The brain is incredibly good at math, just the APIs are not exposed.
Just look at machines that don't do precalculated movements (ASIMO, but even many of its patterns are prepared; Boston Dynamics robots, etc) versus those that do (industrial assembly line robots) and it gap is insanely wide. And even then, the dynamic bots are doing maybe one or two things at a time (walk, stop, pickup, walk, drop) nothing complex or integrated.
Otherwise you're asserting "doing arithmetic" as a property of any analogue system, and would say that a falling ball needs to understand calculus in order to make an arc. Downthread someone is saying that crystal formation is "doing arithmetic". While there may be a philosophical sense in saying that all actions of the universe are in some sense arithmetical as they obey physical laws, this is not a useful way to talk.
(Repost of my comment above)
You almost described a transistor. :)
The physical world, at our scale in inherently analogue.
(Might be digital at a quantum level, but we don't know that yet.)
Inside neuronal systems there doesn't seem to be a direct symbolic representation - and if there is, the neuronal patterns of somebody doing calculus on paper versus e.g. catching a ball are entirely different.
I believe he would argue it's a matter of training.
In the Nature vs Nurture debate, the purists on either side tend to use tortured, hair-splitting definitions to make their arguments, and it's usually those somewhere in the middle that sound the sanest.
Without the appropriate programming they can't do anything.
It is not very meaningful from an information theoretic pov to debate whether the results come from the multiplication algorithms computers follow or via some trained analog network; the result is the same.
I agree (though probably not in the sense you intended) - in fact, the human brain is the only thing we know of in the universe that can do math.
I do not hold the apparently widespread view that anything performing an action that can be modeled mathematically is doing mathematics, but it is clear by now the two sides on this issue are not going to reach an agreement.
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.
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>Therefore the sage goes about doing nothing, teaching no-talking.
>The ten thousand things rise and fall without cease,
>Creating, yet not possessing.
>Working, yet not taking credit.
>Work is done, then forgotten.
>Therefore it lasts forever.
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.
In sum, I was just trying to see through what angle OP was framing their point.
[1] You don't really need to understand _how_ you're moving your arm. You just do it -- it's on autopilot.
Highly recommended if you're interested in philosophical discussions about this sort of stuff. I'm finding it highly entertaining and deliciously provocative.
You can also claim that Google is a giant lookup table. They should stop hiring computer scientists and start repurposing brains!
Saying the brain literally computes is making a philosophical claim as to what exists, as opposed to a useful metaphor.
-- Mother Nature