I'm totally with you on the Penrose tiling, great stuff. I must have first seen those in Hofstadter's SciAm column or the collection thereof. Too bad about Penrose's foray into cognitive science though....
I've read "The Emperor's New Mind" and several other essays by Penrose--they're worth reading even if ultimately (not like I'm an expert in the field) I think he's wrong. He dismisses computational thought simulation but, as far as I know, doesn't offer alternative explanations, though he also doesn't (again, afaik) retreat into mysticism. Like Searle, he might just be saying, "Look, I don't know but you don't either." but that kind of agnostic position seems...unimaginative to me instead of saying something like, "You may in fact be correct, it makes a basic kind of sense, I just think we're much farther away from proving it than you."
The Emperor's New Mind wasn't a bad but it was kind of a not needed critique at the time. There was plenty of that at the time including people like Searle and dreyfus, who've made a career of if and others who are actually in the field. But that's okay anyway, the real issue was the followup book, Shadows of the Mind where he basically does retreat into (a kind of) mysticism. It's been a while but he postulates some sort of quantum homunculus. This book was so widely off base it really ended his foray into this. I personally think that outside perspectives can be great but I think that Penrose was kind of like a creationist pushing "intelligent design" - he had his own agenda and didn't look thoroughly enough into what is a pretty vast field. This leads to a lot of mistakes which buries any valid points you may have. This same thing plagued Wolfram's A New Kind of Science which has tons of interesting concepts into it, but his attempt to "revolutionize" all of science was fraught with errors. So all that good stuff is ignored as everyone creates lengthy lists of these errors.
I never read "Shadows..." though now that you mention it, I do recall reading reviews that had similar criticisms, doubtless what put me off from delving in.I do have that massive Wolfram tome and have waded through it. I kept waiting for that "amazing concept" that was going to revolutionize science and kept reading nothing but elaborations on cellular automata theory, much of which was interesting but nothing, to my lay mind, that seemed fundamentally different than things I already knew. I left open the good possibility that I was missing something but the lack of (as far as I know) enormous response from the scientific community leads me to think that Wolfram was over-reaching. Back to the tilings, their "same but different" aspect causes them to appear as mental images to a good deal of music I enjoy.
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