And yes, I'm serious. Can you please be less confrontational?
I think we have a fundamental disconnect somewhere, so let's try to diagnose it. Where do you start to disagree in the following series of claims:
1. People can have kinematic skills, like throwing and catching balls, without having math or physics skills, like solving kinematic equations.
2. In order to have kinematic skills, something in your brain must be doing something that can be equated by some mapping to solving kinematic equations, because the actions that your muscles perform when performing kinematic skills are the solutions to kinematic equations, so your brain must be producing those (things that map to) solutions somehow.
3. As far as we can tell, brains don't operate symbolically at the neurobiological level. Individual neurons operate according to laws having to do with electrical impulses, synapse firings, neurotransmitters, etc. none of which have anything to do with kinematics.
4. People with kinematic skills generally have only limited insight into how they do what they do when they apply those skills. Being able to catch a ball doesn't by itself give you enough insight to be able to describe to someone how to build a machine that would catch a ball. But someone with math and physics and engineering skills but no kinematic skills (your streotypical geek) could plausibly build a machine that could catch a ball much better than they themselves could. But the workings of a machine built using knowledge of math would almost certainly operate in a very different manner than the brain of a human with kinematic skills.
I think I'll stop there and ask if there is anything you disagree with so far.
Lisper, as I understand this part -
> In order to have kinematic skills, something in your brain must be doing something that can be equated by some mapping to solving kinematic equations
you're talking about an equivalent of YeGoblynQueenne's
> that humans ... do not find solutions to kinematic equations, but instead use simple heuristics that exploit our senses and body configuration, like placing their hands in front of their eyes so that they line up with the ball
So to me the question is, is it correct? Can "mapping to solve kinematic equation" be the same as "simple heuristic... like placing hands in from of eyes"?
Physically this equivalence seems at least plausible.
Now, about
> neurons operate according to laws having to do with electrical impulses
- can't we have those kinematic equations solving, or, in other words, applying simple heuristics, as a trained combination of such neuronal activity?
Me: As an analogy, consider a professional tennis or baseball player.
YeGoblynQueenne: humans e.g. playing baseball do not find solutions to kinematic equations, but instead use simple heuristics that exploit our senses and body configuration, like placing their hands in front of their eyes so that they line up with the ball etc.
At the risk of stating the obvious, being a professional tennis or baseball player involves a lot more than "simple heuristics ... like placing their hands in front of their eyes so that they line up with the ball." That simple heuristic might work for one specific skill -- catching a ball that happens to be heading in your direction. But it won't help much for moving a bat or a raquet in such a way that it will hit a ball moving past you at close to 100mph in such a way that the ball ends up traveling on some desired trajectory.
But even just moving your hand in front of your eyes is nowhere near as trivial as YeGoblynQueenne implies. To do that you have to control seven degrees of freedom: two at your shoulder, two at your elbow, and two at your wrist. Solving those kinematic equations even to find a static solution is elementary but non-trivial, a skill that is solidly at the undergraduate level.
Now consider running to catch a ball. That involves controlling about 20 or 30 degrees of freedom (two arms, two legs, neck, waist, two eyes...) in real time in a situation that involves not just kinematics but also dynamics. Solving that analytically was an unsolved research problem for a long time (maybe still is, I haven't been keeping up with recent developments). A child can learn to do it. But they do have to learn to do it. It's not a skill humans are born with.
It seems pretty obvious to me that the process of learning how to catch a ball while running is very different than the process of learning how to do math. And yet, there must be a mapping between them because the movements required for catching a ball are the solutions to kinematic equations.
Hey, no worries. Thanks for being a gentleman and I'm sorry you're being harassed. Btw, just to be clear: I'm perfectly fine with robust disagreement, I just don't deal well with personal attacks; which you didn't do, I was just worried that's where this conversation was going.
So, thanks for the very detailed analysis of your argument. That indeed makes it much simpler to find common ground. Here's where I disagree: point number 2!
Here's why. It's obvious to me that it's entirely possible to have two distinct models of the same process that compute almost identical results, so it's entirely possible for humans to be using a completely different process to catch balls etc, than kinematic equations.
And here's why I think this is likely: first, because of the point I made above about computational complexity and second because of the observed wide variability in the uh, let's say kinematic capabilities of different humans. If we were all solving kinematic equations, we would all have the same skills. What's more: humans can be wildly inaccurate in their motions (I know I am; don't leave coffee cups on my desk), while robots for example, are distinctly not. That also points to a different computation.
So, to summarise my argument: what we do needs neither be the same computational process, nor be computing the same results, as kinematic equations.
Btw, I'm a bit confused because I thought you were talking about kinematics in classical mechanics, but now I think you're talking about kinematics in robotics, with muscle actions etc. But I think both apply, except the robotics equations are I think much easier to solve than the classical mechanics ones, which I suspect may veer off into the chaotic.
Edit: I had more here on my _agreement_ to your point number 4, but I'm cutting it down to shorten the comment. You don't have all day :)
In any case, I think we just can't say for sure what our brains do, until we can say for sure.
This all turns on what you mean by "completely different". Yes, obviously when you learn to actually catch a ball your brain is not doing anything that maps straightforwardly onto the kinds of symbolic manipulations that happen when you do math. On the other hand, it has to map onto doing math somehow even if that mapping is not straightforward. The only other possibility is that your brain is actually doing something that doesn't map onto math in any way, but still somehow produces the same results that math does by sheer coincidence. If you could actually demonstrate that, it would be one of the biggest breakthroughs in the history of science because it would refute the Church-Turing thesis.
