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A review by leventmolla
Gödel, Escher, Bach: an Eternal Golden Braid by Douglas R. Hofstadter
5.0
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.