Wednesday, December 28, 2005

Gödels Theorem
I was just looking at the fascinating exhibit of equations by Justin Mullins. I'm not sure if I see the exhibit as art, since the visual appearance evokes little in people who do not understand the equations (with the possible exception of the Four Color Theorem), but they are certainly beautiful.

I particularly loved the end of the narrative for Gödel's theorem:

Others have wondered what Gödel’s theorem means for our understanding of the human mind. If our brains are machines that work in a consistent way, then Gödel’s theorem applies. Does that mean that it is possible to think of ideas that are true but be unable to prove them? Nobody knows.

Note the sentence that I highlighted. If it is true, then that sentence is an unprovable idea. I love it.

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