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Gödel, Escher, Bach: An Eternal Golden Braid Paperback – Illustrated, February 5, 1999
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Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers.
The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. --Richard Dragan
Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.
Winner of the Pulitzer Prize in General Nonfiction
Winner of the National Book Award in Science
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."
--- Martin Gardner, Scientific American
"In some ways, Godel, Escher, Bach is an entire humanistic education between the covers of a single book. So, for my next visit to a desert island, give me sun, sand, water and GEB, and I'll live happily ever after."
--- John L. Casti, Nature
"A brilliant, creative, and very personal synthesis without precedent or peer in modern literature."
--- The American Mathematical Monthly
"I have never seen anything quite like this book. It has a youthful vitality and a wonderful brilliance, and I think that it may become something of a classic."
--- Jeremy Bernstein
"A huge, sprawling literary marvel, a philosophy book disguised as a book of entertainment disguised as a book of instruction."
--- Atlanta Journal-Constitution
"A triumph of cleverness, bravura performance."
"A wondrous book that unites and explains, in a very entertaining way, many of the important ideas of recent intellectual history."
"Godel, Escher, Bach was a triumphantly successful presentation of quite difficult concepts for a popular audience. There has been nothing like it in computer science before or since."
--- Ernest Davis, IEEE Expert
- Lexile Measure : 1150L
- Item Weight : 2.37 pounds
- Paperback : 824 pages
- ISBN-10 : 0465026567
- ISBN-13 : 978-0465026562
- Product Dimensions : 6.5 x 1.9 x 9.25 inches
- Publisher : Basic Books; 20th Anniversary ed. Edition (February 5, 1999)
- Language: : English
- Best Sellers Rank: #5,157 in Books (See Top 100 in Books)
- Customer Reviews:
Top reviews from the United States
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Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.
I even think Hofstadter is fundamentally correct in most of what he wrote. Of course, the book is now some decades old and, considering that computer science features prominently in its pages, a fair number of its examples are now comically outdated. Still, this doesn't seem to affect the book's arguments in any meaningful way. The book's fundamental thesis that meaning can arise from "meaningless" formal systems through self-referential hierarchies is a fascinating one.
The trouble is, the book is needlessly difficult to read. I'm not arguing that it's difficult because it explores difficult subject matter. I wouldn't object to that. In fact, some of the subject matter is rather difficult, but it is the author's treatment of his subject matter that leaves much to be desired. Rather than clearly articulating his point, the author presents a meandering and repetitive set of arguments and observations. Some reviewers have complained that his treatment of mathematical content was insufficiently formal. Fair enough, but I don't mind an informal presentation of difficult topics in a work intended for a general audience. That is not really what the author does here, however. Instead, he dumbs down the complicated and complicates the simple or self-evident. The result is a book that, by the author's own admission (n the preface to the 20th anniversary edition), even its fans fail to understand. Of course, the author could have taken this opportunity to offer further clarity, but instead his preface is almost as meandering as the book itself.
The use of dialogues interspersed between the book's chapters seems like an interesting idea. Initially, the dialogues seemed like charming illustrations of the rather fertile intellectual ground explored by the book. By the end, however, they were more annoying than helpful. More than once, I found myself uttering "get on with it" into the book's pages (and I say that as a devotee of long and detailed books). That really seems to be Hofstadter's fundamental problem. It's clear he loves his subject and wants to shout his love to the world. I don't blame him. It's a fascinating subject. But rather than simply stating his thesis and trusting his readers to understand, he felt the need to wax poetic at every possible opportunity, stretching a topic that could easily be explained in a short book (or maybe even a long essay) into a tome of nearly 800 pages.
This book has become something of a classic, so I suppose I have to consider it required reading for anyone interested in things like mathematics, philosophy, or consciousness. And I do admit that, when the author actually bothers to make his points, they're interesting ones. Unfortunately, the book simply wasn't given the editorial treatment it needs so very much, and isn't nearly as enjoyable a read as its subject matter deserves.
Top reviews from other countries
Written in the 70s the concepts presented in this book are timeless. There are lots of things I would want to highlight that has stuck with me after reading this.
Formal systems: The concept of formalizing anything into boundaries. This is the heart of any scientific advancement we have seen as a human civilization since our species started to calculate. The beauty of trying to formalize anything is that you cannot formalize anything. The strange paradox keeps looping in again and again in all sorts of subjects and Hofstadter has asked a lot of interesting questions around this area that directly correlates Science and Philosophy.
Artificial Intelligence: Hofstadter lays all the building blocks needed to clone the human intelligence and what it really takes to completely replicate how a human thinks. Obviously, he himself did not find a solution or gathered one. However, the challenges that face straight on for moving the field of AI forward are clearly laid out. Not just laid out, his attempts to “formalize” them and the difficulties that are faced only suggest that Human species and our “life” is one of the rarest things that ever could have happened and makes us think how many of our limited days we are wasting in hatred, guilt, jealousy, greed. That is why this book gets super interesting when you dive deep into ‘formalising’ anything.
Since the book could get dry at few places, he tells some of the wonderful stories with some fantasical characters that have no least relationships with each other: Achilles, Tortoise, Crab being the main recurring characters. You also get to meet Sloth, Anteater, Author Himself, Charles Babbage, and Alan Turing. A story or a narration takes place between these characters which are highly intriguing in themselves and then is followed by theoretical/mathematical approach towards the subject that was just discussed.
This review is just an attempt and it is impossible to capture all the meta-nuances that this book covers. One thing guaranteed is that you are bound to enjoy the concepts in this book given you have basics of Music and a decent understanding of Mathematics. Since I am in the Engineering field, this book was an amazing journey. Digest it slowly, you will definitely cherish it!
The beginning of the book starts out by explaining some simple concepts, and then chains them together in ever-growing complexity. By the sections on natural-language processing, the symbolic logic can be a little overwhelming if you've not done symbol manipulation before.. Once powered-through (and assuming that you were able to either follow the logic, or trust in Hofstadter's reasoning chain), the book moves into more varied and easier to understand areas which demonstrate the Godel Theorem without going into the maths.
I absolutely loved this book. It's a masterpiece of this generation. It takes some serious bending of the little grey cells to follow all of the logic, but the wonderful interplay of the music, art and maths is truly mind-expanding. Once you see what Hofstadter's pointing out, you simply can't un-see it.
Pretty soon, you'll be making Quine-based quips, or looking for self-disproving theorems (like "This sentence is false"). Ahh, the beauty of a well-laid trap paradox!
so, if you're scientific, technical or just plain interested in maths, then get this. It's a very weighty tome, and a recently added preface and some new sections make it even beefier. But it's so worth it. If I could draw parallels, I'd say it's as mind-expanding as Zen and the Art of Motorcycle Maintenance... that sort of thing.
It's a shame that this wasn't curtailed by the editing process because I wish I had the tenacity to find the signal in amongst the noise. GEB reads like the literary equivalent of "I would have written you a shorter letter, but I did not have the time".