[lisper]

Sorry about that, I'm dealing with a troll on another thread so I'm on a bit of a hair trigger.

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.

[avmich]

It's great to read conversation of towering HN experts in the field.

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?

[lisper]

Let's go back to the original formulation so we don't lose the plot here:

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.

[avmich]

I suspect there's a terminological difference.

> being a professional tennis or baseball player involves a lot more than "simple heuristics ...

Mmm, a combination of simple heuristics, all of which are of course learned, but still simple heuristics, could in itself be a simple heuristic. Yet it could allow performing pretty complex-looking actions, including those you described. Simple heuristic here could be a linear or low degree polynomial approximation of a good solution to kinematic equation - not precise, but enough to get to the goal, while learnable and explainable. But still without actual full-blown abstract, mathematically correct complete solution.

[YeGoblynQueenne]

What's meant by heuristics is some times unclear. I wonder if by heuristics you mean a shortcut. In CS and AI our model of a shortcut is the heuristic cost functions in heuristic search algorithms like A* and its variants.

It's interesting because I've thought along the following lines. A* is a pathfinding algorithm so it's a natural choice for path planning -the process of planning a path through some environment for an autonomous agent to follow. The funny thing is, as it turns out, pathfinding can be abstracted as finding a "path" through a graph: a set of nodes connected by edges; and that's a great abstraction for general task planning - the task of achieving any arbitrary objective - so A* is also widely used for task planning.

Well, isn't path planning an almost universal ability of intelligent animals? Most animals are motile for some part of their lives and they seem to use their intelligence at the very least to navigate their environment. So is it that far-fetched to think that an ancestral ability for path planning, essentially identical to a heuristic search algorithm like A*, evolved into general intelligence? And wouldn't that mean that general intelligence can be, ultimately, modeled as some kind of heuristic search?

The answer I think is: no, and that's a dangerous way to think. A model is a model, it's not the process it models. And I think that's my fundamental disagreement with lisper, disregarding my confusion about the meaning of "kinematics".

[YeGoblynQueenne]

>> But even just moving your hand in front of your eyes is nowhere near as trivial as YeGoblynQueenne implies.

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.

[lisper]

> Yeah, I was actually thinking of kinematics as in classical mechanics. I think you were speaking about kinematic equations as in robotics.

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.

[YeGoblynQueenne]

>> What do you see as the relevant difference?

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?

[lisper]

OK, I'm an expert in both, so I can say the following with some authority:

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.

[YeGoblynQueenne]

>> Sorry about that, I'm dealing with a troll on another thread so I'm on a bit of a hair trigger.

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.

[lisper]

> it's entirely possible for humans to be using a completely different process to catch balls etc, than kinematic equations.

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.

[YeGoblynQueenne]

To be honest I suspect the next scientific revolution would be a refutation of Church-Turing, or maybe something more like an extension of it to phenomena we are not closely studying yet, a bit like my understanding of the relation between Newtonian mechanics, and General Relativity and Quantum mechanics. Unfortunately that won't be me bringing that revolution about, so you won't get to say you exchanged views with a scientific legend :P

For the time being of course we can agree that our brains probably do some kind of maths, as far as we understand it. I'm guessing the way we understand maths has everything to do with the way our brains understand maths because, well, that's my position in our disagreement. But, see, I can do maths by counting on my fingers, so the question is really what kind of maths we're talking about and how complex can they realistically be. My argument is that if it's not the kind of maths a standard human being can calculate very quickly without pen or paper, then that's a no-go, because that leaves plenty of time to be eaten by a sabretooth, or what have you.

[lisper]

> I suspect the next scientific revolution would be a refutation of Church-Turing

I'll give you long odds against. That would be tantamount to discovering a physical phenomenon that could not be described mathematically.

> a bit like my understanding of the relation between Newtonian mechanics, and General Relativity and Quantum mechanics.

Those relationships are well understood: Newton is a low-order approximation of GR in the weak-field limit.

https://en.wikipedia.org/wiki/Post-Newtonian_expansion

The relationship between Newton and QM is explained, at least operationally if not philosophically, by decoherence:

https://en.wikipedia.org/wiki/Quantum_decoherence