Wednesday, August 14, 2013

Turing Crackpottery!

http://scientopia.org/blogs/goodmath/2010/09/08/1069/

" the key to the proof is a program that you can actually write, easily, in a couple of lines of code in a scripting language. And best of all, it's incredibly profound - it proves something very similar to Gödel's incompleteness theorem. It's wonderful."

"The reason that it's so profound is that you can formulate any mechanical proof process as a computer program. If a proof exists for a theorem, then you can write a program which searches for the proof, and will eventually find it. Wecan do that. We can write a program which searches the entire space of first order predicate logic proofs, trying to find a proof for a specific theorem. If it's a theorem of FOPL, it will eventually find a proof. It might take a very, very long time. But if a statement isn't a valid theorem, then the program will never stop. It will keep searching, and searching, and searching. And if the program doesn't stop, you can never actually conclude that "It's not a theorem", because if you just ran the program for another 10, or 100, or 1000 steps, it might stop."

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