4 ms·
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, wh
by 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 agoI 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?