2 ms·

I like and agree with your observation. But I think you can use conceptual tricks to get just a little further: Acceleration is "due" to a force (F=ma), so yo

by xscott 2y ago

I like and agree with your observation. But I think you can use conceptual tricks to get just a little further: Acceleration is "due" to a force (F=ma), so you can think of jerk as a change in that force linearly increasing over time. That doesn't help me recognize a cubic from a quadratic when looking at a small piece of it, but I can imagine an elevator ramping up it's lifting power or similar. It kind of feels like the tricks to conceptualize 4D as 3D position plus a temperature at each spot.

bowsamic 2y ago
I agree the linearisation trick can be used and is often used in physics, but we must do that as a consequence of the thing I'm confused about the origin of, which is not why do we only greatly distinguish between the first few derivatives of position, but why do we only greatly distinguish between the first few derivatives of most functions? I.e. why do we have to do these tricks in the first place?
- xscott 2y ago
  I don't have any answers, but I suspect it's because we're evolved from things that didn't need to know. Related, I sometimes wonder how many derivatives you need to go down in order to find the one that is discontinuous when you decide to make a motion. For instance: pressing the first key to type this reply, my finger didn't instantly jump from zero to non-zero acceleration (or jerk/snap) I assume. How many terms in the Taylor series for moving a muscle?
- thaumasiotes 2y ago
  > the thing I'm confused about the origin of, which is not why do we only greatly distinguish between the first few derivatives of position, but why do we only greatly distinguish between the first few derivatives of most functions? Because higher derivatives are insignificant. That's the entire concept of Taylor series approximation. If you change a high derivative of a function, the value of the function won't noticeably change - why would you care?

by xscott 2y ago

bowsamic 2y ago

I agree the linearisation trick can be used and is often used in physics, but we must do that as a consequence of the thing I'm confused about the origin of, which is not why do we only greatly distinguish between the first few derivatives of position, but why do we only greatly distinguish between the first few derivatives of most functions? I.e. why do we have to do these tricks in the first place?

xscott 2y ago
I don't have any answers, but I suspect it's because we're evolved from things that didn't need to know. Related, I sometimes wonder how many derivatives you need to go down in order to find the one that is discontinuous when you decide to make a motion. For instance: pressing the first key to type this reply, my finger didn't instantly jump from zero to non-zero acceleration (or jerk/snap) I assume. How many terms in the Taylor series for moving a muscle?
thaumasiotes 2y ago
> the thing I'm confused about the origin of, which is not why do we only greatly distinguish between the first few derivatives of position, but why do we only greatly distinguish between the first few derivatives of most functions? Because higher derivatives are insignificant. That's the entire concept of Taylor series approximation. If you change a high derivative of a function, the value of the function won't noticeably change - why would you care?