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user-inactivated · 3277 days ago · link · · parent · post: Set theory and Turing machines from Scott Aaronson
They gave a difficult constructive proof of a statement there's an easy existence proof for. The post argues this is interesting because knowing how big a Turing machine you need before you have to worry about incompleteness gives you an idea where the boundary between nice, safe, well-behaved computations and the twilight zone is. I'm not sure I buy that, from a theoretical perspective the existence proof is all you need, and from a pragmatic perspective the point where you're not going to bother trying to prove properties of your programs comes long before the point where you can't prove properties of your programs.