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Loading... Gödel, Escher, Bach: An Eternal Golden Braidby Douglas R. HofstadterSeries: Godel, Escher, Bach series (1)
A fascinating, wide-ranging, mind-bending, pulitzer prize-winning book on mathematics, art, music, creativity, self-reference, and the nature of consciousness. ( )Fascinating! Full of all kinds of neat, interesting stuff, unbelievably inventive wordplay and structural experiments! I picked it up because of Gödel and logic and so on, but the book is more than that, more than just the names in its title. It does give an introduction to Gödel's theorems, Bach's music and Escher's art, but the underlying theme is more general, related to abstract formal systems and their capabilities. I just love it. I bought the 20th anniversary edition after the first read, it's a must for rereading. I loved the cleverness, and I loved the way it prodded me to think. Many times, I experienced that delightful realization you get, like sunlight bursting from behind clouds, when you suddenly notice that a meta-message is in play, and you go back to re-read a passage and see it in an entirely new light. Intellectual play. However, I bailed at the three-quarters point, a while after Hofstadter stated almost explicitly that the book has a false ending, padded with fluff so that the meta-experience of holding a physical book did not prematurely let you know when you were approaching the end of the work. It didn't seem fair. I _like_ that physical cue of my progress, yet I also have to respect Hofstadter for flouting even that comfortable expectation. (Couldn't muster the fortitude to keep plowing through, though.) "Help. My mind has bent, and now I cannot unbend it!" That was me after I finished reading Godel, Escher, Bach. This book, which is about, well, everything, takes the reader on a journey through mathematics, music, and art, and gives it a little twist just to keep one on one's mental toes. A major theme is recursion, or self-referencing. If you're at all familiar with any of the GEBs, you'll see this in Godel's Incompleteness Theorem, Escher's Drawing Hands, and Bach's Crab Canon. Other mathematicians, artists, and musicians are introduced as well, providing more on this Eternal Golden Braid. Not only does Hofstadter give us so much on logical themes, but he also gives the reader some puzzles too, particularly some that require multiple steps (though the answers are right in front of the reader's face at times). This book is a must read for one who considers oneself a student of mathematics, art, or even music, or who has a strong admiration for most of these things. I suppose computer scientists could read it too. Nevertheless, this is a great book, and a challenge, but definitely worth the read. I really liked this when I first read it (high school, I think) - it's sort of a young geek's dream book. But looking back I find its arguments about consciousness largely unconvincing. Still worth it for the exposition of Godel, etc., though. A must read for anyone truly interested in technology and computers. Best 400 pages long theorem-proof I've ever read (and it's only half of the book). Finally a popular-science book which does not assume you're a dummy. DNF/still reading. Hofstadter argues his perspective on the nature of the mind and the potential of artificial intelligence, particularly with regards to how it relates to Gödel's Theorem (which is essentially about the number-theoretical equivalent of the statment "This sentence is false"). He educates the reader in all the background necessary to understand his arguments, which is a pretty incredible feat for a book that could easily have been purely technical. He goes off on frequent tangents, whimsical diversions and involved analogies (including illustrating his ideas with examples from Escher, Bach, genetics, language and Zen Buddhism). This book is enormous. It's not just 750 pages; it's 750 pages of a very dense book on complex topics. It's accessible to any layperson who wants to make the effort, and it's worth the time involved, but don't start it unless you're willing to commit a lot of time to reading it. I highly recommend getting the 1990's anniversary edition, as the new introduction by the author puts the book into perspective and clearly outlines his argument and the direction it will take, something woefully neglected in the original book. This hurts my tiny brain. An extraordinary romp through self-reference and patterns using mathematics, art, and music as his examples. Funny, witty, erudite and a classic. I have read it twice (the original edition and this newer edition with a new preface) and have no doubt that I will read it again. For some reason, I never read this while I was at university, despite the fact that I was studying Artificial Intelligence, and it was certainly discussed by a number of my peers and tutors. I regret that oversight now that I have finally gotten a copy and read it from cover to cover. Hofstadter has written the most engaging, accessible, and enjoyable discourse into, what is, probably some of the most difficult and complicated topics of science and mathematics - including the fundamental rules (and the system of their proof) without which almost all of our mathematical knowledge would be a useless mass of symbols. Considering the age of the book - it was written almost 30 years - and Hofstadter's determination to not update his text when it is reprinted (you can even spot some of the original typesetting errors he made even in the 1999 edition), the subject matter remains very fresh, and the conclusions towards the end of the book on how intelligence is just another formal system with the same limitations and abilities as any other that can be created and how it is emergent (that is macroscopically chaotic) but, ultimately, governed by deterministic rules, are all just as valid today as they were in the 1970s. Hofstadter has an easy rhythmn to his writing - building on themes in much the same way as Bach would in his fugues (this is no accident, since the works of Bach feature a lot in analogies which relate how systems can also build on themes from simple rules). At no point are you left not understanding the content of the current page (at least not beyond the next page), and each statement is followed by an echo of "oh, yeah, I get that" from somewhere in your own mind. Another aspect of the writing which makes this book stand out from the many texts on science and scientific topics is the use of dialogues. In between each chapter is a sequence involving Achilles and the Tortoise (taking inspiration from Lewis Carroll's own dialogue with these two characters). The discussion between these two figures, and a number of supporting characters, help to bridge the ideas between each of the main chapters, and are also a nice light break from the more serious discussion within the main text. Overall, this book is a fascinating read, and will leave you feeling much smarter than before you picked it up. this is an extremely dense read. but good stuff in here. I first read this book back in April 2004, after coming upon references to it in accounts of the writing of Castrovalva. It was one of five books I read that month, so I knew what I was in for in tackling a rereading. It's a sprawling work, using Gödel's Incompleteness Theorem as its starting point, and traveling through the music of Bach and the artwork of Escher to encompass many diverse ideas: number theory, canons and fugues, recursion, DNA, formal mathematical systems, Zen koans, artificial intelligence, and, ultimately, natural intelligence. It's a bit unfocused, a fact Hofstadter himself attempts to rectify with his new preface to this, the "twentieth anniversary edition", but for obvious reasons, putting a clarification of your conclusions in the front of your book is not entirely effective. Though at times the book can be a bit dense, it's generally comprehensible to someone with no grounding in number theory, thanks to the fact that Hofstadter starts very, very small and works his way up to the big stuff. And I think I could have understood the more confusing stuff with time, but I felt as though I'd already spent more than enough on the book! I find Hofstadter's conclusions about the nature of intelligence most interesting, and I wish that more science fiction dealing with artificial intelligence made use of them, since they make sense to me. Perhaps the most enjoyable part of this dense, lengthy book are the dialogues that appear between chapters, featuring the character of Achilles and Mr. Tortoise discussing the ideas in the text of the book around them, usually in the context of absurdities such as journeying into an Escher print or inventing new and complicated record players. It is here that Hofstadter's deftness with wordplay and ability to twist ideas really sparkles. Overall, I'm not sure if I understood the book more a second time or not. But when I did understand it, I found it quite fascinating and very thought-provoking. There's a ton of diverse ideas in here, and they're all quite good even if they don't always gel. But when he's focused, Hofstadter seems to come immensely close to explaining how our minds work and where they come from. For me, this is the book that started it all. I had no interest at all in science, computing or mathematics before I read GEB. It has been called impossible to read. To be sure, it took me many tries before I got through it cover-to-cover. But the intriguing adventures of Achilles and the Tortoise kept me coming back to it, and I eventually cracked it - at which point I realised what it was all about. Hofstadter elaborates on the theme in his later books (especially "I Am A Strange Loop") but the core of the idea is right here. This book changed my life. I decided to reread this classic of computer science when I learned that Hofstadter is about to release a sequel of sorts. Although it's certainly dated in places, I still found it just as witty and erudite as when I first read it 15 years ago. advice to other reviewers; if you've not read Hostader's 20th anniversary preface, please do. all he want[ed/s] to do [i/wa]s show how self-awareness, the sense of "I", grows out of self-reference. mathematically speaking, which H insists he is not about, observes in Bertrand Russell's Principia Mathematica, while trying to build a Maginot Line in math against "self-reference", lays the seeds for it's own refutation in favor of self-reference. in as few words as possible: it's not about the substance, but the patterns. I ought to reread this book. It is a wonderful read that links ideas from a whole range of sciences and music and art to explain some of the more abstract ideas in philosophy and logic Metamathematics A pun-studded multidisciplinary romp, balanced nicely on the ridge separating known from postulated. This book covers a lot of topics in its search for the understanding and elucidation of the elusive consciousness. Philosophy, maths, logic, physics, genetics, music, art, and artificial intelligence and computer programming are all incorporated in varying measures in this epic trawl of recurring elements and complex ideas. It is a heavily satisfying book to read if you have an interest in this sort of thing, though I imagine that some people really wouldn't have time for it. Despite the serious subject matter the book is lightened in tone by the generous amount of tongue in cheek humour. This is quite a long book, and would have perhaps been too much of a trial to get through without the entertaining dialogues which precede each chapter. They do serve a purpose though, apart from to break up the heavier parts, and that is to introduce concepts, (although often in masked way), that will be discussed in the next chapter. The analogies made between such initially unrelated seeming things throughout the book is sometimes startling, and almost always clever. This author seems to have a great insight into all kinds of interesting things, and I personally found this book fascinating, but I suspect from some of the things I've heard said that this book has had somewhat of a love hate reception. For this reason I can't really recommend this book firmly to anyone, but I think that potential readers will themselves be able to work out if they will enjoy it by checking the main themes off against their interests. It's the best non fiction book I have read in quite a while. Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think. 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 in Amazon.com This is somewhere between a Grand Unified Theory of science, culture, and spirituality, and something ny Ray Kurzweil. It defies description. It's a nonfiction book, this is clear. The topics the book revolves around are Godel's Theorem, the artwork of MC Escher, and music of Bach. These tie in with topics like Zen Buddhism and Zen riddles called koans; Alan Turing and artificial intelligence; recursiveness in nature and everywhere; and DNA. The author does not provide a treatise on each of these topics. Rather, he finds common underpinnings to each of these and finds how they weave together to exist and effect our world. As another reviewer said, if one reads this book, they will never forget it. Interrelationships serve to teach, confuse, and syncretize something beyond all of this. Here's a quote from the description of one of the chapters: "In a way, Zen ideas bear a methaphorical resemblance to some contemporary ideas in the philosophy of mathematics." The 'dialogues' - which is perhaps where Ray Kurzweil got the idea - are a recurring segment having a Turtle converse with Achilles in a Dialogue back and forth using the Socratic method of sorts. It tends to annoy and does not provide educational benefit. Further, my simple mind could not grasp a good 50% of the mathematical formulas in the book - so I suspect this book is more rewarding the more numerical intelligence one has. Even so, everyone should take a crack at this book and for many I suspect it is a mind-changer. Wow. A truly amazing look at intelligence. The first 400 pages or so are pretty difficult to get through. The rest of the book, while not much easier to understand goes much faster. This book provokes some great thoughts. The Dialogues at the beginning of every chapter are worth reading all by themselves. A delightful romp through the world of math, music and philosophy. I am not a math person, but had little trouble following Hofstadter down his various rabbit holes. Engaging, intelligent, articulate. Everything a good book should be. |
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