Customer Rating: 
Summary: Abstruse and over-rated
Comment: The author complains in the new preface that a vast majority of the reviewers, including those who have rated this book very highly, seem to have no idea of what he has been trying to say. In my opinion, this is a self-indictment that does not leave much for others to say. If the author cannot get his ideas across in 700 pages, perhaps people should not waste their time on him. I have learnt it the hard way: after buying this book, five years ago, on high recommendations of friends, only to find it so boring and confused that I could never go beyond a few pages even though I gave it innumerable attempts.
Customer Rating:
Summary: Magnum Opus on Intelligence
Comment: I realized after recommending this to a friend that I've never reviewed it. Strange, since it's one of the dozen most important books I've ever read in my nearly half-century on this planet. I first read it over 20 years ago, and continue to refer to its literate and well-crafted pages frequently.
This book is Doug Hofstadter's religion. Since it's so good and so right about so many things, people run off into strange places with Hofstadter's words, sort of like the Bible. GEB (the shorthand name for the book) is, for me, a meta-level examination of what it is to be human. Some people see the shadows of the gods in there. I'm not trying to be melodramatic, nor do I believe I'm overstating the value of this book.
Hofstadter takes the reader along on a Carrollian trip using metaphor and fable. Then he employs pedagogical, practical exercises, and good old-fashion lecture. Rinse and repeat, again and again. When he tells you to get pen and paper, please do it. Take your time with this book. I tried and failed on my first attempt. When I finally settled into it, it took me three months to joyously work my way through it. Take a year if you need it.
Reception, analysis, recursion, reapplication. Hofstadter examines the basic evidences of intelligence, forms sensible, fundamental meta-rules, and builds from there. This book - as others have said - is hard work, like climbing a mountain. But at the end of the endeavor, the view is dazzling.
Customer Rating:
Summary: Wow... Deep thoughts, and Abstract Perspectives
Comment: I have not completed this book, and I am not sure you can ever say that you are complete with a book of this magnitude, however, it will certainly be a book I will review again and again. If you want to be challenged intellectually, this book would be the ticket. I enjoy a good challenge, and although it isn't a 'fun' read, it is valuable book to have in your personal library if you are interested in a paradigm shift in your reality.
Customer Rating:
Summary: HOFSTADER'S ERROR(By James E. Spinosa)
Comment: 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': 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 www.jimssciencepage.info
Customer Rating:
Summary: A whole new world
Comment: Just like other reviewers of this book, this one is seriously math-challenged. I thought I'd never make it to the end. I had to work hard sometimes. But it was one of the most worthwhile reading experiences of my life, indeed it was fascinating and I ended up recommending it to everybody (almost). This is an eccentric book, which at the beginning seems to be about everything and nothing. The author describes "self-referential systems" and wonders whether they may come to think about themselves and, ultimately, about the possibility of Artificial Intelligence (AI). This is one of the books that have taught me the most and made me think about things that for me are little or not familiar at all, like Typographic Number Theory (TNT) or propositional calculus. I don't pretend to having understood all of it perfectly, but definitely my intellectual horizon and my knowledge widened a lot. The title comes from three people whose work illustrates the wide field of self-referential systems. One is Kurt Godel, a mathematician who formulated the famous and complex Theorem of Incompletitude, which says something like in every formulation of Number Theory there are one or several propositions which are undecidable, that is, it is impossible to affirm if they are theorems of that formulation, or not. What is a formulation of Number Theory? Well, starting from an axiom (a given equation), and according to some precise rules of addition, substraction, or substitution, one develops the equation until finding (or not) some preestablished outcome. These formulations are self-referential because they turn in on themselves, that is, they take the sources of their subsequent development from the very elements present in the original axiom.
OK, where do Bach and Escher enter the picture? Simple: Escher's engravings and illustrations (of which the book offers many beautiful examples), and Bach's music, are self-referential. They present an initial theme, and then they develop by turning in on themselves according to some rules or patterns. This is also how DNA chains and the resulting organisms grow, and even some poetry. The book is written with great sense of humor and didactic skill; it intersperses "technical" chapters with funny and seemingly absurd dialogues between cartoon-like characters, which illustrate with good clarity subjects previously exposed. Mathematics, biology, computers, AI, music, painting, and language are part of the subjects taken on.
For example, this book helped me to understand better how computers and software languages work. In one of the most interesting parts, the author explains how our brains function at different levels: the strictly neuronal, the cellular, the chemical, and the symbolic. In the same way, computers work at different levels, from that which occurs between components of the microcircuits, passing through successive levels of programming, until the "symbolic" level, which is represented by what we see on the screen. Just as people don't need to know or screen what is happening with their pancreas or stomach in order to go about, but they limit themselves to eating, breathing, walking, thinking, computer users don't need to know what is going on with the circuits while they use them. We only take notice of organs or programs ewhen something's wrong: we either feel bad or the computer paralyzes. Finally, the other debate is about the possibility or not of AI, which is far from being resolved. An enormous book.
Summary: Abstruse and over-rated
Comment: The author complains in the new preface that a vast majority of the reviewers, including those who have rated this book very highly, seem to have no idea of what he has been trying to say. In my opinion, this is a self-indictment that does not leave much for others to say. If the author cannot get his ideas across in 700 pages, perhaps people should not waste their time on him. I have learnt it the hard way: after buying this book, five years ago, on high recommendations of friends, only to find it so boring and confused that I could never go beyond a few pages even though I gave it innumerable attempts.
Customer Rating:
Summary: Magnum Opus on Intelligence
Comment: I realized after recommending this to a friend that I've never reviewed it. Strange, since it's one of the dozen most important books I've ever read in my nearly half-century on this planet. I first read it over 20 years ago, and continue to refer to its literate and well-crafted pages frequently.
This book is Doug Hofstadter's religion. Since it's so good and so right about so many things, people run off into strange places with Hofstadter's words, sort of like the Bible. GEB (the shorthand name for the book) is, for me, a meta-level examination of what it is to be human. Some people see the shadows of the gods in there. I'm not trying to be melodramatic, nor do I believe I'm overstating the value of this book.
Hofstadter takes the reader along on a Carrollian trip using metaphor and fable. Then he employs pedagogical, practical exercises, and good old-fashion lecture. Rinse and repeat, again and again. When he tells you to get pen and paper, please do it. Take your time with this book. I tried and failed on my first attempt. When I finally settled into it, it took me three months to joyously work my way through it. Take a year if you need it.
Reception, analysis, recursion, reapplication. Hofstadter examines the basic evidences of intelligence, forms sensible, fundamental meta-rules, and builds from there. This book - as others have said - is hard work, like climbing a mountain. But at the end of the endeavor, the view is dazzling.
Customer Rating:
Summary: Wow... Deep thoughts, and Abstract Perspectives
Comment: I have not completed this book, and I am not sure you can ever say that you are complete with a book of this magnitude, however, it will certainly be a book I will review again and again. If you want to be challenged intellectually, this book would be the ticket. I enjoy a good challenge, and although it isn't a 'fun' read, it is valuable book to have in your personal library if you are interested in a paradigm shift in your reality.
Customer Rating:
Summary: HOFSTADER'S ERROR(By James E. Spinosa)
Comment: After studying Douglas R. Hofstader's brilliant book, I discovered an error in the proof of Godel's first incompleteness theorem that invalidates the proof. The same error is in Newman & Nagel's book Godel's Proof.
The error occurs on page 447. The incorrect statement is, "a' is the arithmoquinification of u." The statement should read: a' is the arithmoquinification of the numeric value of the Godel number u. The term u represents the Godel number of a specific formula, and the word arithmoquinification is a portmanteau word coined by the author.
Godel's theorem is derived by arithmoquining a formula that Hofstader calls the "uncle" formula. On page 447, he writes,"Now all we need to do
is-arithmoquine this very uncle! What this entails is 'booting out' all the free variables-of which there is only one,namely a"-and putting in the
numeral for u everywhere. This gives us: ~Ea:Ea':
he offers this interpretation of the theorem,"There do not exist numbers a
& a' that both(1)they form a TNT-proof-pair, and(2)a' is the arithmoquinification of u." But,as I have pointed out Godel's theorem does
not declare part(2)of his interpretation. Instead, the correct interpretation of part(2)is, a' is the arithmoquinification of the numeral of the Godel number u. The numeral of the Godel number u cannot be
arithmoquined because it is not a formula and therefore has neither a Godel number nor a free variable.
This invalidates the proof because we no longer have a true statement: a'
is the arithmoquinification of u that cannot be proven. Instead we have a
false statement that cannot be proven. For more info & essays on this subject,please go to www.jimssciencepage.info
Customer Rating:
Summary: A whole new world
Comment: Just like other reviewers of this book, this one is seriously math-challenged. I thought I'd never make it to the end. I had to work hard sometimes. But it was one of the most worthwhile reading experiences of my life, indeed it was fascinating and I ended up recommending it to everybody (almost). This is an eccentric book, which at the beginning seems to be about everything and nothing. The author describes "self-referential systems" and wonders whether they may come to think about themselves and, ultimately, about the possibility of Artificial Intelligence (AI). This is one of the books that have taught me the most and made me think about things that for me are little or not familiar at all, like Typographic Number Theory (TNT) or propositional calculus. I don't pretend to having understood all of it perfectly, but definitely my intellectual horizon and my knowledge widened a lot. The title comes from three people whose work illustrates the wide field of self-referential systems. One is Kurt Godel, a mathematician who formulated the famous and complex Theorem of Incompletitude, which says something like in every formulation of Number Theory there are one or several propositions which are undecidable, that is, it is impossible to affirm if they are theorems of that formulation, or not. What is a formulation of Number Theory? Well, starting from an axiom (a given equation), and according to some precise rules of addition, substraction, or substitution, one develops the equation until finding (or not) some preestablished outcome. These formulations are self-referential because they turn in on themselves, that is, they take the sources of their subsequent development from the very elements present in the original axiom.
OK, where do Bach and Escher enter the picture? Simple: Escher's engravings and illustrations (of which the book offers many beautiful examples), and Bach's music, are self-referential. They present an initial theme, and then they develop by turning in on themselves according to some rules or patterns. This is also how DNA chains and the resulting organisms grow, and even some poetry. The book is written with great sense of humor and didactic skill; it intersperses "technical" chapters with funny and seemingly absurd dialogues between cartoon-like characters, which illustrate with good clarity subjects previously exposed. Mathematics, biology, computers, AI, music, painting, and language are part of the subjects taken on.
For example, this book helped me to understand better how computers and software languages work. In one of the most interesting parts, the author explains how our brains function at different levels: the strictly neuronal, the cellular, the chemical, and the symbolic. In the same way, computers work at different levels, from that which occurs between components of the microcircuits, passing through successive levels of programming, until the "symbolic" level, which is represented by what we see on the screen. Just as people don't need to know or screen what is happening with their pancreas or stomach in order to go about, but they limit themselves to eating, breathing, walking, thinking, computer users don't need to know what is going on with the circuits while they use them. We only take notice of organs or programs ewhen something's wrong: we either feel bad or the computer paralyzes. Finally, the other debate is about the possibility or not of AI, which is far from being resolved. An enormous book.