Gödel, Escher, Bach: An Eternal Golden Braid
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Douglas 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 and Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.
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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 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. |
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| 11-29-08 | 1 | 0\1 |
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The book was fine, I guess. Except it was in Spanish instead of English. I'd like to return it and get the English version.
(Review Data Last Updated: 2008-12-04 11:41:18 EST)
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| 10-14-08 | 2 | 2\3 |
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This book is boring. It doesn't really tell you anything, kind of "all form, no substance". A cloud of a book.
I approached it a few times in the past, seeing it on top of many bestseller charts, but each time got scared away by apparent lack of clarity - when you open this book at random, you always face something unexpected - math, music, art, insects, human brains, DNA, viruses, zen, artificial intelligence, talking turtles, you name it, and always in different form. Anyway, I thought to myself one day - it still must be a special book, it is rated so high, and it looks mysteriously clever, and so I have to read it through to understand. And I did. Geez, was it boring. This book is 800 pages of chasing its own tail. It is full of curiousities, but no rigor, no plot, no structure. For the first 200 pages or so, reading tales seems fascinating, just imagine (you think to yourself) what the author has to offer when it gets to the point ! Never happens. As you reach page 600, you clench your teeth still hoping that there must be some sort of revelation ahead, even if on the last page. None. These three things is this book about: 1. Self-reference. The great deal of the book is dedicated to approaching the proof of the Godel's theorem which in some sense says that a system cannot understand itself. 2. Form vs. substance. This ranges from extracting meanings from messages on different levels, to having different levels of interpreting the situation. 3. Infinity and different sorts of infinities. This only helps to fog things up. Can't spit without hitting a paradox. And this is presented rather informally. Speaking of which, EVERYTHING in this book is presented informally. There is no facts, no proofs, no math, no logical reasoning, no conclusions, just a stream of consciousness, which twirls around and around. It doesn't ask nor answer any single question straight. It's a philosophy, I see, but even a philosopher has to take sides, but the author does not. There is no side here really. The discussed topics are indeed interesting and mind-provoking, for the first 200 pages even fascinating, like I said, but then it becomes pointless and boring. The only thing I want to ask after reading this book is "SO WHAT ?". I wish I spent the time on some other book. Something with a plot. (Review Data Last Updated: 2008-11-30 03:42:07 EST)
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| 09-26-08 | 5 | (NA) |
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Godel, Escher and Bach, written by Douglas Hofstadter, while the title would suggest it is discussion of a mathematician, an artist, and a composer, is a complex examination of how human beings develop perception and meaning. More specifically, the book explores, through a series of dialogues and narrations, how symbols, thought and language are all intertwined and how reality is essentially a composition of overlapping meanings and perceptions. The book challenges the reader to observe the system of symbolic meanings around him or her objectively.
(Review Data Last Updated: 2008-10-14 11:26:38 EST)
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| 08-27-08 | 5 | (NA) |
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Early this summer at a computer programming conference I found myself with a group of programmers of different ages and nationalities. The one thing we all had in common is that we'd read this book while in high school or college and found it fascinating. For some of us the book was life changing. Most of us rediscovered a love of math that our high school education had nearly destroyed. Many of us became programmers because of it. The book may seem to be dated in some respects after 20 plus years, but on the whole it is as relevant and exciting today as it was when it was first published.
(Review Data Last Updated: 2008-09-27 03:10:08 EST)
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| 08-12-08 | 5 | (NA) |
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This is a work of incredible depth and scope. From number theory to cognition to genetics, Hofstadter offers some incredible insights about the way we and the world work. One word of advice: don't worry if you can't understand all of his ideas. This book is so chock-full of content that most readers could spend a decade plowing through it, only to find that they've missed something important. Just read it. You'll get some of it, and that's enough.
(Review Data Last Updated: 2008-08-28 00:14:23 EST)
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| 06-09-08 | 5 | (NA) |
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This is one of my favourite book of all time. I first read it twenty years ago as an undergraduate on my computer science degree. The nice thing about getting older, but still remaining young, is that you can go back and revistit master works - and lets make no bones about it, this is a master work. As such, it requires time, effort and mastery of the ideas.
This is not a book that you can just pick up and read in a couple of days. Of course you can delve into it and loose yourself for a few hours, but to obtain mastery will take serious time and effort. Using Howard Gardener's terminology, Hofstadter synthesises across the domains of music, maths and art. This is no mean feat. Buy it, only if you have the time for it. Treasure it, enjot it and love it as much as I do. (Review Data Last Updated: 2008-08-13 02:51:21 EST)
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| 04-20-08 | 1 | 3\10 |
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The author complains in the new preface that a vast majority of the reviewers, including those who have rated this book very highly, seem to have no idea of what he has been trying to say. In my opinion, this is a self-indictment that does not leave much for others to say. If the author cannot get his ideas across in 700 pages, perhaps people should not waste their time on him. I have learnt it the hard way: after buying this book, five years ago, on high recommendations of friends, only to find it so boring and confused that I could never go beyond a few pages even though I gave it innumerable attempts.
(Review Data Last Updated: 2008-06-10 02:44:50 EST)
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| 03-28-08 | 5 | 1\1 |
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I realized after recommending this to a friend that I've never reviewed it. Strange, since it's one of the dozen most important books I've ever read in my nearly half-century on this planet. I first read it over 20 years ago, and continue to refer to its literate and well-crafted pages frequently.
This book is Doug Hofstadter's religion. Since it's so good and so right about so many things, people run off into strange places with Hofstadter's words, sort of like the Bible. GEB (the shorthand name for the book) is, for me, a meta-level examination of what it is to be human. Some people see the shadows of the gods in there. I'm not trying to be melodramatic, nor do I believe I'm overstating the value of this book. Hofstadter takes the reader along on a Carrollian trip using metaphor and fable. Then he employs pedagogical, practical exercises, and good old-fashion lecture. Rinse and repeat, again and again. When he tells you to get pen and paper, please do it. Take your time with this book. I tried and failed on my first attempt. When I finally settled into it, it took me three months to joyously work my way through it. Take a year if you need it. Reception, analysis, recursion, reapplication. Hofstadter examines the basic evidences of intelligence, forms sensible, fundamental meta-rules, and builds from there. This book - as others have said - is hard work, like climbing a mountain. But at the end of the endeavor, the view is dazzling. (Review Data Last Updated: 2008-04-20 02:36:43 EST)
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| 02-08-08 | 5 | (NA) |
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I have not completed this book, and I am not sure you can ever say that you are complete with a book of this magnitude, however, it will certainly be a book I will review again and again. If you want to be challenged intellectually, this book would be the ticket. I enjoy a good challenge, and although it isn't a 'fun' read, it is valuable book to have in your personal library if you are interested in a paradigm shift in your reality.
(Review Data Last Updated: 2008-03-29 11:44:29 EST)
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| 01-28-08 | 4 | 0\2 |
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After studying Douglas R. Hofstader's brilliant book, I discovered an error in the proof of Godel's first incompleteness theorem that invalidates the proof. The same error is in Newman & Nagel's book Godel's Proof.
The error occurs on page 447. The incorrect statement is, "a' is the arithmoquinification of u." The statement should read: a' is the arithmoquinification of the numeric value of the Godel number u. The term u represents the Godel number of a specific formula, and the word arithmoquinification is a portmanteau word coined by the author. Godel's theorem is derived by arithmoquining a formula that Hofstader calls the "uncle" formula. On page 447, he writes,"Now all we need to do is-arithmoquine this very uncle! What this entails is 'booting out' all the free variables-of which there is only one,namely a"-and putting in the numeral for u everywhere. This gives us: ~Ea:Ea': he offers this interpretation of the theorem,"There do not exist numbers a & a' that both(1)they form a TNT-proof-pair, and(2)a' is the arithmoquinification of u." But,as I have pointed out Godel's theorem does not declare part(2)of his interpretation. Instead, the correct interpretation of part(2)is, a' is the arithmoquinification of the numeral of the Godel number u. The numeral of the Godel number u cannot be arithmoquined because it is not a formula and therefore has neither a Godel number nor a free variable. This invalidates the proof because we no longer have a true statement: a' is the arithmoquinification of u that cannot be proven. Instead we have a false statement that cannot be proven. For more info & essays on this subject,please go to www.jimssciencepage.info (Review Data Last Updated: 2008-02-27 03:57:28 EST)
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| 12-18-07 | 5 | (NA) |
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Just like other reviewers of this book, this one is seriously math-challenged. I thought I'd never make it to the end. I had to work hard sometimes. But it was one of the most worthwhile reading experiences of my life, indeed it was fascinating and I ended up recommending it to everybody (almost). This is an eccentric book, which at the beginning seems to be about everything and nothing. The author describes "self-referential systems" and wonders whether they may come to think about themselves and, ultimately, about the possibility of Artificial Intelligence (AI). This is one of the books that have taught me the most and made me think about things that for me are little or not familiar at all, like Typographic Number Theory (TNT) or propositional calculus. I don't pretend to having understood all of it perfectly, but definitely my intellectual horizon and my knowledge widened a lot. The title comes from three people whose work illustrates the wide field of self-referential systems. One is Kurt Godel, a mathematician who formulated the famous and complex Theorem of Incompletitude, which says something like in every formulation of Number Theory there are one or several propositions which are undecidable, that is, it is impossible to affirm if they are theorems of that formulation, or not. What is a formulation of Number Theory? Well, starting from an axiom (a given equation), and according to some precise rules of addition, substraction, or substitution, one develops the equation until finding (or not) some preestablished outcome. These formulations are self-referential because they turn in on themselves, that is, they take the sources of their subsequent development from the very elements present in the original axiom.
OK, where do Bach and Escher enter the picture? Simple: Escher's engravings and illustrations (of which the book offers many beautiful examples), and Bach's music, are self-referential. They present an initial theme, and then they develop by turning in on themselves according to some rules or patterns. This is also how DNA chains and the resulting organisms grow, and even some poetry. The book is written with great sense of humor and didactic skill; it intersperses "technical" chapters with funny and seemingly absurd dialogues between cartoon-like characters, which illustrate with good clarity subjects previously exposed. Mathematics, biology, computers, AI, music, painting, and language are part of the subjects taken on. For example, this book helped me to understand better how computers and software languages work. In one of the most interesting parts, the author explains how our brains function at different levels: the strictly neuronal, the cellular, the chemical, and the symbolic. In the same way, computers work at different levels, from that which occurs between components of the microcircuits, passing through successive levels of programming, until the "symbolic" level, which is represented by what we see on the screen. Just as people don't need to know or screen what is happening with their pancreas or stomach in order to go about, but they limit themselves to eating, breathing, walking, thinking, computer users don't need to know what is going on with the circuits while they use them. We only take notice of organs or programs ewhen something's wrong: we either feel bad or the computer paralyzes. Finally, the other debate is about the possibility or not of AI, which is far from being resolved. An enormous book. (Review Data Last Updated: 2008-01-29 02:53:06 EST)
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| 11-19-07 | 5 | (NA) |
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If pop culture threatens to turn your mind to mush or if Paris Hilton and Rush and Riley leave you wondering whether all those lovely convolutions and synapses evolved for naught, treat yourself to some brain candy. This is not a beach book. If you get it at the library you may be renewing it for a year. Hofstadter ties together Kurt Godel's Theorem (mathematical) with M.C. Escher's art and J.S. Bach's music in a wild intellectual rollercoaster that will leave your thinking muscles feeling frisky as a colt. Of the three heroes, Escher is probably most familiar. His hands drawing each other, endless waterfalls and a fascinating Mott the Hoople album cover have postered him into household art. The recursive loops that form the theoretical base for Escher are the stuff of Bach's genius, and echo in Godel's work. This plunks us smack dab into the invention of computers and the question: Is artificial intelligence possible? This statement is false. Fabulous, difficult, fun.
(Review Data Last Updated: 2007-12-19 03:02:56 EST)
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| 10-29-07 | 2 | 2\3 |
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I love reading books, to me "factual" knowledge really tickles my fancy, however after reading this, and I am in page 420, I am literally entirely bored out of my mind. Although maybe 3 out of all the ideas and concepts he presents were interesting to me such as the caste system, and the discussion and comparison about the ant colony to the process in which the brain functions quite entertaining along with the record discussion between the tortoise and achilles (holy crap, this is like animal farm on weed),(which is what my two starts go to), the remainder of this book is quite annyoing.
I have never taken such a long time to read a book which is so hyped up to be nothing more than half baked ideas. I am not a mathematician by any means of the word, I personally stick to history books and science books and biographies based on FACTS. I seldom read a book based on an individual's ideas and interests and religious beliefs (UGH!). I think it is quite amazing that he is able to drag on such a long discussion about someone's theorem, and for that I applaud him (and feel bad for Godel, he must be rolling over in his grave), but it is not for me. As a "regular" joe when it comes to Math/Logic, this books certainly has turned me away from ever wanting to delve into the subject again and I sincerely recommend the "average" reader to just rent it if this peaks your curiosity. I am still not sure as to whether I want to finish this book, because if I have to look at any more parenthesis and tabs and letters, numbers, drawings, I will punch myself in the face... For those of you who like this book, more power to ya, not for me though. I will stick to my "FACTUAL" books, not "OPINION BASED BOOKS". PS: IF YOU WANT A QUICK OVERVIEW OF GODEL'S THEOREM of INCOMPLETENESS without the "ETERNAL GOLDEN BRAID" portion of it and half baked ideas from the disco era, just google it and read up on it, it's maybe a few pages, so save yourself the waste of time. (Review Data Last Updated: 2007-11-20 14:04:04 EST)
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| 05-18-07 | 5 | 12\15 |
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This is a difficult book.
Difficult to read. Difficult to understand. And, I'm finding, difficult to review. What's it about? Good question. The author, himself, isn't very clear on this point, describing it as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll." I'm not sure I can do better than that. I will tell you this, however: if the book has a "point," it does seem to be that man's consciousness is ultimately mechanical and, therefore, that there is no reason that machines cannot finally be intelligent in the same sense that man is. (And, in fact, be as man in just about every internal way.) While I take issue with this conclusion, and some of Hofstadter's reasoning along the way, I don't think that my debating his points is the basis on which a prospective reader should decide whether or not to pick up this book. Instead, the prospective reader should know: that this is a lengthy and deep work. It will take a *long* time to read properly, and most readers should not read more than a chapter a day. Many of the sections, and especially the various dialogues that preface the chapters, are quite clever. (These dialogues are usually between Achilles and the Tortoise, of Zeno's paradoxes, and their friends.) Some of the chapters grow incredibly technical. The subject matters vary, wildly and rapidly, and there will be points in reading where you will question your investment. In the end, you will feel good for having pushed through the hard bits. It will coalesce, more or less, into a whole. Whether you finally agree with Hofstadter's conclusions or not, you'll have learned much and thought about important topics you might otherwise not have. A good book, certainly not for everyone... but, if you're the "right" audience--someone deeply interested in questions of intelligence, mathematics, computer science and free will, and possessed of a bit of an ironic sense of humor--then this book cannot be recommended highly enough. Five stars, for the work it represents, and the doors it opens to the reader. (Review Data Last Updated: 2007-10-30 02:45:45 EST)
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| 05-16-07 | 5 | 4\10 |
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As you can see from other reviews, people tend to walk away from this book with a variety of different impressions. Math, Art, Logic, Philosophy, Human Perception and Thought, it has it all. This is second to the Bible in my collection as a book I've read multiple times and can still come back to a read again for even more insight and perspective.
(Review Data Last Updated: 2007-10-14 02:52:56 EST)
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| 05-14-07 | 5 | 0\24 |
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Hofstadter combines the awe in math, music, art, artificial intelligence, language and computers into one big book called GEB. Its takes the reader on an ecstatic journey with a clever use of parallels between the structure of math, music and finite but endless loops that appear in Escher's works. Dialogs between Achilles and Tortoise are very interesting.
(Review Data Last Updated: 2007-10-14 02:52:56 EST)
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| 05-14-07 | 5 | 2\11 |
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Can someone tell me, in plain English, what this book is about? On the little matter of determinism--is he for it or against it? He does not seem to have come to praise Godel, Escher, Bach for their strangeness but rather to bury strangeness and its resistance to materialism. He seems to be saying that strangeness is hardwired and can be programmed into a formal system by someone who sees it for what it is--in short, that computers will some day rise to the level of consiousness and self-reference. But wouldn't such a system be curved in upon itself and lack strangeness? If strangeness could be hard-wired into AI, would it still seem strange? Nothingness annihilates strangeness, but then the absense of strangeness is the actual limit of the theories of value seen in those who follow Heidegger. In order to eliminate the difference between soul and matter, they must give up the resistance of soul to the limitations of material existence; at which point "strangeness" becomes a matter of verbal virtuosity and conceptual sleight of hand. "Strangeness" becomes the same thing as cleverness. Or am I misreading this fascinating book?
(Review Data Last Updated: 2007-10-14 02:52:56 EST)
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| 05-14-07 | 5 | 0\19 |
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Item is in good condition and I recommend buying from this seller.
(Review Data Last Updated: 2007-07-10 12:11:54 EST)
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| 03-19-07 | 5 | 24\30 |
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A simple example of recursiveness in music is the song "row, row, row your boat." The song becomes recursive as each new line is started when the original line makes it to "gently down the stream." In this way, we have a musical example of the artistic portrayals of Maurits Cornelius Escher whose paintings invariably fosuc on recursive visual themes such as two hands in the process of drawing each other.
In each case, the depiction challenges our ability to pidgeon hole the phenomenon we are examining. Which line is the harmony, which is the melody in "row, row, row your boat"? Which hand is drawing which in the Escher print? Liguistically, the same effect occurs when we examine the statement "This sentence is false." Logically if we accept the statement at its face value being false then it becomes an accurate representation (in that it correctly asserts its falseness). On the other hand, we are also drawn to the conclusion that the statement is true (again because it is self referentially accurate). Ultimately, we are forced to logically conclude that we can neither bracket the statement "This sentence is false" with either all true statements or all untrue statements. As indicated previously, like the song "row, row, row your boat" or an Escher painting, the sentence defies pidgeon holing owing to its recursive quality. Back in 1931, Kurt Godel shocked the mathematics community with his assertion that mathematically consistent systems themselves necessarily produce formally undecideable propositions (the math equivalent of "This sentence is false"). At the time of presenting his paper, it was Godel's intent to demonstrate the unique nature of human intellect because if we can resolve undecideable propositions then there must be something unique to the process of human intellect. While Godel certainly brought undeniable genius to the creation of his theorem, it doesn't follow that the theorem proves the uniqueness of human intellect. And the reason Godel's theorem doesn't prove the uniqueness of human intellect is because its logical limitations are our own. Just as Godelian mathematics can't prove undecideable propositions, neither can we "prove" them. However, we can "believe" undecideable propositions. (In this regard, two easy cases in point are Goldbach's conjecture -- that all even numbers are the sum of two primes -- and that parallel lines really are parallel.) In this way, Godel's theorem, in combination with modern research on artificial intelligence, shows that it is the emotive side of reason that defies the strict logical limitations of Godelian constructs. These hard won discoveries have combined to make for some surprising findings. Probably the first among these most observable to the general public through the misconception of science fiction is that emotion somehow stagnates the operation of intellect. In this way, it was HAL 9000's personality as much as the creepiness of that personality that was surprising to 1968 movie goers watching "2001: A Space Odessy." As demonstrated in the movie, it was the fact of HAL's emotive connections with the ongoing actions of his crew that prompted "him" to formulate and act on plans. Second, modern research has shown that human intellect is not best characterized as being a "blank slate" but rather a delicate combination of various systems that survey reality in the own ways. An easy example is the human eye which uses a combination of three different light cones to measure redness, greenness and blueness. It is the relative comparisons of these cone findings that nudges your visual perception to observe the color of an object. At the intellectual level, one system is entirely devoted to our understanding of artifacts. How do they work? How can they be modified for use in a situation? Another system comprehends animate creatures. Yet another system recognizes faces. Still another system is devoted to language acquisition. And significantly all these systems acquire information emotively. We see the face of a parent and emotively appreciate it (unless we suffer from a particular cognitive disorder that has disabled our ability to do so as for example discussed by Oliver Sacks in his great book "The man who mistook his wife for a hat"). We remember a concept learned and emotively evaluate it. In this way, freedom, communism, taxes are not just intellectual constructs but ideas that spark real feelings on our part. In creating Godel, Escher, Bach, Douglas Hofstadter displayed true genius in linking three domains wherein recursiveness seems to play such a pivatol role. As he indicated, they are three shadows cast from the same source. In re-concluding this book, however, I couldn't help but think of other possible titles that could be added to a Godel, Escher, Bach type encyclopedia: "Phi, Di Vinci, Bach" -- the story of the "golden ratio" of phi which plays a role in Di Vinci's art work and as it so happens also in the music of Bach; "Pascal, State Lotteries, Happy Birthday" -- the story of Pascal's wager and how an appreciation of statistics will make us understand why states will never lose money running a state lottery for reasons akin to why relatively small groupings of people will have at least two that share the same birthday; and "Klein, Carroll, Kubrick" -- the story of Oscar Klein's bottle which can resort to the fourth dimensionj to fill itself up and how speculations by the physicist J Richard Gott suggest that Alice and all of us may have originallyu gone down the rabbit hole for a real space odessy through time itself. The point here is not that Hofstadter was incorrect but (no pun intended) merely incomplete in his survey when he said that Godel's proof, Escher's paintings and Bach's music were but three shadows cast from the same source. The point here is that -- properly examined -- those three shadows, together with the encyclopedia I've suggested, would direct us not only to the origins of consciousness but also the origin of origins itself. (Review Data Last Updated: 2007-10-14 02:52:56 EST)
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| 02-09-07 | 5 | 4\19 |
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Godel, Escher, Bach (GEB) is an interesting book on...well, it's hard to categorize. It's about "Strange Loops", but it's about way more than that...it's about human reasoning and computer interaction...but it's also about way more than that. Overall, as one of the reviews on the back cover says, this book is "An entire humanistic education between the covers of one book."
(Review Data Last Updated: 2007-10-14 02:52:56 EST)
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| 01-09-07 | 4 | 0\1 |
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A very robust analysis for consciousness and mind, but I think that "The Mind's I" of the same author provides the same "food for thought" in a more attractive way.
(Review Data Last Updated: 2007-02-10 08:22:05 EST)
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| 12-10-06 | 3 | 3\7 |
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The contents of this book are like the remains of a huge building that, unfortunately, collapsed in the middle of construction. It is one vast heap of rubbish, but like all such heaps it contains much that is interesting and a little that is valuable. This is a book to browse -- there is something thought-provoking on almost every page -- but I wouldn't recommend reading it from cover to cover: the structure is only superficial, and any attempt to "follow" the argument would surely be infuriating. One of the best features of the book is its bibliography: most bibliographies are purely technical affairs, but Hofstadter has taken the time in this one briefy to describe the contents of each book he cites as well as to note its relevance to his "project". Coupled with the bibliography, this book is a good source of material for research of one's own. Just take it with a grain of salt: it is not a thesis, but a gesture.
(Review Data Last Updated: 2007-01-10 03:31:00 EST)
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| 11-10-06 | 5 | (NA) |
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There are so many reviews of this book. Many of them assert that the theme is simplistic and presentation of various different "unrelated" subjects and materials don't amount to much. Many reviews try to summarize. I can read the reviews written about this book much like the way I read the book itself. So many variations in thinking by so many different thinking beings.
I agree with some reviewers that the theme seems to be that cognition arises from patterns that seem originally inanimate. A great puzzle, how can we think when we are made of atoms? How does one connect point A (materials that are not capable of consciousness) to point B (human beings capable of cognition and thought)? It is difficult to explain A to B. The author presents many views of the same patterns using Music, Math, Logic, Art and Language arts. The book isn't about any one of these things. It certainly isn't about just AI. It seems to be a unique attempt to lay down the nebulous web of patterns inside author's mind that connect pieces together which illuminate the possibility of connecting point A to B. Mr. Hofstadter has written another book recently (Le Ton Beau De Marot: In Praise of the Music of Language) which is yet another iteration of recursive theme. I go back to this book every several years to read parts of it again. The last time was after reading David Mitchell's Cloud Atlas. The theme in the novel weaves through many different narratives, presented in different styles, stories varying greatly in settings and time period, even the languages used are vastly different. But the pieces are threaded together with the undercurrent of comet shaped birthmark. GEB is threaded similarly, with the idea of patterns, I think. Patterns alive, adrift, amorphous, aware and abiding. The writing is dry but I detected a sort of sadness under all the dry math an logic, which helped me to continue to read despite the difficulties (at least initially). I still don't understand all the little puzzles. But I think I get the gist of it. I hope. (Review Data Last Updated: 2006-11-19 04:12:44 EST)
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| 11-10-06 | 5 | (NA) |
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There are so many reviews of this book. Many of them assert that the theme is simplistic and presentation of various different "unrelated" subjects and materials don't amount to much. Many reviews try to summarize. I can read the reviews written about this book much like the way I read the book itself. So many variations in thinking by so many different thinking beings.
I agree with some reviewers that the theme seems to be that cognition arises from patterns that seem originally inanimate. A great puzzle, how can we think when we are made of atoms? How does one connect point A (materials that are not capable of consciousness) to point B (human beings capable of cognition and thought)? It is difficult to explain A to B. The author presents many views of the same patterns using Music, Math, Logic, Art and Language arts. The book isn't about any one of these things. It certainly isn't about just AI. It seems to be a unique attempt to lay down the nebulous web of patterns inside author's mind that connect pieces together which illuminate the possibility of connecting point A to B. Mr. Hofstadter has written another book recently (Le Ton Beau De Marot: In Praise of the Music of Language) which is yet another iteration of recursive theme. I go back to this book every several years to read parts of it again. The last time was after reading David Mitchell's Cloud Atlas. The theme in the novel weaves through many different narratives, presented in different styles, stories varying greatly in settings and time period, even the languages used are vastly different. But the pieces are threaded together with the undercurrent of comet shaped birthmark. GEB is threaded similarly, with the idea of patterns, I think. Patterns alive, adrift, amorphous, aware and abiding. I hope this doesn't sound too trite. (Review Data Last Updated: 2006-11-12 04:00:51 EST)
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| 11-09-06 | 1 | 2\19 |
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I read this book I don't remember how many years back. I think about 15 years ago. And just remembering makes me nauseous, for the amount of time and effort it took me read it just to get to no point. I was younger, naiver and I got engaged, I confess that. Clever Author no doubt, to make a huge pile of unrelated ideas and make believe you would get somewhere following his lead. Just wandering around and playing with analogies. I had the time back then, I guess. Today I only have the time to write a review stating how surprised I am today I could finish this kind of book. I can't speak for anyone else, suffice to say I was a nerd with a lot of time in my hands.
(Review Data Last Updated: 2006-12-11 03:39:31 EST)
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| 11-05-06 | 5 | 1\2 |
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Hofstadter tickles every curious and philosophical bone in your body. This one is a long read with a lot of dense material. If you take the time to get through it, while understanding all of it (this ain't no dime novel!), you will find yourself sitting on such a mental high as you cannot yet imagine. Plus, you get to boast to all of your nerdy friends that you have read "GEB", but thats just a perk.
(Review Data Last Updated: 2006-12-02 00:44:15 EST)
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| 11-04-06 | 5 | 1\3 |
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This is Professor Hofstadter's Thesis. Those thinking about reading this book should do some research before doing so since it is over 25 years old...
Perhaps that will level set expectations, so that you might objectively evaluate it's merit, and make an informed decision on whether or not it is a good investment for you individually... But then that would be exercising exactly what this book is about... Put that in your pipe and smoke it! If you are intrigued and fascinated by what it means to be human and have a Mind... If you are the type who wonders... Why, or more importantly, how do I wonder? Then you owe it to yourself to read this book... Even if like me, you struggle to comprehend it and read it many, many times until the light grows from a flicker to a full on fire, you will appreciate your self-discipline in the end. This book absolutely stands on it's own as an illuminating discourse on how the animate springs forth from the inanimate. If you don't like it, put it down and read something you do enjoy, but don't take it personal and attack the author. Good, bad, or indifferent this book represents a monumental achievement for a brilliant human mind, and that is irrefutable. Whether or not this is your "cup-of-tea" is inconsequential, we should all be thankful for people like Professor Hofstadter, who dare to live without self-imposed limits, and take on the monumental effort of expanding the human collective consciousness. (Review Data Last Updated: 2006-12-02 00:44:15 EST)
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| 08-23-06 | 5 | 6\7 |
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Whenever I read a book in translation I often wonder if it's the translator I love or hate, or the author themselves. Literature in translation is essentially a complete re-writing of the book itself. Consider Lewis Carroll: How does one go about translating seemingly endless word play and words that are often made up? Now consider the fact that Alice in Wonderland had been translated into over 50 languages. If you could read all 50 languages, some would approximate your understanding of "Alice", and some would appear tangenital, or worse, dishonest to the original.
Machine Translation (MT) is considered AI's hardest problem, and Hofstadter goes to painstaking length to show just why this is so. Despite marketing rhetoric he points out why such a solution is years in the making if it ever occurs at all (to a satisfactory degree - meaning literature, not technical documents). Though many who have read "Gödel, Escher, Bach" or "Metamagical Themas" are sometimes disappointed in this book, to me it is part of the evolution. And being a word geek, a polyglot, and in the constant companion of one who makes translation a living, I have to say this book rates above those other tombs on my list. But be forewarned, you are leaving the world of complex algorithms and entering a world where just such analysis is not forthcoming. (Review Data Last Updated: 2006-12-02 00:44:15 EST)
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| 08-17-06 | 5 | 5\7 |
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I read this book in 1980, and each chapter of it still stands out in my mind in glittering bas-relief against all I read before or have read since. What stands out the most, however, is that my thinking changed after reading this book. Everything since reading it has been inevitably processed through its filter, which has quite simply changed my life. Perhaps a first-reading today would not have an equal effect; in 1980 it was timely. Things we take for granted now were difficult to conceptualize then--the internet, for instance. But I'll leave it for contemporary readers to decide whether Gödel, Escher, Bach: An Eternal Golden Braid is as eternal as the title claims. For me, the answer is a resounding yes. I can say without doubt that my life would have been different if I had not read it at that time.
Ok, if it's so great, then what is it that makes it so? Trying to describe what is great about this book is like trying to say what is great about a particular Bach Fugue, or an Escher print. A fugue doesn't typically have a great melody. The rhythm can be monotonous and predictable. You know where it begins and where it will end up, and the subjects will enter on cue and not deviate from their lines. Escher's prints, similarly, are composed of mediocre representations of their subjects. Shading is not sublime, some of the features may be grotesque. What is it, then, that makes that fugue or that print great? Ahhh... that's the subject of this book, and in beautifully crafted recursion, its own principles apply equally to itself. You will come away with an understanding of the underlying principles of intelligence, beauty, craft, logic, and universal principles of creation. A deeper appreciation for those things does not necessarily mean a simpler or easier means of describing same. In fact, it may be the opposite, sort of "the more you know, the more you know you don't know." This confrontation with, and participation in, the infinite seems to be the root of our longing--a sense that Bach, Escher, and Gödel weaved intuitively into their own work without feeling compelled to explain. So, rather than expect to come away from this book with the answers to the big quiz of life, I would say what one is more likely to find is a deepening of "mu," a rendering of knowledge into its proper place where "answers" in the Western sense dissolve into the questions in a deepening spiral of association and metaphor to the point at which one sees so many possibilities that the original question loses its significance. So is it nirvana? Not this book. But one may get caught up in the craft of the author and his inspirations to the point that one might feel lifted up and deposited at the trailhead of a new path, and the best that one can expect in this life is a new, sublime path. I think Hofstadter would agree that nirvana, should it exist, is the path, not the destination, and this book may well prove the author to be a willing bodhisattva. Shooshie (Review Data Last Updated: 2006-12-02 00:44:15 EST)
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| 08-02-06 | 4 | 5\9 |
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This book is a great way to expose yourself to new ideas, but, in the words of a previous reviewer, it was written by a passionate dilettante.
Its treatment of Godel's proof is occasionally great, but it is sometimes excessively obfuscatory, and sometimes even just plain wrong. I think this book is extremely clever, and I encourage almost anyone to read it, but take everything it says with a grain of salt. It's a great way to start yourself thinking about some fascinating things, but don't take the book too seriously. IF YOU WANT A REAL UNDERSTANDING OF GODEL'S PROOF: read "Godel's Proof" by Nagel and Newman, and then read a good translation of Godel's paper itself. GEB is clever and inspired, but it should not be taken too seriously. (Review Data Last Updated: 2006-12-02 00:44:15 EST)
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| 07-19-06 | 3 | 16\29 |
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I finally finished "Gödel, Escher, Bach" the other day. Does this book deserve a review? Sure, it's over 700 pages long and took me more than a month to read. Not because it was too complicated or difficult but because of my lack of daily reading time. If I were to describe this work in a few words I would say it's mostly a vehicle of self-promotion for the author. Hofstadter seems to yell in a high-pitched tone: "look at me, I know so many things, I know math, computers, molecular biology, ants, zen, logic, artificial intelligence, music and art and philosophy, and I have an opinion on everything" (and he talks about other subjects too which, for the sake of keeping this paragraph within bounds, I chose to omit). What bothered me about the book - which I started reading with the best intentions - and almost made me abandon it, was that this feeling of showing-off pervades quite easily through the superficiality of the story. Hofstadter embarks on a quest to show that many aspects of life are made of "strange loops", which always have a self-referential, unprovable element that leads to incompleteness. His central point seems to be Gödel's theorem of formal systems (I say "seems" because it's never clear what his point actually is), and from there he draws parallels to all things who seem to work by similar rules: the origin of intelligence and logic, the life of ant colonies, Bach's extremely elaborate music, Escher's tricky drawings, the internal mechanisms of the living cell, you name it.
But Hofstadter never offers any insight in any of these subjects, neither for people who are familiar with them nor for those who - like the majority of the readers - have some sort of vague, superficial knowledge about them. He goes on rambling about everything under the sun and at one point, if I remember well, he even starts to dissect and praise his own thought process in relation to how he wrote one of the boring dialogues between Achilles and the Tortoise. He tries to write funny sometimes, but his funny parts become quickly rather annoying. He reminds me of the guy whose class "Debugging Win32 applications" I attended once and who couldn't stop cracking jokes even if nobody was laughing. However, if one is to believe the reviews it gets on Amazon, the book creates an effect of awe on many people, who feel that they belong to a select club for having read it. The average reaction is "This book is awesome although... I didn't understand much of it". Long story short, I was disappointed. I had expected to be captivated and fascinated but I wasn't. I had expected to learn a great deal but I didn't - the book doesn't go past my own murky ideas about infinity, self-reference, origins of though and the other eternal major questions of humanity. But I wouldn't diss the book completely; it is, after all, a book that makes one think and no such book is ever a waste of paper. If you have read this book you have at least asked yourselves the same questions as the author, and although you may not have an answer, you have started on a journey of the mind, a journey that should never stop. If you haven't read the book but were thinking about it, think again - there are only so many books you can read in a lifetime and this one can be safely skipped. Just don't pick "The DaVinci Code" instead... (Review Data Last Updated: 2006-11-02 01:44:11 EST)
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| 07-04-06 | 5 | (NA) |
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Plainly put, this book was a ride. Standing back from a distance and looking at what the author has done really can put you in awe - the sheer scope of this work is breathtaking. He digs into many different scientific, mathematical, and artistic disciplines, and somehow manages to work them all together into a sometimes confusing, but ultimately satisfying whole.
The short dialogues that fit in between each chapter are clever and always thought-provoking, but the bulk of this book's worth comes in the chapters. From the beginning to the end, I constantly found myself having to stop and rethink my perspective on many subjects. As the end of the book nears, he wraps it up by theorizing profoundly on the then-blooming subject of artificial intelligence. While parts of this are dated by this point, much of it isn't, and that is a testament to Hofstadter's powerful intellect and foresight. As you may have guessed from my review's title, this is not a summer beach read. Admittedly I am not the world's fastest reader, but this one took me a few months to complete (I would often put it down for a stretch and pick it up again some time later). So take your time with this one - enjoy it, reread passages you didn't understand the first time, and maybe pick up a different, easier book when you feel bogged down. But for anyone with any interest in mathematics, computer science, or the philosophy of the human mind, this is a must-have and well worth all the time you can give it. (Review Data Last Updated: 2006-11-02 01:44:11 EST)
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| 06-13-06 | 4 | 0\8 |
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I spent a good part of the day yesterday beggining a reading of GEB and was fascinated at the way Hofstadter looked at language and Bach's canons and fugues. And there is much to come, I can tell. Although I consider myself an intellectual, I am not qualified enough in mathematics to really understand what is being said on the subject, but hope that Hofstedter is going to open that up for me, too.
(Review Data Last Updated: 2006-11-02 01:44:11 EST)
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| 06-06-06 | 5 | 2\2 |
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It's the gifted individual who can make math fun: it takes a complete master to do the same with Godel's Theorem.
Godel, Escher, Bach was first recommended to me by my piano accompanist three years ago. I flipped through it--it looked too bizarre and eclectic to bother with. Three years later, when I finally did start reading it, I couldn't put it down. Hofstadter is entertaining, fascinating, earnest, and--above all--unbelievably clever. The puns littered throughout, the triple-decker meanings, the symphonic weaving of the work is enchanting from start to finish. I can't imagine anyone not gaining something from this book, not seeing the world differently after it was finished. Logic seems different to me, music different, truth and math and reality different. And there are moments of just the purest wonder within, moments when I felt almost hyponotized, ready to find out that I was a character within somebody else's book, maybe a Djinn or a God Over one. I admit that even in this easily digestible presentation, I couldn't fully understand the Godelian proof--though I grokked the gist of it. It's no matter though--there's so much within here that I won't spell it out or explicate it, only point out that it is what is claims to be: a synthesis of the three titular men, a work of gold. (Review Data Last Updated: 2006-07-10 19:53:07 EST)
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| 06-05-06 | 4 | 5\5 |
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GEB: an Eternal Golden Braid is a difficult book to explain. It's a book about strange loops, recursivity, paradox, number theory, formal systems, molecular biology, Zen Buddhism, impressionism, and fugues. These concepts are introduced through the works of mathematician Kurt Gödel, artist M.C. Escher, and composer J.S. Bach, as well as some other supporting characters, like Charles Babbage (the first one to think of an Analytical Engine, a mechanical device for churning out algebraic theorems) and Alan Turing (of Turing Test fame). And then, of course, there are the dialogues, populated by the Greek warrior Achilles, a tortoise, a crab, and an anteater. Out of this confusing mess of concepts Hofstadter attempts to grapple with a truth he feels lies at the heart of Artificial Intelligence and Human Consciousness--that it forms from the same tangled hierarchies as Gödel's Incompleteness proof or Escher's "Print Gallery" or Bach's "Canon per Tonos" (a theme that changes notes according to a fixed system that somehow always returns to its starting note, one octave higher in pitch).
Much of the book deals with formal systems--meaningless symbol-shunting procedures for producing theorems from axioms--and the way they are mapped on to "truths" about the world (what Hofstadter calls "isomorphisms"). One of the most extensively used formal system in the book, dubbed TNT for `typographical number theory' (also as one in a series of Hofstadter puns, as TNT, when joined with a process called Gödel Numbering, tends to self-destruct), which is just a new way of expressing simple number-theoretical truths (such as the commutativity and associativity of addition; i.e., b+c=c+b and b+(c+d)=c+(b+d)). Strange loopiness enters formal systems when they can express Epimenide's paradox, a single sentence that reads "This sentence is untrue." Hofstadter explains how this realization came to pass when a German mathematician named Kurt Gödel discovered inconsistencies in Bertrand Russell and Alfred North Whitehead's "Principia Mathematica", a treatise meant to banish self-reference in set and number theories. Any formal system capable of expressing all number-theoretical truths can also be used to represent itself through a system of Gödel Numbering, which is just a way of interpreting symbols in the formal system as large numbers. Any formal system powerful enough to represent itself through Gödel Numbering can make the statement "There is no theorem with Gödel Number G'", where G' is the Gödel number for that statement. In other words, a powerful formal system will inevitably make claims that are paradoxical, inconsistent whether you call them true or false. Hofstadter combines the strange loopiness of formal systems with the concept of isomorphisms to come to some conclusions about human consciousness. First, he claims that the brain has a formal system for representing concepts in the world that exhibits self-reference and self-modification in a tangled hierarchy, just like the simplified formal systems he introduces in the book, Escher illustrates, and Bach incorporates into his music. He takes his time making his case, ending each chapter with a dialogue between Achilles and a Tortoise, a convention Zeno used to prove the impossibility of motion, and Lewis Carroll burrowed in his Two-Part Invention. These dialogue's are usually esoteric and highly amusing, including a series on Achilles' record player and one of the Tortoise's records designed explicitly to create vibrations that destroy the record player. This is a parallel to the explosive self-repudiation of TNT--any record player that can produce a high fidelity representation of the magnetic strips on the record will destroy itself, and any record player that can't is useless as a record player. Another dialogue introduces an anteater who converses with an ant colony that is collectively cognizant, even if each individual ant isn't (a parallel to meaning arising from meaningless formal systems of neuron representations in the human mind). In the main text, Hofstadter introduces the reader to the computer languages of Bloop, Floop, and Gloop (Gloop is just theoretical, a self-altering program reminiscent of the tangled hierarchy of the human mind), simple programs designed to reproduce themselves (an analogue to strings of DNA that encode for DNA synthesizing enzymes), and the Zen concept of MU (where neither `yes` or `no` suffice, say MU, or `unask the question`). Fans of M.C. Escher will want to take another look at his "Print Gallery", a picture of a man looking at a picture of a town that contains the gallery the man is in, and the picture he's looking at. This is a tangled bit of self-reference has a blemish at the lower right-hand corner of the picture frame (the picture frame in the print, which is in the center of the print). In this blemish M.C. Escher writes his signature, but Hofstadter points out that the "blemish" is an inescapable side-effect of the self reference. No consistent image could appear in that blemish, just as no consistent interpretation of Epimenide's paradox is correct. Human's don't have privileges access to the formal system of their representations of the world--the inviolate level of human consciousness is off-limits to our perception. "From this balance between self-knowledge and self-ignorance comes the feeling of free will (p. 713)," says Hofstadter. This is the central idea of his book. Formal systems are ubiquitous, and powerful formal systems exhibit tangled hierarchies. The human mind is no exception, and the "blemish" of human consciousness is that inevitable bit of self-ignorance that gives us free-will. By breaking it down to the saliencies of a formal system, Hofstadter has high regard for the prospects of Artificial Intelligence, which ought to be able to build upon a similar edifice. This is a difficult book to read and understand. It's deeply compelling and reads differently each time. I recommend it to those who have a lot of time on their hands. (Review Data Last Updated: 2006-07-10 19:53:07 EST)
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| 02-21-06 | 5 | 4\4 |
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Wow, this one was a mental workout. The book is very enjoyable, but light reading it ain't. It's amazing how many meanings/interpretations he can give to a single word/symbol of his own book. In a way, of course, that's what this book is about, how words mean instead of what they mean. One effective way to get that across is to reinterpret a single symbol multiple times.
Hofstadter deftly combines heavy speculation on the nature of intelligence with a bizarre sort of humor that will have you convulsing with laughter from its sheer unexpectedness. This book's greatest virtue also makes it difficult to do justice in review. It's so tightly woven together that you can't draw out a single thread to illustrate its quality. (Review Data Last Updated: 2006-07-05 01:39:54 EST)
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| 02-12-06 | 5 | 3\3 |
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I read this book in a seminar earlier this year. I was fortunate, because I'm not sure I'd have been brave enough to read this book on my own. GEB is an incredibly cerebral creation, and not for the faint of heart. It's without a doubt the most challenging thing I've ever read, but also the msot rewarding.
The core of the book is to explicate the complex mathematical theorem of the incompleteness of formal systems in mathematics, something which a lot of math majors don't even understand. I don't really get it either, but even if Godel's Theorem surpasses you, the other concepts presented in this book make it well worth the read. It changes your brain, and the concepts I learned while reading it are ones I find I encounter again and again. It's not just about mathematics; on the contrary, the book is written in such a way that non-mathematicians can understand. It's kind of like core concepts of life through a mathematical lens. If you're willing to put in the time and effort, you won't be disappointed with this book. Even if it does have you bashing your head against the wall sometimes. (Review Data Last Updated: 2006-07-05 01:39:54 EST)
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| 02-01-06 | 5 | 9\9 |
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Overall, the book looks at the author's views on how consciousness and a sense of self can arise from what is nothing more than the mind, a collection of neurons that follow fairly precise rules at a granular enough level. How can something as complex as a symphony be produced by what is nothing more than a collection of cells?
What made the book such an enjoyable read was the author's ability to meld these three individuals' lives (Godel's, Escher's, and Bach's) and work together into a seemingly finely interwoven mosaic. In virtually every chapter there's multiple works by Escher that, upon seeing them within the context of the chapter's topic, makes you think Escher created that work for Hofstadter's book. Similarly, I learned a lot about music structure and the little games and slieghts of hand Bach's works contain. One unique thing about this book was the structure. Between each chapter the author included a dialog between, typically, Achilles and the Tortoise. These two chums would have discourses on topics that played into the material presented in the following chapter. These dialogs are worth the price of admission alone. In particular the Crab Canon is a piece where a new character, the crab, is introduced, and he has one line right smack dab in the middle of the dialog. The first half and second half of the dialog, however, are identical in words, but shifted in meaning. For example, the dialog starts with Achilles saying, "Good day!" as a greeting, and ends with the Tortoise saying "Good day!" as a goodbye. It's amazing how well it all works together. (You can read this particular dialog in its entirety here - http://www.barryland.com/canon.html) In music, a crab canon is a kind of canon in which one line is reversed in time from the other (e.g. FABACEAE <=> EAECABAF). Hofstadter explores these ideas in part by looking at Goedel's incompleteness theorem, which states that given a complex enough of a formal system (such as number theory), there are theorems in the system that are true but cannot be expressed in the system. In other words, interesting formal systems are incomplete. The canonical example used to illustrate Goedel's theorem is the statement, "This sentence is false." Goedel's theorem is founded in number theory, not English, but the point is that given a complex enough system, there are things that are "beyond" the system. The chapters I enjoyed included: * The one on Zen Buddhism, which I knew little to nothing about beforehand, but like the explanation that the author provided. Sounds like a very interesting philosophy. (How honest/complete an overview the author gave, I don't know, not being familiar with the philosophy myself.) * The chapters describing the basics of the cell, how cell's replicate and how DNA, RNA, mRNA, and ribosomes work together to create the proteins used by the cell. * The final chapter, as it posed many open-ended questions about "strange loops and tangled hierarchies" (a concept discussed throughout the book) in everyday life. Overall, I would highly recommend this book to those who are interested in a discussion on what might constitute consciousness, thought, the soul, and existence, and how these concepts can be materialized from lower-level mechanical processes. Furthermore, the author examines how he views things like true artificial intelligence - a computer with a soul, with a sense of self - would have to be accomplished. Understand that the author does not get to these concepts right off; rather, he spends significant time building up the base of understanding to have a discussion on these topics, and the topics are not fluff ones. At times it can take several minutes just to get through a single page (at least for me). But if you put the time in, I think you'll reap the reward by the book's end. Personally I liked every chapter except for the few close to the end that detailed the "progress" in AI research. (I use "progress" in quotes because this book was written back in 1979.) (Review Data Last Updated: 2006-07-05 01:39:54 EST)
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| 12-08-05 | 5 | 9\9 |
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I first read the 1979 edition of this book in 1988, and have been dipping into it periodically for insight and edification ever since. Its richness and depth defy adequate description in a short review.
Hofstadter uses the music, mathematics, and art of the three title figures, as well as examples, concepts, and metaphors from diverse domains such as physics, genetics, computing, language, propositional calculus, Zen Buddhism, artificial intelligence, formal systems theory, and a whole lot more, in order to elucidate such notions as meaning and form, pattern, theoremhood, self-reference, and strange loops. It's a roller-coaster-ride of astuteness and wisdom, and some of the insights such as "Isomorphisms Induce Meaning" simply blew my mind when I first grasped their impact. What makes the book even more special is that it is written with humour, and employs storytelling in the form of dialogues between Archilles, the Tortoise, and the Crab. I recommend it without reservation. For me it was more than a learning experience, it was a formative one. (Review Data Last Updated: 2006-07-05 01:39:54 EST)
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| 12-01-05 | 5 | 7\7 |
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You might have been recommended this by a friend, or come across web recommendations. Almost everyone gives it more than 5 stars! But...
you can think of many reasons why you do NOT want to read this. There is lots of maths (it is a book about maths!?), it is loved by geeks, and it seems to cover too many things (consciousness, intelligence, reductionism, holism, recursion, self and soul!)... You don't know if you want to start on an epic 700 page book about abstruse stuff right now. Perhaps later. Hold it! You can enjoy this book just because of the brilliant writing, the puzzles and wordplay that make it a dream of Renaissance-style writing. The Rule of Four, Hypnerotomachia, Name of the Rose etc can't match this brilliance. I suggest a really easy way to start this book: Read a dialogue. Each chapter has an opening dialogue: Tortoise and Achilles and a few others spar; their verbal wizardry opens up new worlds; each is set to music, imitating the style of a Bach piece so closely you can almsot hear the music while you read. The main chapters discuss the serious stuff seriously. A typical dialogue is less than 5 pages; so give it a quick try NOW.... see if you enjoy the heady mix of literature, puzzles and deep stuff! My favourite is Crab Canon.. this was the first bit written, the whole book was written around it. Crabs (supposedly) walk backwards; see the illustrations (Escher's art, Bach's score, both called Carb Canon) upside down, and then .. read the dialogue backwards. Here it is: http://www.barryland.com/canon.html Or try "Sonata by Unaccompanied Achilles": this has a couple of lovely little puzzles. http://www.rdegraaf.nl/index.asp?sND_ID=141084 Or, ... oh! there's so many little gems to recommend. And if you like the first dialogue you read, get the book. Then read the preface, and then read the dialogues - in order - and skip the chapters .. till later. That makes it a great fun read.. and a short book in itself! Then having enjoyed yourself, read from the beginning and enjoy the whole thing afresh... at yor own pace. I read the dialogues quickly, and absorbed the book over a year, solving word and logic puzzles, tripping over imagery and more ... So, have fun with this great book. It might change your life, as it did mine. (Review Data Last Updated: 2006-07-05 01:39:54 EST)
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| 11-07-05 | 5 | 20\21 |
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There is so much more to GEB than its primary goal: the explication of Godel's famous incompleteness theorem. The interplay of Godel's work with that of Echer's and Bach's involves self-reference. In Echer's work we have a hand painting a hand which is painting the original hand, or a pertual waterfal system. In Bach's fuges the music builds into a complex structure of overwhelming beauty from the repetition of a simple motif: think row, row, row your boat, except it's the Tocata Fugue!
Kurt Godel, who hung out with Albert Einstein at Princeton, "killed" mathematics early during the previous century. He demonstrated that sufficiently large systems that refer to themselves (as is the mathematics of the integers) will have true statements that cannot be so proven within the confines of the system. One can expand the system, prove what couldn't previously be proven, but the new system will suffer the existence of new, true but undemonstrable statements. Alan Turing, thinking about how one could decide if a computer program would either terminate, or suffer endless looping, derived the same conclusion from a computer science point of view. At the heart of this, is the debate on whether a machine can ever be made truly sentient--Hofstadter believes so, and makes his case convincingly in my opinion. You will definitely learn from this entertaining book, written to be accesible to wide audience. Alex Alaniz 1. Please see the reviews of my own strong science fiction book: Beyond Future Shock about the near-terms perils and promise of advanced bio/nano technology in a world still roiled with Middle Age religious conflict and ever growing extreme wealth gradients. 2. I have REVIEWED many books from undergraduate to graduate in: PHYSICS, MATH, ECONOMETRICS, and HISTORY among other areas. (Review Data Last Updated: 2006-07-05 01:39:54 EST)
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| 11-07-05 | 5 | 14\14 |
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There is so much more to GEB than its primary goal: the explication of Godel's famous incompleteness theorem. The interplay of Godel's work with that of Echer's and Bach's involves self-reference. In Echer's work we have a hand painting a hand which is painting the original hand, or a pertual waterfal system. In Bach's fuges the music builds into a complex structure of overwhelming beauty from the repetition of a simple motif: think row, row, row your boat, except it's the Tocata Fugue!
Kurt Godel, who hung out with Albert Einstein at Princeton, "killed" mathematics early during the previous century. He demonstrated that sufficiently large systems that refer to themselves (as is the mathematics of the integers) will have true statements that cannot be so proven within the confines of the system. One can expand the system, prove what couldn't previously be proven, but the new system will suffer the existence of new, true but undemonstrable statements. Alan Turing, thinking about how one could decide if a computer program would either terminate, or suffer endless looping, derived the same conclusion from a computer science point of view. At the heart of this, is the debate on whether a machine can ever be made truly sentient--Hofstadter believes so, and makes his case convincingly in my opinion. You will definitely learn from this entertaining book, written to be accesible to wide audience. Alex Alaniz (Review Data Last Updated: 2005-12-05 09:54:13 EST)
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| 10-24-05 | 5 | 6\8 |
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This is an incredible book. Not only does it make the maze of modern physics, mathematics and philosophy more comprehensible, but it pulls all disciplines together in a wonderful mix of various formats, from dialogues to pictures to complex explanations. The beauty of this all is that you can dip in at any part and find something interesting and inspiring. If you don't get on well with the explanations, try some dialogues, or read the author's commentary about the pictures. If you have time to work through the whole book, it will be well worth it.
As an ex-music student, I found the "Bach" sections less convincing than the rest, but I agree that Bach was quite a mathematician as well as being a musician and a composer. To link his work and his name with John Cage is quite something, but the author pulls it off. I also like the way that these great names are brought together and shown to be speaking about the same things - a universality that perhaps is at theheart of this book. Very much recommended for a user-friendly exploration into sicentific, musical, mathematical, and philosophical ideas. (Review Data Last Updated: 2006-07-03 18:09:31 EST)
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| 09-16-05 | 5 | 0\14 |
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On rare occasions, a work comes along that has monumental implications for the worlds of art and/or science. The reader is simply enveloped by the breadth of the work and the shear love of - oneself. If I could be so bold as to paraphrase Hofstadter, "Ya edit uh textbook, fer cryin' out loud; not a dang master-freakin'-piece (sniff)."
Hence, we have two (of many) issues. Firstly, in this, the 20th anniversary edition, it could have used some editing - perhaps down to the Cliff's Notes version. And secondly, Hof provides a rather lengthy Preface to the book letting us - the unwashed masses - in on what it's about. Apparently, according to The Hoffer, the first 20 years' worth of readers had no idea. Go figger. The book is apparently for a subset of computer science geeks, like myself, except the ones that have had the lobotomy. We can only hope that for the 40th anniversary edition the Preface to the Preface describing what the 20th anniversary Preface was about, doesn't exceed the length of the book; and that The Hofster tapes a quarter to the dust jacket in order to garner some interest on the Closeout table at the bookstore. My advice is to wait for the movie - on DVD... (Review Data Last Updated: 2006-06-20 09:42:13 EST)
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| 08-31-05 | 5 | 3\23 |
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