginary scenes such as Leibniz attempting to tell his patron, the Duke of Brunswick, about his new creation, except that the Duke interrupts him due to an incontinent bladder. You can imagine how that illuminates the invention of the algorithm.
Ok, so maybe it just illustrates how completely beyond the concerns of his time, and his contemporaries, Leibniz was. In fact, that is the most intriguing lesson in Berlinski's book: humans had been imagining something like a computer, and how it might work, for centuries before they ever had one. Charles Babbage is often given credit for inventing the first computer, but in some sense there had been software written and ready for it for about 300 years before the hardware appeared on the scene, and Babbage's scheme was but one of many instances of great thinkers wishing for a device that could execute an algorithm.
What is an algorithm? The key point would seem to be that it is a sequence of steps, each one of which is simple enough as to require no insight or creativity. It's a very peculiar way of thinking, if that is the word for it, and not one which comes very naturally to the human mind. Those who took more naturally to it (e.g. Leibniz or Turing) came along about once every hundred million people.
Which is Berlinski's biggest obstacle to writing a book about this, of course. How do you get people to buy a book about a topic which is intrinsically opaque and alien to almost every potential reader? It is apparent that Berlinski is a man without fear, in this regard; he has also published a book, not a textbook but a book intended for the general public, on the Calculus.
When explaining the idea of the Traveling Salesman problem, he presents us with an imaginary conversation, over dinner at a restaurant, with his editor and his agent. One wonders what his editor and agent feel at being cast as more or less fictional characters in his work. He returns several times to a dinner set by the Cardinal of Vienna, who inquires of physicists concerning time and space, meaning and logic. He concocts a new old story of a merchant who sells dreams, and an until-then satisfied customer comes to return a dream of truth which unfortunately included recursion.
In between, Berlinski juggles equations and graphs, theorems and pseudo-code as elegantly as any writer may, to bring us along with him as he attempts to trace the gestation of an idea across three centuries. Goedel and Church, Post and Peano, Frege and Hilbert, all cross the stage, as his tale hurtles towards its own nearly inexplicable ending.
The ending, is the tricky part. To what end has the algorithm come, thus far? It is hard to tell it in a satisfying way, for the very reason that it has succeeded so well that it has moved beyond what we could as easily calculate ourselves. Berlinski's ending is, perhaps, cruel, and not a little ominous, but it is affecting. The story of the algorithm is the story of our attempt to understand, and then reconstruct, the act of thinking itself, and to look long on such a topic is unsettling to the spirit and dreadful to the soul. Berlinski's periodic tangents into fiction and prose poetry, are like way stations of warmth and light on a trek across a beautiful but deadly landscape of ice and snow. The algorithm is currently transforming the planet, in a way which we have difficulty even perceiving in its entirety, much less comprehending. Come look at the history of how it came to be.
Ok, so maybe it just illustrates how completely beyond the concerns of his time, and his contemporaries, Leibniz was. In fact, that is the most intriguing lesson in Berlinski's book: humans had been imagining something like a computer, and how it might work, for centuries before they ever had one. Charles Babbage is often given credit for inventing the first computer, but in some sense there had been software written and ready for it for about 300 years before the hardware appeared on the scene, and Babbage's scheme was but one of many instances of great thinkers wishing for a device that could execute an algorithm.
What is an algorithm? The key point would seem to be that it is a sequence of steps, each one of which is simple enough as to require no insight or creativity. It's a very peculiar way of thinking, if that is the word for it, and not one which comes very naturally to the human mind. Those who took more naturally to it (e.g. Leibniz or Turing) came along about once every hundred million people.
Which is Berlinski's biggest obstacle to writing a book about this, of course. How do you get people to buy a book about a topic which is intrinsically opaque and alien to almost every potential reader? It is apparent that Berlinski is a man without fear, in this regard; he has also published a book, not a textbook but a book intended for the general public, on the Calculus.
When explaining the idea of the Traveling Salesman problem, he presents us with an imaginary conversation, over dinner at a restaurant, with his editor and his agent. One wonders what his editor and agent feel at being cast as more or less fictional characters in his work. He returns several times to a dinner set by the Cardinal of Vienna, who inquires of physicists concerning time and space, meaning and logic. He concocts a new old story of a merchant who sells dreams, and an until-then satisfied customer comes to return a dream of truth which unfortunately included recursion.
In between, Berlinski juggles equations and graphs, theorems and pseudo-code as elegantly as any writer may, to bring us along with him as he attempts to trace the gestation of an idea across three centuries. Goedel and Church, Post and Peano, Frege and Hilbert, all cross the stage, as his tale hurtles towards its own nearly inexplicable ending.
The ending, is the tricky part. To what end has the algorithm come, thus far? It is hard to tell it in a satisfying way, for the very reason that it has succeeded so well that it has moved beyond what we could as easily calculate ourselves. Berlinski's ending is, perhaps, cruel, and not a little ominous, but it is affecting. The story of the algorithm is the story of our attempt to understand, and then reconstruct, the act of thinking itself, and to look long on such a topic is unsettling to the spirit and dreadful to the soul. Berlinski's periodic tangents into fiction and prose poetry, are like way stations of warmth and light on a trek across a beautiful but deadly landscape of ice and snow. The algorithm is currently transforming the planet, in a way which we have difficulty even perceiving in its entirety, much less comprehending. Come look at the history of how it came to be.
July 9, 2017
No. Just no. Possibly the worst book I've ever finished. There are too many problems to detail, so I'll summarize: the algorithm is not the crowning achievement of 20th century formal mathematical logic. The algorithm is an idea as old as arithmetic, developed and used since at least ancient Egypt. Algorithm is a name derived from Arabic because the Muslim Arab scholars keeping learning alive throughout the Dark Ages eventually bequeathed the formalized process for solving a problem back to Renaissance Europe. You don't need formal logic to understand that you follow a set of steps through a defined procedure to follow an algorithm. Never read a book by a logician - they love their own little mind games and over complicate things. I don't need Leibnitz and certainly don't need Godel to understand an algorithm. Just terrible... pitch this one on the fire next time you're at a good ol' fashioned book burning.
August 28, 2017
I'm still not sure why I pushed so hard hard to finish this brute of a self-involved, obtuse, ramble down through the history of logic and computer science. Berlinsky struggles to stay on topic and never fails to sow confusion through his over-complicated language and baffle-gab. He is also terrifically self-involved sharing dull anecdotes from the failures of his 3 broken marriages and his frustrating conversations with his editor and agent. There are lots of great books on this important topic, but this isn't one of them.
April 7, 2021
2.0 out of 5 stars Overwritten
Reviewed in the United States on April 9, 2019
I think that this is going to be my final David Berlinski book. (I have one more of his that I have purchased, but that I have not yet read.)
For most books, the reader has an idea of exactly what they are within the first 5 or 10 pages.
This book went on for 333 pages, and it's only at around page 218 that I'm beginning to figure out what it is.
It seems to be a synopsis of mathematical developments that culminated in the algorithm and then the computer.
("Algorithm" is one of those words that one hears spoken in English,
to which one would like a more precise definition. In that respect, this book is like drinking water through a fire hose.)
Owing to the fact that mathematicians are on a different plane from the rest of us, this notion of an algorithm takes on overtones that the overwhelming majority of humanity cannot hear.
If the reader wants a better book on algorithms (in the practical sense of the word), I would recommend "The Checklist Manifesto" much in preference to this one.
A series of better books on biological complexity: "Signature in the Cell" and "Darwin's Doubt."
Berlinski is trying to strike the balance between: prose that a normal human being will sit down and read from start to finish versus a textbook-- which nobody would read at all. (That explains his insertion of narrative-creating-fictitious-vignettes, the exact point of any of which I have yet to discern.)
There is his usual assortment of $5 words.
Asseverations
Marmoreal
Transmogrification
Taponade
Greave
Monad
Irrefragable
Indubitable
Lepidopterist
Rubicund
Bezel
Abjured
Dialectician
Stroboscopic
Fiacre
Valetudinarian
Chillblains
Ashram
Arabesques
Empyrean
Ecumenical
Numinous
Apothegms
Desultory
Chiliastic
Escutcheon
Bezel
Irrefrangibly
The single best sentence of this book was probably on page 155: "Logic has always been a dangerous discipline, any number of logicians going mad after finding themselves hopelessly lost in the wilderness of their own thoughts."
The sentence is brilliant precisely because I understand *every* single word in it. And I *understand* every single word in it.
To wit: These people who created all of these wonderful things almost all died from unnatural causes or had serious mental issues. Godel starved himself to death. Turing died after cyanide poisoning. Etc.
Because Pure Mathematics is a discipline that resonates with so few people, this book is not quite the same thing as reading a book on the history of Physics or some history of Molecular Biology. Because Physics and Molecular Biology do correspond to things that we all see in the real world and in everyday life.
Everybody can imagine Newton being thumped on the head by an apple. Nobody can imagine an obscure debate between ways that somebody treats functions.
There are 15 chapters, and just about 21 pages per chapter. But none of the chapters are thematically arranged in such a way that a person can go back and re-read what he may not have understood.
And the scope of topics is vast.
Intro to predicate calculus
Set theory
Lambda conversion
Hilbert spaces
Godel's incompleteness
Approximate differential equations
Computer modeling of statistical mechanics
Shannon information
Turing machines
Complexity (with respect to biological systems)
There are a lot of things that an intelligent person will have heard of in a passing way. Godel incompleteness theorem. Hilbert spaces. But, you can't deduce such things by just reading a book. They take intense and focused practice (i.e., a college course).
And while that book could possibly have been written, this was not that book. Berlinski's prattling was of no use.
One other minor stylistic quibble: Which English is he using? On page 19, I find a word spelled the British way, and then another word spelled the American way just a paragraph later.
Berlinski's gift for writing shines through on every page. That fact notwithstanding: Beautifully dressing up a poorly structured book is the logical equivalent of a brand new Aston Martin with no engine.
Verdict: Not recommended.
Reviewed in the United States on April 9, 2019
I think that this is going to be my final David Berlinski book. (I have one more of his that I have purchased, but that I have not yet read.)
For most books, the reader has an idea of exactly what they are within the first 5 or 10 pages.
This book went on for 333 pages, and it's only at around page 218 that I'm beginning to figure out what it is.
It seems to be a synopsis of mathematical developments that culminated in the algorithm and then the computer.
("Algorithm" is one of those words that one hears spoken in English,
to which one would like a more precise definition. In that respect, this book is like drinking water through a fire hose.)
Owing to the fact that mathematicians are on a different plane from the rest of us, this notion of an algorithm takes on overtones that the overwhelming majority of humanity cannot hear.
If the reader wants a better book on algorithms (in the practical sense of the word), I would recommend "The Checklist Manifesto" much in preference to this one.
A series of better books on biological complexity: "Signature in the Cell" and "Darwin's Doubt."
Berlinski is trying to strike the balance between: prose that a normal human being will sit down and read from start to finish versus a textbook-- which nobody would read at all. (That explains his insertion of narrative-creating-fictitious-vignettes, the exact point of any of which I have yet to discern.)
There is his usual assortment of $5 words.
Asseverations
Marmoreal
Transmogrification
Taponade
Greave
Monad
Irrefragable
Indubitable
Lepidopterist
Rubicund
Bezel
Abjured
Dialectician
Stroboscopic
Fiacre
Valetudinarian
Chillblains
Ashram
Arabesques
Empyrean
Ecumenical
Numinous
Apothegms
Desultory
Chiliastic
Escutcheon
Bezel
Irrefrangibly
The single best sentence of this book was probably on page 155: "Logic has always been a dangerous discipline, any number of logicians going mad after finding themselves hopelessly lost in the wilderness of their own thoughts."
The sentence is brilliant precisely because I understand *every* single word in it. And I *understand* every single word in it.
To wit: These people who created all of these wonderful things almost all died from unnatural causes or had serious mental issues. Godel starved himself to death. Turing died after cyanide poisoning. Etc.
Because Pure Mathematics is a discipline that resonates with so few people, this book is not quite the same thing as reading a book on the history of Physics or some history of Molecular Biology. Because Physics and Molecular Biology do correspond to things that we all see in the real world and in everyday life.
Everybody can imagine Newton being thumped on the head by an apple. Nobody can imagine an obscure debate between ways that somebody treats functions.
There are 15 chapters, and just about 21 pages per chapter. But none of the chapters are thematically arranged in such a way that a person can go back and re-read what he may not have understood.
And the scope of topics is vast.
Intro to predicate calculus
Set theory
Lambda conversion
Hilbert spaces
Godel's incompleteness
Approximate differential equations
Computer modeling of statistical mechanics
Shannon information
Turing machines
Complexity (with respect to biological systems)
There are a lot of things that an intelligent person will have heard of in a passing way. Godel incompleteness theorem. Hilbert spaces. But, you can't deduce such things by just reading a book. They take intense and focused practice (i.e., a college course).
And while that book could possibly have been written, this was not that book. Berlinski's prattling was of no use.
One other minor stylistic quibble: Which English is he using? On page 19, I find a word spelled the British way, and then another word spelled the American way just a paragraph later.
Berlinski's gift for writing shines through on every page. That fact notwithstanding: Beautifully dressing up a poorly structured book is the logical equivalent of a brand new Aston Martin with no engine.
Verdict: Not recommended.
March 24, 2020
Strange book and deeply unsatisfying.
I think that the acknowledgements at the end gave a clue why. In them, he notes that preliminary versions of the last two chapters appeared in periodicals previously. That would explain the mish-mash toward the end as an attempt to marry the first part of the book to existing material.
The first part of the book was fun: A history of mathematical logic and related topics with the personalities involved, including good explanations of the concepts. It was at times wildly self-indulgent in language and form, but that was clearly the author playing around and having fun and rarely, at least for me, interrupted the flow of the book.
The last part of the book was essentially, in physics and math language, a re-hash of the teleological proof for the existence of God, except without the God part...so, I guess, the teleological proof of the existence of meh. That isn't to say the section wasn't worth reading--the narrative and explanation of solving a particular traveling salesman problem using DNA was interesting and informative, if unnecessarily complicated by his little stories.
But the connective part. Oy. It was an abysmal treatment of the P versus NP problem. Lets just say that it started out with incorrectly identifying NP and went downhill from there.
Now, the book is 20 years old and if the author was a generalist maybe there would be some excuses, since a lot has been written in the last 20 years about P vs NP for non-mathematicians. But, he is a mathematical logician and this should have been his bread and butter even in 2000.
So, three stars as (just) worth my time based on lots of interesting, good small scale stuff, even with the failure of the overall argument.
I think that the acknowledgements at the end gave a clue why. In them, he notes that preliminary versions of the last two chapters appeared in periodicals previously. That would explain the mish-mash toward the end as an attempt to marry the first part of the book to existing material.
The first part of the book was fun: A history of mathematical logic and related topics with the personalities involved, including good explanations of the concepts. It was at times wildly self-indulgent in language and form, but that was clearly the author playing around and having fun and rarely, at least for me, interrupted the flow of the book.
The last part of the book was essentially, in physics and math language, a re-hash of the teleological proof for the existence of God, except without the God part...so, I guess, the teleological proof of the existence of meh. That isn't to say the section wasn't worth reading--the narrative and explanation of solving a particular traveling salesman problem using DNA was interesting and informative, if unnecessarily complicated by his little stories.
But the connective part. Oy. It was an abysmal treatment of the P versus NP problem. Lets just say that it started out with incorrectly identifying NP and went downhill from there.
Now, the book is 20 years old and if the author was a generalist maybe there would be some excuses, since a lot has been written in the last 20 years about P vs NP for non-mathematicians. But, he is a mathematical logician and this should have been his bread and butter even in 2000.
So, three stars as (just) worth my time based on lots of interesting, good small scale stuff, even with the failure of the overall argument.
December 15, 2019
David Berlinksi is a polymath. Like a proud peacock, he is not afraid to put his erudition on full display. I suspect, however, that he has (innocently, I'm sure) somehow missed Somerset Maugham, who aphorized: "to write simply is as difficult as to be good."
Berlinsksi valorizes the journey over the destination. I first stumbled across his writing years ago in A Tour of the Calculus --a book I enjoyed despite its rambling (some may say pretentious, verbose, off-topic, unedited) storyline. Tour, indeed.
Advent is not dry intellectual history: au contraire, mes amis (a Berlinskian interjection if ever there was one). The proof in the pudding is the closing Epilogue: Wallace Stevens' "The Idea of Order at Key West." Order, algorithms--you get the idea. Like Dover sole garnished with crisp, skinned Granny Smith apple flesh (because both are vaguely white). And I love Wallace Stevens.
Berlinski can be enjoyable if you know this going in. Like grandparents with spoiled, smarter grandkids, readers can leave--or love.
Berlinsksi valorizes the journey over the destination. I first stumbled across his writing years ago in A Tour of the Calculus --a book I enjoyed despite its rambling (some may say pretentious, verbose, off-topic, unedited) storyline. Tour, indeed.
Advent is not dry intellectual history: au contraire, mes amis (a Berlinskian interjection if ever there was one). The proof in the pudding is the closing Epilogue: Wallace Stevens' "The Idea of Order at Key West." Order, algorithms--you get the idea. Like Dover sole garnished with crisp, skinned Granny Smith apple flesh (because both are vaguely white). And I love Wallace Stevens.
Berlinski can be enjoyable if you know this going in. Like grandparents with spoiled, smarter grandkids, readers can leave--or love.
December 31, 2018
The subject matter of the book appeals to me very much, and it is clear that the author has a mastery of this material. This book displays the author's vast knowledge and comprehension of mathematics, logic, history, and computing.
Unfortunately, the style of the writing interferes constantly with the message that is being delivered. The jacket of the book refers to the style as 'witty', but I found that the constant rhetorical flourishes made it impossible to read.
I did not finish the book, yet this is a loss, because this book is written around numerous subjects that interest me.
Unfortunately, the style of the writing interferes constantly with the message that is being delivered. The jacket of the book refers to the style as 'witty', but I found that the constant rhetorical flourishes made it impossible to read.
I did not finish the book, yet this is a loss, because this book is written around numerous subjects that interest me.
February 8, 2018
More about the history of mathematical logic than what most might expect based on the title. A lot is worth skipping. I also don't like his writing style... but like the topics he discusses. Not sure it's worth the read.
December 11, 2019
While I have to admit that this book is a great historical summary of the development of discrete mathematics, reading it was immensely painful. Berlinski writes with an arrogant and haughty tone that I personally couldn't stand.
May 10, 2021
An interesting overview of the development for a concept so critical to our modern lives.
July 4, 2024
Look this definition up on Wikipedia …..
August 12, 2016
The Advent of the Algorithm is not the only book on mathematics that made my list of books to read, but it is one of a very few. At this point, I am not sure whether I am glad or sorry.
The idea of algorithms is a pivotal concept in the development of the modern computer. David Berlinsky tells the history of the idea of the algorithm by giving the histories of some of the men (and they all seem to be men) who thought up the various concepts that eventually went into the making of the algorithm. The first few of these concepts are relatively easy to understand. Later on, as with most things, they get harder and harder.
He also seems to have some pretensions to literary fiction, and he intersperses the discourse on logical and mathematical ideas with some short vignettes that are mostly every bit as enigmatical as the math talk, but at least they are entertaining.
I think I understand a bit more about the idea of algorithms than I did before. But trust me, I won’t remember it very long.
The idea of algorithms is a pivotal concept in the development of the modern computer. David Berlinsky tells the history of the idea of the algorithm by giving the histories of some of the men (and they all seem to be men) who thought up the various concepts that eventually went into the making of the algorithm. The first few of these concepts are relatively easy to understand. Later on, as with most things, they get harder and harder.
He also seems to have some pretensions to literary fiction, and he intersperses the discourse on logical and mathematical ideas with some short vignettes that are mostly every bit as enigmatical as the math talk, but at least they are entertaining.
I think I understand a bit more about the idea of algorithms than I did before. But trust me, I won’t remember it very long.
May 18, 2014
This book falls somewhere between an okay math text and an okay historical text. It isn't great at either. It suffers from excessive use of metaphors and bathetic prose. I found it very difficult to read, especially since it took, what appeared to be, great liberties with history and historical figures. At times it was hard to decipher what was fact and what was speculative fiction. In that the book presents itself as a history, instead of a text on algorithms or linear algebra, it would have benefited from greater research and scene setting. Additionally, the thesis of this book (whether intended or not) is that there is, in fact, a history of algorithms. To support this it would need to show a coherent story, instead of vignettes from important moments.
I gave up before completing the book. If I want to learn about algorithms there are better and more succinct works out there. And this book fails as a historical text.
I gave up before completing the book. If I want to learn about algorithms there are better and more succinct works out there. And this book fails as a historical text.
February 16, 2009
Computers are important--everyone knows that. But computers aren't nearly as important as the ideas behind them. If you want to understand why computer science is important, then you need to read Berlinski's book on the algorithm. Berlinski ranks the algorithm as the idea, next to calculus, that has most shaped modern science and, consequently, our world.
If there's one things that gives me pause it is that I'm not sure how accessible this book is to the layman. For someone with a Ph.D. in Computer Science its entertaining and thought provoking and very understandable. I'd appreciate knowing what you think of it.
If there's one things that gives me pause it is that I'm not sure how accessible this book is to the layman. For someone with a Ph.D. in Computer Science its entertaining and thought provoking and very understandable. I'd appreciate knowing what you think of it.
October 15, 2009
Yes, everybody knows that the word algorithm comes from the Arabic. And, yes, I am a sucker for books that recount the history and development of logic, mathematics, calculating machines and computers. Even if I've heard or read all the facts before, I like to see what new inferences and connections new contributors bring to the subject.
Even if you are not an engineer (or one that gives a hoot about how we got here) it is a well-written book with good if not great coverage of the topic. If you wonder about the modern world and why things are as they are, sit back, open a copy and enjoy.
Even if you are not an engineer (or one that gives a hoot about how we got here) it is a well-written book with good if not great coverage of the topic. If you wonder about the modern world and why things are as they are, sit back, open a copy and enjoy.
February 24, 2010
There are interesting parts about formal systems and the history of logic, but I knew most of it from reading other books that covered the material in more depth. Berlinski has a tendency towards florid prose, but this book takes a few too many departures into fictional asides that don't connect as strongly to the main narrative as he intended. The last 100 pages veer off into musings on intelligence and the beginnings of life that are as much philosophical musings and speculation as they are interesting extensions of the concept of the algorithm to other fields.
December 28, 2015
What I liked about this book was the serious attention it paid to the algorithm, a topic of great interest to me. Berlinski sketches out a rich history for this idea and he is an odd and interesting writer, playful in ways that are entertaining and annoying in equal measure.
I'm not especially moved by Berlinski's ultimate goal, which is pointing that rich history towards a theory of intelligent design. While the book trailed off as this frame came to the fore I didn't begrudge the style of the book, especially not when he ended with a Wallace Stevens poem.
I'm not especially moved by Berlinski's ultimate goal, which is pointing that rich history towards a theory of intelligent design. While the book trailed off as this frame came to the fore I didn't begrudge the style of the book, especially not when he ended with a Wallace Stevens poem.
April 20, 2008
Beautifully written prose and a good introduction to the topic of Algorithms from middle ages to modern computer. A good thumbnail sketch of many of the actors in development of algorithms especially Turing.
December 20, 2008
This book contains several fictional vignettes that are irrelevant, boring, and incoherent.
Much worse, however, is that the author says that NP stands for non-polynomial! Even if I had liked the rest of the book (which I didn't), that huge a mistake would automatically give this 1 star.
Much worse, however, is that the author says that NP stands for non-polynomial! Even if I had liked the rest of the book (which I didn't), that huge a mistake would automatically give this 1 star.
August 8, 2012
Great whimsical & slightly verbose book, especially if you like computers and math. This book will cause your mind to work, you will not get much out of it if you aren't willing to really think. They book does a pretty good job of appealing to layman...but only if the layman knows math. ;-)
Want to read
June 22, 2010I feel like I need to be smarter to read this book. It's excellent and thought provoking, but I think it is one to "study" and not just pick up for three minutes at a time. David is finishing it, then I'll get into it more.
May 19, 2008
Hilarious. I love the way Berlinski writes- and I especially love his fictional stories that he places throughout the book. It makes me love algorithms all the more.
April 18, 2015
This book is fascinating. I should want to finish it, but it seems like work not pleasure, so LIS.
October 1, 2012
Rough sledding. Had to wave the white flag.
January 16, 2014
A good book, but requires an extensive math background in order to really get something out of it.
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