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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: 2950
Weight:2.45 lbs
Published: 1999 Basic Books
Amazon price $15.61
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Amazon.co.uk info
Paperback 824 pages  
ISBN: 0140289208
Salesrank: 5913
Weight:2.38 lbs
Published: 2000 Penguin
Amazon price £12.23
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Amazon.ca info
Paperback 832 pages  
ISBN: 0465026567
Salesrank: 30137
Weight:2.45 lbs
Published: 1999 Basic Books
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Product Description
This groundbreaking Pulitzer Prize-winning book sets the standard for interdisciplinary writing, exploring the patterns and symbols in the thinking of mathematician Kurt Godel, artist M.C. Escher, and composer Johann Sebastian Bach.
 
Good, but not great ****
I've read this book, on and off, over the better part of the last 4 years. It is certainly a fascinating read, the kind of book that effortlessly discusses everything from computers to art, from paradoxes to physics, from philosophy to tortoises, and seemingly everything in between.

However, the reason I don't give it a 5/5 is that I didn't think that it all ever really coalesced into any singular idea. Other reviewers see it as a profound meditation on the concept of consciousness or something. To me, it just seemed like a hodge-podge of neat stuff. Not that there's anything wrong with that, but I think if you go in expecting a revolutionary work, you might be a bit disappointed.

Still, it's such a hefty book, its easy to recommend as a sort of "desert island" kind of book. It's not just the thickness of the book, but the sheer density on each page. Most chapters contain logic games and stuff which you really should try out if you want to get the most out of the book. It's not the kind of book that you can just zip right through. Taken purely as a value proposition it's hard to beat the amount of insight and entertainment this book provides.
 
I thought I was wrong but I was mistaken ... ***
Finally finished it! It's entertaining to visit the realms at the edge of human understanding. There are plenty of excellent reviews well before mine but I feel compelled to write a review none the less to celebrate the long read's conclusion. From a technical standpoint, much of the 'controversial/interesting' material feels overcome by the 2 decades and more since the writing. Although the topics are 'better understood now, the new understanding gets us no closer to an explanation. Proceeding time has not answered the same underlying questions. We are no further along in our quest for understanding `understanding'. If anything, the mystery has deepened.

Gödel's incompleteness theorems may be taken for granted by Hofstadter from my understanding and reflection but it's not fatal. If you take Gödel straight up ... mathematics and numbers might never be understood, let alone proven. Our minds have great difficulty constructing vocabulary to rationalize mathematics. That's not `news'. The multiplicity of examples and variants that Hofstadter provides regarding this subtle reality of human understanding are fun. I suppose we all comprehend the fuzziness that words contribute or fail completely in communicating mathematical constructs. Hofstadter reinforces the notion that we can't put our finger on our mind's dilemma with the exactitude we desire. I came away with a better appreciation that I'm not alone in the quagmire.

Many, many years ago, I simply enjoyed the whimsy of Escher's art. As a young physicist, I had not come to appreciate the relationship between "art" with science beyond the medium. The curious and repetitious appearance of unconscious ratios in non-mathematical, natural and abstract contexts does `feel' a bit (should I say it?) unnatural. The golden ratio, Fibonacci numbers, Euler characteristics, omega constant, etc affect everything but nothing that can be verbally expressed. Why? No idea. It just does. Hofstadter expresses this `feeling' perhaps as well as we can elucidate it.

Bach ... I got it! I enjoyed Hofstadter's excursions with Bach. Why? ... I was a terrible piano student. I didn't get it. My sister did. It bothered me to no end as a kid. Some few years ago I ran across a detailed Pythagorean statement about how tone/music is recognized as concordant and related by small integer ratios. It was magic to my mind. I'm ready to try again. It seems so simple!

Hofstadter uses narrative `gimmicks' (for lack of a better word ) to link the Gödel, Escher and Bach theme into vertical and horizontal systems and system of systems that may or may not withstand peer review. That's not really the point. I'd call it mind fertilizer ... lots and lots of it.

And that's my criticism ... the read is massive. You have to want to press on through verbosity and detours. It's a book that I would imagine not every reader will preserver to finish. I must admit I was almost one.

In reflection upon the six months or so that I took to read it I'd say it was worth it. There will be times that you'll ask yourself why you ever picked the book up. It's mind candy ... that's what it is.
 
Kindle watershed *****
I have been working as a professional software engineer and computer scientist for about 27 years now, and I can still point back to the college summer I spent reading this book as one of the most profound experiences in my intellectual life and a significant influencing factor in my choice of career. I own two original hardbound copies and another in paperback. I periodically reread sections of the book for a bit of nostalgic timetravel. But I must ask, where the devil is the kindle edition? I can load up my kindles with countless dry reads on number theory and I am quite thankful for that (iPad bookstore is a pure void in this regard) but good old GEB, of all books, has never made the jump. Please, Amazon, resolve this gap in the kindle library. Shall I be forced to develop a botnet purely for the purpose of generating a billion clicks on the "tell the publisher" link?
 
Don't let the math scare you *****
If you pick up a copy of GED and leaf through it, it might intimidate you to see pages and pages of extrapolated number theory formulations, but truth be told, you don't have to be a mathematician, or a member of MENSA to enjoy and appreciate this book. It wouldn't hurt of course, but Hofstadter didn't write GED to show off to his academic brethren, provide the syllabus for courses in math or computer science (although they do have an MIT course based on GED), or even to illuminate with searing insight, the work of Kurt Godel, MC Escher, and J.S. Bach. Hofstadter uses the work of those men (and others) in an attempt to explore a mystery.. perhaps the greatest mystery known to man..the mystery of intelligence and human consciousness. How does the hardware (human brain) interact with the software (intelligence) to produce the Self (consciousness), and what implications does this suggest for the development of what we call Artificial Intelligence?

A layman's understanding of Godel's incompleteness theorems would help in comprehending the key themes of this book, which illustrate connections to the graphic work of Escher, and the contrapuntal music of Bach as typified by his "Musical Offering". Hofstadter attempts to weave this remarkable braid of human ideas represented by number theory, visual art, and music, pointing to the self referential (recursive) aspect of each and the resultant "strange loops" which are keys to understanding human thought processes. GED is loaded with puzzles and brain teasers, both visual and mathematical, concrete and abstract, which lead us down the path to making some sense of it all. Aside from music, art, and mathematics, GED references computer science, language, biology and psychology as well as people like Alan Turing, Charles Babbage, Rene Magritte, John Cage, Alfred Tarski, and Marvin Minsky, whose work help illuminate many of the points made in the book.

Another thing worth mentioning is the ingenious way the book is designed. The chapter preludes consist of dialogues between the Tortoise and Achilles (characters from Lewis Carroll's famous article) and they introduce us to the ideas of each ensuing chapter in clever and amusing fashion. Additional characters, such as the Crab, the Anteater, and the Sloth, act as mediators in some of those dialogues. Hofstadter entertains while he enlightens. The Crab Canon prelude to chapter 8 is nothing short of a tour de force. All told, GED is a work of brilliance, both challenging and uniquely thought provoking.
 
I just started this book, but Amazon is buggin for a review ***
This edition has a very lengthy "30 years since GEB" introduction added to it. That new intro was boring the crap out of me so I skipped ahead to the original start of the book. So far, within the first 10-20 pages, I've learned about what are effectively scientific discoveries in music, art and math. I wouldn't have thought there was so much to be scientific about in the realm of music, and the perspectives on the art and math discoveries was almost equally intriguing.
 
Stunning *****
I've just read over 100 pages therefore my opinion is based rather on first impressions than anything else.
Every now and then, I read books that are truly amazing. My last one was the The Kindly Ones from Littell (2006!).
GEB is an impressive masterpiece. My only regret: not finding out about this book before...
Go on, get it!
 
Fantastically in-depth, whilst still light enough to enjoy reading if you don't understand it all! ****
I have to admit that this book was sitting on my bookshelf for a while before I started reading it. In fact, I think it was about three years (I hadn't heard of the book's reputation, and so wasn't aware that I shouldn't have been intimidated). Once I got going, however, it was immensely enjoyable. The book covers a wide range of topics (number theory, art, consciousness and so on...), all of which are beautifully intertwined, as the title suggests. Some of the maths is pretty heavy going, I can't claim to have fully understood it on a single read, and I didn't do as the book suggested and worked through some of the examples (which would undoubtedly have made later ideas easier to understand), but even so, there is so much else in the book that it really doesn't matter. Different chapters tend to deal with different themes, so maths doesn't enter them all, and all are preceded by a dialogue which sets up the theme and keeps the mood light. These are beautifully crafted, with many hidden meanings, and, once again, probably require several reads to spot all the layers of meaning (however, a single read will illuminate several of these). The dialogues are so well-written, in fact, that they really kept me reading, as I was determined to plow through some of the heavier stuff to get to the next one.

Overall, I thoroughly enjoyed reading this book and look forward to coming back to it at some point in the future to see what else I can get out of it.
 
This will make you think *****
Like no other book I've read before, Godel, Escher, Bach really made me think. An incredibly clever author, dealing with hard to explain issues (- consciousness and identity primarily), Hofstadter still manages to keep the reader interested and entertained (mostly) throughout. Having said that, it's not an easy read or a relaxing read- I felt like I'd been put through a gruelling mental workout after most chapters. But... no pain, no gain I suppose, as the rewards are well worth it in the end.
 
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.
 
Brings back memories. ****
I bought this because I remember browsing through it when i was a teenager, and found it intriguing, even though I didn't understand most of it at the time, and didn't even come close to reading it all. So, currently being a little "wannabe" erudite, I figured I'd give it another look, from a more experienced perspective.
 
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.

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