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Douglas Hofstadter

Godel, Escher, Bach

Gödel, Escher, Bach: an Eternal Golden Braid is Douglas Hofstadter's classic work on self-reference, and its application to the mind, music, art and of course Gödel's incompleteness theorem.

The book deals with the way things can be studied at several different levels - a mathematical proof may be just marks on a piece of paper, but it shows the reader that something is true. If there is interaction between different levels then this can lead to weird results. But this is all done in such a playful way that it makes even highly abstract ideas accessible to a wide readership. There are plenty of conversations between Achilles and the tortoise, as well as several of their guests (including the author himself). The book is now available as a 20th anniversary edition, and for this a new preface has been added but the main text of the book has been left as it was - Hofstadter explains in the preface why attempting to make any changes would have lead to writing a new book. (I felt he ought to have sneaked a request into the original text, supposedly from his younger self asking that his older self didn't make any revisions).

I think Gödel has the upper hand in this book - there are interesting ideas on music and art, but Escher and Bach tend to play the role of supporting characters. Hofstadter also explains in the preface some of his 'strange loop' ideas on the nature of the mind, which also tended to get hidden in the original book.

I didn't actually read Gödel, Escher, Bach until some time after it had been published, and I realised after I'd read it that I should have done so much earlier. There's no doubt about it - if you are interested in the puzzles and paradoxes of self-reference then this book is a must read.

Amazon.com info
Paperback 832 pages  
ISBN: 0465026567
Salesrank: 3755
Weight:2.65 lbs
Published: 1999 Basic Books
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Amazon.co.uk info
Paperback 824 pages  
ISBN: 0140289208
Salesrank: 4931
Weight:2.38 lbs
Published: 2000 Penguin Books Ltd
Amazon price £11.99
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Amazon.ca info
Paperback 832 pages  
ISBN: 0465026567
Salesrank: 7894
Weight:2.65 lbs
Published: 1999 Basic Books
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Product Description
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.
 
An Incredible Intellectual Romp *****
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.
 
Literate, Facinating, Readable *****
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.
 
My favourite book - ever! *****
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.
 
Abstruse and over-rated *
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.
 
Magnum Opus on Intelligence *****
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.
 
Engaging and mind bending *****
Even though it is old, it still holds all its qualities intact. To me it is the bible of everything that begins with "meta". It hovers elegantly around so many subjects and still ties them together into self-reference and I doubt anyone can help but be charmed. The challenges are put forward in such a playful manner that only the crankiest stick in the stickiest mud could not help but swaying their way. But be warned - it does take an effort - and all other books will feel both easy, shallow and... well... literally light by comparison.
 
A great intro to some profound mathematics *****
I read this when it was published back in '79 and it helped inspire me to more fully understand the massive achievments of Kurt Godel and his quite astonishing incompletness theorem.
For the casual reader, this is a wonderful book that will inspire you and give you a glimpse into the unsettling world of axiomatic set theory and it's uncany relationship to the music of Bach and the artistry of Esher.
 
Do buy this edition! *****
A wonderful book well worth reading.

I feel obliged to note that contrary to a previous review the book supplied to me had not lost '...the aesthetic appeal the previous editions had'. In fact the paper quality was not '...really bad' but rather good and the pages were certainly not '...almost transparent'. The book's size is very similar to a previous edition I have encountered and the margins are not smaller than they should be. I really cannot find fault with this edition of the book and strongly recommend that you buy a copy.
 
It is big and it is clever ****
This enormous book is a hymn to the "strange loop", a term coined by the author. Loosely, a strange loop occurs when, after moving up a level in a conceptual hierachy, one is brought strangely back to where one started. It's closely related to those paradoxes of self-reference which can occur when form and content become intertwined.

An example is the old joke about the park keeper angry that his park has been littered with leaflets entitled "Keep Britain Tidy". Another is building one computer system to test another computer system, and then needing a third system to test the one you've just built. Yet another is the Wikipedia entry of Douglas Hofstadter which, at the time of writing, contains a quote from Hofstadter stating that his Wikipedia entry is full of inaccuracies. (So, do you trust the entry enough to believe this quote claiming it's unreliable?) You get the idea.

Hofstadter sees these strange loops everywhere: in the music of Bach, the art of Escher and, most significantly, Gödel's incompleteness theorem, in which an algebraic system is used to prove a result about itself (rather than about numbers). After he's presented the various variations on these ideas, he then moves on to Artificial Intelligence, examining the "state of the art" as he sees it and discussing the implications of the earlier material for this subject.

Along the way he delves into various other diverse subjects such as the structure of the human brain or the challenges of translating a novel into different (human) languages. Much of this is fascinating stuff and if you are mathematically inclined, there is plenty to love about this book.

Given all the above, why not give the man 5 stars - what more could one possibly ask for?! Well, personally I have a number of objections to this work which I'll mention briefly before the crowd throws rotten fruit at me. Firstly, I am not sure that *all* Hofstadter's examples are on the ball. For example, the loop in Bach's "endlessly rising" canon is simply a consequence of there being 12 semitones in an octave, rather than any subtle paradox of self-reference. Similarly, the main theme from Bach's Musical Offering is not "Babbage" backwards, however you push it! In short, I suspect the author's obsessions can cause him to see patterns in the world around him which aren't really there.

Secondly, his would-be humorous writing style, quirky and lively though it is, will not be to everyone's taste ("Why, you don't say, Mr T!"). Thirdly, some readers will wish he had been more honest up-front about the book really being about AI (and something of a polemic, as evidenced by his almost mean-spirited attack on the philosopher John Lucas in several places): personally, it's not a subject close to my heart and I would have been rather more interested in delving into, say, what makes Bach's music beautiful and spiritual, as the cover suggests we will be doing. And fourthly, and most seriously, I am not convinced that Hofstadter is that great a pedagogue: the facetious style and inordinate length of the book can serve to obscure, rather than illuminate, his meaning.

These niggles notwithstanding, this book really is a fine achievement and, if you have the time and inclination (you'll need both in spades), likely to be a very rewarding read.
 
Brilliant! *****
Scientists seem to love quoting Alice in wonderland, as it seems applicable in so many fields. This book is a grown up version of Alice, an invaluable reference for anyone interested in the universe around them.
 
A wonderful read for all aspiring thinkers *****
The Atlanta Journal Constitution describes Gödel, Escher, Bach (GEB) as "A huge, sprawling literary marvel, a philosophy book, disguised as a book of entertainment, disguised as a book of instruction." That is the best one line description of this book that anybody could give. GEB is without a doubt the most interesting mathematical book that I have ever read, quickly making its place into the Top 5 books I have ever read.
The introduction of the book, "Introduction: A Musico-Logical Offering" begins by quickly discussing the three main participants in the book, Gödel, Escher, and Bach. Gödel was a mathematician who founded Gödel's Incompleteness Theorem, which states, as Hofstadter paraphrases, "All consistent axiomatic formulations of number theory include undecidable propositions." This is what Hofstadter calls the pearl. This is one example of one of the recurring themes in GEB, strange loops.
Strange loops occur when you move up or down in a hierarchical manner and eventually end up exactly where you started. The first example of a strange loop comes from Bach's Endlessly rising canon. This is a musical piece that continues to rise in key, modulating through the entire chromatic scale, ending at the same key with which he began. To emphasize the loop Bach wrote in the margin, "As the modulation rises, so may the King's Glory."
The third loop in the introduction comes from an artist, Escher. Escher is famous for his paintings of paradoxes. A good example is his Waterfall; Hofstadter gives many examples of Escher's work, which truly exemplify the strange loop phenomenon.
One feature of GEB, which I was particularly fond of, is the 'little stories' in between each chapter of the book. These stories which star Achilles and the Tortoise of Lewis Carroll fame, are illustrations of the points which Hofstadter brings out in the chapters. They also serve as a guidepost to the careful reader who finds clues buried inside of these sections. Hofstadter introduces these stories by reproducing "What the Tortoise Said to Achilles" by Lewis Carroll. This illustrates Zeno's paradox, another example of a strange loop.
In GEB Hofstadter comments on the trouble author's have with people skipping to the end of the book and reading the ending. He suggests that a solution to this would be to print a series of blank pages at the end, but then the reader would turn through the blank pages and find the last one with text on it. So he says to print gibberish throughout those blank pages, again a human would be smart enough to find the end of the gibberish and read there. He finally suggests that authors need to write many pages more of text than the book requires just fooling the reader into having to read the entire book. Perhaps Hofstadter employs this technique.
GEB is in itself a strange loop. It talks about the interconnectedness of things always getting more and more in depth about the topic at hand. However you are frequently brought back to the same point, similarly to Escher's paintings, Bach's rising canon, and Gödel's Incompleteness theorem. A book, which is filled with puzzles and riddles for the reader to find and answer, GEB, is a magnificently captivating book.
 
A readable Mobius strip *****
If you have never read this book, then I'd like to say that it has a lot of the most greatest knowledge out there. It doesn't just deal with math, art, and music, but also with zen, philosophy, self-ref, self-rep, holism, reductionism, and everything else that is considered pure knowledge of cognitive science and general intelligence. I don't know why some of the people rating it have no idea of what's it about; it's not about Godel's theorem like many think it is, it's about consciousness and how the power of the mind and the "I" comes out of the inanimate matter that creates us. That's not it, the second part of the book talks about computer programming and AI. Can a computer program ever have a sense of self or compose meaningful music? Hofstadter's response to the second one was: "Only if that AI could go through the maze of life on it's own, fighting it's way through it and feeling the cold of a chilly night, the longing for a cherished hand, the inaccessibility of a distant town, the regenaration after a human death, the...and only then can it be considered to do so."
This book really has more than that. I can't say all of the things mentioned in it, not in this tiny little review, but I can say that you should probably read it and hopefully understand it because it truly is a masterpiece.
 
Pseudo-science at best *
I quite agree with the reviewer from East Hartford. Maybe I am not extremely eligible to comment on the portions dealing with Escher and Bach, respectively (I have no appetite for Escher. I like chamber music of Bach and somtimes play his keyboard music but my performance level is, of course, that of amateur.)
But I must say the part dealing with Gödel's Theorem of Incompleteness is *complete garbage*. I am convinced anyone with a degree of mathematics will agree with me: for those who have no background in mathematics, I assure you that Gödel's theorem concerns a problem in "formal logic" and has nothing to do with human-cogno-something.
If this book were meant to be a cult literature, that would be okay: I don't care anyway.
But if this is meant to be an entertainment for people with no scientific background, I rate this alchemy or pseudo-science at best.
 
A book that is about more than Godel, Escher, and Bach *****
This book is an excellent introduction to several ideas in cognitive science, biology, mathematics, linguistics, computer science, art, and other fields. It cleverly reveals how different fields influence each other in a cross disciplinary fashion and actually "embeds" this structure inside the book. I won't go into more detail, but as soon as you read the book, you will see how this is done. The writing is crisp and engaging, almost as if Lewis Carroll, Noam Chomsky, and your favorite professor in college gave birth to a book. The concepts are revealed through parables, koans, and other forms involving characters named Tortoise, Achilles, and Crab and at one point involve a metagenie.(...)

The only criticisms that I have about the book are
1)Some radically new things have been discovered/done in many of the fields discussed in the book, especially artificial intelligence. The book doesn't talk about some of these developments, and some of the statements in the book are inaccurate or outdated (ex: chess playing computer that can beat human will never be built, replication in biolgy is A LOT more complicated/different than its rather cursory rendering in this book)
2)This book is more helpful as an introduction to spark your interest in various topics than a detailed guide to the many interesting ideas that have arisen in science. After reading about concepts in the book, if they are interesting, it would be helpful to read a more detailed and recent book on the topic.
3)Sometimes, but not usually, the author's desire to be witty or find connections overwelms the actual truth of his statements--at these points the connections made are rather weak.

 
Pretty good book! *****
I haven't really heard any hype about the book (a lot of the other reviewers are saying the book doesn't live up to its hype). I'm about 2/3 through, and it's really interesting! I'm not really sure what the message is, but I just like that it makes me think about interesting things. I'm an undergrad student doing a summer research project in math, so when I get a bit tired of really rigorous math, this is a nice break for me, but it still keeps me thinking.

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