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.
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?
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.
> 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.
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".
>> 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.
> 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.
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?
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.
>> 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.
> 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.
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.
> 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.
>> That's possible. It's actually a deep philosophical question. Do planets "solve Newton's equations of motion" when they move?
Yes, that's an interesting question- that I'm really not equipped to answer. Probably for the best.
>> 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.
I'm really new to the field so I don't know your work. In fact I wouldn't even say I am in the field as such. An academic sibling suggested I take a post doc job and now I'm collaborating with roboticists. I'm just working on autonomous behaviour- I'm not allowed near hardware.
It's an interesting field although I have to constantly be on my toes to avoid violating my principles. See I'm a peacenick, but it seems with the work I do, as soon as I got that stuff working, someone will want to put it on a drone, strap a gun on its back and send it to kill people. And I'm dead set against that sort of thing.
I had a quick look at your site and you've worked with NASA. Respect! We can send autonomous rovers to explore far away planets and people want to keep them here wreaking havoc and death. Unbelievable.
Do you have any pointers to your work? Something you are really proud of that you did in the past? I'm curious.
>> 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.
> 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.
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.
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.