Yeah, I was actually thinking of kinematics as in classical mechanics. I think you were speaking about kinematic equations as in robotics. My bad, I misunderstood.
I agree that moving your hand in the right place is not a simple problem, and I don't actually have an insight into that, but I think it's easier than calculating the trajectory of an object, let alone many at once (think juggling). Maybe that's another source of our disagreement- but see my comment about having multiple models for a process.
What do you see as the relevant difference?
> I think it's easier than calculating the trajectory of an object, let alone many at once
Well, yeah, but there isn't anything fundamentally more difficult about juggling. It all boils down to Newton's laws.
My point is that there are two different ways that human brains can apply Newton's laws. We can do it intuitively, without even being consciously aware of Newton's laws, which is why humans were able to throw and catch objects before 1687. Or we can do it consciously by manipulating symbolic representations of the equations of motion. Those two activities are in some sense equivalent because they both involve producing a model of a physical system in our brains and using that model to make accurate predictions about that system. But they are also obviously radically different in other ways, and being skilled at one in now way implies being skilled at the other.
I'm not an expert in either, so I'm possibly overemphasizing the difference.
[Edit: As far as I understand it, one is useful in predicting the movement of objects outside the body, the other the position of the limbs etc.]
>> My point is that there are two different ways that human brains can apply Newton's laws. We can do it intuitively, without even being consciously aware of Newton's laws, which is why humans were able to throw and catch objects before 1687. Or we can do it consciously by manipulating symbolic representations of the equations of motion. Those two activities are in some sense equivalent because they both involve producing a model of a physical system in our brains and using that model to make accurate predictions about that system. But they are also obviously radically different in other ways, and being skilled at one in now way implies being skilled at the other.
I totally agree with that. Can we agree that we can model whatever our brains do with kinematic equations, but we have no idea what is the true process that is being modeled?
No, we cannot model what our brains do with kinematic equations. Our brains operate according to the laws of neurobiology, which we do not yet fully understand, but which we know enough about to know that they bear absolutely no resemblance to the laws of kinematics. Your brain is not made of mechanical linkages.
Nonetheless, despite the fact that the laws of neurobiology and the laws of kinematics bear no resemblance to each other, our brains somehow manage to produce solutions to problems that require solving kinematic equations. Not only that, but our brains can do this in two completely different ways, one of which is conscious and deliberate (what we call "doing math") and the other of which is instinctive and subconscious (developing sensory-motor skills).
We get leverage out of doing math despite the fact that our brains can solve some of the same problems innately. Likewise, I believe that LLMs could get a lot of leverage if they were augmented with special-purpose modules for doing math and other specific tasks.
I've confused you. My apologies. What I meant with this sentence:
"we can model whatever our brains do with kinematic equations"
Was that we can model whatever our brains do _while catching a ball etc_ by means of kinematic equations. I did not mean that we can model everything our brains do, i.e. the function of the brain, in general. If we could model an entire brain just by kinematic equations we wouldn't need any AI research, and I wouldn't be arguing that we don't know what our brains do when they solve problems that we solve using kinematic equations. Our disagreement is about the solutions our brain finds to that kind of problem.
>> Not only that, but our brains can do this in two completely different ways, one of which is conscious and deliberate (what we call "doing math") and the other of which is instinctive and subconscious (developing sensory-motor skills).
That's my problem with all this - the "subconscious" part. I don't really understand what it means. When I catch a ball, I do it entirely consciously, and I know exactly what I'm doing: I'm extending my hand to catch the ball. I may not be able to articulate every little muscle movement, or describe precisely the position of my arms, my hand, my fingers, the ball, etc, but I do know with great accuracy where those objects are in space, and where they are in relation with each other. I cannot introspect into the intellectual mechanisms by which I know those things, but I do know them, so they're not "subconscious".
The difference you point out, between doing maths with pen-and-paper (or computers) and performing a task without having to do maths-with-pen-and-paper, is, I think, the difference between having a formal language that is powerful enough to describe all the objects and functions I describe above (hand position, muscle movement etc), on the one hand, and not having such a language on the other hand. Somehow humans are able to come up with formal languages with the power to describe some of the things we do, like catching balls etc, and many other things besides. As a side note, we do not have a formal language -we do not have the mathematics- to describe our ability to come up with formal languages, yet. That was be one of the original goals of AI research, although it has now fallen by the wayside, in the process of chasing benchmark performance.
I digress. When I speak of "formal languages", I mean more broadly formal systems, like mathematics (of which logic is one branch, btw). When I speak of a "model" in my earlier comment, I mean a formalism that describes various kinds of human capability, like our catching-balls example. Kinematic equations, that's one such model. But a model is not the thing it, well, models. Is my claim.
I hope this is clear and apologies if it's not. Most of our discussion is not on things of my expertise so I'm trying to find the best way to say them. Also, this is a much less technical discussion and so much less precise, than I'm used to. I hope I'm not wasting your time with needless philosophising.
On the other hand, I think this kind of conversation would be made much easier if we didn't assume human brains. Our ability to navigate, and interact with, our environment, is shared to a greater or lesser extent with many animals that aren't humans and don't have human brains, so whatever we can do with our brains thanks to that shared ability, must also share an underlying system- because we all evolved from the same, very distant, animal ancestors, ultimately, and we must have inherited the same basic firmware as it were.
