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What I find interesting are the claims Penrose[1] and others make about human versus machine intelligence based on Godel's results.

[1] https://en.wikipedia.org/wiki/Philosophy_of_artificial_intel...

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I'm sceptical of Penrose's arguments. We don't see human brains as symbol-manipulating formal systems, but that doesn't mean that aren't (or, more correctly, that doesn't mean that there is no symbol-manipulating formal system which is isomorphic to a particular brain, or brains in general).

Brains aren't implementing any known algorithm, but that doesn't mean they aren't implementing any unknown algorithm.

It brings to mind Minksky's advice to Sussman http://en.wikipedia.org/wiki/Hacker_koan#Uncarved_block

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