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

Basically yeah, it stops corresponding to anything with a physical interpretation.

Position is a directly-observable quantity. First derivative is proportional to momentum and second derivative is proportional to kinetic energy. Even if the derivative is kind of an abstract operation, momentum and energy are conserved quantities so they are “real” to the laws of physics.

The Jerk is a number you can calculate, but even that isn’t meaningful to physics the way that conserved quantities are. Human perception happens to map to it, but it doesn’t describe reality the way that acceleration (kinetic energy) does. It’s an emergent description of the behavior of a system.

Further derivatives don’t represent physical quantities, and they also don’t map to any definite human perception. They’re just increasingly abstract numbers.