3 ms·

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. YeGoblynQueenn

by lisper 3y ago

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 3y ago
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 3y ago
  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 3y ago
>> 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 3y ago
  > 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 3y ago
    >> 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?

by lisper 3y ago

avmich 3y ago

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 3y ago
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 3y ago

>> 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 3y ago
> 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 3y ago
  >> 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?