Why 3rd derivative? Do you think that because we don't typically work with 3rd derivatives to explain physical phenomenon that there is a lot we are missing? Or are there particular scenarios where you see 3rd derivative as being critical to causality? 1st derivative = direct causality, 2nd derivative = ability to affect change, 3rd derivative = ?? tertiary causes.
Wait. Doesn't a derivative mathematically define a causal relationship?
EDIT: nevermind re: derivative = causal ... that's just a correlation relationship. dx/dt. Still I'm curious as to what is special about the 3d derivative (besides jerk).
3rd derivative is a simple filter on acceleration. Obvious feature in something like fault prediction on heavy machinery.
What you really want, though are the ability to decouple and infer relationships between short and long term features (something like the cepstrum transform from speech analysis).
Wait. Doesn't a derivative mathematically define a causal relationship?
EDIT: nevermind re: derivative = causal ... that's just a correlation relationship. dx/dt. Still I'm curious as to what is special about the 3d derivative (besides jerk).