Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. HofstadterMy rating: 5 of 5 stars
This book is about a lot of things but its essence has to do with Gödel’s incompleteness theorem.
As you might know, mathematical systems start off with axioms. Axioms are ingredients with which mathematical theories are built on, these ingredients are assumed to be true without any formal proof. The following statement is an example of an axiom: if a equals b and b equals c, then a must equal c; the last part is assumed to be self-evident. A system built through the use of axioms and their logical derivations is called a formal system.
Put simply, Gödel's incompleteness theorem shows (via mathematical proofs) formal systems are unable to reach certain truths. In other words, formal systems are not complete. This means there are certain things that exist out there that we will never know by using formal systems; i.e., with the formal systems we have now, we will never be able to build an all knowing system. The book shows this using art, biology and music.
As a student of Computer Science I can say that a great deal of the content is outdated. I wish it was written more recently, I would be very curious to see what the author makes out of the current boom in artificial intelligence.
Water cannot rise higher than its source, neither can human reason. — Samuel Taylor Coleridge
Difficulty: 7/10
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