Bach: An Eternal Golden Braid, Escher, Gödel
ByDouglas R. Hofstadter★ ★ ★ ★ ★ | |
★ ★ ★ ★ ☆ | |
★ ★ ★ ☆ ☆ | |
★ ★ ☆ ☆ ☆ | |
★ ☆ ☆ ☆ ☆ |
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Readers` Reviews
★ ★ ★ ★ ★
tucker
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.
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.
★ ★ ★ ☆ ☆
smrati thakur
On reading Iain Mcgilchrist' Master and his Emissary, I see the trouble with this sort of book. Douglas R. Hofstadter is a classic left brain sort of guy.
I won't get into all this here, but I will like to mention that the implications of the brain science will never be accepted.
Sam Harris talks about this in his latest book. Harris says that we accept wacky ideas like AI and parallel universes and we even accept that we have no free will (from brain science), but the idea that we can be half blind (also from brain science) will, by definition, be not noticed, let alone accepted.
So is Hofstadter half blind? If we see with our brain, and not the eyes, then sure!
Many 1 star reviews have pointed out that this book is way too long and very self indulgent. I bought it anyway. Douglas R. Hofstadter has written a feast of ideas and brilliance and the book is packed with artwork. I even enjoyed the dialogues. Unfortunately, Hofstadter has trouble getting to the point. Imagine a man telling you a joke, but to never getting to the joke? This is what this book felt like.
It isn't hard getting to the point. When Einstein said that he can explain his theory to a 7 year old, he meant that a guy who really knows, can encapsulate his position in a short and sweet manner.
We can reinterpreted what Einstein said bu saying that a right hemisphere guy can explain it to a 7 year old. A left hemisphere guy will go on and on.
Iain Mcgilchrist writes that a left hemisphere guy will enjoy pages upon pages of tight logical, almost algorithmic, excess, but he can never 'just say it'. You don't need an entire page to quote an 18 century man talking about the promise of a machine being able to beat J.S. Bach at music, followed then half a page quoting a guy who reckons the music of J'S Bach is not reducable to an algorithm because of the transcendental element contained (think Godel here). Just say it in one page man! Also, the page long quotes are in a very small font, thus, the book should have been even thicker!
Kurt Godel's theorem, and why it matters, and the overthrow of the apparent truths of Euclid, which is more important that Godel, and the transcendental will one day be explained in under 200 pages and become a best seller. Alas, people who know about those things probably won't need to dive into this book and those who don't know will only get frustrated by a thick jungle of words and logical symbols.
If Douglas R. Hofstadter had something else to say in this big book, he should just say it!
Overall this book feels like, well, have you ever watched one of those documentaries about those annoying child prodigies who can do advanced tensors, flip pancakes, and read a thick book in 22 minutes whilst talking to the camera? Well Douglas R. Hofstadter was one such prodigy. In love with his brilliance, and informing the reader that as a little boy, he could think in French and in English at the same time, Hofstadter's genius shines.
I won't get into all this here, but I will like to mention that the implications of the brain science will never be accepted.
Sam Harris talks about this in his latest book. Harris says that we accept wacky ideas like AI and parallel universes and we even accept that we have no free will (from brain science), but the idea that we can be half blind (also from brain science) will, by definition, be not noticed, let alone accepted.
So is Hofstadter half blind? If we see with our brain, and not the eyes, then sure!
Many 1 star reviews have pointed out that this book is way too long and very self indulgent. I bought it anyway. Douglas R. Hofstadter has written a feast of ideas and brilliance and the book is packed with artwork. I even enjoyed the dialogues. Unfortunately, Hofstadter has trouble getting to the point. Imagine a man telling you a joke, but to never getting to the joke? This is what this book felt like.
It isn't hard getting to the point. When Einstein said that he can explain his theory to a 7 year old, he meant that a guy who really knows, can encapsulate his position in a short and sweet manner.
We can reinterpreted what Einstein said bu saying that a right hemisphere guy can explain it to a 7 year old. A left hemisphere guy will go on and on.
Iain Mcgilchrist writes that a left hemisphere guy will enjoy pages upon pages of tight logical, almost algorithmic, excess, but he can never 'just say it'. You don't need an entire page to quote an 18 century man talking about the promise of a machine being able to beat J.S. Bach at music, followed then half a page quoting a guy who reckons the music of J'S Bach is not reducable to an algorithm because of the transcendental element contained (think Godel here). Just say it in one page man! Also, the page long quotes are in a very small font, thus, the book should have been even thicker!
Kurt Godel's theorem, and why it matters, and the overthrow of the apparent truths of Euclid, which is more important that Godel, and the transcendental will one day be explained in under 200 pages and become a best seller. Alas, people who know about those things probably won't need to dive into this book and those who don't know will only get frustrated by a thick jungle of words and logical symbols.
If Douglas R. Hofstadter had something else to say in this big book, he should just say it!
Overall this book feels like, well, have you ever watched one of those documentaries about those annoying child prodigies who can do advanced tensors, flip pancakes, and read a thick book in 22 minutes whilst talking to the camera? Well Douglas R. Hofstadter was one such prodigy. In love with his brilliance, and informing the reader that as a little boy, he could think in French and in English at the same time, Hofstadter's genius shines.
The Hero with a Thousand Faces (The Collected Works of Joseph Campbell) :: Reflections on the Art of Living (The Collected Works of Joseph Campbell) :: The Hero with a Thousand Faces by Joseph Campbell (2016-03-22) :: The Collected Works of Joseph Campbell - Myths to Live By :: A Romance of Many Dimensions (Dover Thrift Editions)
★ ★ ★ ★ ★
unfunnyjester
For me this book has become the "Book of the books"....how to say...? I mean, it is something more than a simple book that you can find in the open shelves worldwide. The book is `just' about self-reference and self-referential systems and Hofstadter explains you that self-reference is that fundamental `natural' law which moves everything, at every level of complexity as the human intelligence can recognize it: in music, mathematics, art, physics, genetics,...and so on. Hofstadter has the exceptional skill of making the reader to understand these concepts by means of lots of examples, simplified images borrowed from every field of human knowledge, just step by step towards the deep understanding of the so destabilizing Godel's Theorem of Incompleteness. "Gödel, Escher, Bach" is the book which makes you to think and to develop your thinking even beyond the contents of the book itself, trying to catch what should be the last and fardest level of the self-referential systems. The book is however structured in order to talk about artificial intelligence (AI) and how powerful such an intelligence can become if just we can really fully understand how our own brain does work, since AI is 'simply' a way for creating something perfectly imitating ourselves, without being God. And such a process is a so-called a 'strange loop', because we have to go inside our self for creating something outside it. In conclusion, the book represented for me something like "Wonderland" (actually, the reference to Lewis Carrol is a constant in the book), and more..., because once you finished it, you realizes that the book itself is a strange loop as well, and that you would like to start to read it again...and again....
★ ★ ★ ★ ★
maria swailes
Excuse me for the long-winded review. I have a lot to say. No one's forcing you to read this, but I think it would be useful for you to wade through.
I will begin by making two brief notes. Firstly, my 5-star rating does not imply that this book is flawless. I will expound on the book's flaws shortly. However, I do not believe that the flaws are enough to warrant subtracting a full star. I will even go as far to say that this book is fully deserving of its Pulitzer prize, and it has become one of my most treasured books in my extensive collection.
Secondly, I want to give some background about myself and I will explain why. I believe in subjectivity and I believe that the depth of one's background can reveal a lot about this book. The book jumps between many subjects, and if one has a weak background in one area, then we can assess the author's clarity. If one has a strong background in another area, then we can assess the author's accuracy and even pinpoint areas where he is inaccurate or presents questionable results. So I will mention my background in regards to the relevant areas. These areas are: Mathematics, Logic, Artificial Intelligence, Art, Music, Biology, Neurology, and Zen Buddhism.
My background:
Fairly strong: Mathematics, Logic
Intermediate: Biology, Zen Buddhism (studied, not accepted), Artificial Intelligence
Minimal, but existent: Music Theory (barely), Neurology (as much as my AI studies have revealed to me)
Nil: Art
Degrees, research, areas of emphasis:
ABD in Statistics (Ph.D. in about 2 years hopefully) - Highly mathematical research area (essentially a high-dimensional Euclidean geometry problem in a statistical framework)
BA in Mathematics - Numerical Analysis
BS in Computer Science - Parallel Computing, Neural Nets, Truth Maintenance Systems
Field experience in microarray analysis and immunology.
The areas of emphasis for my undergraduate degrees should be taken with a grain of salt. I completed no respectable research in those areas.
With that out of the way (we will return to the importance of that shortly), let us figure out what in the world this book is about, and that is one question that has evaded many. I see an intended purpose in the book, and an important implicit one. Here, the path is as important as the goal. According to the author, the book is about how animate beings can come from inanimate matter. That is, it is about how minds and consciousness can come from something as material as a brain, and how true A.I., one that is conscious, is plausible.
The implicit meaning of the book deals with structure and meaning. While building up to the end goal, the author discusses, within the context of the areas that I already mentioned, the nature of structure and meaning. How does meaning arise? Why are we quicker to attach meaning to structures than to atomic elements, yet recognize that there are "meaningless" structures? When and how does meaning come into play? How do structures result from processes? How are self-reference and self-replication possible and what role do they play? These questions and their possible answers are what make this book captivating. The author, though he doesn't "prove" much, illustrates these concepts through beautiful, meaningful examples, and most of his arguments are both eloquent and quite convincing. I will say that I learned MUCH from this book. In fact, he puts forth his arguments so naturally and with so much confidence that I wonder how much I have been duped. Am I gullible in accepting so many of these "farout" concepts? It's hard to say, but it does show that the author has amazing skills in argumentation, and he has a very pleasing and effective literary style. He would make a good brainwasher (some of his critics would claim that he is).
So, is he going to convince you? Well, though I believe he wants to, it doesn't look like he tries very hard. That is, his arguments are less about "this is how things are" as "this is plausible". For example, he starts from the platform of materialism, but he doesn't really argue that materialism is correct. He just says "assume this, and let's work from here" (not a literal quote). As another example, he doesn't so much argue that true A.I. will exist as he does the argument that true A.I. CAN exist. He doesn't extensively argue that the mind is completely contained in the brain. He says that it is plausible that the seemingly immaterial concept that is the mind CAN be contained in something as material as the brain. He builds these arguments up from his discussions on meaning and structure and constantly draws parallels between areas of applications and between the practical and the theoretical. The big emphasis is on self-reference and self-replication. He discusses how these non-intuitive concepts are not only possible, but very real. The implications of self-reference/replication are quite profound as the author shows. These things he refers to as "strange loops" and they are indeed strange.
The glue that holds these together is what I consider to be the most beautiful, profound, and earth-shattering theorem in all of mathematics: Godel's Incompleteness Theorem. The weight of this theorem comes from two places: the result and the proof. The theorem basically states that the formulation of a perfect mathematical system, one that explains all that there is to know about mathematics (or even something a little less grand...like number theory) and is contradiction-free, is essentially impossible (the existence of Godel-circumventing methods to achieve the original goal have been discussed by mathematicians, but they have not yet materialized - the theorem is just too strong and relies on minimal assumptions). The proof of this theorem relies on a self-referential statement. Kurt Godel showed that any recursively enumerable (i.e. "sufficiently powerful") formal system contains a statement (a self-referential one) which is true but unprovable. Although the author discusses the implications of this result, particularly in relation to artificial intelligence, he puts stronger emphasis on its proof. How can something as abstract as a formal system talk about itself? He discusses this and relates how this idea is connected with the concepts of structure and meaning.
Okay, he's eloquent and profound. So what? What matters are the big questions: Is he accurate? Is he clear? Is he fair?
1.) Pretty much.
2.) In most areas, but not others.
3.) Not really.
First off, don't worry about your background. Having a strong background in one area may make the reading go quicker, but he is exceptionally clear in most areas and can explain almost anything in layman's terms. As I said before, my background in areas such as art and music theory are pretty weak. Yet, though I had to slow down a bit for these sections, I never felt lost. In fact, I can say that as a side effect, I learned at least a little bit about these areas.
Then there are the areas where my background is stronger. Here we run into a little bit of trouble, particularly in his mathematical statements. I say "particularly", but readers with a stronger background in areas such as music or neurology may run into similar problems. I originally saw the problems as problems of accuracy, but they really have to do with clarity. These problems have to do with consistency, completeness, and Godel's Incompleteness theorem. A person without the proper mathematical background won't catch these problems, but I will say be on guard.
For example, he states that a complete and consistent formal system is impossible. If a system is too weak for Godel's theorem to apply, i.e. it cannot be self-referential, then it is incomplete by its own weaknesses ("incomplete in an uninteresting way" as the author puts it).
Hogwash.
Well, sort of hogwash. The problem lies not in the factuality of the statement (he wasn't REALLY lying to you) but in definitions. Mathematicians have formulated formal systems which are provably both consistent AND complete. The problem is that they go by a different definition of "complete". It turns out that there are multiple mathematical definitions of "complete". There's syntactically complete, semantically complete, strongly complete, extremely complete, and so on. Without a qualifier, when mathematicians discuss "completeness", they usually mean syntactical completeness. Syntactical completeness essentially means that for every legitimate string in the system, either it or its negation can be proven to be a theorem. What the author means by complete is that the system contains everything there is to know about number theory (or mathematics in general). Under the conventional definition, a system which does not contain every number-theoretical theorem as a provable theorem can still be complete if these statements are simply not allowed, i.e. they don't form "legitimate" strings. Naturally, most of these systems don't contain much (e.g. for arithmetic, you can prove properties related to addition in a complete and consistent system, but you cannot do the same for multiplication). Now, the author's definition is perfectly valid, but he doesn't really clarify what definition he's going by. When he talks about completeness and consistency, I was confused not by a lack of background, but because of my background.
In regards to his discussions of consistency, we run into the same kind of problem. "Consistency" basically means "contradiction-free". He tries to make some kind of distinction between what he calls "internal" and "external" consistency, and though I applaud him for trying, he doesn't really clarify the distinction and he doesn't help the reader keep track of what kind of consistency he is talking about at a particular time. When discussing external consistency, he mentions that we can remove this kind of consistency by changing our interpretation. So, can we defeat Godel's Theorem by changing the interpretation of Godel's statement from "This is not a theorem in this formal system" to something a little more meaningless? No, of course not, but understanding why requires a deeper analysis than would have been necessary if the author had been more clear on such matters.
Then there is the issue of fairness. Does he present the "other side"? There is always an "other side". He doesn't do this very often. Potential criticism of his theories are largely ignored for the largest portion of this book, and this in and of itself, makes his arguments slightly weaker. Where he does bring in significant criticism are the sections on artificial intelligence. He fortunately presents critics of his views on A.I. in a respectable way. There are no straw-men here. However, his counters are not exactly strong, but sometimes this is, surprisingly, a good thing. In some cases, he virtually ignores the question (then why mention the question??!!). In others, instead of a strong refutation, he sticks with the style that I mentioned before. He doesn't claim his ideas are necessarily correct. He argues that they are plausible. I respect this. The author presents himself as a man of integrity who, unlike so many of his colleagues, doesn't remain stubborn or throw a fit when someone disagrees with him. This may be why I was so disappointed with this book's followup, "I am a Strange Loop". There, he switches from "this is plausible" mode to "I am right - deal with it" mode. So sad.
Now, something should be said about style. The author calls the concepts here his "religion". You can tell. This books oozes passion and inspiration. One can tell very quickly that the author is absolutely in love with his own ideas. From a less skilled writer, this would result in an air of arrogance, but in GEB, his love helps you build your love. Also, he is an absolute master at creating analogies and tying together concepts. The beauty in this book is not in what he says, but how the concepts are structured and intertwined and the analogies that are drawn. It is just like the concepts that he discusses in the book. Meaning was largely created, not from what the structure is made of, but from the structure itself.
Another thing of note is the collection of dialogues. Before most chapters, he includes a dialogue between Achilles and Tortoise modeled after Lewis Carroll's "What the Tortoise Said to Achilles". Whimsical dialogues such as these would induce eye-rolling in most serious texts, but he writes these dialogues confidently and they illustrate the concepts of the book in a silly, but meaningful way. Yes, it all sounds very silly, especially for such an academic book, but I fully welcome the dialogues for reasons I can't fully express. I simply can't imagine this book without them.
Whew! That was long. If you made it this far, you'll be glad to know that I'm wrapping up. I know I spent more time presenting criticisms than you would expect in a 5-star review, but I find it much easier to find words of criticism than words of praise. I'll never write an inspirational book. Just rest assured that whatever flaws the book may contain, it is at its core, unbelievably fascinating. It can also be quite an eye-opener. I don't hesitate in the least in giving this book my very highest recommendation. If this is not on one's "must-read" list, that list is surely "incomplete".
I will begin by making two brief notes. Firstly, my 5-star rating does not imply that this book is flawless. I will expound on the book's flaws shortly. However, I do not believe that the flaws are enough to warrant subtracting a full star. I will even go as far to say that this book is fully deserving of its Pulitzer prize, and it has become one of my most treasured books in my extensive collection.
Secondly, I want to give some background about myself and I will explain why. I believe in subjectivity and I believe that the depth of one's background can reveal a lot about this book. The book jumps between many subjects, and if one has a weak background in one area, then we can assess the author's clarity. If one has a strong background in another area, then we can assess the author's accuracy and even pinpoint areas where he is inaccurate or presents questionable results. So I will mention my background in regards to the relevant areas. These areas are: Mathematics, Logic, Artificial Intelligence, Art, Music, Biology, Neurology, and Zen Buddhism.
My background:
Fairly strong: Mathematics, Logic
Intermediate: Biology, Zen Buddhism (studied, not accepted), Artificial Intelligence
Minimal, but existent: Music Theory (barely), Neurology (as much as my AI studies have revealed to me)
Nil: Art
Degrees, research, areas of emphasis:
ABD in Statistics (Ph.D. in about 2 years hopefully) - Highly mathematical research area (essentially a high-dimensional Euclidean geometry problem in a statistical framework)
BA in Mathematics - Numerical Analysis
BS in Computer Science - Parallel Computing, Neural Nets, Truth Maintenance Systems
Field experience in microarray analysis and immunology.
The areas of emphasis for my undergraduate degrees should be taken with a grain of salt. I completed no respectable research in those areas.
With that out of the way (we will return to the importance of that shortly), let us figure out what in the world this book is about, and that is one question that has evaded many. I see an intended purpose in the book, and an important implicit one. Here, the path is as important as the goal. According to the author, the book is about how animate beings can come from inanimate matter. That is, it is about how minds and consciousness can come from something as material as a brain, and how true A.I., one that is conscious, is plausible.
The implicit meaning of the book deals with structure and meaning. While building up to the end goal, the author discusses, within the context of the areas that I already mentioned, the nature of structure and meaning. How does meaning arise? Why are we quicker to attach meaning to structures than to atomic elements, yet recognize that there are "meaningless" structures? When and how does meaning come into play? How do structures result from processes? How are self-reference and self-replication possible and what role do they play? These questions and their possible answers are what make this book captivating. The author, though he doesn't "prove" much, illustrates these concepts through beautiful, meaningful examples, and most of his arguments are both eloquent and quite convincing. I will say that I learned MUCH from this book. In fact, he puts forth his arguments so naturally and with so much confidence that I wonder how much I have been duped. Am I gullible in accepting so many of these "farout" concepts? It's hard to say, but it does show that the author has amazing skills in argumentation, and he has a very pleasing and effective literary style. He would make a good brainwasher (some of his critics would claim that he is).
So, is he going to convince you? Well, though I believe he wants to, it doesn't look like he tries very hard. That is, his arguments are less about "this is how things are" as "this is plausible". For example, he starts from the platform of materialism, but he doesn't really argue that materialism is correct. He just says "assume this, and let's work from here" (not a literal quote). As another example, he doesn't so much argue that true A.I. will exist as he does the argument that true A.I. CAN exist. He doesn't extensively argue that the mind is completely contained in the brain. He says that it is plausible that the seemingly immaterial concept that is the mind CAN be contained in something as material as the brain. He builds these arguments up from his discussions on meaning and structure and constantly draws parallels between areas of applications and between the practical and the theoretical. The big emphasis is on self-reference and self-replication. He discusses how these non-intuitive concepts are not only possible, but very real. The implications of self-reference/replication are quite profound as the author shows. These things he refers to as "strange loops" and they are indeed strange.
The glue that holds these together is what I consider to be the most beautiful, profound, and earth-shattering theorem in all of mathematics: Godel's Incompleteness Theorem. The weight of this theorem comes from two places: the result and the proof. The theorem basically states that the formulation of a perfect mathematical system, one that explains all that there is to know about mathematics (or even something a little less grand...like number theory) and is contradiction-free, is essentially impossible (the existence of Godel-circumventing methods to achieve the original goal have been discussed by mathematicians, but they have not yet materialized - the theorem is just too strong and relies on minimal assumptions). The proof of this theorem relies on a self-referential statement. Kurt Godel showed that any recursively enumerable (i.e. "sufficiently powerful") formal system contains a statement (a self-referential one) which is true but unprovable. Although the author discusses the implications of this result, particularly in relation to artificial intelligence, he puts stronger emphasis on its proof. How can something as abstract as a formal system talk about itself? He discusses this and relates how this idea is connected with the concepts of structure and meaning.
Okay, he's eloquent and profound. So what? What matters are the big questions: Is he accurate? Is he clear? Is he fair?
1.) Pretty much.
2.) In most areas, but not others.
3.) Not really.
First off, don't worry about your background. Having a strong background in one area may make the reading go quicker, but he is exceptionally clear in most areas and can explain almost anything in layman's terms. As I said before, my background in areas such as art and music theory are pretty weak. Yet, though I had to slow down a bit for these sections, I never felt lost. In fact, I can say that as a side effect, I learned at least a little bit about these areas.
Then there are the areas where my background is stronger. Here we run into a little bit of trouble, particularly in his mathematical statements. I say "particularly", but readers with a stronger background in areas such as music or neurology may run into similar problems. I originally saw the problems as problems of accuracy, but they really have to do with clarity. These problems have to do with consistency, completeness, and Godel's Incompleteness theorem. A person without the proper mathematical background won't catch these problems, but I will say be on guard.
For example, he states that a complete and consistent formal system is impossible. If a system is too weak for Godel's theorem to apply, i.e. it cannot be self-referential, then it is incomplete by its own weaknesses ("incomplete in an uninteresting way" as the author puts it).
Hogwash.
Well, sort of hogwash. The problem lies not in the factuality of the statement (he wasn't REALLY lying to you) but in definitions. Mathematicians have formulated formal systems which are provably both consistent AND complete. The problem is that they go by a different definition of "complete". It turns out that there are multiple mathematical definitions of "complete". There's syntactically complete, semantically complete, strongly complete, extremely complete, and so on. Without a qualifier, when mathematicians discuss "completeness", they usually mean syntactical completeness. Syntactical completeness essentially means that for every legitimate string in the system, either it or its negation can be proven to be a theorem. What the author means by complete is that the system contains everything there is to know about number theory (or mathematics in general). Under the conventional definition, a system which does not contain every number-theoretical theorem as a provable theorem can still be complete if these statements are simply not allowed, i.e. they don't form "legitimate" strings. Naturally, most of these systems don't contain much (e.g. for arithmetic, you can prove properties related to addition in a complete and consistent system, but you cannot do the same for multiplication). Now, the author's definition is perfectly valid, but he doesn't really clarify what definition he's going by. When he talks about completeness and consistency, I was confused not by a lack of background, but because of my background.
In regards to his discussions of consistency, we run into the same kind of problem. "Consistency" basically means "contradiction-free". He tries to make some kind of distinction between what he calls "internal" and "external" consistency, and though I applaud him for trying, he doesn't really clarify the distinction and he doesn't help the reader keep track of what kind of consistency he is talking about at a particular time. When discussing external consistency, he mentions that we can remove this kind of consistency by changing our interpretation. So, can we defeat Godel's Theorem by changing the interpretation of Godel's statement from "This is not a theorem in this formal system" to something a little more meaningless? No, of course not, but understanding why requires a deeper analysis than would have been necessary if the author had been more clear on such matters.
Then there is the issue of fairness. Does he present the "other side"? There is always an "other side". He doesn't do this very often. Potential criticism of his theories are largely ignored for the largest portion of this book, and this in and of itself, makes his arguments slightly weaker. Where he does bring in significant criticism are the sections on artificial intelligence. He fortunately presents critics of his views on A.I. in a respectable way. There are no straw-men here. However, his counters are not exactly strong, but sometimes this is, surprisingly, a good thing. In some cases, he virtually ignores the question (then why mention the question??!!). In others, instead of a strong refutation, he sticks with the style that I mentioned before. He doesn't claim his ideas are necessarily correct. He argues that they are plausible. I respect this. The author presents himself as a man of integrity who, unlike so many of his colleagues, doesn't remain stubborn or throw a fit when someone disagrees with him. This may be why I was so disappointed with this book's followup, "I am a Strange Loop". There, he switches from "this is plausible" mode to "I am right - deal with it" mode. So sad.
Now, something should be said about style. The author calls the concepts here his "religion". You can tell. This books oozes passion and inspiration. One can tell very quickly that the author is absolutely in love with his own ideas. From a less skilled writer, this would result in an air of arrogance, but in GEB, his love helps you build your love. Also, he is an absolute master at creating analogies and tying together concepts. The beauty in this book is not in what he says, but how the concepts are structured and intertwined and the analogies that are drawn. It is just like the concepts that he discusses in the book. Meaning was largely created, not from what the structure is made of, but from the structure itself.
Another thing of note is the collection of dialogues. Before most chapters, he includes a dialogue between Achilles and Tortoise modeled after Lewis Carroll's "What the Tortoise Said to Achilles". Whimsical dialogues such as these would induce eye-rolling in most serious texts, but he writes these dialogues confidently and they illustrate the concepts of the book in a silly, but meaningful way. Yes, it all sounds very silly, especially for such an academic book, but I fully welcome the dialogues for reasons I can't fully express. I simply can't imagine this book without them.
Whew! That was long. If you made it this far, you'll be glad to know that I'm wrapping up. I know I spent more time presenting criticisms than you would expect in a 5-star review, but I find it much easier to find words of criticism than words of praise. I'll never write an inspirational book. Just rest assured that whatever flaws the book may contain, it is at its core, unbelievably fascinating. It can also be quite an eye-opener. I don't hesitate in the least in giving this book my very highest recommendation. If this is not on one's "must-read" list, that list is surely "incomplete".
★ ★ ★ ★ ★
wei lin
I'm just starting to dip my toes into the water of some of this stuff, but I thought this was one of the most mind-bending and beautiful books I've ever read. There were a couple chapters I had to skip and another that I had to read about online after completing the chapter to make full sense of it but it was a challenge well worth taking.
★ ★ ★ ★ ★
lona yulianni
A few years ago, a friend lent me this book, and I started to read. 24 hours later, with no sleep and little food, I'd finished it. Each concept in this book was presented in such a clear way, and leading from one thread to the next. A wonderful work, giving part-time and amature philosophers, mathematitians, and computer scientists something to think about! Everyone should read this book at least once. *smile*
★ ★ ★ ☆ ☆
oliver sheppard
An engaging book - Hofstadter does well to link Bach and Escher to Godel, and to illustrate difficult concepts such that average readers can gain an appreciation of them.
Hofstadter is at his best in the dialogues, as well as when he treats Bach, Escher and Godel. He is at his worst when he treats the elusive concept of meaning.
Indeed, his treatment of meaning is a very simplistic version of psycho-physical reductionism, and, worse, he does not argue for his position, but assumes that it is indeed true.
When reading his first chapter explicitly treating meaning, I was forced to look ahead to the index. To my dismay, there is no mention of Kant, no mention of the empiricist/rationalist debate, and no nuance in his hasty generalization regarding the identical states of people's brains, or an argument that would suggest that 'brain' and 'mind' have anything to do with each other.
Entertaining, for the dialogue, penetrating in the treatment of Bach, Escher and Godel, but simplistic in its treatment of what intelligence actually is - disappointing . . .
Hofstadter is at his best in the dialogues, as well as when he treats Bach, Escher and Godel. He is at his worst when he treats the elusive concept of meaning.
Indeed, his treatment of meaning is a very simplistic version of psycho-physical reductionism, and, worse, he does not argue for his position, but assumes that it is indeed true.
When reading his first chapter explicitly treating meaning, I was forced to look ahead to the index. To my dismay, there is no mention of Kant, no mention of the empiricist/rationalist debate, and no nuance in his hasty generalization regarding the identical states of people's brains, or an argument that would suggest that 'brain' and 'mind' have anything to do with each other.
Entertaining, for the dialogue, penetrating in the treatment of Bach, Escher and Godel, but simplistic in its treatment of what intelligence actually is - disappointing . . .
★ ★ ★ ★ ★
gwendolyn casey
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.
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.
★ ★ ★ ★ ★
chelsea d
For those people always on the lokout for something to really mull over and appreciate, here is a book that provides it.. Abook that in its own way has gained an almost cult like status... It is an intersting exploration of interconnectedness of seemingly disparate themes. A intersting read, that never fails to fascinate. One ponders over the richness of thought that created such a book. Surely a different book, well worth the time spent unravelling it!
★ ★ ★ ★ ☆
caryn winslow
Don't buy into the wild hype surrounding this book that many of these reviews spout. No this in NOT the greatest book ever written. However, it is a pretty good "soft" introduction to many interesting areas of mathematics and computer science. In particular, this book covers mathematical logic, Godel's Theorems, the theory of computation, and artificial intelligence. The major flaw with this book is its length. Hofstadter is a very longwinded writer, and much of this book could be considerably shortened without losing much. In spite of this, I heartily recommend this book. It is the best introduction to Godel's theorems and computation that I know of. In addition, the whimsical dialogs are an excellent exploration of form and content, just beautiful.
★ ★ ★ ★ ★
jugemu
I've read GEB in French then in English. It is fascinating
in both languages. It must have been one of the most difficult
books to translate. But D. Hofstadter took part in the work
(he speaks fluent French) and it is as enchanting and captivating
to read in French as in English.
I second [email protected]: if you read only one book in
your life let GEB be this book.
in both languages. It must have been one of the most difficult
books to translate. But D. Hofstadter took part in the work
(he speaks fluent French) and it is as enchanting and captivating
to read in French as in English.
I second [email protected]: if you read only one book in
your life let GEB be this book.
★ ★ ☆ ☆ ☆
chris richards
I gotta side with the minority here. That the book is omnipresent even after many years and has such a loyal following boggles my mind. I suppose the same people who get off on elaborate dungeons and dragons fantasies played over months and years would enjoy this. I did not. It is over-complicated, trite and sometimes positively obnoxious in its desire to be cute. If Hofstadter's desire was to write a nonfiction "Finnegan's Wake," he's succeeded, but without the artistic accomplishment, only the chaos. If ever there were a case of the "emporer's new clothes," this book is it. As a mathematician and attorney, I object to this kind of obsfucation.
★ ★ ★ ★ ★
czaja
The book primarily starts to talk about the "core" of the famous GEB figure. And it can basically said to be the Godel theorem. In the introduction, author explicitly states that he has thought of an essay about Godel theorem at first and that his ideas "growed like a sphere" then. It is credible and nice that Escher is involved significantly with his famous, brain teasing works and the concept of "self reference" in these figures is well presented together with the great analogies of Godel theorem that is also intimately related with this concept. Another important thing that the author constantly points out is the idea of "isomorphism". The meaning of patterns and the actual meaninglessness of formal systems is related to this idea before rushing into the AI topics. By the way, Bach is just a little flavor for the book which is subjectively included for the sake of completeness of the trio.
Things start to get a little bit mysterious and annoying when Zen Buddhism is presented to make some kind of convincing relationship between the main plot, but I think it's not convincing. The author is not sure that whether he really understood what Zen is. But I'm sure that he misuses it. What lies beneath the eastern philosophies is some kind of Pantheism and its reflections to the practical life. That's all. Anyway, the chapter about Zen can be totally omitted. It's an unnecessary part of the book.
It's vital to see that the author is not a blind defender of strong AI as some intellectuals were so in the era the book is written. He stresses the complexity of intelligence, but more importantly in what way it is complex and how. He tries to make "isomorphisms" and "mappings" of the brain and thought and finally suggests that if sufficiently large layers of abstraction and sophisticated symbol manufacturing and processing units are established we can have an intelligence on a machine. By the way, the relationship presented between Godelian issues and the intelligence is not strong as the ones described in the first part. I mean, we really have to be sure that intelligence is not a "brain-bound phenomenon" (a term exactly used in the book) if we are to ignore low level details. It's not guaranteed that we'll achieve intelligence on a machine if we do abstractions and use some other kind of hardware. (Though, we can go very far) Physical and biological rules might be more effective than we think and it might be that the way neurons work presents a scheme that is very specific and hard (maybe impossible) to implement on any other platform. (This idea is proposed by Penrose, but very speculatively. Indeed, we don't have much knowledge about these issues)
As for the nature of a possible AI (that he suggests), the author stresses that this machine would not be prone to programming for example, since the obvious programming statements (or say simplest, atomic operations) get lost in the layers and we actually don't know how it does a certain operation.
So, what? This book has lots of beautiful ideas that are well presented and it's really easy to read although the concepts may seem unfamiliar at first. What makes it more valuable is that the author has a certain sense of literature and the text gets extremely nice at times. The creative dialogues of Achilles and Tortoise also indicate this feature.
This book is a classic. BUT, it's neither a Bible of any kind nor a "metabook" (or any kind of thing that it's sometimes regardes as) and a book in this field is not expected to be so. (That's why he still get 5 stars from me) Author dubs it as a statement of his religion and it really is, as there are lots of excitement and mystery throughout the book. I asked myself why this book is so popular. People putting it very high is probably influenced by the "style" of the book. It pulls the reader into the bizarre world of the author even if you don't notice it. The artistic value is important here. This book could well be an above average book by a monotone and uninspired writing. But, it's a very good piece of art with valuable, ingenius ideas and what can we expect more?
In short, I strongly advice this book if you want to have some sense of the topics it touches, but don't get hypnotized. I also advice you to read Penrose's work "Emperor's New Mind". For me, these two form a good couple while most do not think that way.
Things start to get a little bit mysterious and annoying when Zen Buddhism is presented to make some kind of convincing relationship between the main plot, but I think it's not convincing. The author is not sure that whether he really understood what Zen is. But I'm sure that he misuses it. What lies beneath the eastern philosophies is some kind of Pantheism and its reflections to the practical life. That's all. Anyway, the chapter about Zen can be totally omitted. It's an unnecessary part of the book.
It's vital to see that the author is not a blind defender of strong AI as some intellectuals were so in the era the book is written. He stresses the complexity of intelligence, but more importantly in what way it is complex and how. He tries to make "isomorphisms" and "mappings" of the brain and thought and finally suggests that if sufficiently large layers of abstraction and sophisticated symbol manufacturing and processing units are established we can have an intelligence on a machine. By the way, the relationship presented between Godelian issues and the intelligence is not strong as the ones described in the first part. I mean, we really have to be sure that intelligence is not a "brain-bound phenomenon" (a term exactly used in the book) if we are to ignore low level details. It's not guaranteed that we'll achieve intelligence on a machine if we do abstractions and use some other kind of hardware. (Though, we can go very far) Physical and biological rules might be more effective than we think and it might be that the way neurons work presents a scheme that is very specific and hard (maybe impossible) to implement on any other platform. (This idea is proposed by Penrose, but very speculatively. Indeed, we don't have much knowledge about these issues)
As for the nature of a possible AI (that he suggests), the author stresses that this machine would not be prone to programming for example, since the obvious programming statements (or say simplest, atomic operations) get lost in the layers and we actually don't know how it does a certain operation.
So, what? This book has lots of beautiful ideas that are well presented and it's really easy to read although the concepts may seem unfamiliar at first. What makes it more valuable is that the author has a certain sense of literature and the text gets extremely nice at times. The creative dialogues of Achilles and Tortoise also indicate this feature.
This book is a classic. BUT, it's neither a Bible of any kind nor a "metabook" (or any kind of thing that it's sometimes regardes as) and a book in this field is not expected to be so. (That's why he still get 5 stars from me) Author dubs it as a statement of his religion and it really is, as there are lots of excitement and mystery throughout the book. I asked myself why this book is so popular. People putting it very high is probably influenced by the "style" of the book. It pulls the reader into the bizarre world of the author even if you don't notice it. The artistic value is important here. This book could well be an above average book by a monotone and uninspired writing. But, it's a very good piece of art with valuable, ingenius ideas and what can we expect more?
In short, I strongly advice this book if you want to have some sense of the topics it touches, but don't get hypnotized. I also advice you to read Penrose's work "Emperor's New Mind". For me, these two form a good couple while most do not think that way.
★ ★ ★ ★ ★
twisty
This is one of the most deeply brilliant books ever written. Rarely do I meet someone who actually understood it, which is only superficially about weaving together the seemingly disparate works of Godel, Escher and Bach. The book is mostly about consciousness, but not explicitly -- it approaches its subject by poking and prodding at the Godelian limits to self-understanding, the "snake eating itself"-like recursivity of consciousness, from different angles, and often being cute and playful along the way.
Zen koan are meant to provoke enlightenment through the momentary extrication from Godelian-limited logic. They point toward ideas that cannot be contained explicitly in syntax. I think this book works very much on the same principle, except rather than being terse and purposefully enigmatic, Hofstadter earnestly tries to explain himself.
Zen koan are meant to provoke enlightenment through the momentary extrication from Godelian-limited logic. They point toward ideas that cannot be contained explicitly in syntax. I think this book works very much on the same principle, except rather than being terse and purposefully enigmatic, Hofstadter earnestly tries to explain himself.
★ ★ ★ ★ ★
tasidia
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.
★ ★ ★ ★ ★
alexei dolganov
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.
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.
★ ★ ★ ★ ★
christy halstead
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.
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.
★ ★ ★ ★ ☆
bridgette
I'm in the middle of the book GEB, and I'm taking it kind of slowly, because my not-so-mathematical brain has to rest between exercises. This is an unusual and interesting book; I have never read anything quite like it. I quickly get lost during the sections of math and formal systems, but if I ever do follow a thought through, I feel very accomplished. If you think the book sounds interesting but you aren't sure you're going to like it, try it. There are many different sections and many of them don't rely on the previous sections to be coherent. I am especially amazed by the dialogues. Just when I am about to applaud myself for following along with the simple content of the discussion, I find that the external structure of the dialogue exactly parallels whatever topic the speakers have been talking about--amazing! Whenever I make a discovery like that, I feel dizzy with glee and pride. It's a great experience--try it ourself; read the dialogues! (And maybe the rest of the book too.)
★ ★ ★ ★ ★
lynne o brien
That's just it. This is the best book I've ever read, and that's not a judgement that comes easily believe me. It just embraces so many themes, so elegantly, and so deeply as to leave such a lasting mark upon the reader that it is difficult to match.
The one criticisim it might draw is that it is not on the whole, light reading and is rather a heavy read, but that is something difficult to avoid when you embrace significant themes designed to make the reader think and feel at the same time. Light reading after all is not something that forces you to think after every paragraph or page, it just flows ...
I have in all honesty met many more people that started this book than have read it through. Now there's a challenge or an interesting reflection on the company I keep :-).
The one criticisim it might draw is that it is not on the whole, light reading and is rather a heavy read, but that is something difficult to avoid when you embrace significant themes designed to make the reader think and feel at the same time. Light reading after all is not something that forces you to think after every paragraph or page, it just flows ...
I have in all honesty met many more people that started this book than have read it through. Now there's a challenge or an interesting reflection on the company I keep :-).
★ ★ ★ ★ ★
telesa
This book rewards you in proportion to your effort, the more carefully you read it, the more intriguing, entertaining, and enjoyable it becomes. It is a challenging read, but every section helps you understand every other section, so keep at it, you will find much enjoyment within its pages. And it will introduce a world of thought.
Ignore the negative critics, the book would not win so many awards if it was a waste of time.
Ignore the negative critics, the book would not win so many awards if it was a waste of time.
★ ★ ★ ★ ★
darcy glenn
This book is so great, I think it's the best book that I've ever read.
The red line throughout the whole story is Godel's theorem and it's wonderful proof. This main theme is mixed with nice dialogs between Achilles and the Toirtoise, Escher's works, Bach's music and more.
The thing that makes this book exceptional is that Hofstadter connects all these diverse topics and shows you similarities. Zen bhuddism is even mentioned. I found myself constantly suprised.
This book gave me a warm feeling for the beauty of mathematics and logic. I feel lucky I found the book.
The red line throughout the whole story is Godel's theorem and it's wonderful proof. This main theme is mixed with nice dialogs between Achilles and the Toirtoise, Escher's works, Bach's music and more.
The thing that makes this book exceptional is that Hofstadter connects all these diverse topics and shows you similarities. Zen bhuddism is even mentioned. I found myself constantly suprised.
This book gave me a warm feeling for the beauty of mathematics and logic. I feel lucky I found the book.
★ ★ ★ ★ ★
john gardner
This book is, like I said above, great. I'm only 13 years old (no joke.) I was getting really sick of sci-fi one day and was looking for Joseph Heller books at our bookstore, when I spied this one. The title was what really grabbed me. Godel I had never heard of. Escher is (I think) the greatest artist that has ever lived, same for Bach only music. Also the subtitle, which compared it to the works of Lewis Carroll, who I think is a very good author and mathemetician (sp?). It took me two readings to fully comprehend this book. The translating of zen koans into the prepositional calculus explained in this book is both hard to understand (for me, at least) and interesting. This book didn't really change my life; the only book that has ever done that to me is maybe the Illuminatus! trology. But this was one of the best books that I have ever read.
★ ★ ★ ★ ★
sheba
Absolute, unmitigated genius. Hofstadter takes difficult concepts in several different fields (mathematics, philosophy, psychology, music, biology, art, and even religion), explains them lucidly and even humorously, and brings them all together into a single unified whole. This book is an absolutely indispensible part of a modern liberal arts education.
★ ★ ★ ☆ ☆
sarah kohn
GEB could have sparkled like a brilliant iridescent gem. The book isn't flawless, consequently its glitter is somewhat dimmed.
The book itself is the manifestation and the epitome of Gödel incompleteness theorem. I.e. the author insists that the main theme of his book is "I", as he writes in his preface to the book. But "I" which represent a human being is nowhere found. Creativity and thinking does not constitute a human which is a more complex being. Hence "I" a human is indemonstrable in GEB which fits Gödel's incompleteness theorem like a glove. Creativity and thinking are the sole human characteristics dealt in this book.
After all humans aren't just mere thinker and creative beings.
Another point of incompleteness is the lack of glossary. If the book was intended only for students or majors in logic, math, or computer science then glossary would be a superfluous. But for readers who come from other disciplines (as I am), it's a huge disadvantage one has to search for supplementary literature to be able to understand the specific terminology used in this book.
There are some amiss in Molecular Biology for example the descriptions of protein biosynthesis from amino acids, which might lead readers to error.
There are some seemingly "scientific jokes" which are out of place as the conversation between the Tortoise with Achilles. They wish to retrieve Bach's premiere playing of his composition "Musical Offering", which took place over 250 years ago. This "joke" suggests that sound waves behavior is identical to those of light waves; since stars that no longer exist are seen on the night sky. Actually sound heard in a room dies off in matter of seconds. Therefore retrieving sound after 250 years seems like a bad joke.
On the other hand GEB is an eye and mind opener book. People tend to take many issues for granted, without being aware to it. I'll list some points that directly affected me after reading this book.
Although the author had in mind the "I" concept as the protagonist of his book; I as a reader see in my mind total different themes: language and creativity. The first thought that crossed my mind was creativity as manifested in various and diverse fields, as music, literature, figurative arts, mathematic, logic et cetera, all conceived by the human mind. I find it stunning that three celebrated masters as Gödel Escher and Bach, each a giant in his field, with different tools expresses similar ideas, as paradoxes, self-reference, infinity and so forth. Had I not read the book I wouldn't be aware to such possibility. Before reading this book I considered art merely as a cultural activity in which the various artists expressed themselves in different media. Suddenly it hit me that these different arts are actually different languages with different communicating devices which are the building blocks: notes in music, word and phrases in literature ,symbols in math and logic, as DNA RNA and amino acids are the building blocks of LIFE.
GEB has given me a new perspective and deeper outlook while reading a new book, listening and analyzing music or paintings. Here are some examples:
I realize that in Escher's work there is more to it than just esthetics and optical illusions per se. Escher's work is intellectually intriguing and arousing curiosity by his usage of mathematical and logical concepts of which I was unaware prior to reading this book. Yet another example "Jabberwocky", when I first read it I couldn't make a head or tail of what these meaningless words actually convey. Now it seems to me that the obscure and meaningless words actually create an abstract and versatile poem; interpreted differently by each reader as any other abstract art does. By using phonetic symbols i.e. syllables as a language to express mood, atmosphere and trigger self-imagination which is actually conversion of music into vowels (supplementary to singing), which is an additional expressive media.
With great pain I give this book only 3 stars
The book itself is the manifestation and the epitome of Gödel incompleteness theorem. I.e. the author insists that the main theme of his book is "I", as he writes in his preface to the book. But "I" which represent a human being is nowhere found. Creativity and thinking does not constitute a human which is a more complex being. Hence "I" a human is indemonstrable in GEB which fits Gödel's incompleteness theorem like a glove. Creativity and thinking are the sole human characteristics dealt in this book.
After all humans aren't just mere thinker and creative beings.
Another point of incompleteness is the lack of glossary. If the book was intended only for students or majors in logic, math, or computer science then glossary would be a superfluous. But for readers who come from other disciplines (as I am), it's a huge disadvantage one has to search for supplementary literature to be able to understand the specific terminology used in this book.
There are some amiss in Molecular Biology for example the descriptions of protein biosynthesis from amino acids, which might lead readers to error.
There are some seemingly "scientific jokes" which are out of place as the conversation between the Tortoise with Achilles. They wish to retrieve Bach's premiere playing of his composition "Musical Offering", which took place over 250 years ago. This "joke" suggests that sound waves behavior is identical to those of light waves; since stars that no longer exist are seen on the night sky. Actually sound heard in a room dies off in matter of seconds. Therefore retrieving sound after 250 years seems like a bad joke.
On the other hand GEB is an eye and mind opener book. People tend to take many issues for granted, without being aware to it. I'll list some points that directly affected me after reading this book.
Although the author had in mind the "I" concept as the protagonist of his book; I as a reader see in my mind total different themes: language and creativity. The first thought that crossed my mind was creativity as manifested in various and diverse fields, as music, literature, figurative arts, mathematic, logic et cetera, all conceived by the human mind. I find it stunning that three celebrated masters as Gödel Escher and Bach, each a giant in his field, with different tools expresses similar ideas, as paradoxes, self-reference, infinity and so forth. Had I not read the book I wouldn't be aware to such possibility. Before reading this book I considered art merely as a cultural activity in which the various artists expressed themselves in different media. Suddenly it hit me that these different arts are actually different languages with different communicating devices which are the building blocks: notes in music, word and phrases in literature ,symbols in math and logic, as DNA RNA and amino acids are the building blocks of LIFE.
GEB has given me a new perspective and deeper outlook while reading a new book, listening and analyzing music or paintings. Here are some examples:
I realize that in Escher's work there is more to it than just esthetics and optical illusions per se. Escher's work is intellectually intriguing and arousing curiosity by his usage of mathematical and logical concepts of which I was unaware prior to reading this book. Yet another example "Jabberwocky", when I first read it I couldn't make a head or tail of what these meaningless words actually convey. Now it seems to me that the obscure and meaningless words actually create an abstract and versatile poem; interpreted differently by each reader as any other abstract art does. By using phonetic symbols i.e. syllables as a language to express mood, atmosphere and trigger self-imagination which is actually conversion of music into vowels (supplementary to singing), which is an additional expressive media.
With great pain I give this book only 3 stars
★ ★ ★ ★ ★
sean comeaux
This is the most challenging book I've ever read, but also one of the best. Hoftstadter starts by trying to explain the genius of the three titular characters. He's extraordinarily conversant in mathematics, art, and music- enough to challenge me on my strengths (I was already familiar with Godel's Incompleteness Theorem, but I never appreciated how astounding an impact it deservedly had), but also to buttress my weaknesses (I knew nothing of formal music theory, and getting a reader through the structure of Bach's fugues and other works isn't exactly tossing them softballs). As he talks you through each one, he gradually builds his main thesis- all three of these people were able to understand and apply the concept of self-reference (thinking about thinking). It sounds grim and serious, but chapters are written as fables, palindromes, and poems, with diversions into Zen koans, horrible puns, and arguments between cartoonish characters. It's the best book I've read on a number of apparently simple questions like "What makes someone smart?"
★ ★ ★ ★ ★
katybeth
This is not a review of John Sundman's "Cheap Complex Devices" (CCD). If it were, the first sentence of this paragraph would be false, forming a rather simplistic example of a "strange loop", one of those inherently self-contradictory structures whose existence is postulated by Goedel's theorem to be possible in any "sufficiently complex" system that can represent statements in logic.
After the obligatory snippets of glowing reviews, the back cover proudly declares that CCD was awarded the Hofstadter Prize for computer-generated fiction. Douglas Hofstadter is the Pulitzer Prize winning author of one of the seminal literary works related to computer science, "Goedel, Escher, Bach: the Eternal Golden Braid". Goedel, as mentioned above, was a mathematician whose most famous work dealt with self contradiction in logical systems; Escher was an artist who created many famous works that play upon our interpretations of "3 dimensional" drawings done on flat surfaces. Bach, of course, was a 17th century German organist of some repute.
The first key to understanding CCD is to realize that there is, in fact, no Hofstadter prize, and no Society for Analytical Engines to award it. This book was not written by a military surplus AWACS computer with (or without) a faulty floating point unit. Even the review snippets on the back cover are fictional. All of these fictions regarding the book could be described as "meta fiction", which exist on a different conceptual level from the book itself. The clever use of meta-fiction justifies this volume's claim on the Hofstadter Award. Except that, if the award actually existed, the metafiction would not, and this book would no longer merit the award. Strange loops indeed.
Continuing in Hofstadterian fashion, references, contrasts, and comparisons are made repeatedly to Sundman's first novel, "Acts of the Apostles" forming the illusion of a dual with the earlier book. But "Acts" doesn't deul back, and there is no compelling reason to read "Acts" before CCD.
But this is not a review of "Acts of the Apostles", any more than it is of Lewis Carrol's "Through the Looking Glass", Steve Martin's "Pure Drivel", or any other work to which "Cheap Complex Devices" might be reasonably compared. None of those works are prerequisite to this one.
After all, this has actually been a review of "Goedel, Escher, Bach"
After the obligatory snippets of glowing reviews, the back cover proudly declares that CCD was awarded the Hofstadter Prize for computer-generated fiction. Douglas Hofstadter is the Pulitzer Prize winning author of one of the seminal literary works related to computer science, "Goedel, Escher, Bach: the Eternal Golden Braid". Goedel, as mentioned above, was a mathematician whose most famous work dealt with self contradiction in logical systems; Escher was an artist who created many famous works that play upon our interpretations of "3 dimensional" drawings done on flat surfaces. Bach, of course, was a 17th century German organist of some repute.
The first key to understanding CCD is to realize that there is, in fact, no Hofstadter prize, and no Society for Analytical Engines to award it. This book was not written by a military surplus AWACS computer with (or without) a faulty floating point unit. Even the review snippets on the back cover are fictional. All of these fictions regarding the book could be described as "meta fiction", which exist on a different conceptual level from the book itself. The clever use of meta-fiction justifies this volume's claim on the Hofstadter Award. Except that, if the award actually existed, the metafiction would not, and this book would no longer merit the award. Strange loops indeed.
Continuing in Hofstadterian fashion, references, contrasts, and comparisons are made repeatedly to Sundman's first novel, "Acts of the Apostles" forming the illusion of a dual with the earlier book. But "Acts" doesn't deul back, and there is no compelling reason to read "Acts" before CCD.
But this is not a review of "Acts of the Apostles", any more than it is of Lewis Carrol's "Through the Looking Glass", Steve Martin's "Pure Drivel", or any other work to which "Cheap Complex Devices" might be reasonably compared. None of those works are prerequisite to this one.
After all, this has actually been a review of "Goedel, Escher, Bach"
★ ★ ★ ★ ★
karla verdin
I did not review this book immediately after reading it, thinking that my opinion was already well represented by any number of two star reviews on here. I'm glad I didn't.
My initial impression was nonplussed. A lot of the ideas in here are nothing new to any junior-level computer science undergraduate, with one or two neat ways of looking at them. The Tortoise/Achilles segments were occasionally funny, and only his analysis of "ant cognition" and the record story were anything novel to me. This was a sentiment that seemed echoed over and over in reviews.
However, in retrospect, I find that this book did much more for me than I had ever thought. While the ideas in here were nothing new, the things they were applied to were. GEB, despite my initial dismissal, radically changed the framework in which I thought about things, without me even knowing it. The value if GEB is not so much in the ideas it contains (although if you've never been exposed to them before, you'll no doubt find them interesting). It is in the way they are used.
So, for anybody considering whether you should read this book: Yes. It will be long, and in parts tedious. You may find yourself nodding your head impatiently, waiting for the bits that aren't old news to you. You may not even like it. But you may find yourself slightly changed by it nonetheless.
My initial impression was nonplussed. A lot of the ideas in here are nothing new to any junior-level computer science undergraduate, with one or two neat ways of looking at them. The Tortoise/Achilles segments were occasionally funny, and only his analysis of "ant cognition" and the record story were anything novel to me. This was a sentiment that seemed echoed over and over in reviews.
However, in retrospect, I find that this book did much more for me than I had ever thought. While the ideas in here were nothing new, the things they were applied to were. GEB, despite my initial dismissal, radically changed the framework in which I thought about things, without me even knowing it. The value if GEB is not so much in the ideas it contains (although if you've never been exposed to them before, you'll no doubt find them interesting). It is in the way they are used.
So, for anybody considering whether you should read this book: Yes. It will be long, and in parts tedious. You may find yourself nodding your head impatiently, waiting for the bits that aren't old news to you. You may not even like it. But you may find yourself slightly changed by it nonetheless.
★ ★ ★ ★ ★
david garrison
It's a classic book and it's becoming old. I've read it when I'm in High Scholl. After 20 years it is amazingly refreshing. But I think that some parts is becoming outdated ( However, a classic book never loses its charm). Being an unsual work, between Knuth's "The Art of Computer Programming" and Carl Sagan's "Broca's Brain", it's somewhat difficult to read. Written in a pre-internet (as we use today), it loses some appeal for the young ones ( except for the gifted ones). I hope that Mr. Hofstadter has some plans to update and refresh with new format, new insights and appeal to the young ones.
★ ★ ★ ★ ☆
jen kelchner
I just finished reading this book as part of my Sophmore Math 2 AP class in high school. It was very interesting and insightful. Some of the ways that Hofstadter described certain things were brilliant. It is definitely worth reading. You will learn many things that you never even dared to think about before. Once in while it gets a bit boring, but overall it is fascinating.
★ ★ ★ ★ ★
tomsikjr
Its an ingeniously Carrollian take on a bunch of themes from genetic replication through recursion theory and into self-representational art, itself falling into this last category. On top of all this it tries to further our understanding of the human mind. Good fun, and just about anyone will at least enjoy the first half. Be prepared though for a long haul. This is a BIG book.
Is it the best book of non-fiction ever written? Nah! Surely that award must go to Euclid's 'Elements'. 2000 years of spectacular reviews and still wowing anyone who touches it. Nevertheless GEB is the best science popularization I have read.
Is it the best book of non-fiction ever written? Nah! Surely that award must go to Euclid's 'Elements'. 2000 years of spectacular reviews and still wowing anyone who touches it. Nevertheless GEB is the best science popularization I have read.
★ ★ ★ ★ ★
osmaan
I've been reading reviews of GEB for years, and the most fascinating thing about them, aprt from the near-uniform enthusiasm of the readers, is that almost none of the enthusiatic readers have any idea of what the book is actually about! The typical reader seesm to think of GEB as a jouyous romp through any number of fascinating bits of logic, math and science without any idea as to what Hofstader's actually doing.
Yes, it's about Goedel, and recursion, and "strange loops", and linguistics Bach and ants and all that- but only trivially. The bulk of the book is taken up with what amounts to a very entertaining tutorial that sets the reader up for the real thesis of the book. What Hofstadter has attempted in GEB is nothing less than a concise, bottom-up theory of mind. You can read it as a theory of AI, or a theory of human intelligence, but either way he's telling you how to construct an intelligent entity.
True, he doesn't really have a theory of *how* a self-aware being should arise from his metaphorical anthill, but then, neither does anyone else. But he does have a very good story as to how intelligence does arise in such conditions.
If you've read this book before without understanding what his aim was, read it again, with that notion in mind. And if you haven't read it, and you're the sort of person who enjoys mathematic and scientific amusements of any sort, well, read it and discover how much fun a speculative theory can be.
Yes, it's about Goedel, and recursion, and "strange loops", and linguistics Bach and ants and all that- but only trivially. The bulk of the book is taken up with what amounts to a very entertaining tutorial that sets the reader up for the real thesis of the book. What Hofstadter has attempted in GEB is nothing less than a concise, bottom-up theory of mind. You can read it as a theory of AI, or a theory of human intelligence, but either way he's telling you how to construct an intelligent entity.
True, he doesn't really have a theory of *how* a self-aware being should arise from his metaphorical anthill, but then, neither does anyone else. But he does have a very good story as to how intelligence does arise in such conditions.
If you've read this book before without understanding what his aim was, read it again, with that notion in mind. And if you haven't read it, and you're the sort of person who enjoys mathematic and scientific amusements of any sort, well, read it and discover how much fun a speculative theory can be.
★ ★ ★ ★ ★
jeanne harrison
For me, this was the book that proved the cliche: it changed my life. I was working as a musician, studying biochemistry, when I read it and fell in love with AI, and mathematics, and complexity and emergent intelligence. The next 30 years of my life were spent in Computer Science. A must read.
★ ★ ★ ★ ★
patcholi1961
This book first came out when I was entering graduate school. Intrigued by reviews, I vowed to pick it up and see what all the fuss was about, but that intention continued to be overruled by the time constraints of graduate research, as well as various other life experiences. Eventually, a few other misadventurous choices I made sucked a lot of time out of life, and I gradually forgot about GEB.
Then, a little more than ten years ago, an internet acquaintance I had met in a newsgroup referred to GEB, and I was intrigued enough at that time to seek out and purchase an out-of-print copy at a used book store. What a life saver, literally! How? Bear with me, and I will explain...
It would be hyperbole to credit GEB solely for giving me the inspiration to change a very bad personal situation several years ago, without also crediting family, friends, myself, and a bit of good luck as well, but it would also be negligent to not credit GEB at all. After purchasing the book, I started reading short passages occasionally and working through various mental challenges and puzzles, albeit secretly, lest my activity be perceived as futile and thus evoke the ire of a certain someone in my life at the time. I certainly did not want my dearly sought, out-of-print (at the time) book to end up being destroyed.
If you are still with me here, you are probably thinking by now, she needed a few self help books, new locks on the doors, court orders, and maybe even a baseball bat; not GEB! Well, this is a book review, so let me continue. It sounds trite, but Hofstadter's book helped me realize the truth of "I think, therefore, I am." Of course, it certainly helped that I have always enjoyed puzzles in mathematics and logic, but by going through GEB, I began to recover a certain sense of self that I had pretty much neglected. It was a defining moment in turning my life around.
Now, with regard to the book itself...
Some reviewers here have critiqued GEB as if they are reviewing a paper for journal publication. Excuse me, but the book is what it is. Surely if these reviewers are as serious and scholarly as they present themselves to be, they could stroll over to their nearest university library and find all sorts of very scholarly writing with which they could impress themselves. However, I do not understand why they seem to expect GEB to be in the same category as peer reviewed journals. The ideas presented in the book are most definitely impressive, but GEB was published to be read and enjoyed by an educated public, not just by a scholarly few within one discipline.
I will not pretend to have found the "hidden message" of the entire book, though I think I have a pretty good idea what it is. I find that I enjoy the book most by slowly taking in various ideas to be savored and digested. It is a meditative work. Indeed, as someone now well along in a career as a computer professional, e.g., programmer analyst (hey, my life really did change!), I sometimes find the development in my thinking skills nurtured by GEB, and I also find my understanding of GEB nurtured by the development of my thinking skills. This understanding extends into all areas of life.
GEB is very inspirational on multidimensional levels, e.g., serious, recreational, challenging, etc. If you enjoy logic, puzzles, philosophy, and knowledge in general, I think you will enjoy this book. If you have a reasonably good grounding in mathematics, you will probably enjoy GEB even more, but if you do not have such a background, do not let that stop you from diving in anyway. Peruse a few passages, and see if you like it!
Then, a little more than ten years ago, an internet acquaintance I had met in a newsgroup referred to GEB, and I was intrigued enough at that time to seek out and purchase an out-of-print copy at a used book store. What a life saver, literally! How? Bear with me, and I will explain...
It would be hyperbole to credit GEB solely for giving me the inspiration to change a very bad personal situation several years ago, without also crediting family, friends, myself, and a bit of good luck as well, but it would also be negligent to not credit GEB at all. After purchasing the book, I started reading short passages occasionally and working through various mental challenges and puzzles, albeit secretly, lest my activity be perceived as futile and thus evoke the ire of a certain someone in my life at the time. I certainly did not want my dearly sought, out-of-print (at the time) book to end up being destroyed.
If you are still with me here, you are probably thinking by now, she needed a few self help books, new locks on the doors, court orders, and maybe even a baseball bat; not GEB! Well, this is a book review, so let me continue. It sounds trite, but Hofstadter's book helped me realize the truth of "I think, therefore, I am." Of course, it certainly helped that I have always enjoyed puzzles in mathematics and logic, but by going through GEB, I began to recover a certain sense of self that I had pretty much neglected. It was a defining moment in turning my life around.
Now, with regard to the book itself...
Some reviewers here have critiqued GEB as if they are reviewing a paper for journal publication. Excuse me, but the book is what it is. Surely if these reviewers are as serious and scholarly as they present themselves to be, they could stroll over to their nearest university library and find all sorts of very scholarly writing with which they could impress themselves. However, I do not understand why they seem to expect GEB to be in the same category as peer reviewed journals. The ideas presented in the book are most definitely impressive, but GEB was published to be read and enjoyed by an educated public, not just by a scholarly few within one discipline.
I will not pretend to have found the "hidden message" of the entire book, though I think I have a pretty good idea what it is. I find that I enjoy the book most by slowly taking in various ideas to be savored and digested. It is a meditative work. Indeed, as someone now well along in a career as a computer professional, e.g., programmer analyst (hey, my life really did change!), I sometimes find the development in my thinking skills nurtured by GEB, and I also find my understanding of GEB nurtured by the development of my thinking skills. This understanding extends into all areas of life.
GEB is very inspirational on multidimensional levels, e.g., serious, recreational, challenging, etc. If you enjoy logic, puzzles, philosophy, and knowledge in general, I think you will enjoy this book. If you have a reasonably good grounding in mathematics, you will probably enjoy GEB even more, but if you do not have such a background, do not let that stop you from diving in anyway. Peruse a few passages, and see if you like it!
★ ★ ★ ★ ★
maged hassaan
I first discovered this book at age 14 while at a welcome home party for my cousin. He was studying education in college and brought a copy along with him. One look at the title had me hooked, I was already a longtime fan of the artist M.C. Escher's paradoxical artwork.Although a lot of the book rode above my head at the time, there were intriguing and sometimes intertwining themes such as zen koans, Lewis Carroll, as well as patterns and self-reference in art and language. Now, 19 years later, I still don't understand some of the more complex ideas, but my copy is well dog eared and I plan on keeping it for a long time.
★ ★ ★ ☆ ☆
haidee
Douglas Hofstadter's imaginative and engaging GEB:EGB asks the question, "Can machines be conscious?" and answers in effect, "Certainly, because we ourselves are such machines." And there is no doubt that he earned his Pulitzer Prize for this fascinating book.
But watch out! His reliance on imagination actually masks the real problem.
The "real problem" is this: mind can't arise _simply_ from self-reference and self-representation, because reference and representation presume the existence of a mind to begin with. Only minds refer and represent; _resemblances_ (even fancy ones like "isomorphisms") aren't references/representations.
And in Hofstadter's undeniably well-presented examples, his reliance on imagination serves to distract from the absolutely crucial fact that the reference and the representation are always provided by a mind _outside_ the system in question: the reader. A formal system complex enough to "represent itself" doesn't become conscious; it takes a mind _outside_ the system to "see" the isomorphisms in question as references/representations. The system _itself_ can't do so unless mind is _already_ there -- so Hofstadter's bootstrapping "explanation" fails.
As an _argument_, then, GEB:EGB is a tremendous begging of the question. Invoking Godel's Theorems and waving one's hands about "strange loops" doesn't alter the fact that Godel's Theorem itself delivers a killing blow to "computational" theories of consciousness: semantics is _not_ reducible to syntax; truth is not reducible to provability within a formal system; reason is not reducible to purely formal logic; meaning is not reducible to isomorphism; and mind is not reducible to computation. (And indeed, this reading has much more in common with what Godel himself thought he had shown than does Hofstadter's attempt to reinterpret Godel's work in favor of strong AI.)
But GEB:EGB is still a remarkable intellectual accomplishment and a joy to read. Just be careful!
But watch out! His reliance on imagination actually masks the real problem.
The "real problem" is this: mind can't arise _simply_ from self-reference and self-representation, because reference and representation presume the existence of a mind to begin with. Only minds refer and represent; _resemblances_ (even fancy ones like "isomorphisms") aren't references/representations.
And in Hofstadter's undeniably well-presented examples, his reliance on imagination serves to distract from the absolutely crucial fact that the reference and the representation are always provided by a mind _outside_ the system in question: the reader. A formal system complex enough to "represent itself" doesn't become conscious; it takes a mind _outside_ the system to "see" the isomorphisms in question as references/representations. The system _itself_ can't do so unless mind is _already_ there -- so Hofstadter's bootstrapping "explanation" fails.
As an _argument_, then, GEB:EGB is a tremendous begging of the question. Invoking Godel's Theorems and waving one's hands about "strange loops" doesn't alter the fact that Godel's Theorem itself delivers a killing blow to "computational" theories of consciousness: semantics is _not_ reducible to syntax; truth is not reducible to provability within a formal system; reason is not reducible to purely formal logic; meaning is not reducible to isomorphism; and mind is not reducible to computation. (And indeed, this reading has much more in common with what Godel himself thought he had shown than does Hofstadter's attempt to reinterpret Godel's work in favor of strong AI.)
But GEB:EGB is still a remarkable intellectual accomplishment and a joy to read. Just be careful!
★ ★ ★ ★ ★
neil clench
As far as the layout and design of the book go, I find this piece to be particularly structured in a way that one studying abstract and modern mathematics might find appealing. It gives specific axioms for use with each topic and in doing so defines more than just what the topic might imply. As the content goes, for those taking an introduction course in abstract algebra, this book may be slightly heavy and unwieldy, however, for those well-learned in some of its background material, this book is enjoyable and pleasurable to read. The author even makes use of antecdotes to enforce his topics. Overall, this book has been one of the most pleasurable assigned readings I have endured.
★ ★ ★ ★ ★
jessica blogeared books
I was given G.E.B. as a gift in 1981 but didn't get around to reading it for the first time for two years. I've made up for it since by reading it twice. Each time another layer is peeled away and I marvel at the depth and range of the author's mind. Don't consider yourself 'well read' until you read this book.
★ ★ ★ ★ ★
ravi
I bought the book quite awhile ago and just happened to reread a few parts and found it just as thought provoking as I did then. There are many deep questions which are worth thinking over and remain as fresh as they were then. Many of the expectations were not realized because we are still very far from answers but the problems he poses are just as relevant today as they were when he wrote it.
★ ★ ★ ★ ★
pelham123
This book is worth buying for the dialogues between the tortoise and Achilles alone. The more serious chapters are worth reading as well, but get a bit slow and turbid toward the end. What is consciousness? How did this get here? I am not a computer.
★ ★ ★ ★ ★
jane haase
This fine work, the first book by Hofstadter, is a marvel. He integrates classical philosophy, AI, set theory, Fermat's last theorem (now proven!), music and musical progressions and M.C. Escher's self-referential style of art into one coherent whole. All I can add is that every copy of this book I have loaned out has never come back!
★ ★ ☆ ☆ ☆
jess roth
This book richly deserved its Pulitzer prize. It's one of the great pieces of popular science writing and it's remarkable that it has lost so little in 25 years. You learn the intricacies of Bach's music, of Godel's Incompleteness theorem, Escher's drawings and DNA replication. Although his purpose seems to have been very general, with everything tied together loosely as ideas for his future work in artifical intelligence, one could view this as a book about some parts of cognitive psychology-- how the templates we inherit in our DNA create and interpret sounds and images and theorems and how these seem to relate to one another via the concepts of recursiveness, tangled hierarchies, and incompleteness. It is mostly the lack of these inference engines that accounts for the fact that to this day AI has still not been able to make a machine with the brains of an ant(ie, go out into an arbitrarily complex world, recognize and deal with friend and foe, eat, reproduce, and stay out of the sun and rain and keep doing it for years).
His followup the next year with Daniel Dennet--`The Mind's I` complements this book nicely(see my review).
So one could say that this is really a psychology text. It is about human behavior and reasoning-about why we think and act the way we do. But(like all such discussions until recently) none of the explanations are really explanations. Nobody at that time had much understanding of the mental mechanisms involved. Like most 'explanations` of behavior, the comments here are often more interesting for what kinds of things he tries to use (and omits) than for the actual content. As with all reasoning and explaining, art, math, music, etc, one now wants to know which of the brains inference engines are activated. This book and most books and AI research were largely oblivious to such explanations until quite recently.
Cognitive and evolutionary psychology are still not evolved enough to provide full explanations but an interesting start has been made. Boyer's `Religion Explained` is a good place to see what a modern scientific explanation of human behavior looks like,and works on art, music and math are sure to appear soon. Pinker's `How the mind Works` is a good general survey. They do not explain all of intelligence or thinking but give an idea of how to start. See several of the recent texts(ie, 2004 onwards) with evolutionary psychology in the title or the web for further info.
We now recognize that the bases for art, music, math, philosophy, psychology, sociology, language and religion are found in the automatic functioning of templates or inference engines. This is why we can expect similarities and puzzles and inconsistencies or incompleteness and often, dead ends. The brain has no general intelligence but numerous specialized modules, each of which works on certain aspects of some problem and the results are then added, resulting in the feelings which lead to behavior. Hofstadter, like everyone, can only generate or recognize explanations that are consistent with the operations of his own inference engines, which were evolved to deal with such things as resource accumulation, coalitions in small groups, social exchanges and the evaluation of the intentions of other persons. It is amazing they can produce philosophy and science, and not surprising that figuring out how they themselves work together to produce consciousness or choice or spirituality is way beyond reach.
He does not try to deal with the endlessly vexing issue of whether these correlations are out there in the world or in here in the mind. Yes, we use our templates, but why did we evolve those and was there another possibility? Some will say this will all become clear when psychology and genetics are sufficiently advanced, while others say the same of physics and mathematics or programming. And, did they all evolve from some prototype engine in a precambrian invertebrate or did they come much later and from many sources?
It occurred to me that some of the most complex products of human reasoning --superstring theory and the associated math--are recursive( in some nontrivial sense) to quantum field theory, subatomic particle behavior and the entire universe. Physics unites many areas of the most advanced math because it needs self consistent structures, but since we know math is logically proven to be inescapably incomplete and math is a product of the mind, it seems reasonable that there must be a sense in which the mind is incomplete also. We expect since they use math that computers must be incomplete. We know that Turing's halting theorem for computation(we can not discover in advance when a computer will stop) is logically equivalent to Godel's incompleteness theorem. It might follow that physics will be incomplete as well and there will be many physical laws or phenomena that will never be compatible with or derivable from the others. Or perhaps physics can be complete and selfconsistent in one universe but not in others
Just as he did not go very far into the many realms of psychology or physics, neither did he venture far into philosophy. Perhaps the book could have benefited greatly from an understanding of the infinitely subtle relationships between language, thought and reality. An acquaintance with Wittgenstein would have helped immensely, especially his 'Lectures on the Foundations of Mathematics: Cambridge, 1939' edited by Cora Diamond(1990). It is better to get this one rather than the earlier `Remarks on the Foundations of Mathematics, Vol. 1` edited by Rush Rhees( as they are based on different sets of notes if you are really into it you should get both).
Although I've never seen anyone say so, W can be regarded as a pioneer in cognitive psychology. All of his research was thought experiments and introspection into the relations between language, thought and reality. Perhaps nobody ever approached his talent for describing the mind at work. The point is that Hofstadter is trying to understand how the mind works as a preliminary to making programs that work the same way(or at least get similar results) so anyone who is interested in this book(or nearly any area of philosophy, language, psychology, or intellectual discourse) can look into W with great profit(but be forewarned W may seem very shallow, but if you jump in you may never stop swimming)!
Just after reading this book I happened to read Wittgensteins ``Culture and Value``(published the same year(1980), but written decades earlier), and, though it's his least interesting book, I picked out a few comments that may be regarded as pertinent to much of this book and of course to a large part of modern intellectual life.
``There is no religious denomination in which the misuse of metaphysical expressions has been responsible for so much sin as it has in mathematics.``
``People say again and again that philosophy doesn't really progress, that we are still occupied with the same philosophical problems as were the Greeks. But the people who say this don't understand why is has to be so. It is because our language has remained the same and keeps seducing us into asking the same questions. As long as there continues to be a verb 'to be' that looks as if it functions in the same was as 'to eat' and 'to drink', as long as we still have the adjectives 'identical', 'true', 'false', 'possible', as long as we continue to talk of a river of time, of an expanse of space, etc., etc., people will keep stumbling over the same puzzling difficulties and find themselves staring at something which no explanation seems capable of clearing up. And what's more, this satisfies a longing for the transcendent, because, insofar as people think they can see `the limits of human understanding', they believe of course that they can see beyond these.``
Whenever one gets philosophical it is relevant to take a step back from time to time and see just what is really going on. Hofstadter is not a philospher and he does not seem to take that step. Incompleteness seems well defined in math but what about elsewhere? In what sense is music or art or biology incomplete? And exactly what will count as a tangled hierarchy, and recursiveness or self referencing in such different realms(and as W would say, such different language games)? Its not really so clear that the recursiveness in art, music, biology and math are the same sort of thing at all an, insofar as they are, what exactly that means. What should count as ``same` here?
H does not address these questions in any depth but one might find them by far the most interesting theme of the book. We are tantalized at the seeming connections but do they mean anything? Do they go to the core of our being(how the mind works)? Are they merely the result of the use of some of the same templates by art, math, and music? Do they relate to the molecular structure of matter or to particle physics and string theory? Is it useful to extend these analogies(or are they homologies?)almost endlessly further into philosophy, language, psychology, biology(e.g., not only the recursive nature of DNA, RNA and proteins, but the many levels of feedback in the nucleus, cytoplasm, intercellular, interorgan, intracerebral, exchange of chemicals and genes between nucleus, mitochondria and chloroplasts as well as with the bacteria and viruses that wander in out of our bodies into other bodies and other organisms happily picking up and dropping off genes as they go--tangled, recursive, hierarchical and in some sense, incomplete).
Or, to take it further, one might find yet more connections between art and music, math and biology, computer programs, physics and chemistry and biochemistry and add such dimensions as color, geometric shapes, measurements , self organizing abilities, chaos, and other temporal, spatial or purely psychological ways(emotions, sensations, dreams etc). There are many books in art, music, math, biology, psychology, physics and chemistry that already touch upon these themes but I think the most progress is being made in cognitive psychology. The brain is highly recursive in many ways. We converse with ourselves internally and many times externally. The schizophrenic commonly hears voices, but they rarely say nice things.
One is reminded of the cut-ups that William Burroughs and Byron Gysin created. They cut up books or even newspapers and stuck them back together randomly. There was usually some perverse kind of logic to the result showing the hidden threads in discourse. Burroughs later did the same thing with films, with similar results.
Of course pursuing hidden relationships between seemingly unconnected things quickly leads to numerology, pyrimidology and madness. One can find codes or algorithms to connect or derive anything from anything. Hofstadter does not go into this here but he mentions it in his next book, The Minds I(1981). I am reminded of string theory which has math so powerful it can probably explain any possible universe and so it is very suspect as an explanation of ours.
He suggest that incompleteness, tangled hierarchies etc may be responsible for the emergence of higher phenomena which do not exist and cannot be explained at lower levels(eg, consciousness and in fact, everything)and seems to be something of a holist( but in other places he seems clearly behaviorist or reductionist). You might say he is suggesting we look for the explanation of emergence in the bizarre phenomena of the foundations of math, rather than in those in the foundations of physics. Given a universe where life is possible, is it not inevitably full of recursiveness, tangled hierarchies, incompleteness etc.
As H is well aware, Zen can be regarded as using these aspects of the world to trick the mind into stopping-- at which point all relationships become irrelevant. However he was just starting in Zen at the time so he does not go very far with it. For those who want to go into it further, probably the best and most readable recent books on Zen are the various volumes by Osho.
Its a pity he has not been able to write another book like this as there is now a vast amount of information available about DNA and RNA, the inflationary theory of the universe, quantum theory, and the beautiful fusion of string theory and advanced math, which could greatly extend and amplifiy the themes of recursion, tangledness, hierarchies, and incompleteness. One could make a good case that the basic structure of the universe has these properties at its smallest and largest scales. Both quantum physics and string theory have complex sets of laws that appear tangled,nested, hierarchical and incomplete-- and so far no one can unify them, unless one accepts string theory on faith-but nobody can solve string theory and physics, like mathematics which it mirrors (or expresses?)may remain forever incomplete( Kaku's `Hyperspace` gives a summary up to 1994-see my review).
It was one of the few times he stuck his neck out when he predicted that the future of AI would involve recursive programs but are neural nets and fuzzy logic recursive? And do these relate at all to how the brain works or to anything Wittgenstein has to say about language and reality? The diligent might want to look at B.A. Worthington's book--`Self Consciousness and Self Referencing:an interpretation of Wittgenstein's Tractatus`.
Since this book appeared, mathematician Gregory Chaitin has made major extensions of incompleteness and alsodeveloped the amazing omega number defining the limits of math(his popular and tech books easy to find on the net and his most recent on omega-- Meta Math --appeared in 2005).
Some readers will find interesting a vaguely similar book ``Labyrinth`` by Peter Pesic (2000) which uses the form of the triple fugue to link symbolic mathematics to the pursuit of science.
He does not mention that Godel showed that (if the universe is rotating) time travel is possible(ie, time is recursive), nor that all theories of physics, including quantum field theory, remain incomplete. Also the highest product of the mind--Superstring Theory is recursive to quantum field theory and the behavior of particles and the entire universe. A good bit of this was known in 1980 and Hofstadter was a physicist so it''s surprising it does not appear here. We know that the most advanced physics and the most advanced math fuse in superstring theory and this seems amazingly holistic. Physics must have the self consistent structures of mathematics but as math is inescapably incomplete does it follow that physics is also? And worse, as math is a product of the mind is not the mind forever incomplete too? Does this mean there will always be physical laws or phenomena that are not deriveable from(compatible with) the others or can physics be complete and self consistent in one universe(however we delimit or describe that) but inconsistent in others? All these questions seem likely to go on forever.
It is now a decade later and I have drastically changed my views on this book and its whole approach. It is a massive confusion that repeats on every page the standard mistakes of philosophy. For my current views please see my postings on the net or my collected writings now available on the store as paperbacks and Kindles
https://www.the store.com/dp/B071P1RP1B
https://www.the store.com/dp/B0711R5LGX
https://www.the store.com/dp/B071HVC7YP
His followup the next year with Daniel Dennet--`The Mind's I` complements this book nicely(see my review).
So one could say that this is really a psychology text. It is about human behavior and reasoning-about why we think and act the way we do. But(like all such discussions until recently) none of the explanations are really explanations. Nobody at that time had much understanding of the mental mechanisms involved. Like most 'explanations` of behavior, the comments here are often more interesting for what kinds of things he tries to use (and omits) than for the actual content. As with all reasoning and explaining, art, math, music, etc, one now wants to know which of the brains inference engines are activated. This book and most books and AI research were largely oblivious to such explanations until quite recently.
Cognitive and evolutionary psychology are still not evolved enough to provide full explanations but an interesting start has been made. Boyer's `Religion Explained` is a good place to see what a modern scientific explanation of human behavior looks like,and works on art, music and math are sure to appear soon. Pinker's `How the mind Works` is a good general survey. They do not explain all of intelligence or thinking but give an idea of how to start. See several of the recent texts(ie, 2004 onwards) with evolutionary psychology in the title or the web for further info.
We now recognize that the bases for art, music, math, philosophy, psychology, sociology, language and religion are found in the automatic functioning of templates or inference engines. This is why we can expect similarities and puzzles and inconsistencies or incompleteness and often, dead ends. The brain has no general intelligence but numerous specialized modules, each of which works on certain aspects of some problem and the results are then added, resulting in the feelings which lead to behavior. Hofstadter, like everyone, can only generate or recognize explanations that are consistent with the operations of his own inference engines, which were evolved to deal with such things as resource accumulation, coalitions in small groups, social exchanges and the evaluation of the intentions of other persons. It is amazing they can produce philosophy and science, and not surprising that figuring out how they themselves work together to produce consciousness or choice or spirituality is way beyond reach.
He does not try to deal with the endlessly vexing issue of whether these correlations are out there in the world or in here in the mind. Yes, we use our templates, but why did we evolve those and was there another possibility? Some will say this will all become clear when psychology and genetics are sufficiently advanced, while others say the same of physics and mathematics or programming. And, did they all evolve from some prototype engine in a precambrian invertebrate or did they come much later and from many sources?
It occurred to me that some of the most complex products of human reasoning --superstring theory and the associated math--are recursive( in some nontrivial sense) to quantum field theory, subatomic particle behavior and the entire universe. Physics unites many areas of the most advanced math because it needs self consistent structures, but since we know math is logically proven to be inescapably incomplete and math is a product of the mind, it seems reasonable that there must be a sense in which the mind is incomplete also. We expect since they use math that computers must be incomplete. We know that Turing's halting theorem for computation(we can not discover in advance when a computer will stop) is logically equivalent to Godel's incompleteness theorem. It might follow that physics will be incomplete as well and there will be many physical laws or phenomena that will never be compatible with or derivable from the others. Or perhaps physics can be complete and selfconsistent in one universe but not in others
Just as he did not go very far into the many realms of psychology or physics, neither did he venture far into philosophy. Perhaps the book could have benefited greatly from an understanding of the infinitely subtle relationships between language, thought and reality. An acquaintance with Wittgenstein would have helped immensely, especially his 'Lectures on the Foundations of Mathematics: Cambridge, 1939' edited by Cora Diamond(1990). It is better to get this one rather than the earlier `Remarks on the Foundations of Mathematics, Vol. 1` edited by Rush Rhees( as they are based on different sets of notes if you are really into it you should get both).
Although I've never seen anyone say so, W can be regarded as a pioneer in cognitive psychology. All of his research was thought experiments and introspection into the relations between language, thought and reality. Perhaps nobody ever approached his talent for describing the mind at work. The point is that Hofstadter is trying to understand how the mind works as a preliminary to making programs that work the same way(or at least get similar results) so anyone who is interested in this book(or nearly any area of philosophy, language, psychology, or intellectual discourse) can look into W with great profit(but be forewarned W may seem very shallow, but if you jump in you may never stop swimming)!
Just after reading this book I happened to read Wittgensteins ``Culture and Value``(published the same year(1980), but written decades earlier), and, though it's his least interesting book, I picked out a few comments that may be regarded as pertinent to much of this book and of course to a large part of modern intellectual life.
``There is no religious denomination in which the misuse of metaphysical expressions has been responsible for so much sin as it has in mathematics.``
``People say again and again that philosophy doesn't really progress, that we are still occupied with the same philosophical problems as were the Greeks. But the people who say this don't understand why is has to be so. It is because our language has remained the same and keeps seducing us into asking the same questions. As long as there continues to be a verb 'to be' that looks as if it functions in the same was as 'to eat' and 'to drink', as long as we still have the adjectives 'identical', 'true', 'false', 'possible', as long as we continue to talk of a river of time, of an expanse of space, etc., etc., people will keep stumbling over the same puzzling difficulties and find themselves staring at something which no explanation seems capable of clearing up. And what's more, this satisfies a longing for the transcendent, because, insofar as people think they can see `the limits of human understanding', they believe of course that they can see beyond these.``
Whenever one gets philosophical it is relevant to take a step back from time to time and see just what is really going on. Hofstadter is not a philospher and he does not seem to take that step. Incompleteness seems well defined in math but what about elsewhere? In what sense is music or art or biology incomplete? And exactly what will count as a tangled hierarchy, and recursiveness or self referencing in such different realms(and as W would say, such different language games)? Its not really so clear that the recursiveness in art, music, biology and math are the same sort of thing at all an, insofar as they are, what exactly that means. What should count as ``same` here?
H does not address these questions in any depth but one might find them by far the most interesting theme of the book. We are tantalized at the seeming connections but do they mean anything? Do they go to the core of our being(how the mind works)? Are they merely the result of the use of some of the same templates by art, math, and music? Do they relate to the molecular structure of matter or to particle physics and string theory? Is it useful to extend these analogies(or are they homologies?)almost endlessly further into philosophy, language, psychology, biology(e.g., not only the recursive nature of DNA, RNA and proteins, but the many levels of feedback in the nucleus, cytoplasm, intercellular, interorgan, intracerebral, exchange of chemicals and genes between nucleus, mitochondria and chloroplasts as well as with the bacteria and viruses that wander in out of our bodies into other bodies and other organisms happily picking up and dropping off genes as they go--tangled, recursive, hierarchical and in some sense, incomplete).
Or, to take it further, one might find yet more connections between art and music, math and biology, computer programs, physics and chemistry and biochemistry and add such dimensions as color, geometric shapes, measurements , self organizing abilities, chaos, and other temporal, spatial or purely psychological ways(emotions, sensations, dreams etc). There are many books in art, music, math, biology, psychology, physics and chemistry that already touch upon these themes but I think the most progress is being made in cognitive psychology. The brain is highly recursive in many ways. We converse with ourselves internally and many times externally. The schizophrenic commonly hears voices, but they rarely say nice things.
One is reminded of the cut-ups that William Burroughs and Byron Gysin created. They cut up books or even newspapers and stuck them back together randomly. There was usually some perverse kind of logic to the result showing the hidden threads in discourse. Burroughs later did the same thing with films, with similar results.
Of course pursuing hidden relationships between seemingly unconnected things quickly leads to numerology, pyrimidology and madness. One can find codes or algorithms to connect or derive anything from anything. Hofstadter does not go into this here but he mentions it in his next book, The Minds I(1981). I am reminded of string theory which has math so powerful it can probably explain any possible universe and so it is very suspect as an explanation of ours.
He suggest that incompleteness, tangled hierarchies etc may be responsible for the emergence of higher phenomena which do not exist and cannot be explained at lower levels(eg, consciousness and in fact, everything)and seems to be something of a holist( but in other places he seems clearly behaviorist or reductionist). You might say he is suggesting we look for the explanation of emergence in the bizarre phenomena of the foundations of math, rather than in those in the foundations of physics. Given a universe where life is possible, is it not inevitably full of recursiveness, tangled hierarchies, incompleteness etc.
As H is well aware, Zen can be regarded as using these aspects of the world to trick the mind into stopping-- at which point all relationships become irrelevant. However he was just starting in Zen at the time so he does not go very far with it. For those who want to go into it further, probably the best and most readable recent books on Zen are the various volumes by Osho.
Its a pity he has not been able to write another book like this as there is now a vast amount of information available about DNA and RNA, the inflationary theory of the universe, quantum theory, and the beautiful fusion of string theory and advanced math, which could greatly extend and amplifiy the themes of recursion, tangledness, hierarchies, and incompleteness. One could make a good case that the basic structure of the universe has these properties at its smallest and largest scales. Both quantum physics and string theory have complex sets of laws that appear tangled,nested, hierarchical and incomplete-- and so far no one can unify them, unless one accepts string theory on faith-but nobody can solve string theory and physics, like mathematics which it mirrors (or expresses?)may remain forever incomplete( Kaku's `Hyperspace` gives a summary up to 1994-see my review).
It was one of the few times he stuck his neck out when he predicted that the future of AI would involve recursive programs but are neural nets and fuzzy logic recursive? And do these relate at all to how the brain works or to anything Wittgenstein has to say about language and reality? The diligent might want to look at B.A. Worthington's book--`Self Consciousness and Self Referencing:an interpretation of Wittgenstein's Tractatus`.
Since this book appeared, mathematician Gregory Chaitin has made major extensions of incompleteness and alsodeveloped the amazing omega number defining the limits of math(his popular and tech books easy to find on the net and his most recent on omega-- Meta Math --appeared in 2005).
Some readers will find interesting a vaguely similar book ``Labyrinth`` by Peter Pesic (2000) which uses the form of the triple fugue to link symbolic mathematics to the pursuit of science.
He does not mention that Godel showed that (if the universe is rotating) time travel is possible(ie, time is recursive), nor that all theories of physics, including quantum field theory, remain incomplete. Also the highest product of the mind--Superstring Theory is recursive to quantum field theory and the behavior of particles and the entire universe. A good bit of this was known in 1980 and Hofstadter was a physicist so it''s surprising it does not appear here. We know that the most advanced physics and the most advanced math fuse in superstring theory and this seems amazingly holistic. Physics must have the self consistent structures of mathematics but as math is inescapably incomplete does it follow that physics is also? And worse, as math is a product of the mind is not the mind forever incomplete too? Does this mean there will always be physical laws or phenomena that are not deriveable from(compatible with) the others or can physics be complete and self consistent in one universe(however we delimit or describe that) but inconsistent in others? All these questions seem likely to go on forever.
It is now a decade later and I have drastically changed my views on this book and its whole approach. It is a massive confusion that repeats on every page the standard mistakes of philosophy. For my current views please see my postings on the net or my collected writings now available on the store as paperbacks and Kindles
https://www.the store.com/dp/B071P1RP1B
https://www.the store.com/dp/B0711R5LGX
https://www.the store.com/dp/B071HVC7YP
★ ★ ★ ★ ★
abd rsh
I am just finishing the last dialog of GEB and had, what for me, is a strange reaction to it. I found it very entertaining though I have some problems with a few of the techniques the author uses in atempting to make the book more accessable to the average reader (arithmoquining, etc.). I would prefer it to have been a bit more mathematically rigouous, but that's the physicist in me coming out.
I was sitting on the train, on my way into work, reading the book and decided to look aheasd to see how much was left. I suddenly found myself saying "I will miss this book like an old friend who suddenly anounced that he is moving away". For me, a strange reaction, but one that speaks of the entertaining and enjoyable nature of the book.
I was sitting on the train, on my way into work, reading the book and decided to look aheasd to see how much was left. I suddenly found myself saying "I will miss this book like an old friend who suddenly anounced that he is moving away". For me, a strange reaction, but one that speaks of the entertaining and enjoyable nature of the book.
★ ★ ★ ★ ★
alex tell
This may be a difficult read, but I think it's worth it. There's a definate payoff to be had; this book contains stuff that can be downright exciting, when things start connecting in ways you'd never considered before. (Or maybe that's just me : )
If you hate "thinking" and deliberately avoid math just on principle, you might not like this book. If you do puzzles, you probably will enjoy it.
If you hate "thinking" and deliberately avoid math just on principle, you might not like this book. If you do puzzles, you probably will enjoy it.
★ ★ ★ ★ ★
william
I would never give anything 10 out of 10.
My copy of this book is sitting on the desk to the left to me. It usualy lives on the bookshelves about 40cms to the left of that. It is battered, worn and the paper cover's torn. It is the 1980 Penguin edition. It's been read about 10 times. It's been skimmed a hundred times more.
Max Escher visited my life when I became fascinated with the process of lithography after initially discovering the work of William Heath-Robinson. J S Bach wrote some wonderful blues baselines which I shamelessly plagerised when doing my music O-level. Godel was a strange name (despite my background in mathematics).
I write computer programs for a living. Alan Turing has always been my hero (he died 3 months before I was born). Pictures and music have always been part of my life. Formal systems more so. Zen came in the 60s (via, indirectly, Pirsig's "Zen and the Art of Motorcycle Maintenance").
There are those who find this book trivial and the jokes facile. There are those who find this book difficult and confusing. The former are those who lack the joy of a child finding magic in numbers and who have their own intellectual agenda to impose. The latter need encouragement: this book needs work, it makes you think and thinking has consequences. You do not need to accept Hofstadter's thesis (though it is a damn sight more convincing than that of Roger Penrose's "The Emperor's New Clothes), but you *must* find joy in its presentation. The only comparable book (though far more limited in its domain) is Raymond Smullyan's "What is the Name of this Book?".
The very exsitence of GEB adds colour to our lives and gives us, in Ian Drury's immortal words, "reasons to be cheerful". This book is the starting point for thought, converstation and discovery. It presents concepts as a process of revalation. It is the work of a unique mind. Some people don't like that. I do. Try it and see.
My copy of this book is sitting on the desk to the left to me. It usualy lives on the bookshelves about 40cms to the left of that. It is battered, worn and the paper cover's torn. It is the 1980 Penguin edition. It's been read about 10 times. It's been skimmed a hundred times more.
Max Escher visited my life when I became fascinated with the process of lithography after initially discovering the work of William Heath-Robinson. J S Bach wrote some wonderful blues baselines which I shamelessly plagerised when doing my music O-level. Godel was a strange name (despite my background in mathematics).
I write computer programs for a living. Alan Turing has always been my hero (he died 3 months before I was born). Pictures and music have always been part of my life. Formal systems more so. Zen came in the 60s (via, indirectly, Pirsig's "Zen and the Art of Motorcycle Maintenance").
There are those who find this book trivial and the jokes facile. There are those who find this book difficult and confusing. The former are those who lack the joy of a child finding magic in numbers and who have their own intellectual agenda to impose. The latter need encouragement: this book needs work, it makes you think and thinking has consequences. You do not need to accept Hofstadter's thesis (though it is a damn sight more convincing than that of Roger Penrose's "The Emperor's New Clothes), but you *must* find joy in its presentation. The only comparable book (though far more limited in its domain) is Raymond Smullyan's "What is the Name of this Book?".
The very exsitence of GEB adds colour to our lives and gives us, in Ian Drury's immortal words, "reasons to be cheerful". This book is the starting point for thought, converstation and discovery. It presents concepts as a process of revalation. It is the work of a unique mind. Some people don't like that. I do. Try it and see.
★ ★ ★ ★ ☆
angela gillis
Mathematical theories shape-shift like ice cream on a tin roof in Tijuana, time and space invert, and talking tortoises demolish record players-and that's the simple stuff. Its a tall drink for the casual reader, but those who've secretly yearned for more surrealism in their algebra or who won't look both ways before approaching the intersection of art, mathematics, and philosophy will be rewarded. GEB presents a view of mind mechanics, the nature of intelligence, and the challenges of creating both artificially that is at best enlightening, and, at worst, unparalleled in most readers' experience. Take five months off and tackle it.
★ ★ ★ ★ ★
anne simpson
I first picked up this book as a pretentious college freshman and went in head first thinking that I would get some sort of badge from completing this immense Pulitzer Prize winning novel in the mathematic community. Nearly 20 years later, I re-read the book and truly understood the intense themes and real significance of the book for the book itself... not for the challenge of completing it. It's a long and challenging read, even for math types, but what you gain from Dr. Hofstadter is the definitive work of cognitive science and it is amazing!
★ ★ ★ ★ ★
ellie
Sorry for the crass title, but I really couldn't think of a better way to describe it. The book is about strange loops and paradoxes, which by their very nature screw with your head. I love this book. It's the most intellectually stimulating book I've ever read. It truly challenges the way you think, and does so in an entertaining and beautiful way. For anyone who has a strong multidisciplinary pull in their lives (Personally, I'm a programmer and an artist), just read it. It's worth it.
★ ★ ★ ★ ★
andi purwanto
It is quite likely that the hardest question I've ever been asked is, "What's that book about?" This book manages to discuss, coherently, cohesively, and interestingly, everything from molecular biology to quantum physics to computer science to music theory to philosophy to advanced mathematics to Elizabethan literature and beyond. Reading this will definitely change the way you see the world, and if you read one book this entire year, this should probably be it. VERY highly recommended.
★ ★ ★ ★ ★
jakob b born
I came across this book in 1993. I had to prepare for a seminar on AI as part of my curriculum. My then tutor recommended that I read this book before preparing for my seminar.
The journey started at this point. No matter however hard I tried, I couldnt keep the book down.
One could not help repeatedly starring at Escher's paintings on relativity and admiring it. It seems to be whole new world out there. Another painting that is great is the 'Waterfall'.
The dialogues between Achiless and the tortoise are simply great. It gives us the insight on how great men think.
WONDERFUL WONDERFUL WONDERFUL It is indeed creditable of Mr. Hofstadter to bring out this masterpiece.
The journey started at this point. No matter however hard I tried, I couldnt keep the book down.
One could not help repeatedly starring at Escher's paintings on relativity and admiring it. It seems to be whole new world out there. Another painting that is great is the 'Waterfall'.
The dialogues between Achiless and the tortoise are simply great. It gives us the insight on how great men think.
WONDERFUL WONDERFUL WONDERFUL It is indeed creditable of Mr. Hofstadter to bring out this masterpiece.
★ ★ ★ ★ ★
cindy halsey
This is an amazing book if you have ever wondered if Math, Music and Art were somehow linked. Yes, the are and this book will explain how.
If you are interested in the subject but are a novice in the area, reading 'Art and Physics' by Leonard Shlain will set a good platform for this book.
If you are interested in the subject but are a novice in the area, reading 'Art and Physics' by Leonard Shlain will set a good platform for this book.
★ ★ ★ ★ ★
amalie
Seemingly unrelated topics (art, music, mathematics and even Zen Buddhism) have been beautifully interwoven to illustrate a central point. Very powerful and even enlightening. I really like the dialogues (hidden) meaning which makes the following chapters so much easier to follow.
★ ★ ★ ★ ★
josh evans
Even though Thomas Cleary claims Hofstadter doesn't really grok Zen, any serious student of the nature of the mind should read this Pulitzer-Prize winning labor of love.
--Richard Brodie, author, Virus of the Mind: The New Science of the Mem
--Richard Brodie, author, Virus of the Mind: The New Science of the Mem
★ ★ ★ ★ ★
tamuna
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.
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.
★ ★ ★ ★ ★
claudio
Hofstadter has done a original work combining art, mathematics, computer and philosophy. He presents the core similarity between the greatest work of art and mathematic which has a great implication on mind. The book is very readable, enjoyable and interlectual. It is a non-fiction which can be read like a fiction. A great book!!!
★ ★ ★ ★ ★
diane uhl
This book is great! It discusses some very serious matters, and it is not an easy book to tackle. However, it is very enjoyable to read, as Hofstadter augments each subject with examples from very diverse sources. The joy of discovering the puns and other playful gems hidden in the book is part of what makes it so special. Anecdotes, word plays and Zen koans are additional aspects that help make the 777 pages an experience that many readers consider to be a turning point in their lives. Other books I liked are Paul Omeziri's Descent into Illusions and Steven Pinker's How the Mind Works.
★ ★ ★ ☆ ☆
yumiko
I first started reading G, E, B at the recommendation of a friend. I did not start at the conventional beginning, but instead with the TNT chapter. I took my time, insisting that I at least tried to understand everything said. Finishing this chapter with a huge sigh of relief, I read on to the next, and the next. Having finished this outstanding book, I thought about what I had learnt. The Answer? Absolutely nothing useful, except that nothing is definitive, and that there are an infinite number of perceptions. I will read this book again in a year or so, not to understand more, or to learn anything of "real" value, but to be swallowed again and again in the thoughts, and ideas of some of our greatest, most contraversial minds. Don't try to disprove what is said in this book, or you could well succeed. Just allow yourself to be swept away by the magic of the mind.
★ ★ ★ ☆ ☆
brandon uttley
Telling people not to read "Gödel, Escher, Bach" is like telling people not to read Harry Potter. This book has become so much of a cultural touchstone that everyone should read it, just to see what the hype is about. In fact, Hofstadter has written a very careful exploration of the nature of consciousness. Now, I don't find the questions that he raises, of self-reference or the consistency of systems of axioms, very interesting, but reading "Gödel, Escher, Bach" reminded me of all the problems that *do* interest me. In that respect, the book's "negative space" had a very deep influence on me, and, since one of the book's themes is negative and positive space, I like to think that my reading is in a spirit that Hofstadter would approve of.
If you're interested in theories of consciousness or Gödel's theorem, this book may appeal to you, especially if you appreciate a playful treatment of these topics and don't mind the author's long-windedness. Now, I was not enthusiastic to begin with, so I don't feel qualified to comment on the flaws in the book's argument. But I will recommend 3 other books on related topics which complement "Gödel, Escher, Bach" nicely, even for more sympathetic readers.
A more accessible, better contextualized, and more enlightening treatment of Gödel's Incompleteness Theorem can be found in "Logicomix" by Doxiadis and Papadimitriou.
Descartes' theory of consciousness assumes, like Hofstadter's, that consciousness is an individual (rather than a social) phenomenon. Descartes' approach is axiomatic without taking into account problems of self-reference. (You might say that Hofstadter tries to update Descartes for the post-Gödel era, which forces Hofstadter to place less faith in deductive reasoning.) You might read the "Discourse on Method" or the "Meditations on First Philosophy". Those books are both much shorter and much wittier than "Gödel, Escher, Bach".
Finally, Ramachandran has interesting things to say on the subject of consciousness and sees self-reference as only one of several defining characteristics of consciousness. He makes some remarks to that effect at the end of "Phantoms in the Brain".
If you're interested in theories of consciousness or Gödel's theorem, this book may appeal to you, especially if you appreciate a playful treatment of these topics and don't mind the author's long-windedness. Now, I was not enthusiastic to begin with, so I don't feel qualified to comment on the flaws in the book's argument. But I will recommend 3 other books on related topics which complement "Gödel, Escher, Bach" nicely, even for more sympathetic readers.
A more accessible, better contextualized, and more enlightening treatment of Gödel's Incompleteness Theorem can be found in "Logicomix" by Doxiadis and Papadimitriou.
Descartes' theory of consciousness assumes, like Hofstadter's, that consciousness is an individual (rather than a social) phenomenon. Descartes' approach is axiomatic without taking into account problems of self-reference. (You might say that Hofstadter tries to update Descartes for the post-Gödel era, which forces Hofstadter to place less faith in deductive reasoning.) You might read the "Discourse on Method" or the "Meditations on First Philosophy". Those books are both much shorter and much wittier than "Gödel, Escher, Bach".
Finally, Ramachandran has interesting things to say on the subject of consciousness and sees self-reference as only one of several defining characteristics of consciousness. He makes some remarks to that effect at the end of "Phantoms in the Brain".
★ ★ ★ ★ ★
kat o b
It seems highly appropriate that Douglas Hofstatder should re-release his epic work now. His central theme plays so eloquently in this place and time: Every system folds in on itself, be it physics, mathematics, or any form of language. All these systems are inherently self-referential, and as such, take on a life of their own. A life their creators could never imagine. Many reviewers have focused on the explicit messages of the book, their likes or dislikes, but the great beauty of this work lies within the realm of what it does not say. It is, no doubt, the most difficult book I have ever read, and I have to admit it took me several false starts to finally get through the thing. It is so incredibly deep - one cannot simply wade through it like a sci-fi novel. But if you take your time, spend, say about a year on it - work through the TNT exercises, discover the hidden messages the author has left, read the bibliography - and at some point it will strike you; the incredible richness of the message. The book, you, the world, all of it IS open. The pages of this universe are blank, unwritten. Dr. Hofstadter has woven a message of eternal optimism, one that transcends even the infinite depth to the tapestry of topics spread before us: The great freedom that we, nature's most remarkable matrix, are part of a future without destiny. Even if we were created, any purpose impressed upon us is lost in a cacophany of unexpected relationships. Deterministic, yet infinitely complex and unpredictable. We can never understand anything completely, and thus every life can experience the magic of observing that which cannot be explained. This is a book of wonders, and you will never regret the time you spent on it.
★ ★ ★ ★ ★
nikky
Even though Thomas Cleary claims Hofstadter doesn't really grok Zen, any serious student of the nature of the mind should read this Pulitzer-Prize winning labor of love.
--Richard Brodie, author, Virus of the Mind: The New Science of the Mem
--Richard Brodie, author, Virus of the Mind: The New Science of the Mem
★ ★ ★ ★ ★
loni
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.
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.
★ ★ ★ ★ ★
diane mccarrick
Hofstadter has done a original work combining art, mathematics, computer and philosophy. He presents the core similarity between the greatest work of art and mathematic which has a great implication on mind. The book is very readable, enjoyable and interlectual. It is a non-fiction which can be read like a fiction. A great book!!!
★ ★ ★ ★ ★
lulyy
This book is great! It discusses some very serious matters, and it is not an easy book to tackle. However, it is very enjoyable to read, as Hofstadter augments each subject with examples from very diverse sources. The joy of discovering the puns and other playful gems hidden in the book is part of what makes it so special. Anecdotes, word plays and Zen koans are additional aspects that help make the 777 pages an experience that many readers consider to be a turning point in their lives. Other books I liked are Paul Omeziri's Descent into Illusions and Steven Pinker's How the Mind Works.
★ ★ ★ ☆ ☆
zac mccoy
I first started reading G, E, B at the recommendation of a friend. I did not start at the conventional beginning, but instead with the TNT chapter. I took my time, insisting that I at least tried to understand everything said. Finishing this chapter with a huge sigh of relief, I read on to the next, and the next. Having finished this outstanding book, I thought about what I had learnt. The Answer? Absolutely nothing useful, except that nothing is definitive, and that there are an infinite number of perceptions. I will read this book again in a year or so, not to understand more, or to learn anything of "real" value, but to be swallowed again and again in the thoughts, and ideas of some of our greatest, most contraversial minds. Don't try to disprove what is said in this book, or you could well succeed. Just allow yourself to be swept away by the magic of the mind.
★ ★ ★ ☆ ☆
reyhan syifa
Telling people not to read "Gödel, Escher, Bach" is like telling people not to read Harry Potter. This book has become so much of a cultural touchstone that everyone should read it, just to see what the hype is about. In fact, Hofstadter has written a very careful exploration of the nature of consciousness. Now, I don't find the questions that he raises, of self-reference or the consistency of systems of axioms, very interesting, but reading "Gödel, Escher, Bach" reminded me of all the problems that *do* interest me. In that respect, the book's "negative space" had a very deep influence on me, and, since one of the book's themes is negative and positive space, I like to think that my reading is in a spirit that Hofstadter would approve of.
If you're interested in theories of consciousness or Gödel's theorem, this book may appeal to you, especially if you appreciate a playful treatment of these topics and don't mind the author's long-windedness. Now, I was not enthusiastic to begin with, so I don't feel qualified to comment on the flaws in the book's argument. But I will recommend 3 other books on related topics which complement "Gödel, Escher, Bach" nicely, even for more sympathetic readers.
A more accessible, better contextualized, and more enlightening treatment of Gödel's Incompleteness Theorem can be found in "Logicomix" by Doxiadis and Papadimitriou.
Descartes' theory of consciousness assumes, like Hofstadter's, that consciousness is an individual (rather than a social) phenomenon. Descartes' approach is axiomatic without taking into account problems of self-reference. (You might say that Hofstadter tries to update Descartes for the post-Gödel era, which forces Hofstadter to place less faith in deductive reasoning.) You might read the "Discourse on Method" or the "Meditations on First Philosophy". Those books are both much shorter and much wittier than "Gödel, Escher, Bach".
Finally, Ramachandran has interesting things to say on the subject of consciousness and sees self-reference as only one of several defining characteristics of consciousness. He makes some remarks to that effect at the end of "Phantoms in the Brain".
If you're interested in theories of consciousness or Gödel's theorem, this book may appeal to you, especially if you appreciate a playful treatment of these topics and don't mind the author's long-windedness. Now, I was not enthusiastic to begin with, so I don't feel qualified to comment on the flaws in the book's argument. But I will recommend 3 other books on related topics which complement "Gödel, Escher, Bach" nicely, even for more sympathetic readers.
A more accessible, better contextualized, and more enlightening treatment of Gödel's Incompleteness Theorem can be found in "Logicomix" by Doxiadis and Papadimitriou.
Descartes' theory of consciousness assumes, like Hofstadter's, that consciousness is an individual (rather than a social) phenomenon. Descartes' approach is axiomatic without taking into account problems of self-reference. (You might say that Hofstadter tries to update Descartes for the post-Gödel era, which forces Hofstadter to place less faith in deductive reasoning.) You might read the "Discourse on Method" or the "Meditations on First Philosophy". Those books are both much shorter and much wittier than "Gödel, Escher, Bach".
Finally, Ramachandran has interesting things to say on the subject of consciousness and sees self-reference as only one of several defining characteristics of consciousness. He makes some remarks to that effect at the end of "Phantoms in the Brain".
★ ★ ★ ★ ★
hallie wachowiak
It seems highly appropriate that Douglas Hofstatder should re-release his epic work now. His central theme plays so eloquently in this place and time: Every system folds in on itself, be it physics, mathematics, or any form of language. All these systems are inherently self-referential, and as such, take on a life of their own. A life their creators could never imagine. Many reviewers have focused on the explicit messages of the book, their likes or dislikes, but the great beauty of this work lies within the realm of what it does not say. It is, no doubt, the most difficult book I have ever read, and I have to admit it took me several false starts to finally get through the thing. It is so incredibly deep - one cannot simply wade through it like a sci-fi novel. But if you take your time, spend, say about a year on it - work through the TNT exercises, discover the hidden messages the author has left, read the bibliography - and at some point it will strike you; the incredible richness of the message. The book, you, the world, all of it IS open. The pages of this universe are blank, unwritten. Dr. Hofstadter has woven a message of eternal optimism, one that transcends even the infinite depth to the tapestry of topics spread before us: The great freedom that we, nature's most remarkable matrix, are part of a future without destiny. Even if we were created, any purpose impressed upon us is lost in a cacophany of unexpected relationships. Deterministic, yet infinitely complex and unpredictable. We can never understand anything completely, and thus every life can experience the magic of observing that which cannot be explained. This is a book of wonders, and you will never regret the time you spent on it.
★ ★ ★ ★ ★
lisa alonso
This is the most intriguing book I have ever read. Extraodinary and perplexing... very clearly exposed. The author is brilliant. Obligatory reading, to be taken with care. Often times more disturbing than fascinating. Never boring.
★ ★ ★ ★ ★
rashi
This is perhaps one of the most ingenius books ever written. Douglas Hofstadter has managed to tie together music, art, mathematics, biology and so much more to make this masterpiece. There has never been a book quite like this.
★ ★ ★ ★ ★
ciaran kerr
I'm surprised not to see more discussion of the chapter on translation and meaning. I thought it was one of the best parts of the book. The Japanese translation of the book also included a Japanese version of Jabberwocky.
Though I read the book several years ago, it made a deep and lasting impression in many ways. What actually brought it to mind just now was the coming year of the dragon, which reminded me of Escher's amazing wannabe 3D dragon image used in the book. I don't think anyone can deal with this book in the few weeks a library would allow you to have it...
Though I read the book several years ago, it made a deep and lasting impression in many ways. What actually brought it to mind just now was the coming year of the dragon, which reminded me of Escher's amazing wannabe 3D dragon image used in the book. I don't think anyone can deal with this book in the few weeks a library would allow you to have it...
★ ★ ★ ★ ★
talime
I was blessed with a few great professors in college. Interestingly, two of them were recipients of Nobel and Pulitzer Prizes. I recently took the time to re-read a few of their important works, so I thought a review of these two important authors plus another newly published book by an exciting new author would be appropriate - as all three books share similar traits. I will review these books collectively, and I recommend all three without reservation!
The books are: Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter; Governing the Commons: The Evolution of Institutions for Collective Action (Political Economy of Institutions and Decisions) by Elinor Ostrom; and The Blueprint: Averting Global Collapse by Daniel Rirdan.
Whether it's Hofstadler's Pulizter Prize winning words about artificial intelligence, Ostrom's Nobel Prize winning economic and political comparison of state versus private ownership of common lands, or Rirdan's amazing ability to set political and economic realities aside and probe possible solutions to potential environmental chaos... the trait shared by all three writers and all three books is that they think big.
Because of this, some people will not like these books - one or all. In fact, some people will hate them... and that's OK. Some people are deep thinkers, and some are not. When I sat in Hofstadler's class decades ago, he had already won the awards for his book... and I understood why! When I listened to Professor Ostrom, she was not even the most famous political scientist or economist in her home, as that title belonged to her equally talented husband... but her words rang with clarity and purpose and inspired like few others! When I read the words of Mr. Rirdan, I feel the same way... in fact, his book was what enticed me to pull my well-worn dog-eared books by Ostrom and Hofstadler out of mothballs to be read yet again.
It's a shame that Professor Ostrom (both of them actually) passed away last month, as I think she would have enjoyed reading Rirdan's discussion of what is required to facilitate the great change that's needed for our world to survive and flourish - as this deeply impacts the common pool resources that she loved to examine and discuss...and much more. The economist in her likely also would have been a bit fascinated by his analysis of our globes biomass footprint and how this total anchors our sustainable economic realities into the future of a planet with 7 billion people already on board. While I've not spoken with Professor Hofstadler in decades, I have a feeling that he would admire the way Rirdan set aside some limits of current reality to examine and quantify future possibilities... not altogether different than a dreamlike division of the plane by M.C. Escher that Hofstadler held so dear, or even Ostrom's enjoyable game-theory ramblings.
Frankly, I don't agree with every one of Rirdan's conclusions, and in fact he is seemingly far left of my normally libertarian stance on most issues - but I don't agree necessarily with all of what Ostrom and Hofstadler wrote either. (I will resist the urge to call Hofstadler a strange loop! LOL) That said, I recognize genius when I read it... and all three of these books can be described accordingly. You will be a better person from examining all or any of these three books... I know I am!
The books are: Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter; Governing the Commons: The Evolution of Institutions for Collective Action (Political Economy of Institutions and Decisions) by Elinor Ostrom; and The Blueprint: Averting Global Collapse by Daniel Rirdan.
Whether it's Hofstadler's Pulizter Prize winning words about artificial intelligence, Ostrom's Nobel Prize winning economic and political comparison of state versus private ownership of common lands, or Rirdan's amazing ability to set political and economic realities aside and probe possible solutions to potential environmental chaos... the trait shared by all three writers and all three books is that they think big.
Because of this, some people will not like these books - one or all. In fact, some people will hate them... and that's OK. Some people are deep thinkers, and some are not. When I sat in Hofstadler's class decades ago, he had already won the awards for his book... and I understood why! When I listened to Professor Ostrom, she was not even the most famous political scientist or economist in her home, as that title belonged to her equally talented husband... but her words rang with clarity and purpose and inspired like few others! When I read the words of Mr. Rirdan, I feel the same way... in fact, his book was what enticed me to pull my well-worn dog-eared books by Ostrom and Hofstadler out of mothballs to be read yet again.
It's a shame that Professor Ostrom (both of them actually) passed away last month, as I think she would have enjoyed reading Rirdan's discussion of what is required to facilitate the great change that's needed for our world to survive and flourish - as this deeply impacts the common pool resources that she loved to examine and discuss...and much more. The economist in her likely also would have been a bit fascinated by his analysis of our globes biomass footprint and how this total anchors our sustainable economic realities into the future of a planet with 7 billion people already on board. While I've not spoken with Professor Hofstadler in decades, I have a feeling that he would admire the way Rirdan set aside some limits of current reality to examine and quantify future possibilities... not altogether different than a dreamlike division of the plane by M.C. Escher that Hofstadler held so dear, or even Ostrom's enjoyable game-theory ramblings.
Frankly, I don't agree with every one of Rirdan's conclusions, and in fact he is seemingly far left of my normally libertarian stance on most issues - but I don't agree necessarily with all of what Ostrom and Hofstadler wrote either. (I will resist the urge to call Hofstadler a strange loop! LOL) That said, I recognize genius when I read it... and all three of these books can be described accordingly. You will be a better person from examining all or any of these three books... I know I am!
★ ★ ★ ★ ★
trevor
EGB is a tremendous work in the field of cognitive science. Not only does Hofstadter draw together many of the findings of his field into a concise and readable format, but he also draws the reader into thinking about the genesis and consequences of the mental process. EGB's socratic, and often humorous, dialogs are a work of art unto themselves. Highly recommended.
★ ☆ ☆ ☆ ☆
nick bicknell
Allow me to rant a bit- this involves issues I feel most keenly about (or, you can skip ahead to the final paragraph for a summary). I read this book in the early 90's, after reading glowing reviews. I pored over it, pondered it; some things didn't add up (which I attributed to my own intellectual deficiencies- I was then an undergraduate, likely in WAY over my head), but I ultimately concluded that its central theses were that wholes can be greater than the sum of their parts, that systems are not really "closed", only appear to be, and that strange loops seem to defy the normal laws of physics in some quantum sense.
Hofstadter's avowed intent to analyze the world and the mind in the spirit of Lewis Carroll (whom I'd read and delighted in), his celebration of the genius of three men who infused their work with their spirituality, his koan-like meditations, and multiple levels of analysis seemed to me a valentine to the complexities and irreducibility of the universe and human consciousness, implying that human thought, "the mind" could exceed the confines of the human brain, just as Escher's paintings and Godelian knots escaped being defined or constrained by dimensional space. The phenomena described so poetically by Hofstadter seemed to me to suggest the possibility of ever widening spheres of analysis, of perception, of consciousness. Or so I thought. In any case, I was tremendously inspired by it. In my naivete, I thought he embodied perspectives simultaneously scientific and spiritual, as did the book's namesakes, in varying degrees. (Note that this is from memory, which cannot be other than selective- I donated the book years ago. These are the impressions that have stuck with me.) In succeeding years I read his next two books, although I have little memory of those.
It wasn't until a few years later, after I'd read World Hypotheses: A Study in Evidence by Stephen Pepper (must reading for anyone seeking to understand how knowledge is organized and "truth" derived), as well as At Home in the Universe by John Archibald Wheeler, The Mathematical Foundations of Quantum Mechanics by John von Neumann, works by Ilya Prigogine, Hermann Lotze, William James, and others (as part of advanced study in cognitive neuroscience, philosophy, and the philosophy of science), books that directly addressed the issues hinted at, or at least suggested to me by Hofstadter, that I went back and re-read GEB.
I had an epiphany, muddied by a sense of betrayal at being utterly duped, that, in fact, not only did Hoffstadter not mean what I thought he had (MY bad), but the book actually said very little and proved nothing. Just prior to revisiting it I'd read an article by Hofstadter asserting that GEB was actually about mind/consciousness as a mere epiphenomenon that arises as an emergent property of individual neurons, themselves non-conscious (his ant analogy). This was not even then a new idea, and he didn't provide proof of it, indeed, seemed to contradict it. More egregiously, it's a mechanistic notion, yet he cited Godel, a non-mechanistic theorist, whose theorem, according to Godel himself, demonstrates that symbolic thought can NOT arise from inanimate matter, due to the necessity of recursion in logical thought. Moreover, Godel thought it proof, along with other axioms he'd developed, of God's existence (btw, his bff Albert Einstein thought so too). Dirty pool indeed, to subvert, misrepresent and try to twist a mathematical proof to fit, to subserve one's own incompatible and biased agenda, WITHOUT owning up to what you're doing- intellectually dishonest in the extreme (if he's not a passive-aggressive, I'll eat my hat, though that's hardly pertinent). In any event, he was unsuccessful, but that fact seems to have escaped nearly everyone's notice.
Cognitive psychology is rife with intriguing mysteries to be solved. Neurons seem to have a mind of their own, changing their receptor sites at the flick of an eye, firing, responding or not responding to stimuli by mechanisms we've yet to discover. And they respond not only to electrical signals, but to chemical/magnetic changes and a vast array of neurotransmitters and hormones. Cells in the immune system also sport rapidly morphing receptor sites, making the situation even more complex.
In one study, a neuron was transplanted from a grasshopper's brain to its belly. The neuron grew into the surrounding tissue, but to the surprise of researchers, grew one, abnormally long dendrite [for receiving neural signals] directly back to the exact spot from which it had been excised, presumably so that it could keep abreast of developments in its old stomping grounds. The question of course is, how did it know from whence it came?
There's a long-standing debate amongst cognitivists and philosophers about the seeming irreconcilability of symbolic thought processes and observations of actual neuronal processes (a focus of Godel's work). Hofstadter's likening of neurons to ants did nothing to reconcile the two perspectives, nor did stories of tortoises or hares, though he seemed to suggest otherwise, without ever actually explaining how they did. In fact, Hofstadter's book, though lyrical, shed no new light on ANY of the pressing issues in cognitive science. As I remember, the entire book boils down to this (though I had to look long and hard to find it): strange loops exist in nature. Since we know there's no divine or organizing principle extant in nature, they must occur by natural means. Period. No actual proof is provided. No experiments are conducted. It's not science- it's a faith assumption.
GEB leads us down myriad garden paths that go nowhere. It's smoke and mirrors, an elaborate exercise in obfuscation and intellectual masturbation, AND full of errant premises- Pulitzer Prize, zen-master-like countenance and assured, authoritative tone not withstanding. I'd have no beef with Hofstadter if he'd presented his musings in a less duplicitous fashion, if he'd said "These are musings, part prose, part metaphysical speculation, draw from them what you will, but they're offered as proof of nothing." Or, he could have laid bare the real issues involved, presenting both sides of the materialism VS idealism debate, for example (he didn't, of course, because he actually had nothing new to add). It's the inherent DISHONESTY, the cloaking of the real issues involved, that irks me so. SPIT IT OUT- what do you believe, what evidence do you have in support of your contentions, what dilemmas still remain for you, how might these be studied/resolved? If you want to read works simultaneously scientific, substantive, inspiring, achingly poetic, and USEFUL, curl up with anything by French neuroscientist/philosopher Gaston Bachelard, or Jerome Bruner. If you want to be challenged by perplexities both tantalizing and profound, try the inimitable Chuang Tzu (by either Burton Watson or A.C. Graham), World Hypotheses by Stephen Pepper, or the WAY out there A Course In Miracles by psychologist and Columbia University Medical School Professor Helen Schucman. As supplemental reading for my own students I've recommended Oliver Sacks, Roger Penrose, Howard Gardner, and Jerome Bruner, among others- Hofstadter not included, obviously.
It's fitting that Hofstadter succeeded Martin Gardner as mathematical columnist for Scientific American, who opined in the preface of his The Annotated Alice: Alice's Adventures in Wonderland & Through the Looking Glass, also supposedly in "tribute" to Lewis Carroll, that:
"The last level of metaphor in Alice is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by an idiot mathematician. At the heart of things science finds only a mad, never-ending quadrille of Mock Turtle Waves and Gryphon Particles. For a moment the waves and particles dance in grotesque, inconceivably complex patterns capable of reflecting on their own absurdity. We all live slapstick lives, under an inexplicable sentence of death."
Metaphysical assumptions aside, just look at the nihilistic bent of the words employed. Grotesque? Mad? Absurd? These terms are not only value-ridden (i.e., suggestive of mechanistic bias), but one could argue, in stark contrast to the spirit of those chosen by Lewis Carroll, particularly in the poems which preface and conclude his beloved Alice's adventures. Carroll was a devoutly religious man, a clergyman who saw the mind of God as the substrate for the material world, and I think we can safely say that he had no such metaphor in mind when he put pen to paper. Indeed, I'm sure it would horrify him (as would the fact that Gardner made hefty royalties highjacking and subverting his labors of love). While still not cricket where Carroll is concerned, at least Gardner made no attempt to obscure his mechanistic (er, atheistic) agenda.
Perhaps the issues I raise here are now old hat in philosophical circles, I haven't kept up with this aspect of the field (my career took an applied, clinical turn, years ago). Recently I happened upon a brief synopsis of Hofstadter's 2007 book, and my sense of outrage at his devious sleight of hand and hucksterism came flooding back, thus, this review. So as not to obscure my own bias, I admit I think it more likely than not that essence precedes existence, that the material world is a projection of mind or minds, the result of conscious intentionality, as Blaise Pascal, and John von Neumann ultimately concluded (and the latter thought he'd demonstrated mathematically). Other scientists, brilliant and rigorous, have arrived at the same conclusion (Irwin Schrodinger, Roger Sperry, many more).
It is possible, as philosopher George Howison contended (circa 1902), that: "It is not simply that there are many minds behind the scenes, but that these minds are OURS- our GENUINE selves." And: "The real past is a flowing whole, and we are forever pouring the future into the flood, through the gate of the present. Our past is really always changing, and it is we who initiate the change, and so the past, though no part can be re-called, is perpetually being re-created and transformed, now for the worse, now for the better, as the whole goes on unfolding." This last assertion was later echoed by physicist John Wheeler, in his theory of the participatory universe.
But I digress. I should give Hofstadter some credit- had I not misconstrued his gobbledygook, not sought to reconcile contradictions, not attended closely to Godel's theorizing and its implications, in particular, investigating further, I would not have gained knowledge and convictions that would later inform and enrich my personal and professional life. Thanks in part to Hofstadter, I think for myself and am more discerning and critical minded than I would likely have been otherwise, it has served me (and most importantly, my patients) well. And, his enthusiasm (along with brilliant Michael Mahoney's) spurred me to pursue cognitive neuropsychology in the first place. However, in retrospect, I would also quibble about the fact that Hofstadter teaches at a publicly-funded university, and that our tax dollars paid for him to write his flippant, irrelevent clap-trap, dross that may well lead other promising young minds ASTRAY, rather than encouraging them to seek real solutions to the egregious psychological/neurological ills that plague our society and resound for other more socially responsible cognitive scientists (cognitive science being, after all, an outgrowth of psychology and an applied discipline). Douglas Hofstadter is instead a huge distraction, a dilettante, the Kim Kardashian of the Neuroscientific community (sorry, Kim). What a waste of brilliance.
In a nutshell, with GEB I think Hofstadter perpetrated some measure of fraud on the scientific community. We should have been more discerning. He had one seminal idea, that Godel's theorem, Escher's drawings, and Bach's fugues had something in common, were "strange loops". This he could have been presented in a 10 page paper in a peer-reviewed professional journal, but instead, he swaddled it in hundreds of pages of self-indulgent, pretentious, masturbatory ramblings and rehashed, arcane mathematical computations (that he perhaps knew few would scrutinize, and which have little to do with his prose). In the final analysis, very little of it is germaine, valid, or useful, scientifically. But gosh, it sounds so good, seems so...profound. For me it's sort of the literary equivalent of Terence Malick's The Tree of Life- a lot to take in, flash and style galore, but ultimately little of substance, nothing remotely explanatory or USEFUL. THIS is the main reason I find Hoftadter so contemptible, along with his deceitful methods, not the fact that his metaphysical faith assumptions differ from mine. It's NOT the fact that he's mechanistic, atheistic (there are plenty of mechanists I esteem greatly, e.g., Stephen Jay Gould, Loren Eiseley, Milton Erickson, Steven C. Hayes)- it's the fact that he obscured his ideology and agenda, and worst of all, cited and twisted the work of noble men who believed the polar opposite, without owning up to it- having a sly, slithery laugh at their (and our) expense, to the detriment of us all. Disgusting.
Hofstadter's avowed intent to analyze the world and the mind in the spirit of Lewis Carroll (whom I'd read and delighted in), his celebration of the genius of three men who infused their work with their spirituality, his koan-like meditations, and multiple levels of analysis seemed to me a valentine to the complexities and irreducibility of the universe and human consciousness, implying that human thought, "the mind" could exceed the confines of the human brain, just as Escher's paintings and Godelian knots escaped being defined or constrained by dimensional space. The phenomena described so poetically by Hofstadter seemed to me to suggest the possibility of ever widening spheres of analysis, of perception, of consciousness. Or so I thought. In any case, I was tremendously inspired by it. In my naivete, I thought he embodied perspectives simultaneously scientific and spiritual, as did the book's namesakes, in varying degrees. (Note that this is from memory, which cannot be other than selective- I donated the book years ago. These are the impressions that have stuck with me.) In succeeding years I read his next two books, although I have little memory of those.
It wasn't until a few years later, after I'd read World Hypotheses: A Study in Evidence by Stephen Pepper (must reading for anyone seeking to understand how knowledge is organized and "truth" derived), as well as At Home in the Universe by John Archibald Wheeler, The Mathematical Foundations of Quantum Mechanics by John von Neumann, works by Ilya Prigogine, Hermann Lotze, William James, and others (as part of advanced study in cognitive neuroscience, philosophy, and the philosophy of science), books that directly addressed the issues hinted at, or at least suggested to me by Hofstadter, that I went back and re-read GEB.
I had an epiphany, muddied by a sense of betrayal at being utterly duped, that, in fact, not only did Hoffstadter not mean what I thought he had (MY bad), but the book actually said very little and proved nothing. Just prior to revisiting it I'd read an article by Hofstadter asserting that GEB was actually about mind/consciousness as a mere epiphenomenon that arises as an emergent property of individual neurons, themselves non-conscious (his ant analogy). This was not even then a new idea, and he didn't provide proof of it, indeed, seemed to contradict it. More egregiously, it's a mechanistic notion, yet he cited Godel, a non-mechanistic theorist, whose theorem, according to Godel himself, demonstrates that symbolic thought can NOT arise from inanimate matter, due to the necessity of recursion in logical thought. Moreover, Godel thought it proof, along with other axioms he'd developed, of God's existence (btw, his bff Albert Einstein thought so too). Dirty pool indeed, to subvert, misrepresent and try to twist a mathematical proof to fit, to subserve one's own incompatible and biased agenda, WITHOUT owning up to what you're doing- intellectually dishonest in the extreme (if he's not a passive-aggressive, I'll eat my hat, though that's hardly pertinent). In any event, he was unsuccessful, but that fact seems to have escaped nearly everyone's notice.
Cognitive psychology is rife with intriguing mysteries to be solved. Neurons seem to have a mind of their own, changing their receptor sites at the flick of an eye, firing, responding or not responding to stimuli by mechanisms we've yet to discover. And they respond not only to electrical signals, but to chemical/magnetic changes and a vast array of neurotransmitters and hormones. Cells in the immune system also sport rapidly morphing receptor sites, making the situation even more complex.
In one study, a neuron was transplanted from a grasshopper's brain to its belly. The neuron grew into the surrounding tissue, but to the surprise of researchers, grew one, abnormally long dendrite [for receiving neural signals] directly back to the exact spot from which it had been excised, presumably so that it could keep abreast of developments in its old stomping grounds. The question of course is, how did it know from whence it came?
There's a long-standing debate amongst cognitivists and philosophers about the seeming irreconcilability of symbolic thought processes and observations of actual neuronal processes (a focus of Godel's work). Hofstadter's likening of neurons to ants did nothing to reconcile the two perspectives, nor did stories of tortoises or hares, though he seemed to suggest otherwise, without ever actually explaining how they did. In fact, Hofstadter's book, though lyrical, shed no new light on ANY of the pressing issues in cognitive science. As I remember, the entire book boils down to this (though I had to look long and hard to find it): strange loops exist in nature. Since we know there's no divine or organizing principle extant in nature, they must occur by natural means. Period. No actual proof is provided. No experiments are conducted. It's not science- it's a faith assumption.
GEB leads us down myriad garden paths that go nowhere. It's smoke and mirrors, an elaborate exercise in obfuscation and intellectual masturbation, AND full of errant premises- Pulitzer Prize, zen-master-like countenance and assured, authoritative tone not withstanding. I'd have no beef with Hofstadter if he'd presented his musings in a less duplicitous fashion, if he'd said "These are musings, part prose, part metaphysical speculation, draw from them what you will, but they're offered as proof of nothing." Or, he could have laid bare the real issues involved, presenting both sides of the materialism VS idealism debate, for example (he didn't, of course, because he actually had nothing new to add). It's the inherent DISHONESTY, the cloaking of the real issues involved, that irks me so. SPIT IT OUT- what do you believe, what evidence do you have in support of your contentions, what dilemmas still remain for you, how might these be studied/resolved? If you want to read works simultaneously scientific, substantive, inspiring, achingly poetic, and USEFUL, curl up with anything by French neuroscientist/philosopher Gaston Bachelard, or Jerome Bruner. If you want to be challenged by perplexities both tantalizing and profound, try the inimitable Chuang Tzu (by either Burton Watson or A.C. Graham), World Hypotheses by Stephen Pepper, or the WAY out there A Course In Miracles by psychologist and Columbia University Medical School Professor Helen Schucman. As supplemental reading for my own students I've recommended Oliver Sacks, Roger Penrose, Howard Gardner, and Jerome Bruner, among others- Hofstadter not included, obviously.
It's fitting that Hofstadter succeeded Martin Gardner as mathematical columnist for Scientific American, who opined in the preface of his The Annotated Alice: Alice's Adventures in Wonderland & Through the Looking Glass, also supposedly in "tribute" to Lewis Carroll, that:
"The last level of metaphor in Alice is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by an idiot mathematician. At the heart of things science finds only a mad, never-ending quadrille of Mock Turtle Waves and Gryphon Particles. For a moment the waves and particles dance in grotesque, inconceivably complex patterns capable of reflecting on their own absurdity. We all live slapstick lives, under an inexplicable sentence of death."
Metaphysical assumptions aside, just look at the nihilistic bent of the words employed. Grotesque? Mad? Absurd? These terms are not only value-ridden (i.e., suggestive of mechanistic bias), but one could argue, in stark contrast to the spirit of those chosen by Lewis Carroll, particularly in the poems which preface and conclude his beloved Alice's adventures. Carroll was a devoutly religious man, a clergyman who saw the mind of God as the substrate for the material world, and I think we can safely say that he had no such metaphor in mind when he put pen to paper. Indeed, I'm sure it would horrify him (as would the fact that Gardner made hefty royalties highjacking and subverting his labors of love). While still not cricket where Carroll is concerned, at least Gardner made no attempt to obscure his mechanistic (er, atheistic) agenda.
Perhaps the issues I raise here are now old hat in philosophical circles, I haven't kept up with this aspect of the field (my career took an applied, clinical turn, years ago). Recently I happened upon a brief synopsis of Hofstadter's 2007 book, and my sense of outrage at his devious sleight of hand and hucksterism came flooding back, thus, this review. So as not to obscure my own bias, I admit I think it more likely than not that essence precedes existence, that the material world is a projection of mind or minds, the result of conscious intentionality, as Blaise Pascal, and John von Neumann ultimately concluded (and the latter thought he'd demonstrated mathematically). Other scientists, brilliant and rigorous, have arrived at the same conclusion (Irwin Schrodinger, Roger Sperry, many more).
It is possible, as philosopher George Howison contended (circa 1902), that: "It is not simply that there are many minds behind the scenes, but that these minds are OURS- our GENUINE selves." And: "The real past is a flowing whole, and we are forever pouring the future into the flood, through the gate of the present. Our past is really always changing, and it is we who initiate the change, and so the past, though no part can be re-called, is perpetually being re-created and transformed, now for the worse, now for the better, as the whole goes on unfolding." This last assertion was later echoed by physicist John Wheeler, in his theory of the participatory universe.
But I digress. I should give Hofstadter some credit- had I not misconstrued his gobbledygook, not sought to reconcile contradictions, not attended closely to Godel's theorizing and its implications, in particular, investigating further, I would not have gained knowledge and convictions that would later inform and enrich my personal and professional life. Thanks in part to Hofstadter, I think for myself and am more discerning and critical minded than I would likely have been otherwise, it has served me (and most importantly, my patients) well. And, his enthusiasm (along with brilliant Michael Mahoney's) spurred me to pursue cognitive neuropsychology in the first place. However, in retrospect, I would also quibble about the fact that Hofstadter teaches at a publicly-funded university, and that our tax dollars paid for him to write his flippant, irrelevent clap-trap, dross that may well lead other promising young minds ASTRAY, rather than encouraging them to seek real solutions to the egregious psychological/neurological ills that plague our society and resound for other more socially responsible cognitive scientists (cognitive science being, after all, an outgrowth of psychology and an applied discipline). Douglas Hofstadter is instead a huge distraction, a dilettante, the Kim Kardashian of the Neuroscientific community (sorry, Kim). What a waste of brilliance.
In a nutshell, with GEB I think Hofstadter perpetrated some measure of fraud on the scientific community. We should have been more discerning. He had one seminal idea, that Godel's theorem, Escher's drawings, and Bach's fugues had something in common, were "strange loops". This he could have been presented in a 10 page paper in a peer-reviewed professional journal, but instead, he swaddled it in hundreds of pages of self-indulgent, pretentious, masturbatory ramblings and rehashed, arcane mathematical computations (that he perhaps knew few would scrutinize, and which have little to do with his prose). In the final analysis, very little of it is germaine, valid, or useful, scientifically. But gosh, it sounds so good, seems so...profound. For me it's sort of the literary equivalent of Terence Malick's The Tree of Life- a lot to take in, flash and style galore, but ultimately little of substance, nothing remotely explanatory or USEFUL. THIS is the main reason I find Hoftadter so contemptible, along with his deceitful methods, not the fact that his metaphysical faith assumptions differ from mine. It's NOT the fact that he's mechanistic, atheistic (there are plenty of mechanists I esteem greatly, e.g., Stephen Jay Gould, Loren Eiseley, Milton Erickson, Steven C. Hayes)- it's the fact that he obscured his ideology and agenda, and worst of all, cited and twisted the work of noble men who believed the polar opposite, without owning up to it- having a sly, slithery laugh at their (and our) expense, to the detriment of us all. Disgusting.
★ ★ ★ ★ ★
shasta
I would fall short in characters if I even tried to review this book.
This book analyzes patters from DNA to smoking habits. Gives a run down on how patterns are perceived and why they become "logical"... It gets interesting once the theories of the reverses come in place, it opens a door to endless logic and the theorems keep on coming.
Beyond my full understanding still, I plan on reading this book in a couple of years again... And for the intriguing love of it's quest... Again.
This book analyzes patters from DNA to smoking habits. Gives a run down on how patterns are perceived and why they become "logical"... It gets interesting once the theories of the reverses come in place, it opens a door to endless logic and the theorems keep on coming.
Beyond my full understanding still, I plan on reading this book in a couple of years again... And for the intriguing love of it's quest... Again.
★ ★ ★ ★ ★
henna helmi heinonen
If you're stranded upon a deserted (not desert: unless of course one can find an island in the desert), you better hope this book is the one with you.
This is the Russian Dolls of books. Hofstadter pulled a great trick over readers, which, like the trick itself, is a trick of infinite regress.
This is the Russian Dolls of books. Hofstadter pulled a great trick over readers, which, like the trick itself, is a trick of infinite regress.
★ ★ ★ ★ ★
tracy vantracy
A truly wonderful book: beautifully written, engaging, stimulating, and extremely original. I have read and reread it many, many times, and each time I have had new insights and appreciations; it so exquisite in detail. The only (potential) flaw is that it is not for everyone, since the beauty of the book is not revealed superficially. A tour-de-force not easy to emulate, even in a generation, even to its own author.
★ ★ ★ ★ ★
michael wade
This epic voyage into the world of the philosophy of AI and human intelligence is made accessible by Hofstadters absorbing style. One gets the impression that no matter how many times one read the dialogues, based around 4 / 5 characters, there would always be more to find. The layers of complexity in the dialogues makes for an amazing read, especially as layers of complexity is one of the main themes of the book. This book covers all the bases, it will set you thinking in totally new ways.
★ ★ ★ ★ ★
joanie calder
I love this book because it touches on many universal concepts using examples from art, science, music, math, and more. If you are an intellectual, or you consider yourself intelligent, you should take a few moments to read this. You'll love it...
★ ★ ★ ★ ★
lokanath
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.
★ ★ ★ ★ ★
craig
A true "desert island" tome, GEB will put more wrinkles in your brain with every page you struggle to understand. That struggle is more fulfilling than frustrating, as Hofstadter steadily leads you down a path marked "Artificial Intelligence" to the true destination of Real Intelligence. You will probably want to read it several times, but this book will change the way you think about the way you think.
★ ★ ★ ★ ★
dena sanders
If there was ever a book to take to an eternal isolated spot (or even prison), this is it. You will never be bored, even if you do figure it all out - it is mental gymnastics, brain sex and worth every bit of the Pulitzer it got.
★ ★ ★ ★ ☆
amalia
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.
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.
★ ★ ★ ★ ★
lillian
This is possibly the best book written in the twentieth century. It links mathematics, philosophy, art, music and genetics in very clever and natural ways. It is laced with excellent humor. It presents no less than a way of viewing the universe. Everyone who thinks themself educated should read this book.
★ ★ ★ ★ ★
kate ck
I was once told there are two kinds of people: those who get past chapter 7 in GEB, and those who don't. It saddens me to be in the second group, but the part I did read has left an intangible pattern weaving somewhere back there in my mind.
★ ★ ★ ★ ★
ikhlasul
Read it once, twice and trice: GEB Will surprise you again and again. In a delightful manner, Hofstadter presents us to his reach inner world, from his love to art to molecular biology and mathematical logic, all in search of the paradoxes ensuing from our recursive World.
★ ★ ★ ★ ★
andrei taraschuk
a cursory glance at a random passage of godel, escher, and bach, will likely appear to be jabberwocky, with its unapologetic, evolving vocabulary and sparkles of inside jokes based on such, this is ironic, because the right arm of this book is recursion, which implies that the whole is implied by each part, far from while reading, one most certainly must read godel, escher, and bach in its sequential order, too funny
★ ★ ★ ★ ★
sue cccp
I will simply add my "Amen" to the chorus that found this book wonderful. An illuminating, entertaining and profound discussion about a difficult subject. Lewis Carroll would have loved the dialogues. I only wish I knew enough to appreciate Western Classical music.
★ ★ ★ ★ ★
kathleen w wilson
Finally, a book to make people think. Hofstadter has created a text for those who are bored with the general complacency exhibited in the modern world. I encourage anyone who wants to be challenged in thought and perception to read this book. Enjoy.
★ ★ ★ ★ ★
ibunyaima notodisurjo
If creativity (thought) starts with two or more systems which were not designed to work together, but that seem to interact in some meaningful way anyway, then the Internet my be the first artificial exo-organ, which connects humans together as a super-organism. The question becomes, how much of it is alive?
★ ★ ★ ★ ★
tess n
This masterpiece has changed the way I think. I pity those have only read it once, or, even worse, didn't finish it. Only on the second reading can you understand that the entire book is itself a glorious ricercar and an endlessly rising canon. If you don't understand what I mean, read the book. And read it again, and again, and. . . .
★ ★ ★ ★ ★
hope baxter
I read this book in its entirety five years ago. This is after I made some unsuccessful initial attempts to finish it several years before that. I love the way the author gently teases and prods the reader into the magical realm of Gödel Incompleteness. Hofstadter doesn't just vomit the complex ideas of Gödel but rather coddles the reader to think in a manner that is conducive to understanding Gödel. By the end of the book, the reader who is willing to put in the effort changes his or her manner of thinking and starts to breath in Gödel's ideas as effortlessly and unthinkingly as breathing air.
I remember seeing the movie The Karate Kid back in the Eighties. I was fascinated with the way Mr. Miyagi was prodding Daniel LaRusso (Ralph Macchio) to repetitively wax his car, much to Daniel's annoyance. What did this have to do with learning Karate? We learn eventually that Mr. Miyagi was instilling in Daniel a manner of thinking and moving that is necessary before effectively learning Karate. Daniel learned not how to do Karate but rather how to become Karate. This is what Hofstadter's book does in teaching Gödel's ideas. The assiduous reader learns how to instinctively think in a Gödel-like manner rather than trying to awkwardly struggle with the foreign and strange world of Gödel.
My only criticism of the book is that Hofstadter is actually too meek and conservative in his application of Gödel's ideas to understanding physical and abstract phenomenon. Hofstadter claims that consciousness is a product of Gödel Incompleteness. I go a step further by claiming that all of reality is due to Gödel Incompleteness. The Big Bang itself is probably a Gödel type of self referential system. Here comes a shameless self promotion. In my novella Shards Of Divinities I gently introduce the reader to a Gödel-like way of thinking (without even mentioning Gödel for much of the book) and towards the end of the book I spell out my view point that all of reality is a Gödel-like loop. I also employ the same gentle prodding of the reader to almost imperceptibly start thinking in a Gödel-like way.
In the TV series of the late 70s The Paper Chase professor Kingsfield tells his first year law class: You come in here with a skull full of mush and you leave thinking like a lawyer.
You start reading Gödel Escher Bach with a skull full of mush and you leave thinking like a Gödel loop - the eternal golden braid.
I remember seeing the movie The Karate Kid back in the Eighties. I was fascinated with the way Mr. Miyagi was prodding Daniel LaRusso (Ralph Macchio) to repetitively wax his car, much to Daniel's annoyance. What did this have to do with learning Karate? We learn eventually that Mr. Miyagi was instilling in Daniel a manner of thinking and moving that is necessary before effectively learning Karate. Daniel learned not how to do Karate but rather how to become Karate. This is what Hofstadter's book does in teaching Gödel's ideas. The assiduous reader learns how to instinctively think in a Gödel-like manner rather than trying to awkwardly struggle with the foreign and strange world of Gödel.
My only criticism of the book is that Hofstadter is actually too meek and conservative in his application of Gödel's ideas to understanding physical and abstract phenomenon. Hofstadter claims that consciousness is a product of Gödel Incompleteness. I go a step further by claiming that all of reality is due to Gödel Incompleteness. The Big Bang itself is probably a Gödel type of self referential system. Here comes a shameless self promotion. In my novella Shards Of Divinities I gently introduce the reader to a Gödel-like way of thinking (without even mentioning Gödel for much of the book) and towards the end of the book I spell out my view point that all of reality is a Gödel-like loop. I also employ the same gentle prodding of the reader to almost imperceptibly start thinking in a Gödel-like way.
In the TV series of the late 70s The Paper Chase professor Kingsfield tells his first year law class: You come in here with a skull full of mush and you leave thinking like a lawyer.
You start reading Gödel Escher Bach with a skull full of mush and you leave thinking like a Gödel loop - the eternal golden braid.
★ ★ ★ ☆ ☆
nolybab
If you're new to computer science, then this book introduces you to some interesting topics in decideability and recursion. These ideas have implications for people who contemplate the possibility of intelligent computers or the design of intelligent systems.
Since most of the computer science theory is over 50 years old, none of it is new to anyone who is familiar with the subject. That said, the presentation is a rather weak play on Lewis Carroll combined with the cloying childishness of A. A. Milne.
Most readers claim to find the book fascinating. They're either genuinely fascinated by the AI topics, which are great - just not the author's own ideas. Or they're faking it because you're supposed to say you like stuff that sounds clever. Or they're faking it.
Since most of the computer science theory is over 50 years old, none of it is new to anyone who is familiar with the subject. That said, the presentation is a rather weak play on Lewis Carroll combined with the cloying childishness of A. A. Milne.
Most readers claim to find the book fascinating. They're either genuinely fascinated by the AI topics, which are great - just not the author's own ideas. Or they're faking it because you're supposed to say you like stuff that sounds clever. Or they're faking it.
★ ★ ★ ★ ★
bunty
If there was one book I was allowed, it would be this, even if I don't understand it - and that is why I would take it to an eternal isolated spot (or even prison) - it would take me years of mental gymnastics to figure out. I would be entertained. The book is worth every bit of the Pulitzer it got.
★ ★ ★ ★ ★
penelope
and FEEL the world within you and without you.
The book is a masterpiece of recursiveness
The book is a masterpiece of recursivenes
The book is a masterpiece of recursivene
The book is a masterpiece of recursiven
The book is a masterpiece of recursive
The book is a masterpiece of recursiv
The book is a masterpiece of recursi
The book is a masterpiece of recurs
The book is a masterpiece of recur
The book is a masterpiece of recu
The book is a masterpiece of rec
The book is a masterpiece of re
The book is a masterpiece of r
The book is a masterpiece of
The book is a masterpiece of
The book is a masterpiece o
The book is a masterpiece
The book is a masterpiece
The book is a masterpiec
The book is a masterpie
The book is a masterpi
The book is a masterp
The book is a master
The book is a maste
The book is a mast
The book is a mas
The book is a ma
The book is a m
The book is a
The book is
The book is
The book i
The book
The book
The boo
The bo
The b
The
The
Th
T
But you might have to squint your eyes to see it . . .
See it? . . .
It's right here.
Yes, here.
But not in this review.
Get it?
Hofstadter does . . .
Good Luck!
-Zhil
The book is a masterpiece of recursiveness
The book is a masterpiece of recursivenes
The book is a masterpiece of recursivene
The book is a masterpiece of recursiven
The book is a masterpiece of recursive
The book is a masterpiece of recursiv
The book is a masterpiece of recursi
The book is a masterpiece of recurs
The book is a masterpiece of recur
The book is a masterpiece of recu
The book is a masterpiece of rec
The book is a masterpiece of re
The book is a masterpiece of r
The book is a masterpiece of
The book is a masterpiece of
The book is a masterpiece o
The book is a masterpiece
The book is a masterpiece
The book is a masterpiec
The book is a masterpie
The book is a masterpi
The book is a masterp
The book is a master
The book is a maste
The book is a mast
The book is a mas
The book is a ma
The book is a m
The book is a
The book is
The book is
The book i
The book
The book
The boo
The bo
The b
The
The
Th
T
But you might have to squint your eyes to see it . . .
See it? . . .
It's right here.
Yes, here.
But not in this review.
Get it?
Hofstadter does . . .
Good Luck!
-Zhil
★ ★ ★ ★ ★
jenna m
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.
★ ★ ★ ★ ★
mrs harris librarian
I read this book years ago and thought it was terrific then. This isn't "dumbed down" for the mass market reader and requires some time to finish but it is well worth it. To prospective readers- enjoy.
★ ★ ★ ★ ★
justine gieni
what can i say that has not already been said? i have never read another book that relates ideas (particularly concepts as complex as those discussed in the book) so clearly, let alone with such imagination.
★ ★ ☆ ☆ ☆
lisa rapaport
Godels' Theory is just that. Theory. Nothing is proven although some enlightening mathematical juxtipositions are called into play. It is highly entertaining. But I would not call it life changing. I would be very malicious if I did not maintain a skeptical view of this work.
★ ★ ★ ☆ ☆
kirstin
In his classic work, Hofstadter basically defines the postmodern idea of what a reference is: It is anything. The author pulls in more loose ends than the DaVinci Code, and perhaps with less success. Most notable is his prescient reference to crabmap, given the rise of culinary terrorism that has plagued the twenty first century. In one of his recent radio interviews, Putrid Pink author Norton Mansefield compared Hofstadter to Willy McGilly, a character in many of R.A. Lafferty's short stories.
A really good read, although it didn't get my gas logs going as quick as I would have liked.
A really good read, although it didn't get my gas logs going as quick as I would have liked.
★ ★ ★ ★ ★
abdullah almusned
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?
★ ★ ★ ★ ★
damon
The book is excellent. The relationships between music,math, and art are thoroughly explored in an interesting way. The images in the book are very relative to the topics discussed. Overall, I am very satisfied with my purchase.
★ ★ ★ ★ ★
gordon dawson tibbits
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...
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...
★ ★ ★ ☆ ☆
julie walsh
I was slightly disappointed. The actual proof is easier to read than this book, which is rich in interesting anecdotes, nice paintings but a bit verbose for my taste. Although I certainly wouldn't say it is an easy read, I do get the impression that many long pages and complicated analogies could be summarized in a few lines of formulas. Then again, in that case it would be a math book.
I particularly enjoyed the information about Bach, one of my favorite composers. Otherwise, a lot of text but few key concepts.
I particularly enjoyed the information about Bach, one of my favorite composers. Otherwise, a lot of text but few key concepts.
★ ★ ★ ☆ ☆
wyatt
In his classic work, Hofstadter basically defines the postmodern idea of what a reference is: It is anything. The author pulls in more loose ends than the DaVinci Code, and perhaps with less success. Most notable is his prescient reference to crabmap, given the rise of culinary terrorism that has plagued the twenty first century. In one of his recent radio interviews, Putrid Pink author Norton Mansefield compared Hofstadter to Willy McGilly, a character in many of R.A. Lafferty's short stories.
A really good read, although it didn't get my gas logs going as quick as I would have liked.
A really good read, although it didn't get my gas logs going as quick as I would have liked.
★ ★ ★ ★ ★
kim gregory
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?
★ ★ ★ ★ ★
traci dziatkowicz
The book is excellent. The relationships between music,math, and art are thoroughly explored in an interesting way. The images in the book are very relative to the topics discussed. Overall, I am very satisfied with my purchase.
★ ★ ★ ★ ★
shawn elkins
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...
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...
★ ★ ★ ☆ ☆
mike votta
I was slightly disappointed. The actual proof is easier to read than this book, which is rich in interesting anecdotes, nice paintings but a bit verbose for my taste. Although I certainly wouldn't say it is an easy read, I do get the impression that many long pages and complicated analogies could be summarized in a few lines of formulas. Then again, in that case it would be a math book.
I particularly enjoyed the information about Bach, one of my favorite composers. Otherwise, a lot of text but few key concepts.
I particularly enjoyed the information about Bach, one of my favorite composers. Otherwise, a lot of text but few key concepts.
★ ★ ☆ ☆ ☆
paula
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.
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.
★ ★ ★ ★ ☆
sara mutchler
I really was not sure what to think of it before reading the book. I was disaapointed to find so much math, because I am terrible at math. But with so many different and obscure topics, I was so pleased with the overall content. Extremely thought provoking. Youll wish you could remember 1/10th of the book when you're finished with it.
★ ★ ☆ ☆ ☆
maude
I can't really give this one star, as it helped spur some thoughts in me and got me thinking about some things, but it definitely does not deserve higher than 2 stars. While I know a lot of people found meaning in this book, it's lack of structure, boorish nature, and lack of efficiency lead me to question that those readers found their meaning in the book itself. I'd equate this book to a poem where it has sufficient ambiguous meaning to allow readers to latch on and attach their own meaning to it. Ironic that this is an example of the meaning being found in the reader, not the text. That obviously means that readers can get something out of it, but if you're looking for the holy grail of non-fiction that it's made out to be, then you'll be sorely disappointed. If you have never seen things like academic philosophy or logic or don't have a degree in mathematics, this book will be even worse and unbearable. Read it if you must, but don't be surprised if it doesn't work out for you...
★ ★ ★ ☆ ☆
deborah simon
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). The sheer number of topics covered is not the problem; what bothered me about the book - which I started reading with the best intentions - and almost made me abandon it, was that this attitude of "showing-off" pervades everywhere 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 inane 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 workshop I attended once and who couldn't stop cracking jokes for the audience even if nobody was laughing. However, if one is to believe the reviews it gets on the store, 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...
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 inane 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 workshop I attended once and who couldn't stop cracking jokes for the audience even if nobody was laughing. However, if one is to believe the reviews it gets on the store, 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...
★ ☆ ☆ ☆ ☆
sonne lore
There's some bizarre cult following to this book I will never understand.
Although it does a nice job stroking both your and the authors' ego, this book is a waste of time for anyone even marginally mathematically inclined. Some 80% of the book is full of tired arguments whose conclusion you've probably already considered if you've graduated middle school. Another 5% is passable as a Playskool(TM) My First Logic Book. The remaining 15% is full of Hofstadter's pseudoscientific quackery. The connections the author tries tries to make between Godel and Escher/Bach are entirely banal, and can be applied to the work of basically any mathematician since Fibonacci, who lived closer to the Plague of Justinian than to the birth of Hofstadter.
If you want to actually learn something, just read a decent 160-page book on Godel's work (example: Gödel's Proof) and never worry about pseudo-philosophical smart-Alec turtles again. The Great Courses has an amazing course on Bach Lectures on Bach. The works of Escher can be fully understood by passing a high school math class. Identifying a superset of Hofstadter's connections between the three requires the firing of maybe a neuron or two.
Although it does a nice job stroking both your and the authors' ego, this book is a waste of time for anyone even marginally mathematically inclined. Some 80% of the book is full of tired arguments whose conclusion you've probably already considered if you've graduated middle school. Another 5% is passable as a Playskool(TM) My First Logic Book. The remaining 15% is full of Hofstadter's pseudoscientific quackery. The connections the author tries tries to make between Godel and Escher/Bach are entirely banal, and can be applied to the work of basically any mathematician since Fibonacci, who lived closer to the Plague of Justinian than to the birth of Hofstadter.
If you want to actually learn something, just read a decent 160-page book on Godel's work (example: Gödel's Proof) and never worry about pseudo-philosophical smart-Alec turtles again. The Great Courses has an amazing course on Bach Lectures on Bach. The works of Escher can be fully understood by passing a high school math class. Identifying a superset of Hofstadter's connections between the three requires the firing of maybe a neuron or two.
★ ★ ★ ☆ ☆
shelley wead
I can only warn you of this book: It might give you a nervous breakdown if you are a spiritual person. The sickly intelligent author has a devilish and almost violent joy in convincing you that you don't have a soul, that your mind and self is a product of the complexity of your brain, and that is the ideology that pours out of every sentence in this book! He believes so strongly that everything can be objectified and symbolized that he kind of neglects his very own existence ...The thrill is: you have to hand it to him: he's real logical! It took me some time to get over it, but I felt he was wrong... and he is wrong, but it's not easy to put in words, because words are just words. No matter how you try to cover up the truth... someday it will prevail, because it IS! What traumatic experience made this author so loveless, cynical and blind?
★ ★ ★ ★ ☆
ellyce
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':<TNT-PROOF-PAIR{a,a'}/\ARITHMOQUINE{SS...SS0/a",a'}> where the number of S's equals the numeral for u." That is Hofstader's version of Godel's theorem or G. On page 447
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 [...]
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':<TNT-PROOF-PAIR{a,a'}/\ARITHMOQUINE{SS...SS0/a",a'}> where the number of S's equals the numeral for u." That is Hofstader's version of Godel's theorem or G. On page 447
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 [...]
★ ☆ ☆ ☆ ☆
thebassplayerswife
When I opened the package there was a lot of a mysterious powdery substance, which I soon discovered was the decaying binding of the book. (Glue, paper, ?) It was a mess. The book was in very poor condition, nearly unreadable, because the binding will not hold.
★ ★ ☆ ☆ ☆
annez
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.
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.
★ ★ ★ ★ ★
heather
Arrived on time, in good condition (as advertised). As for content, I read this a few years back. It is one of those "Aha!" books that makes you see the world a bit differently. The book itself is denser than lead (both in content and physically! you could start a gym with a few dozen of these), but you definitely get more out of it than what you put in.
★ ☆ ☆ ☆ ☆
run2birth
Godel, Escher and Bach (GEB) is about the question of how a Self (something which can refer to itself, like a human being) can arise from things which do not have a Self (i.e. nucleotides (molecules)), and the author of GEB makes a connection (he calls isomorphism) between Gödel's incompleteness theorem and the workings of DNA and the Genetic Code. This connection is explained by describing how a self-referential `sentence' of meaningless symbols within a sufficiently powerful formal system like Typographical Number Theory (TNT) can be derived using rules which `shunt' these meaningless symbols around, akin to how symbols are shunted in Algebra. The author then shows a connection to this with the Genetic Code and its seemingly similar operation of shunting DNA nucleotides to form the proteins that lead to the development of phenotypes (i.e. like you or me).
The other themes in GEB relate to describing the concepts of thought, consciousness and artificial intelligence which includes a famously incorrect prediction relating to computers and chess. There are things in GEB which are disconcerting...the ever-expanding "GOD" acronym caused discomfort to me because it lacks respect, as well as the author's refusal to volunteer an opinion or theory of the origin of the Genetic Code in the one small paragraph devoted to it at the end of chapter 16. The sequel to GEB ("I am a strange loop") reveals that Hofstadter is swayed more to atheism, but this book is a vastly inferior work than the original GEB (I would say it gives a strong impression that GEB was authored by another).
Interestingly, the author's first wife, Carol, died suddenly in the early 1990s (just over ten years after the first publication of GEB) of a brain-related disease. The author attributes this as a "random" event also...
GEB is a very important book to read and it was central to events that occurred in 2000/2001 that changed the course of history...The Tuesday Operations of C******e, 9/11 and Amerithrax, where the REAL perpetrator embedded a coded message in three texts, with each text consisting of two halves, with one misspelling in each text pair, and the misspelling letters ("A", "A" and "y") forming a diagonal which is analogous to that of the "Cantor" puzzle in the "Aria with Diverse Variations" dialogue in GEB.
The other themes in GEB relate to describing the concepts of thought, consciousness and artificial intelligence which includes a famously incorrect prediction relating to computers and chess. There are things in GEB which are disconcerting...the ever-expanding "GOD" acronym caused discomfort to me because it lacks respect, as well as the author's refusal to volunteer an opinion or theory of the origin of the Genetic Code in the one small paragraph devoted to it at the end of chapter 16. The sequel to GEB ("I am a strange loop") reveals that Hofstadter is swayed more to atheism, but this book is a vastly inferior work than the original GEB (I would say it gives a strong impression that GEB was authored by another).
Interestingly, the author's first wife, Carol, died suddenly in the early 1990s (just over ten years after the first publication of GEB) of a brain-related disease. The author attributes this as a "random" event also...
GEB is a very important book to read and it was central to events that occurred in 2000/2001 that changed the course of history...The Tuesday Operations of C******e, 9/11 and Amerithrax, where the REAL perpetrator embedded a coded message in three texts, with each text consisting of two halves, with one misspelling in each text pair, and the misspelling letters ("A", "A" and "y") forming a diagonal which is analogous to that of the "Cantor" puzzle in the "Aria with Diverse Variations" dialogue in GEB.
★ ☆ ☆ ☆ ☆
hubert
After hearing for years effusive praise heaped on this book by one reviewer/reader after the other, I thought I'd better look at it. Now,we are living in an age that "naturalizes" everything, that treats virtually all issues (including, e.g., the nature of consciousness, perception, language, self), all topics, all domains, as formalizable and treatable by some version or variety of natural sciences/math. (See, for example, the thinking, "research", and practices in current mainstream psychiatry.) Nevertheless, there is a good deal of impressive, very well informed minority literature that counters this trend--one which, according to some, started in ancient Greece and got its major boost in the Cartesian era. (My own publications have dealt with this issue peripherally, and I'm currently at work on a ms. that makes it central.) Apart from several rather lame discussions of Zen and of the limitations of logic and formalisms, Hofstadter's book is predicated on the veneration of formalization. I propose that it plays into the rampant societal pathology of abuse and inappropriate veneration of rationality--an abuse, I might add, which is also accompanied by its opposite polarity, a non-thinking mindlessness, an infantile way of operating. This polarized pathology devalues, ignores, misses what ought to be central to our lives--matters related to what the Jungian James Hillman somewhat ponderously calls our "soul". Hence, my hatred of this pretentious, smug work, and its collusion with scientism.
★ ☆ ☆ ☆ ☆
ben peters
A complete waste of money. Though the book contains some interesting ideas, it is very, very, very wordy. Everything is explained ve-e-ery slowly and repeated a few times. But when the narration approaches a really interesting point, the author switches to a different topic, leaving the interesting point for later. If the book were 1/10 of its size, it might be a good recreational reading. However, in its current form, it is extremely boring, nearly unbearable.
Could not read it past a couple of chapters, though tried several times. Trying to skip a few chapters did not help: it is dead boring all the way to the end.
Could not read it past a couple of chapters, though tried several times. Trying to skip a few chapters did not help: it is dead boring all the way to the end.
★ ☆ ☆ ☆ ☆
michelle taylor
I wish i had ordered through kindle it would have been easjer to return this bulls***. Half of the theores supported on te book have been discarded during the last 20 years as dumbful constructs. A lot of the science stuff have no place, there isnt any reflection but literary misinformation and entertaiment and of course the neuroscience stuff is crap from 20 years ago. Please someone read wittgenstein and realize what a circular logic piece of crap this book is.
Forgit to say. Turing tet have been proven to be pure nonsense.
Forgit to say. Turing tet have been proven to be pure nonsense.
★ ☆ ☆ ☆ ☆
neeta
This book is probably the primary way that the public learns about some of Gödel's ideas. That is has to be in such a naive misrepresentation is typical of the way that Gödel's entire life of thought and work has pretty much been completely missed by the public and even by academia.
This works is really a waste of time...go read some of Gödel's papers or books by Hao Wang. This book does make a great gift to your friend who has no interest in reality but loves smart looking books on his/her shelf though so it's not completely without merit.
This works is really a waste of time...go read some of Gödel's papers or books by Hao Wang. This book does make a great gift to your friend who has no interest in reality but loves smart looking books on his/her shelf though so it's not completely without merit.
★ ☆ ☆ ☆ ☆
shayne moore
The Emperor is naked!
The author has tried to 'show-off' his knowledge of various subjects.
He could have still done it - but with less words.
The people who want to to rate this book high are trying to belong to a group who think they are intelligent.
One of these elitist should at least try writing an abridged version.
A verbose waste of time, as you follow the author in an endless loop as he chases his tail around.
And finally...
I believe that if someone cannot be precise and concise about what they are saying, they themselves don't have a clue.
If that is the case, then we must be idiots to be listening to their rhetoric.
The author has tried to 'show-off' his knowledge of various subjects.
He could have still done it - but with less words.
The people who want to to rate this book high are trying to belong to a group who think they are intelligent.
One of these elitist should at least try writing an abridged version.
A verbose waste of time, as you follow the author in an endless loop as he chases his tail around.
And finally...
I believe that if someone cannot be precise and concise about what they are saying, they themselves don't have a clue.
If that is the case, then we must be idiots to be listening to their rhetoric.
★ ★ ★ ★ ★
aron
I bought this as a git for an intelligent friend.
This is one of those books you read, and then remember forever.
Using Godel the mathematician, Escher the patternist painter/artist and Bach the composer, Douglas Hofstadter, in this timeless book unites mathematics, art and music through thought illustrations (then problem/questions) and informative Platonic-inspired dialogues (including the composite character Aunt Hillary, the massed intelligence of an ant colony.
It's a must read. Supposedly, it was written for high school age nerdish boys, but I greatly enjoyed it in my mid-20's and fondly remember it in my late 60's.
A truly timely book, with my highest recommendation.
This is one of those books you read, and then remember forever.
Using Godel the mathematician, Escher the patternist painter/artist and Bach the composer, Douglas Hofstadter, in this timeless book unites mathematics, art and music through thought illustrations (then problem/questions) and informative Platonic-inspired dialogues (including the composite character Aunt Hillary, the massed intelligence of an ant colony.
It's a must read. Supposedly, it was written for high school age nerdish boys, but I greatly enjoyed it in my mid-20's and fondly remember it in my late 60's.
A truly timely book, with my highest recommendation.
★ ☆ ☆ ☆ ☆
tera
Allow me to rant a bit- this involves issues I feel most keenly about (or, you can skip ahead to the final paragraph for a summary). I read this book in the early 90's, after reading glowing reviews. I pored over it, pondered it; some things didn't add up (which I attributed to my own intellectual deficiencies- I was then an undergraduate, likely in WAY over my head), but I ultimately concluded that its central theses were that wholes can be greater than the sum of their parts, that systems are not really "closed", only appear to be, and that strange loops seem to defy the normal laws of physics in some quantum sense.
Hofstadter's avowed intent to analyze the world and the mind in the spirit of Lewis Carroll (whom I'd read and delighted in), his celebration of the genius of three men who infused their work with their spirituality, his koan-like meditations, and multiple levels of analysis seemed to me a valentine to the complexities and irreducibility of the universe and human consciousness, implying that human thought, "the mind" could exceed the confines of the human brain, just as Escher's paintings and Godelian knots escaped being defined or constrained by dimensional space. The phenomena described so poetically by Hofstadter seemed to me to suggest the possibility of ever widening spheres of analysis, of perception, of consciousness. Or so I thought. In any case, I was tremendously inspired by it. In my naivete, I thought he embodied perspectives simultaneously scientific and spiritual, as did the book's namesakes, in varying degrees. (Note that this is from memory, which cannot be other than selective- I donated the book years ago. These are the impressions that have stuck with me.) In succeeding years I read his next two books, although I have little memory of those.
It wasn't until a few years later, after I'd read World Hypotheses: A Study in Evidence by Stephen Pepper (must reading for anyone seeking to understand how knowledge is organized and "truth" derived), as well as At Home in the Universe by John Archibald Wheeler, The Mathematical Foundations of Quantum Mechanics by John von Neumann, works by Ilya Prigogine, Hermann Lotze, William James, and others (as part of advanced study in cognitive neuroscience, philosophy, and the philosophy of science), books that directly addressed the issues hinted at, or at least suggested to me by Hofstadter, that I went back and re-read GEB.
I had an epiphany, muddied by a sense of betrayal at being utterly duped, that, in fact, not only did Hoffstadter not mean what I thought he had (MY bad), but the book actually said very little and proved nothing. Just prior to revisiting it I'd read an article by Hofstadter asserting that GEB was actually about mind/consciousness as a mere epiphenomenon that arises as an emergent property of individual neurons, themselves non-conscious (his ant analogy). This was not even then a new idea, and he didn't provide proof of it, indeed, seemed to contradict it. More egregiously, it's a mechanistic notion, yet he cited Godel, a non-mechanistic theorist, whose theorem, according to Godel himself, demonstrates that symbolic thought can NOT arise from inanimate matter, due to the necessity of recursion in logical thought. Moreover, Godel thought it proof, along with other axioms he'd developed, of God's existence (btw, his bff Albert Einstein thought so too). Dirty pool indeed, to subvert, misrepresent and try to twist a mathematical proof to fit, to subserve one's own incompatible and biased agenda, WITHOUT owning up to what you're doing- intellectually dishonest in the extreme (if he's not a passive-aggressive, I'll eat my hat, though that's hardly pertinent). In any event, he was unsuccessful, but that fact seems to have escaped nearly everyone's notice.
Cognitive psychology is rife with intriguing mysteries to be solved. Neurons seem to have a mind of their own, changing their receptor sites at the flick of an eye, firing, responding or not responding to stimuli by mechanisms we've yet to discover. And they respond not only to electrical signals, but to chemical/magnetic changes and a vast array of neurotransmitters and hormones. Cells in the immune system also sport rapidly morphing receptor sites, making the situation even more complex.
In one study, a neuron was transplanted from a grasshopper's brain to its belly. The neuron grew into the surrounding tissue, but to the surprise of researchers, grew one, abnormally long dendrite [for receiving neural signals] directly back to the exact spot from which it had been excised, presumably so that it could keep abreast of developments in its old stomping grounds. The question of course is, how did it know from whence it came?
There's a long-standing debate amongst cognitivists and philosophers about the seeming irreconcilability of symbolic thought processes and observations of actual neuronal processes (a focus of Godel's work). Hofstadter's likening of neurons to ants did nothing to reconcile the two perspectives, nor did stories of tortoises or hares, though he seemed to suggest otherwise, without ever actually explaining how they did. In fact, Hofstadter's book, though lyrical, shed no new light on ANY of the pressing issues in cognitive science. As I remember, the entire book boils down to this (though I had to look long and hard to find it): strange loops exist in nature. Since we know there's no divine or organizing principle extant in nature, they must occur by natural means. Period. No actual proof is provided. No experiments are conducted. It's not science- it's a faith assumption.
GEB leads us down myriad garden paths that go nowhere. It's smoke and mirrors, an elaborate exercise in obfuscation and intellectual masturbation, AND full of errant premises- Pulitzer Prize, zen-master-like countenance and assured, authoritative tone not withstanding. I'd have no beef with Hofstadter if he'd presented his musings in a less duplicitous fashion, if he'd said "These are musings, part prose, part metaphysical speculation, draw from them what you will, but they're offered as proof of nothing." Or, he could have laid bare the real issues involved, presenting both sides of the materialism VS idealism debate, for example (he didn't, of course, because he actually had nothing new to add). It's the inherent DISHONESTY, the cloaking of the real issues involved, that irks me so. SPIT IT OUT- what do you believe, what evidence do you have in support of your contentions, what dilemmas still remain for you, how might these be studied/resolved? If you want to read works simultaneously scientific, substantive, inspiring, achingly poetic, and USEFUL, curl up with anything by French neuroscientist/philosopher Gaston Bachelard, or Jerome Bruner. If you want to be challenged by perplexities both tantalizing and profound, try the inimitable Chuang Tzu (by either Burton Watson or A.C. Graham), World Hypotheses by Stephen Pepper, or the WAY out there A Course In Miracles by psychologist and Columbia University Medical School Professor Helen Schucman. As supplemental reading for my own students I've recommended Oliver Sacks, Roger Penrose, Howard Gardner, and Jerome Bruner, among others- Hofstadter not included, obviously.
It's fitting that Hofstadter succeeded Martin Gardner as mathematical columnist for Scientific American, who opined in the preface of his The Annotated Alice: Alice's Adventures in Wonderland & Through the Looking Glass, also supposedly in "tribute" to Lewis Carroll, that:
"The last level of metaphor in Alice is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by an idiot mathematician. At the heart of things science finds only a mad, never-ending quadrille of Mock Turtle Waves and Gryphon Particles. For a moment the waves and particles dance in grotesque, inconceivably complex patterns capable of reflecting on their own absurdity. We all live slapstick lives, under an inexplicable sentence of death."
Metaphysical assumptions aside, just look at the nihilistic bent of the words employed. Grotesque? Mad? Absurd? These terms are not only value-ridden (i.e., suggestive of mechanistic bias), but one could argue, in stark contrast to the spirit of those chosen by Lewis Carroll, particularly in the poems which preface and conclude his beloved Alice's adventures. Carroll was a devoutly religious man, a clergyman who saw the mind of God as the substrate for the material world, and I think we can safely say that he had no such metaphor in mind when he put pen to paper. Indeed, I'm sure it would horrify him (as would the fact that Gardner made hefty royalties highjacking and subverting his labors of love). While still not cricket where Carroll is concerned, at least Gardner made no attempt to obscure his mechanistic (er, atheistic) agenda.
Perhaps the issues I raise here are now old hat in philosophical circles, I haven't kept up with this aspect of the field (my career took an applied, clinical turn, years ago). Recently I happened upon a brief synopsis of Hofstadter's 2007 book, and my sense of outrage at his devious sleight of hand and hucksterism came flooding back, thus, this review. So as not to obscure my own bias, I admit I think it more likely than not that essence precedes existence, that the material world is a projection of mind or minds, the result of conscious intentionality, as Blaise Pascal, and John von Neumann ultimately concluded (and the latter thought he'd demonstrated mathematically). Other scientists, brilliant and rigorous, have arrived at the same conclusion (Irwin Schrodinger, Roger Sperry, many more).
It is possible, as philosopher George Howison contended (circa 1902), that: "It is not simply that there are many minds behind the scenes, but that these minds are OURS- our GENUINE selves." And: "The real past is a flowing whole, and we are forever pouring the future into the flood, through the gate of the present. Our past is really always changing, and it is we who initiate the change, and so the past, though no part can be re-called, is perpetually being re-created and transformed, now for the worse, now for the better, as the whole goes on unfolding." This last assertion was later echoed by physicist John Wheeler, in his theory of the participatory universe.
But I digress. I should give Hofstadter some credit- had I not misconstrued his gobbledygook, not sought to reconcile contradictions, not attended closely to Godel's theorizing and its implications, in particular, investigating further, I would not have gained knowledge and convictions that would later inform and enrich my personal and professional life. Thanks in part to Hofstadter, I think for myself and am more discerning and critical minded than I would likely have been otherwise, it has served me (and most importantly, my patients) well. And, his enthusiasm (along with brilliant Michael Mahoney's) spurred me to pursue cognitive neuropsychology in the first place. However, in retrospect, I would also quibble about the fact that Hofstadter teaches at a publicly-funded university, and that our tax dollars paid for him to write his flippant, irrelevent clap-trap, dross that may well lead other promising young minds ASTRAY, rather than encouraging them to seek real solutions to the egregious psychological/neurological ills that plague our society and resound for other more socially responsible cognitive scientists (cognitive science being, after all, an outgrowth of psychology and an applied discipline). Douglas Hofstadter is instead a huge distraction, a dilettante, the Kim Kardashian of the Neuroscientific community (sorry, Kim). What a waste of brilliance.
In a nutshell, with GEB I think Hofstadter perpetrated some measure of fraud on the scientific community. We should have been more discerning. He had one seminal idea, that Godel's theorem, Escher's drawings, and Bach's fugues had something in common, were "strange loops". This he could have been presented in a 10 page paper in a peer-reviewed professional journal, but instead, he swaddled it in hundreds of pages of self-indulgent, pretentious, masturbatory ramblings and rehashed, arcane mathematical computations (that he perhaps knew few would scrutinize, and which have little to do with his prose). In the final analysis, very little of it is germaine, valid, or useful, scientifically. But gosh, it sounds so good, seems so...profound. For me it's sort of the literary equivalent of Terence Malick's The Tree of Life- a lot to take in, flash and style galore, but ultimately little of substance, nothing remotely explanatory or USEFUL. THIS is the main reason I find Hoftadter so contemptible, along with his deceitful methods, not the fact that his metaphysical faith assumptions differ from mine. It's NOT the fact that he's mechanistic, atheistic (there are plenty of mechanists I esteem greatly, e.g., Stephen Jay Gould, Loren Eiseley, Milton Erickson, Steven C. Hayes)- it's the fact that he obscured his ideology and agenda, and worst of all, cited and twisted the work of noble men who believed the polar opposite, without owning up to it- having a sly, slithery laugh at their (and our) expense, to the detriment of us all. Disgusting.
Hofstadter's avowed intent to analyze the world and the mind in the spirit of Lewis Carroll (whom I'd read and delighted in), his celebration of the genius of three men who infused their work with their spirituality, his koan-like meditations, and multiple levels of analysis seemed to me a valentine to the complexities and irreducibility of the universe and human consciousness, implying that human thought, "the mind" could exceed the confines of the human brain, just as Escher's paintings and Godelian knots escaped being defined or constrained by dimensional space. The phenomena described so poetically by Hofstadter seemed to me to suggest the possibility of ever widening spheres of analysis, of perception, of consciousness. Or so I thought. In any case, I was tremendously inspired by it. In my naivete, I thought he embodied perspectives simultaneously scientific and spiritual, as did the book's namesakes, in varying degrees. (Note that this is from memory, which cannot be other than selective- I donated the book years ago. These are the impressions that have stuck with me.) In succeeding years I read his next two books, although I have little memory of those.
It wasn't until a few years later, after I'd read World Hypotheses: A Study in Evidence by Stephen Pepper (must reading for anyone seeking to understand how knowledge is organized and "truth" derived), as well as At Home in the Universe by John Archibald Wheeler, The Mathematical Foundations of Quantum Mechanics by John von Neumann, works by Ilya Prigogine, Hermann Lotze, William James, and others (as part of advanced study in cognitive neuroscience, philosophy, and the philosophy of science), books that directly addressed the issues hinted at, or at least suggested to me by Hofstadter, that I went back and re-read GEB.
I had an epiphany, muddied by a sense of betrayal at being utterly duped, that, in fact, not only did Hoffstadter not mean what I thought he had (MY bad), but the book actually said very little and proved nothing. Just prior to revisiting it I'd read an article by Hofstadter asserting that GEB was actually about mind/consciousness as a mere epiphenomenon that arises as an emergent property of individual neurons, themselves non-conscious (his ant analogy). This was not even then a new idea, and he didn't provide proof of it, indeed, seemed to contradict it. More egregiously, it's a mechanistic notion, yet he cited Godel, a non-mechanistic theorist, whose theorem, according to Godel himself, demonstrates that symbolic thought can NOT arise from inanimate matter, due to the necessity of recursion in logical thought. Moreover, Godel thought it proof, along with other axioms he'd developed, of God's existence (btw, his bff Albert Einstein thought so too). Dirty pool indeed, to subvert, misrepresent and try to twist a mathematical proof to fit, to subserve one's own incompatible and biased agenda, WITHOUT owning up to what you're doing- intellectually dishonest in the extreme (if he's not a passive-aggressive, I'll eat my hat, though that's hardly pertinent). In any event, he was unsuccessful, but that fact seems to have escaped nearly everyone's notice.
Cognitive psychology is rife with intriguing mysteries to be solved. Neurons seem to have a mind of their own, changing their receptor sites at the flick of an eye, firing, responding or not responding to stimuli by mechanisms we've yet to discover. And they respond not only to electrical signals, but to chemical/magnetic changes and a vast array of neurotransmitters and hormones. Cells in the immune system also sport rapidly morphing receptor sites, making the situation even more complex.
In one study, a neuron was transplanted from a grasshopper's brain to its belly. The neuron grew into the surrounding tissue, but to the surprise of researchers, grew one, abnormally long dendrite [for receiving neural signals] directly back to the exact spot from which it had been excised, presumably so that it could keep abreast of developments in its old stomping grounds. The question of course is, how did it know from whence it came?
There's a long-standing debate amongst cognitivists and philosophers about the seeming irreconcilability of symbolic thought processes and observations of actual neuronal processes (a focus of Godel's work). Hofstadter's likening of neurons to ants did nothing to reconcile the two perspectives, nor did stories of tortoises or hares, though he seemed to suggest otherwise, without ever actually explaining how they did. In fact, Hofstadter's book, though lyrical, shed no new light on ANY of the pressing issues in cognitive science. As I remember, the entire book boils down to this (though I had to look long and hard to find it): strange loops exist in nature. Since we know there's no divine or organizing principle extant in nature, they must occur by natural means. Period. No actual proof is provided. No experiments are conducted. It's not science- it's a faith assumption.
GEB leads us down myriad garden paths that go nowhere. It's smoke and mirrors, an elaborate exercise in obfuscation and intellectual masturbation, AND full of errant premises- Pulitzer Prize, zen-master-like countenance and assured, authoritative tone not withstanding. I'd have no beef with Hofstadter if he'd presented his musings in a less duplicitous fashion, if he'd said "These are musings, part prose, part metaphysical speculation, draw from them what you will, but they're offered as proof of nothing." Or, he could have laid bare the real issues involved, presenting both sides of the materialism VS idealism debate, for example (he didn't, of course, because he actually had nothing new to add). It's the inherent DISHONESTY, the cloaking of the real issues involved, that irks me so. SPIT IT OUT- what do you believe, what evidence do you have in support of your contentions, what dilemmas still remain for you, how might these be studied/resolved? If you want to read works simultaneously scientific, substantive, inspiring, achingly poetic, and USEFUL, curl up with anything by French neuroscientist/philosopher Gaston Bachelard, or Jerome Bruner. If you want to be challenged by perplexities both tantalizing and profound, try the inimitable Chuang Tzu (by either Burton Watson or A.C. Graham), World Hypotheses by Stephen Pepper, or the WAY out there A Course In Miracles by psychologist and Columbia University Medical School Professor Helen Schucman. As supplemental reading for my own students I've recommended Oliver Sacks, Roger Penrose, Howard Gardner, and Jerome Bruner, among others- Hofstadter not included, obviously.
It's fitting that Hofstadter succeeded Martin Gardner as mathematical columnist for Scientific American, who opined in the preface of his The Annotated Alice: Alice's Adventures in Wonderland & Through the Looking Glass, also supposedly in "tribute" to Lewis Carroll, that:
"The last level of metaphor in Alice is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by an idiot mathematician. At the heart of things science finds only a mad, never-ending quadrille of Mock Turtle Waves and Gryphon Particles. For a moment the waves and particles dance in grotesque, inconceivably complex patterns capable of reflecting on their own absurdity. We all live slapstick lives, under an inexplicable sentence of death."
Metaphysical assumptions aside, just look at the nihilistic bent of the words employed. Grotesque? Mad? Absurd? These terms are not only value-ridden (i.e., suggestive of mechanistic bias), but one could argue, in stark contrast to the spirit of those chosen by Lewis Carroll, particularly in the poems which preface and conclude his beloved Alice's adventures. Carroll was a devoutly religious man, a clergyman who saw the mind of God as the substrate for the material world, and I think we can safely say that he had no such metaphor in mind when he put pen to paper. Indeed, I'm sure it would horrify him (as would the fact that Gardner made hefty royalties highjacking and subverting his labors of love). While still not cricket where Carroll is concerned, at least Gardner made no attempt to obscure his mechanistic (er, atheistic) agenda.
Perhaps the issues I raise here are now old hat in philosophical circles, I haven't kept up with this aspect of the field (my career took an applied, clinical turn, years ago). Recently I happened upon a brief synopsis of Hofstadter's 2007 book, and my sense of outrage at his devious sleight of hand and hucksterism came flooding back, thus, this review. So as not to obscure my own bias, I admit I think it more likely than not that essence precedes existence, that the material world is a projection of mind or minds, the result of conscious intentionality, as Blaise Pascal, and John von Neumann ultimately concluded (and the latter thought he'd demonstrated mathematically). Other scientists, brilliant and rigorous, have arrived at the same conclusion (Irwin Schrodinger, Roger Sperry, many more).
It is possible, as philosopher George Howison contended (circa 1902), that: "It is not simply that there are many minds behind the scenes, but that these minds are OURS- our GENUINE selves." And: "The real past is a flowing whole, and we are forever pouring the future into the flood, through the gate of the present. Our past is really always changing, and it is we who initiate the change, and so the past, though no part can be re-called, is perpetually being re-created and transformed, now for the worse, now for the better, as the whole goes on unfolding." This last assertion was later echoed by physicist John Wheeler, in his theory of the participatory universe.
But I digress. I should give Hofstadter some credit- had I not misconstrued his gobbledygook, not sought to reconcile contradictions, not attended closely to Godel's theorizing and its implications, in particular, investigating further, I would not have gained knowledge and convictions that would later inform and enrich my personal and professional life. Thanks in part to Hofstadter, I think for myself and am more discerning and critical minded than I would likely have been otherwise, it has served me (and most importantly, my patients) well. And, his enthusiasm (along with brilliant Michael Mahoney's) spurred me to pursue cognitive neuropsychology in the first place. However, in retrospect, I would also quibble about the fact that Hofstadter teaches at a publicly-funded university, and that our tax dollars paid for him to write his flippant, irrelevent clap-trap, dross that may well lead other promising young minds ASTRAY, rather than encouraging them to seek real solutions to the egregious psychological/neurological ills that plague our society and resound for other more socially responsible cognitive scientists (cognitive science being, after all, an outgrowth of psychology and an applied discipline). Douglas Hofstadter is instead a huge distraction, a dilettante, the Kim Kardashian of the Neuroscientific community (sorry, Kim). What a waste of brilliance.
In a nutshell, with GEB I think Hofstadter perpetrated some measure of fraud on the scientific community. We should have been more discerning. He had one seminal idea, that Godel's theorem, Escher's drawings, and Bach's fugues had something in common, were "strange loops". This he could have been presented in a 10 page paper in a peer-reviewed professional journal, but instead, he swaddled it in hundreds of pages of self-indulgent, pretentious, masturbatory ramblings and rehashed, arcane mathematical computations (that he perhaps knew few would scrutinize, and which have little to do with his prose). In the final analysis, very little of it is germaine, valid, or useful, scientifically. But gosh, it sounds so good, seems so...profound. For me it's sort of the literary equivalent of Terence Malick's The Tree of Life- a lot to take in, flash and style galore, but ultimately little of substance, nothing remotely explanatory or USEFUL. THIS is the main reason I find Hoftadter so contemptible, along with his deceitful methods, not the fact that his metaphysical faith assumptions differ from mine. It's NOT the fact that he's mechanistic, atheistic (there are plenty of mechanists I esteem greatly, e.g., Stephen Jay Gould, Loren Eiseley, Milton Erickson, Steven C. Hayes)- it's the fact that he obscured his ideology and agenda, and worst of all, cited and twisted the work of noble men who believed the polar opposite, without owning up to it- having a sly, slithery laugh at their (and our) expense, to the detriment of us all. Disgusting.
★ ★ ★ ☆ ☆
amita
It's too intellectually heavy. I agree with the other 4 and 5 star reviews, it's just too heavy for a single read. It is strange to think that one can learn calculus and statistics and some computer science within a year but to know that there are people who haven't been able to finish the book after a year? Very strange. Maybe if the book were split into two or three it would be a better read and it wouldn't feel like some sections have too much in them.
Please RateBach: An Eternal Golden Braid, Escher, Gödel
Whatever the case may be, this is a very interesting book. Take a look at it in the bookstore, then buy or order it from the store if you find that you like what 'interesting' can mean.