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.
Yeah, think about how complicated it is to play a sport like tennis or frisbee. Running with co-moving objects and players. Integrating the position, velocity, and acceleration of all these things in order to compute a solution. That's some decent undergrad math!
I don't think it is a mathimatical computation in that way. Let's say you want to press the powerbutton on your pc with your finger. It's not like the brain takes the 3D position in space of your finger and the position of the power button in 3D space and calculates the way it has to move your body/arm etc. to press the button. That would be insane inefficient..
Assuming computation has ontological existence, as opposed to cultural demarcation, where we arrange certain physical devices to have predictable behavior we can modify, and call that computation. Or before computers, denoting the markings human beings make on paper as computation.
Saying the brain literally computes is making a philosophical claim as to what exists, as opposed to a useful metaphor.
Walking usually involves ending up in distant places so you can say get food or something to drink etc. A top generally falls over within a few feet of where it was spun.
