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Yep, this is a much less prone to confusion way of saying it than "the mind is a computer".
And this is utterly confused. Douglas Hofstadter's cartoon illustrated the error pithily way back in Gödel, Escher, Bach. The algorithm is exact (the small, correct sums in the Hofstadter cartoon), but it's also too precise and constrained to do mind-like stuff directly in the small. Instead, the mind runs on a sort of virtual machine (big numbers built from the small sums in the cartoon) built up by the algorithm that can do complex pattern recognition and creative solutions, but is also constantly getting things wrong. As we see from AIs, virtual machines like this can be implemented on silicon just fine and they exhibit the same behavior of being able to do difficult useful stuff but also constantly getting details wrong on their own.
I sorta agree here. It's basically an accident of history that "computers", things with hard drives, keyboards, operating systems, files, RAM and CPUs, and "computation", the evaluation of primitive recursive mathematical functions which matches what a Turing machine (which, again, isn't a "machine" that you build from wires and bolts, but a mathematical construct), ended up using the same terminology up to "computer" being right there in the name "computer science". This is why the cognitive science school is called "computationalism" instead of "computerism" and the practitioners optimistically thought that given a name like that, obviously people would think Turing machines, not quad core Mac Pros.
The problem with Penrose's argument is that humans are doing math pretty much as you'd expect if constrained by Gödel. By stumbling into theorems, working hard trying to prove them, and sometimes finding themselves stuck and unable to show something as either true or untrue. The crackpot smell with the physics paper is that Gödel's theorem is ultimately pretty limited. It says that any formal system powerful enough to do any sort of interesting math in allows stating the equivalent of the liar's paradox, which cannot logically resolve to be either true or false, therefore you can't have a mechanism for determining the truth of any proposition because you have liar's paradox propositions floating around. The equivalent impossibility theorem for computer science is the halting problem, you can't write a program that looks at the source code of any program and tells whether the program will terminate. For simulations, this would be saying something like that you need to actually run the simulation to see what kind of state it ultimately ends up in (and whether it stops at a steady state or goes on forever), and can't just look at the simulation's source code and figure it out. But it doesn't prohibit running the simulation and looking at what happens in it while it's running.
Even assuming the article is correct, I'm not sure it'll tell us anything useful about human capabilities versus silicon. Halting problem style arguments do claim that we can't build a literal machine-god that can figure out the exact trajectory of our universe ahead of time just by thinking hard. But that's not necessary to have machines that are better at doing everything humans value doing.
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