Customer Rating: 
Summary: "This sentence is false."
Comment: 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.
Customer Rating:
Summary: An amazing and weird look at...everything!
Comment: Godel, Escher, Bach (GEB) is an interesting book on...well, it's hard to categorize. It's about "Strange Loops", but it's about way more than that...it's about human reasoning and computer interaction...but it's also about way more than that. Overall, as one of the reviews on the back cover says, this book is "An entire humanistic education between the covers of one book."
Customer Rating:
Summary: Relativity and Complexity
Comment: A very robust analysis for consciousness and mind, but I think that "The Mind's I" of the same author provides the same "food for thought" in a more attractive way.
Customer Rating:
Summary: A mishmash of unrelated ideas. A waste of time.
Comment: I read this book I don't remember how many years back. I think about 15 years ago. And just remembering makes me nauseous, for the amount of time and effort it took me read it just to get to no point. I was younger, naiver and I got engaged, I confess that. Clever Author no doubt, to make a huge pile of unrelated ideas and make believe you would get somewhere following his lead. Just wandering around and playing with analogies. I had the time back then, I guess. Today I only have the time to write a review stating how surprised I am today I could finish this kind of book. I can't speak for anyone else, suffice to say I was a nerd with a lot of time in my hands.
Customer Rating:
Summary: Exceptional book
Comment: 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.
Summary: "This sentence is false."
Comment: 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.
Customer Rating:
Summary: An amazing and weird look at...everything!
Comment: Godel, Escher, Bach (GEB) is an interesting book on...well, it's hard to categorize. It's about "Strange Loops", but it's about way more than that...it's about human reasoning and computer interaction...but it's also about way more than that. Overall, as one of the reviews on the back cover says, this book is "An entire humanistic education between the covers of one book."
Customer Rating:
Summary: Relativity and Complexity
Comment: A very robust analysis for consciousness and mind, but I think that "The Mind's I" of the same author provides the same "food for thought" in a more attractive way.
Customer Rating:
Summary: A mishmash of unrelated ideas. A waste of time.
Comment: I read this book I don't remember how many years back. I think about 15 years ago. And just remembering makes me nauseous, for the amount of time and effort it took me read it just to get to no point. I was younger, naiver and I got engaged, I confess that. Clever Author no doubt, to make a huge pile of unrelated ideas and make believe you would get somewhere following his lead. Just wandering around and playing with analogies. I had the time back then, I guess. Today I only have the time to write a review stating how surprised I am today I could finish this kind of book. I can't speak for anyone else, suffice to say I was a nerd with a lot of time in my hands.
Customer Rating:
Summary: Exceptional book
Comment: 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.