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12: Intelligence, Art, Music, and Life are a Strange Loop: Godel, Escher, Bach by Douglas Hofstadter

Made You Think

CHAPTER

Is There a Loop in Number Theory?

In mathematics, any system which tries to define itself will fail. Sobasically saying that that is not possible. The downfall occurs essentially because the system is powerful enough to have self referential sentences. In physics, the notion exists of a critical mass of fisionable substance such as uranium,. A solid lump of he substance will just there if its mass is less than critical. But beyond the critical mass, such a lump will undergo a chain reaction and blow up. It seems that with formal systems, there is an analogous critical point. Below that point, a system is harmless and does not even approach defining arithmetical truth.

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