[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]

>> No, we cannot model what our brains do with kinematic equations.

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.

[lisper]

> Was that we can model whatever our brains do _while catching a ball etc_ by means of kinematic equations.

No, we can't even do that. All we can do is observe that the results of what our brains do happen to be the solutions to kinematic equations. It does not follow that we can model the process of producing those solutions by kinematic equations. It does not even follow that the process of producing those solutions bears any resemblance to what we do when we do math to find them.

Here is an analogy: we can observe that the motions of objects obeys the principle of least action [1] and that to compute the action we have to integrate the Lagrangian. It does not follow that there is anything happening in the physical mechanism that causes particles to move that is even remotely analogous to integrating a Lagrangian.

> When I catch a ball ... I know exactly what I'm doing

No, I don't think you do. If you did, you would be able to describe what you are doing to someone else, and they would be able to reproduce your actions based on that description alone. Alternatively, you would be able to render your knowledge into computer code and build a robot that could do it. But I doubt you can actually do either of those things if your only skill is catching a ball and you are not trained in math.

By way of very stark contrast, I am absolutely terrible at hand-eye coordination tasks, but I can build a machine that is much better at it than I am [2]. Just to be clear, I didn't actually build that particular machine, but I do know how. And so I can tell you that the process of learning how to build a machine that can catch a ball is radically different than the process of learning how to catch a ball yourself.

---

[1] https://en.wikipedia.org/wiki/Stationary-action_principle

[2] https://www.youtube.com/watch?v=FycDx69px8U

[YeGoblynQueenne]

Sorry for the lag. Productive day yesterday and today my friendly neighbourhood rock band was in a great mood early in the bloody morning.

>> No, we can't even do that. (...)

OK well I'm very confused. I thought our disagreement was on whether our brains actually calculate actual kinematic equations, or just the same results by some other means. It feels to me like we're arguing the same corner but we don't have a common language.

>> No, I don't think you do. (...)

"I can't put my finger on it, but I know it when I see it". My claim is that there is a difference between tacit knowledge, and articulable knowledge. I can not articulate the knowledge I have of how I am catching a ball; but I certainly know how I catch a ball, otherwise I wouldn't be able to do it. In machine learning, we replace explicit, articulable knowledge with examples that represent our tacit knowledge. I might not be able to manually define the relation betwen a set of pixels and a class of objects that might be found in a picture, but I can point to a picture that includes an image of a certain class and label it, with the class. And so can everyone else, and that's how we get tons of labelled examples to train image classifiers with, without having to know how to hand-code an image classifier.

Here's a little thing I'm working on. Assume that, in order to learn any concept we need two things: some inductive bias, background knowledge of the relevant concepts; and "forward knowledge" of the target concept. In statistical machine learning the inductive bias comes in the form of neural net architectures, function kernels, Bayesian priors etc. and the knowledge of a target concept comes in the form of labelled examples. Now, there are four learning settings; tabulating:

  Background    Target      Error
  ----------    --------    -----
  Known         Known       Low
  Known         Unknown     Moderate
  Unknown       Known       Moderate
  Unknown       Unknown     High

Where "Error" is the error of a learned hypothesis with respect to the target theory. In the first setting, where we have knowledge of both the background and the target, and the error is low, we're not even learning anything: just calculating. We can equally well match the first three settings to deductive, inductive, and abductive reasoning. You can also replace "known" and "unknown" with "certain" and "uncertain".

Now, I'd say that the invention of kinematic equations by which we can model the way we move our hands to catch balls etc is in the setting where the background theory and the target are both known: the background being our theory of mathematics, and the target being some obsrvations about the behaviour of humans catching balls. I don't know if the kinematic equations you speak of where really derived from such observations, but they could have. Humans are very good at modelling the world in this way.

We're in deep trouble when we're in the last setting, where we have no idea of the right background theory nor the target theory. And that's not a problem solved by machine learning. We only make progress in that kind of problem very slowly, with the scientific method, and it can take us thousands of years, during which we're stuck with bad models. For 15 centuries, the model is epicycles, until we have the laws of planetary motion and universal gravitation. And, suddenly, there are no more epicycles.

This also adressses your earlier comment about betting against a scientific upheaval in the science of computation.

Cool machine, btw, in that video. So you're a roboticist? I work on machine learning of autonomous behaviour for mobile robotics.

[lisper]

> Sorry for the lag.

No worries.

> It feels to me like we're arguing the same corner but we don't have a common language.

That's possible. It's actually a deep philosophical question. Do planets "solve Newton's equations of motion" when they move? On the one hand, they move in ways that correspond to solutions to those equations, and so one could say that they "find solutions" to those equations. On the other hand, the process by which they do this is pretty clearly radically different than what a mathematician does when they solve equations.

> So you're a roboticist?

I used to be. I've been out of the field for over 20 years now. But back in the day I was pretty well known.