Exactly. I always have to make this clear to people. The conscious mind is incapable of fast arithmetic, but the subconscious mind is amazingly capable. It's doing complex, freebase (relative vs static) calculations constantly. The ability to track and accurately move your limbs with a non-determined base point with a few hundred nanosecond-millesecond latency (proactive) or 150-250ms latency (responsive) is without compare.
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.
Is it? Is there any evidence that it's converting the signals to symbols and performing arithemtic on the symbols? Or is the signal processing being performed "directly", through the essentially analogue operation of the neurons?
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.
What's the difference between "crystal formation" and cpu processing? They are both physical processes that don't understand the mathematical concepts that underpin their functioning. Maybe they do computation, but not math. Only humans can do math so far, and maybe some AIs, in a limited sense. Understanding math is harder than computing.
The point I'm trying to make is that computers "do arithmetic" through digital operations where there is a symbolic representation (through assigning analogue state to discrete symbolic values). Not through transistors operating continuously in their linear region.
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.
The symbolic representation is just a language though.
We might not be equipped to understand a language different from the formalisms we came up with.
To expand on that point, the brain is not good at simple products of large numbers, but is fantastic at doing things like triangulation. Or calculating how much muscle to contract to keep your balance going into a turn whilst running. Or eyeballing quantities - we notice when we get it wrong, but the vast majority of the time, we're pretty good at getting estimates correct about the human-scale world around us.
What we do regularly (..say.. move your hand to reach something or catch a ball) does take a large amount of very precise products though (i.e. Inverse Kinematics).
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.
Well, yes, but that's not a very useful distinction. You train computers as well by programming them. In meatspace, there was a famous experiment in the '60s where kittens had their heads locked into position so that they only saw vertical lines - their nascent neuroplastic brains then trained that way, and as they matured, they simply couldn't see horizontal lines (eg: would walk into horizontal bars).
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.
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.
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.
