He also enjoys taking pot shots at composer John Cage for basically no reason. Hofstadter has an axe to grind with Zen Buddhism, and the first application of a formal logical system he develops in the text is to refute a Zen koan about grinding axes.
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The book’s chapters are separated by entertaining Carrollian dialogues which illustrate key ideas that reappear later in the text, imitating the way themes reappear in Bach’s fugues. Gödel numbering really is just like RNA translation, I promise, but if you want to know why you’ll have to check out GEB from your local library, sorry.Īnd third, GEB is really idiosyncratic in a way no one can imitate. Second, this review will leave out the fascinating interconnections Hofstadter draws throughout the text. In a previous draft of this review, I tried quoting out of GEB for a few simple things, but it would always turn out like “Hofstadter thinks humans are sometimes different than machines: (page 37).” The reason is simple: there’s way too many of them. That said, I’ll also briefly touch on part II at the end.īefore I start, let me tell you some things that won’t be in this review because you really can’t get them from anywhere but GEB itself.įirst, this review will feature very few of Hofstadter’s actual words. This “book review” is really an in-depth explainer of the key ideas in GEB part I. Part II, roughly speaking, claims that the ideas of part I have something to do with artificial intelligence and the nature of consciousness. These ideas build to the statement and proof of Godel’s Incompleteness Theorem. Part I is an exposition of many interesting and deeply related ideas: formal systems like math and physics acquire meaning by modeling the world recursion gives these systems power but also enables self-reference and self-reference ultimately poses a serious problem for these systems.
![godel escher bach godel escher bach](http://thirdmonk.net/postcont/2014/08/godel-escher-bach-20-anniversary.png)
Who knew? GEB author Douglas Hofstadter did, and he wrote a 700-page exploration of the ideas behind Gödel’s incompleteness theorem so that you could too. Gödel numbering actually is just like RNA translation, and recursive transition networks really are similar to renormalization of elementary particles. But reading on, you come to see the magic: all of the conspiracies are actually true. Initially, Gödel, Escher, Bach comes across as a perplexingly well-regarded conspiracy theory text. Self-reference and the proof of Gödel’s theorem