Take a photo of a barcode or cover
4.31 AVERAGE
4.31 AVERAGE
challenging
informative
reflective
slow-paced
I was 16 when this book first came out. I read bits and pieces of it constantly from that time until I finally read the whole book from beginning to end when I was 37. By then I had read the whole book several times over, but never sequentially. Many of my personality traits can be traced back to this book: a love of Lewis Carroll, my career as a computer programmer, my interest in robotics and [b:artificial intelligence|27543|Artificial Intelligence A Modern Approach (2nd Edition)|Stuart J. Russell|http://photo.goodreads.com/books/1167881696s/27543.jpg|1362], and several Bach CD's in my collection (including the Musical Offering). I love this book. I'll leave it next to my son's bed when he's old enough to start understanding it.
I was probably in the first year of my M.S. study at the university where I first heard about Douglas Hofstadter's Book Gödel, Escher, Bach: An Eternal Golden Braid. The first description of it was that "It is a book that only less than 10 people in the whole world fully understand". If any of you know me, you would understand that this was the perfect trigger for me to get interested in the book! The appeal of the book was that it was establishing similarities in the works of Kurt Gödel (A 20th century mathematician), Johann Sebastian Bach (An 18th century classical musician, and one of the greatest musicians ever) and Maurits Cornelius Escher (A 20th century Dutch painter).
Later on we recruited a person for my software company, and he claimed to understand the book almost entirely. This guy was an Electrical Engineer who attended high-level Math classes and just listened to the professor without taking any notes, then could show you any proof in its entirety without so much of an effort. He had been studying in the U.S. for a Ph.D. but eventually lost interest and came back to work in the software business.
While struggling with the intricacies of the M.S. work in Industrial Engineering, I was also working on my second major in Mathematics. Along with the inconceivable dimensions and abstract contraptions of Topology, I had to understand the intricate mechanism of being able to prove or disprove any given theorem or conjecture. Gödel had shown in his famous Incompleteness theorem published in 1931 that any mathematical system which has a consistent set of axioms will always have some propositions the value of which (TRUE or FALSE) can not be decided within that mathematical system. Namely, there would be an infinite number of propositions that would be undecidable using the program. This generalization of of the Liar's Paradox (The person who says "I'm a Liar" creates a paradox that makes it impossible to decide whether this statement is true or false) has some negative implications for Information Technology, since it would not be possible to write a computer program that would be able to decide whether a given statement is correct or incorrect.
I had started to get interested in Classical Music while in High School. I was a boarding student, and the mother of one of my good friends was a real classic music lover. She started taking us to the Friday evening concerts in the Classical Music Concert Hall. These usually consisted of real classics, usually with a concerto and maybe a symphony if we were lucky. Since these concerts would normally cover anybody from Mozart to Sostakovich, but would rarely touch Baroque and composers like Back, it took me several years before I got introduced to Bach's music. I used to go to the University library to get an album (Long-play, of course this was way before CDs!) and listen to it with a good headphone in the absolute silence of the library.
Hofstadter's book points to the way Bach has woven his compositions with recursive patterns, with almost mathematical perfection. These recursive patterns form the way counterpoint and other classical techniques are used in his music to reach harmony, that was the crux of early and Baroque era classical music, getting its justification from the religious idea of musical harmony mimicking the perfectness of God's vision.
The concept of recursion is also apparent in Escher's works. He is famous for building impossible worlds in his woodprints, where he has depicted scenes that could not happen in real life, such as rectangular stairs seemingly climbing continuously up to infinity, a waterfall that seems to defy gravity by means of water continually moving upward to create the power with which the waterfall falls down, and similar constructions. He has also formed infinitely recursive patterns and structures on some his paintings. (Use this link to find out about the Escher Museum in The Hague)
Hofstadter has structured his book to cover these three genius individuals in three major divisions of the book, but has interspersed the regular chapters with philosophical fables that look into some of the recursive concepts in philosophy, such as Zeno's paradox, where the philosopher Zeno decides that the perceived world can not be real. He uses the argument of halving the distance to the target and showing that no matter how far the arrow goes, there is still a short distance to cover, and thus the arrow can not reach the target. Since we do see the arrow reaching the target, the perceived reason must be an illusion. His fables are quite interesting, since they usually follow the structure of one of Bach's musical pieces, and they include puns, acrostiches and other literary mechanisms.
Although I read the book a few times, I don't think I have really covered all of the book's explicit and tacit knowledge, so I recently ordered a new copy of the book - which is revised as the 20th anniversary edition, with some additional material and a new preface by the author - so that I could try to fathom its mysteries further.
Later on we recruited a person for my software company, and he claimed to understand the book almost entirely. This guy was an Electrical Engineer who attended high-level Math classes and just listened to the professor without taking any notes, then could show you any proof in its entirety without so much of an effort. He had been studying in the U.S. for a Ph.D. but eventually lost interest and came back to work in the software business.
While struggling with the intricacies of the M.S. work in Industrial Engineering, I was also working on my second major in Mathematics. Along with the inconceivable dimensions and abstract contraptions of Topology, I had to understand the intricate mechanism of being able to prove or disprove any given theorem or conjecture. Gödel had shown in his famous Incompleteness theorem published in 1931 that any mathematical system which has a consistent set of axioms will always have some propositions the value of which (TRUE or FALSE) can not be decided within that mathematical system. Namely, there would be an infinite number of propositions that would be undecidable using the program. This generalization of of the Liar's Paradox (The person who says "I'm a Liar" creates a paradox that makes it impossible to decide whether this statement is true or false) has some negative implications for Information Technology, since it would not be possible to write a computer program that would be able to decide whether a given statement is correct or incorrect.
I had started to get interested in Classical Music while in High School. I was a boarding student, and the mother of one of my good friends was a real classic music lover. She started taking us to the Friday evening concerts in the Classical Music Concert Hall. These usually consisted of real classics, usually with a concerto and maybe a symphony if we were lucky. Since these concerts would normally cover anybody from Mozart to Sostakovich, but would rarely touch Baroque and composers like Back, it took me several years before I got introduced to Bach's music. I used to go to the University library to get an album (Long-play, of course this was way before CDs!) and listen to it with a good headphone in the absolute silence of the library.
Hofstadter's book points to the way Bach has woven his compositions with recursive patterns, with almost mathematical perfection. These recursive patterns form the way counterpoint and other classical techniques are used in his music to reach harmony, that was the crux of early and Baroque era classical music, getting its justification from the religious idea of musical harmony mimicking the perfectness of God's vision.
The concept of recursion is also apparent in Escher's works. He is famous for building impossible worlds in his woodprints, where he has depicted scenes that could not happen in real life, such as rectangular stairs seemingly climbing continuously up to infinity, a waterfall that seems to defy gravity by means of water continually moving upward to create the power with which the waterfall falls down, and similar constructions. He has also formed infinitely recursive patterns and structures on some his paintings. (Use this link to find out about the Escher Museum in The Hague)
Hofstadter has structured his book to cover these three genius individuals in three major divisions of the book, but has interspersed the regular chapters with philosophical fables that look into some of the recursive concepts in philosophy, such as Zeno's paradox, where the philosopher Zeno decides that the perceived world can not be real. He uses the argument of halving the distance to the target and showing that no matter how far the arrow goes, there is still a short distance to cover, and thus the arrow can not reach the target. Since we do see the arrow reaching the target, the perceived reason must be an illusion. His fables are quite interesting, since they usually follow the structure of one of Bach's musical pieces, and they include puns, acrostiches and other literary mechanisms.
Although I read the book a few times, I don't think I have really covered all of the book's explicit and tacit knowledge, so I recently ordered a new copy of the book - which is revised as the 20th anniversary edition, with some additional material and a new preface by the author - so that I could try to fathom its mysteries further.
challenging
funny
informative
inspiring
reflective
slow-paced
challenging
funny
informative
reflective
medium-paced
It took me 6 years (lol!) to finish this book and turned out to be way more than I had signed up for. So much thinking about thinking.
I had to DNF after slogging 1/4 way through it. I wanted to like it, but wasn’t getting enough reward for reading through text drier than most of my undergrad math textbooks to keep my interest and warrant sleeping and reading through another 500 or so pages. Not for me; I will skip further library renewals (bad choice for vacation reading for me) and let the next poor soul waiting for it to have their turn.
challenging
funny
informative
reflective
slow-paced
Parts were thought provoking. Parts were mind numbing. Parts were interesting and parts were wtf. I'm glad I read it, but not likely to ever read again.
It took a while to read because I wanted to savor the experience.
It became apparent to me after only about three chapters that this is a book that would stay with me. And now that I've finished the entire thing, I am only further convinced of this.
The book was arranged differently than most books I've ever read. Each chapter is prefaced by what Hofstadter calls "Dialogues." These dialogues are based on Lewis Carroll's dialogue between Achilles and the Tortoise, with other characters added from time to time. In each dialogue, he demonstrates--often abstrusely, but never completely opaquely--the topics he will discuss in the coming chapter. The dialogues interweave the music of J. S. Bach with the art of M. C. Escher and the mathematics of Kurt Gödel. Often in a way that, once you realize what he's done, leave you with goosebumps, in awe of his abilities. He even gives insight into how he created one of the most artful of these dialogues in a later chapter (The Crab Canon, in which each character says the others' lines in reverse order, and it makes sense).
He starts the reader off with simple concepts and builds ever upwards to complex mathematics, genetics, computer science, philosophy, and the nature of consciousness and intelligence. No small feat.
In the final dialogue (which has no chapter following it), he himself becomes a character in his own book, introducing the other characters to the fact that he created them, allowing them to read over the book that we are reading....and becoming part of an eternal golden braid--a 'strange loop'--himself.
But why Gödel? Why Escher? Why Bach?
Gödel proposed a mathematical theory that (and I'm grossly simplifying this, here) states that it is possible to state the mathematical equivalent of "This theorem is incorrect" in any sufficiently complete number theory, thereby making it incomplete, until one adds either the positive or the negative of the theorem to the set of theorems...and then you start all over again, stating "This theorem is not a theorem." Etc.
Escher's pictures often represent paradoxical concepts such as two hands drawing each other, 2D beings crawling off their page into a 3D world, human figures climbing an impossible stairway, or paintings which contain the viewer viewing the painting which contains the viewer viewing the painting which....
Bach's fugues are one of the human race's crowning achievements of music, curling and twisting in upon themselves in ways that it is nearly impossible to hear all at once.
Hofstadter's ideas on the nature of "intelligence" or "consciousness" strike me as being as beautiful in their own right as a fugue by Bach, a drawing by Escher, or a mathematical theorem by Gödel.
It is a set of ideas that will percolate through my mind for years to come, and I will probably read the book again, gaining further insight each time through.
As a final hint: It's all about self-reference, baby. This sentence knows that.
It became apparent to me after only about three chapters that this is a book that would stay with me. And now that I've finished the entire thing, I am only further convinced of this.
The book was arranged differently than most books I've ever read. Each chapter is prefaced by what Hofstadter calls "Dialogues." These dialogues are based on Lewis Carroll's dialogue between Achilles and the Tortoise, with other characters added from time to time. In each dialogue, he demonstrates--often abstrusely, but never completely opaquely--the topics he will discuss in the coming chapter. The dialogues interweave the music of J. S. Bach with the art of M. C. Escher and the mathematics of Kurt Gödel. Often in a way that, once you realize what he's done, leave you with goosebumps, in awe of his abilities. He even gives insight into how he created one of the most artful of these dialogues in a later chapter (The Crab Canon, in which each character says the others' lines in reverse order, and it makes sense).
He starts the reader off with simple concepts and builds ever upwards to complex mathematics, genetics, computer science, philosophy, and the nature of consciousness and intelligence. No small feat.
In the final dialogue (which has no chapter following it), he himself becomes a character in his own book, introducing the other characters to the fact that he created them, allowing them to read over the book that we are reading....and becoming part of an eternal golden braid--a 'strange loop'--himself.
But why Gödel? Why Escher? Why Bach?
Gödel proposed a mathematical theory that (and I'm grossly simplifying this, here) states that it is possible to state the mathematical equivalent of "This theorem is incorrect" in any sufficiently complete number theory, thereby making it incomplete, until one adds either the positive or the negative of the theorem to the set of theorems...and then you start all over again, stating "This theorem is not a theorem." Etc.
Escher's pictures often represent paradoxical concepts such as two hands drawing each other, 2D beings crawling off their page into a 3D world, human figures climbing an impossible stairway, or paintings which contain the viewer viewing the painting which contains the viewer viewing the painting which....
Bach's fugues are one of the human race's crowning achievements of music, curling and twisting in upon themselves in ways that it is nearly impossible to hear all at once.
Hofstadter's ideas on the nature of "intelligence" or "consciousness" strike me as being as beautiful in their own right as a fugue by Bach, a drawing by Escher, or a mathematical theorem by Gödel.
It is a set of ideas that will percolate through my mind for years to come, and I will probably read the book again, gaining further insight each time through.
As a final hint: It's all about self-reference, baby. This sentence knows that.