If you can take an infinite number of derivatives of position, then why is it so hard to visualize/think of real world examples beyond the jerk? Does the function essentially become meaningless to the physical world?

Question

If you can take an infinite number of derivatives of position, then why is it so hard to visualize/think of real world examples beyond the jerk? Does the function essentially become meaningless to the physical world?

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Answer 1

Mostly because we don’t have any way of reliably identifying experiences that correspond to those higher derivatives.

Humans primarily feel *acceleration* (i.e., we feel force, which is related to acceleration by Newton’s second law of motion). We can’t directly feel position or velocity.

We can feel the change in acceleration (jerk) fairly clearly. But derivatives beyond that? I have no clue what I’m trying to feel for.

Do you know what a change in the change in acceleration feels like? I don’t. The derivative of jerk has no physical meaning to me, because I can’t feel it happen. I only feel its effects. The instantaneous value found by taking the derivative of jerk is a purely conceptual tool to me that I would only bother with it if helped me solve a problem.