Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R Hofstadter (PDF)

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Winner of the Pulitzer PrizeA metaphorical fugue on minds and machines in the spirit of Lewis CarrollDouglas Hofstadter’s book is concerned directly with the nature of “maps” or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

User’s Reviews

Editorial Reviews: Amazon.com Review 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 DraganTopics 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. Review 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.”— Parabola “A wondrous book that unites and explains, in a very entertaining way, many of the important ideas of recent intellectual history.”— Commonweal “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 About the Author Douglas R. Hofstadter is College of Arts and Sciences Professor of Cognitive Science and Computer Science at Indiana University, Bloomington, where he also directs the Center for Research on Concepts and Cognition. He is the author or co-author of nine books, including I Am a Strange Loop and Surfaces and Essences, and has contributed to ten more. He lives in Bloomington. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book has a preface by the author. After twenty (20) or so pages, I was thinking, “Can I understand what he wrote about in the rest of this book?” but I persevered and read the whole book. This book is intense, like any philosophical book. His motive is to “suggest ways of reconciling the software of the mind with the hardware of brain” and that is quite an endeavor he succeeds at, sort of. No wonder he won the Pulitzer prize for this book. He talks of how he came to write and develop the book, and then, upon preparing for republication, he decides to not redo the book: it is what it is, from back then, any addition or correction would create a new book, and it can been seen every so often he imagines some stuff that we use daily, like spell correction, that were just not available back then. If he was to do that, he might as well write a whole new book, and that was not in the cards, nor was it the purpose of the new edition. Gödel goosed him to realize the notions he writes about, but Escher and Bach represent examples of what Gödel was writing and he is thinking about. As you read the introduction you realize this is one educated and well rounded fellow. He describes the development of Bach’s preludes and fugues like a music teacher (I realized that I have a recording of Wanda Landowsky playing “The Well-Tempered Clavier” Book 1, preludes and fugues, but that did not help me understand as you will see). Bach worked up various themes and notions through his music and than then did some fancy finagling and out came some thing wild and crazy wonderful. I listened to the recording I have to no avail. This is something you get to know by playing and playing the tunes, a lot, for yourself, but Mr. Hofstadter’s exposition explains what is what for you. Escher is easier (visual experiences are more important or easier to comprehend than aural experiences). The pictures are presented as examples of repetition or growth from one thing into another. The idea of repeating or self-reference is important: it is one thing that computers do not do. We can do imagining things as well, but at a more basic level we self-reference creating a hump of ability that computers have to accomplish if they are to get to be self aware or intelligent. As he said, he wants to understand the hardware of the brain, but in comparison, computers are simpler, but getting more complicated. He is working from the bottom up with computers: machine language, assembly, programing languages, etc. Fro our brains he is working from the top down, trying to see how the thoughts (software) we think get from one point to another. It is difficult because we do not have access to the basic growth of each thought (neurons firing). Logic tries, yet, as that one guy two (2) or three (3) thousand years ago said, “All I know is that I do not know anything.” Mr. Hofstadter just comes to that thought in another roundabout way. I kept thinking of sex deviants doing what they do and that if we could look into their heads, we would be hard pressed to see where the impetus for their deviant behavior comes from, how it develops or why they do it. It is somewhere in there, but the thoughts (software) are so complicated that we can not see how it develops into what is expressed. I also think of how we all speak. We talk without thinking (something I am accused of constantly and embarrassingly), but in reality we just do not follow the thought process from what we hear and see, etc., to what we think of it, to what we will say, to saying it. Another thought is what is happening in the brains of mediators, you know, those Zen folks who quiet the mind, what is happening in there then? The mind is just amazing in what it does. Throughout this book Mr. Hofstadter writes of the mind and the brain like a psychologist, how it works and what it does. He also delves into genetics. His forte is math and all its intricacies. He develops a couple of different math models to illustrate Gödel’s incompleteness theorem. The logic starts out straight forward enough, then veers off into some esoteric realm where the notion of paradox lives, and this is where we have to develop our math notions. We can study the properties of prime numbers or infinities, but we always must end up knowing we do not know everything, because our logic can not encompass paradoxes, and they will be somewhere in all we do, or something like that. As you can see, I was not able to understand his math models, but I think I got the jist of it. This book reminds me of another book published in 1978, “The Seven Mysteries of Life” by Guy Murchie. It is amazing that they talk of the same things in the same way and for the same reasons. Though this is a treatise on computers and artificial intelligence, and the other is a religious book, sort of, about the awesomeness of life. As for the artificial intelligence aspect, I like his development towards that goal, but, and I find no fault in the imagining of it, I am disappointed that computers will just be like us. It will not create a Spock like machine, or what science fiction has led us to hope for (see Isaac Asimov, “I, Robot” etc.). I did like his notion of combining genotypes to create new genes, but I am a guy and I like that sort of stuff. I find that I agree with someone who said, “There are much more fun ways to create intelligence, and it is not artificial.” If artificial intelligence is not going to be all that great, it is only good to try to develop it for the exercise and the experience it will give us, but otherwise, eh, no big deal.

⭐This book is a replacement for my original copy I bought more than 40 years ago because I wished to dive in again. If you’re interested in mathematics, art, music, physics, philosophy and how & where they intersect-This Is The Book!I will not lie. There is a learning curve to this book(I didn’t finish college), but it isn’t insurmountable.Oh, I feel stupid now…I forgot to mention Quantum Physics which I know lots of people are interested in now be they scientists or psychonauts.The title consists of 3 names: Godel, Escher, and Bach. Most of us are familiar with J.S. Bach. The same goes for M.C. Escher. Kurt Godel is most likely familiar to those involved with mathematics, logic, etc.one of the best features of the book is it’s use of monologue and dialogue to explain/clarify specific points of a chapter, using humor and science.So, if you’re interested in these heady subjects and willing to put on your thinking caps-buy this book.

⭐GEB: EGB is basically an exploration of the idea of intelligence, artificial and otherwise. Hofstader’s goal is to shed some light on how intelligence / consciousness / self-awareness happens. I would call him a materialist, in the sense that he believes that there is a physical basis for thoughts, feelings and emotions. He is dismissive of “soulists,” who believe that there is some sort of inexplicable metaphysical aspect to consciousness.The question, in Hofstader’s mind, is, “If the human brain is made of essentially the same stuff as a kitchen table or a pocket calculator or a tree, why does the first have a sense of of self — of being an ‘I’ — whereas the others do not? Hofstader explores how physical activity in the brain, which seems completely mechanistic and completely unlike the process of thought that we experience, can in fact give rise to a qualitatively different sort of activity occurring at the “higher levels” of the brain. He gives several examples of such systems, such as an ant colony: the individual ants are stupid, acting in response to basic stimula, but the colony as a whole is much smarter.This kind of qualitative difference between the different levels of a system is key to Hofstader’s thesis that critics of the possibility of artificial intelligence have misinterpreted the implications of such limitative notions as Godel’s theorem. Godel’s theorem states, in essence, that any sufficiently powerful system will contain truths that are not provable within the system. The problem with computers, these critics charge, is that they are stuck within a particular system — there is no way to program them to realize that there is no solution to a particular problem within the system, even though such a fact would be perfectly obvious to an intelligent person who can “jump out of the system.” So the computer is stuck trying to solve the problem with a method that is doomed to fail.Hofstader argues, on the other hand, that there is nothing magical about being able to jump out of the system and reflect on whether it is the appropriate system to be using. In fact, in doing this one is still “in” a system — it’s just a bigger system, one that has the ability to think about lower level systems. And one can jump out of that top level system and reflect on it as well — but then of course one has entered a new system again. There’s always another system, at a higher level, no matter how high up you go.At a certain point these levels blur together, because they are recursive — meaning they reflect back on themselves. Hofstader uses the works of Escher and Bach to illustrate the concept of recursivity. For example, there is Escher’s stairway that goes up and up until you are back where you started, or the two hands, each of which is drawing the other.Hofstader believes that self-awareness — the “I” — arises from this kind of recursivity. To put it very simply, at the highest levels the brain is a system that deals with symbols, and the “I” is the symbol for the system itself.There is much, much more to this book. There are lengthy tangents into mathematics, philosophy, biology (the section about the recursion that takes place in the copying of DNA is particularly fascination), etc.Thankfully the book is organized into sections that alternate between straight exposition of some concept and a fictional dialogue that illustrates the concept. Still, it’s not light reading, and I did wish at points that there was a Reader’s Digest version that would just give me the main points without going off on a tangent for 30 pages about wasps or something.Godel, Escher, Bach made me rethink a lot of my preconceptions about consciousness and artificial intelligence, and is well worth reading the next time you have three months to spare.

⭐This review comes after my second attempt to tackle GEB, both of which were thwarted by the author’s insufferable style. The content, while intellectual, is hardly as difficult as Hofstadter makes it out to be with his roundabout explanations—he seems more concerned with intellectual flexing than with concise rhetoric.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”.

⭐GEB is pretty much the must-read book for anyone interested in computers and/or general philosophy of mind. Hofstadter has had a long, interesting career in the field of interesting mathematics and links between theory and real life. In his magnum opus, GEB, he explores what it is to be a self-thinking machine, and how, by looking at it from some other perspectives, we can learn a lot about how we think and do.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.

⭐A book that caused a bit of a sensation when first appeared but seems quite dated now apart from being completely on the wrong lines philosophically as far as I am concerned. Beautifully produced and illustrated and the author has considerable erudition but he is very wordy, woolly and ultimately has very little to say. He puts me off Zen rather than attracts me to it and Escher’s drawings though clever are terrifying. Nature never does fall or ever will fall into the sort of infinite regress, serpent eats its tail &c. that the author finds so sexy. In some ways a dangerous book.

⭐Practically new, unmarked copy, carefully packed and promptly delivered. No way can I yet give a blow by blow account of the book itself. Have you seen it? Have you weighed it? Remember, too, this is no ordinary book, which is why I was so keen to find it. For an intelligent review, ask me again in around 5 years’ time. This one is going to be like swimming the English Channel. I look forward to it enormously.

⭐This is a really engaging book. It has twists and turns, rythms, conundrums and a great mixture of different media to keep you going in an exploration of the possibility of identity arising from ‘machine-like’ operants. There are great illustrations and a good use of humour that permeates the dialogue format that carries the book from section to section. You can learn alot from this tome and enjoy learning it.

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