At least in so far as living macroscopic beings are concerned, they're all doing computation of some sort by processing environmental information and using the results to produce behavior. They're about as good at math as any other computer programmed to reproduce those algorithms.
So long as "processing" information isn't the same as actually producing that behavior, as in the case of crystal growth, they're doing something besides what they're doing.
Though I'd prefer to think that crystals are actually doing math too, but they're so good they don't even need to think about it.
Aren't you overshooting what you mean by linking to that paper? Treating some physical processes as computational processes might lead to some intractable problems, but it also might lead so some insights. Aaronson's section on space seems like an example of this.
Neither is an issue that some way of thinking might raise more questions than it answers. Actually, if any of those questions is both interesting and solvable, that is a virtue.
I don't believe I am overshooting. I am pursuing this conversation thread in light of the original claim; that the brain is incredibly good at math. I just wanted to poke at this statement a bit, to show that if you accept this claim (that the brain is "incredibly good at math" based on its inherent structure), it opens the door to a whole other discussion around what constitutes computation.
In sum, I was just trying to see through what angle OP was framing their point.
Daniel Dennett has a nice phrase for what plants, etc. do: Competence without comprehension. I think it sort of applies here. (And broadly to a lot of human activities, but I would definitely classify "good at math" as requiring some degree of comprehension whereas limb movement... not so much[1].)
[1] You don't really need to understand _how_ you're moving your arm. You just do it -- it's on autopilot.
I'm reading Dennet's From Bacteria to Bach and Back right now.
Highly recommended if you're interested in philosophical discussions about this sort of stuff. I'm finding it highly entertaining and deliciously provocative.
