Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter
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Book Reviews of Gödel, Escher, Bach: An Eternal Golden Braid
Book Review: A Beautiful Discourse on Meaning and Structure
Summary: 5 Stars
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".
Book Review: "This sentence is false."
Summary: 5 Stars
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.
Book Review: Can we build intelligent devices?
Summary: 5 Stars
How do we put the thinking power of the human brain into a man-made device? Godel, Escher, Bach is a jolly tour of this great intellectual challenge.The title of this book is a metaphor for the concept of metaphor. If Hofstadter had called the book "Metaphor, Isomorphism, Mapping" or "Self-reference, Tangled-hierarchies and Strange-loops" it might have sold a few thousand copies. But many millions of people are familiar with Escher or Bach, so the book leaps off of book shelves into people's minds and they can get hooked on the exploration of strange-loops before they realize what they have gotten themselves into.
The mathematics of Godel, the art work of Escher, and the music of Bach are related by the fact that they all included examples of what Hofstadter calls a strange-loop. Hofstadter explores these three specific examples of strange-loopiness and then goes on to explain his belief that it is our struggle to understand and codify strange-loopiness that lies at the heart of Artificial Intelligence research.
The most concise example of a strange-loop is, "This sentence is false." As a self-referential sentence, it gets itself into trouble and defies our desire that all propositions be either true or false. What is the origin of our desire that human reasoning and human language fit nicely into the binary logic of 0 and 1, false and true? Hofstadter reviews some of the history of this idea and explains how Godel was able to shatter its Platonic purity just at the time when digital electronic computers were being invented.
Godel showed that any formal system complex enough to capture the intricacies of number theory must contain propositions that cannot be proven either true or false. Godel accomplished this by showing that such formal systems are inherently self-referential, like the sentence "This sentence is false." Formal systems are capable of not only making statements IN number theory but they can also make self-referential statements ABOUT themselves.
What does this mathematical strange-loopiness have to do with computers, artificial intelligence, and human minds? About the same time that Godel was showing that formal systems are irreversibly tainted with strange-loopiness, people like Alan Turing were discovering how to embed formal systems in electronic computers. So the challenge became how to produce creativity and mindfulness out of formal computing systems, systems which seem the ultimate design for only mindless yes-or-no behavior.
But, as Hofstadter points out, these seemingly mindless computing devices inherently contain the Godelian power of self-reference and strange-loopiness. So wouldn't it be cool if it is strange-loopiness that turns out to be the basis for human intelligence? If so, then we must be able to exploit the strange-loopiness of computers so as to make true artificial intelligences that are just as intelligent as people.
Hofstadter provides a tour of the human brain in an attempt to reveal the sorts of strange-loopiness that make human intelligence. Hofstadter's goal is to find the essential features of biological strange-loopiness so that we can then return to our digital electronic computers and embed that necessary strange-loopiness in them.
One of the main reasons why Hofstadter's book "Godel, Escher, Bach" remains my favorite book is because it chisels out Hofstadter's position so clearly that the shape of the negative space outside of Hofstadter's position is also distinctly defined. His book paradoxically manages to show the importance of just those things he did not want to be important for artificial intelligence research. It is as if he started with a block of marble and chipped off pieces, each of which he describes. What is left standing, the statue, he did not explicitly describe but it is left standing there before our eyes, cleared of all the surrounding waste material. For example, the word "learning" is not even listed in the index yet the book can be taken as a demonstration of the importance of learning for intelligent behavior.
Hofstadter does not want to confront the details of brain hardware, in fact, one of HIS major objectives is to convince himself that it is safe to ignore those details. His research program is to "skim off" the essential "high level" symbols (in modern, post-Dawkin's jargon we'd say "memes" where he says "symbols") from the brain, but he does explain that there have to be "low level" hardware features of the brain that make possible the symbols. Hofstadter's goal is for the "symbols" to be put into a computer where they will have a different "low level" foundation (electronic circuits rather than neurons).
Hofstadter's research program abandons the brain's "low level" unconscious features because they are an untouchable (mentally) common foundation at the base of every human mind. Most human learning takes place in what George Lakoff calls the "cognitive unconscious". We are unconscious of the means by which humans learn the "semantic content" of symbols. This fact deflects Hofstadter (and most AI researchers) away from trying to make robots that would learn about the world in the way human children learn. If you make this move the only games left to play are: 1) program all the needed semantic content by hand, or 2) implement inefficient trial-and-error learning algorithms. These are the methods that most AI researchers use, but decade after decade they fail to give us man-made devices with human-like intelligence.
The alternative, which Hoftadter discusses and then abandons, is to first study the human brain and come to understand how human children learn from their interactions with the world. Once we know that, we will be able to apply that understanding to the task of making robotic devices that can learn the way children learn. This book is a gem in how it draws attention to this road not taken. But it is never too late to take it.
Book Review: reconciling the software of the mind with the hardware of brain
Summary: 5 Stars
This book has a preface by the author. After twenty (20) or so pages, I was thinking, "Can I understand what he wrote about in the rest of this book?" but I persevered and read the whole book. This book is intense, like any philosophical book. His motive is to "suggest ways of reconciling the software of the mind with the hardware of brain" and that is quite an endeavor he succeeds at, sort of. No wonder he won the Pulitzer prize for this book. He talks of how he came to write and develop the book, and then, upon preparing for republication, he decides to not redo the book: it is what it is, from back then, any addition or correction would create a new book, and it can been seen every so often he imagines some stuff that we use daily, like spell correction, that were just not available back then. If he was to do that, he might as well write a whole new book, and that was not in the cards, nor was it the purpose of the new edition.
Gödel goosed him to realize the notions he writes about, but Escher and Bach represent examples of what Gödel was writing and he is thinking about. As you read the introduction you realize this is one educated and well rounded fellow. He describes the development of Bach's preludes and fugues like a music teacher (I realized that I have a recording of Wanda Landowsky playing "The Well-Tempered Clavier" Book 1, preludes and fugues, but that did not help me understand as you will see). Bach worked up various themes and notions through his music and than then did some fancy finagling and out came some thing wild and crazy wonderful. I listened to the recording I have to no avail. This is something you get to know by playing and playing the tunes, a lot, for yourself, but Mr. Hofstadter's exposition explains what is what for you. Escher is easier (visual experiences are more important or easier to comprehend than aural experiences). The pictures are presented as examples of repetition or growth from one thing into another. The idea of repeating or self-reference is important: it is one thing that computers do not do. We can do imagining things as well, but at a more basic level we self-reference creating a hump of ability that computers have to accomplish if they are to get to be self aware or intelligent.
As he said, he wants to understand the hardware of the brain, but in comparison, computers are simpler, but getting more complicated. He is working from the bottom up with computers: machine language, assembly, programing languages, etc. Fro our brains he is working from the top down, trying to see how the thoughts (software) we think get from one point to another. It is difficult because we do not have access to the basic growth of each thought (neurons firing). Logic tries, yet, as that one guy two (2) or three (3) thousand years ago said, "All I know is that I do not know anything." Mr. Hofstadter just comes to that thought in another roundabout way. I kept thinking of sex deviants doing what they do and that if we could look into their heads, we would be hard pressed to see where the impetus for their deviant behavior comes from, how it develops or why they do it. It is somewhere in there, but the thoughts (software) are so complicated that we can not see how it develops into what is expressed. I also think of how we all speak. We talk without thinking (something I am accused of constantly and embarrassingly), but in reality we just do not follow the thought process from what we hear and see, etc., to what we think of it, to what we will say, to saying it. Another thought is what is happening in the brains of mediators, you know, those Zen folks who quiet the mind, what is happening in there then? The mind is just amazing in what it does.
Throughout this book Mr. Hofstadter writes of the mind and the brain like a psychologist, how it works and what it does. He also delves into genetics. His forte is math and all its intricacies. He develops a couple of different math models to illustrate Gödel's incompleteness theorem. The logic starts out straight forward enough, then veers off into some esoteric realm where the notion of paradox lives, and this is where we have to develop our math notions. We can study the properties of prime numbers or infinities, but we always must end up knowing we do not know everything, because our logic can not encompass paradoxes, and they will be somewhere in all we do, or something like that.
As you can see, I was not able to understand his math models, but I think I got the jist of it.
This book reminds me of another book published in 1978, "The Seven Mysteries of Life" by Guy Murchie. It is amazing that they talk of the same things in the same way and for the same reasons. Though this is a treatise on computers and artificial intelligence, and the other is a religious book, sort of, about the awesomeness of life.
As for the artificial intelligence aspect, I like his development towards that goal, but, and I find no fault in the imagining of it, I am disappointed that computers will just be like us. It will not create a Spock like machine, or what science fiction has led us to hope for (see Isaac Asimov, "I, Robot" etc.). I did like his notion of combining genotypes to create new genes, but I am a guy and I like that sort of stuff. I find that I agree with someone who said, "There are much more fun ways to create intelligence, and it is not artificial." If artificial intelligence is not going to be all that great, it is only good to try to develop it for the exercise and the experience it will give us, but otherwise, eh, no big deal.
Book Review: A very good piece of art, but not a "metabook" in anyway...
Summary: 5 Stars
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.