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I think this hacker/kernel bug analogy is confusing the issue. I don't think that it is quote appropriate, so I am going to move to the next paragraph. The lan

I think this hacker/kernel bug analogy is confusing the issue. I don't think that it is quote appropriate, so I am going to move to the next paragraph. The language of bugs also serves to mask what the issue is. It is true that Penrose (as best I can remember) spends time talking about the limits of algorithms. I don't remember the "neural plasticity" stuff, but I do remember he was much impressed by our ability to understand Godel's theorem. Let's just pause here. Does that make sense to you? That our ability to understand the incompleteness theorem is somehow evidence against the algorithmic nature of the mind? Or do you think it shows we have a poor grasp of what it means to "understand" something, and of how symbolic reasoning and proof interacts with our mind? I understood neither his, nor your summary of his, explanation of how QM is supposed to plug this hole in our understanding. In fact, your little discussion of QM has, if anything, bolstered my point. Note: we know that biological laws rely on physical laws, and that QM (and, say, relativity) are our best theories so far. That is not in dispute. But please explain how QM plugs in this Godel hole. When the crux of the matter comes, there seems to be general hand waving (on his part).

drostie 9y ago
I think you're maybe expecting much more than you should, which is why you think that "the language of bugs also serves to mask what the issue is" (it doesn't; both are deep-dives into the causation of unexpected behavior). I think if you get more clear about what you're expecting from Penrose you'll have a better foothold for why you're not getting what you're expecting. It does make sense that our ability to understand the incompleteness theorem is very close to self-contradictory -- I don't know that I'd say it is, without a doubt, self-contradictory; I have not dove deep into how provability logics might force □(a → (p ∧ ¬□p)) into a contradiction, and what you need for that (possibly with reasonable axioms it merely derives ¬□a which just means that if there is an algorithm for understanding then we'll never uncover it?). QM does not by itself plug the hole in our understanding; Penrose has never said that to my knowledge. However a tiny part of quantum physics is the only known part of physics that's capable of producing nonalgorithmic results (the vast majority of QM is linear algebra in funny hats), hence if we've got a nonalgorithmic result it makes sense to follow our "best theories so far" towards that tiny part of quantum physics.

drostie 9y ago

I think you're maybe expecting much more than you should, which is why you think that "the language of bugs also serves to mask what the issue is" (it doesn't; both are deep-dives into the causation of unexpected behavior). I think if you get more clear about what you're expecting from Penrose you'll have a better foothold for why you're not getting what you're expecting. It does make sense that our ability to understand the incompleteness theorem is very close to self-contradictory -- I don't know that I'd say it is, without a doubt, self-contradictory; I have not dove deep into how provability logics might force □(a → (p ∧ ¬□p)) into a contradiction, and what you need for that (possibly with reasonable axioms it merely derives ¬□a which just means that if there is an algorithm for understanding then we'll never uncover it?). QM does not by itself plug the hole in our understanding; Penrose has never said that to my knowledge. However a tiny part of quantum physics is the only known part of physics that's capable of producing nonalgorithmic results (the vast majority of QM is linear algebra in funny hats), hence if we've got a nonalgorithmic result it makes sense to follow our "best theories so far" towards that tiny part of quantum physics.