Jeffrey's Reviews > Gödel, Escher, Bach: An Eternal Golden Braid

Gödel, Escher, Bach by Douglas R. Hofstadter
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Aug 23, 07

bookshelves: science
Read in January, 1999

Conversation overheard at a diner in Upstate NY between Rabbit and Dante. They have been arguing about the existence of God. Dante has been arguing against the proposition.

Rabbit: I have been recently reading a book which helps me to counter many of your points Dante. You should take a look at it. Godel, Escher, Bach: an Eternal Golden Braid by Douglas R. Hofstadter carries within it the seed of an answer to your skepticism. Hofstadter argues, using the pictures of Escher, the music of Bach and the mathematical formulas of Godel, that for those inside a system of any kind, be it music, art or mathematics, you can never prove everything which is true about the system! He does this in the most entertaining way, through dialogues and examples that lead even a Rabbit like me to the obvious conclusion.

Dante: it may be obvious to Mr. Hofstadter, and even to you, but to me, there may be an entirely different conclusion from the same information. Can you give me an example?

Rabbit: Of course. Let’s see.... Ah, imagine an Escher drawing, one of those odd drawings where the stairs seem to lead endlessly upward, yet always end back at the bottom.

Dante: I believe that Bach wrote a similar “Endlessly Rising Cantata”.

Rabbit: Exactly Right Comrade! Well, the drawing seems consistent, internally, to the characters in it. They can not imagine the world any other way. Yet for us, standing outside the picture, we can see the obvious tricks that were used to construct it.

Dante: So Mr. Hofstadter somehow argues that this proves there is a God?

Rabbit: Not exactly. He points out that those inside an internally consistent system can never fully understand the forces outside the system. Godel proves it mathematically by showing that there are true equations in mathematics which cannot be proven. (“This statement is false” is an example of a true statement which Godel translates into numbers, then transmutates into a number which cannot exist but does. It is all very confusing to a Rabbit!)

Dante: “Is a statement that is false” is a statement that is false. Is that a true statement? You do have a way with words, Rabbit!

Rabbit: But they are not my words. Hofstadter says that Godel said something like that. And he proves it, I think.

Dante: Whatever.
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