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Periodic functions like sin(x) are the solutions to differential equations like dy/dx = -y that describe for example, oscillations of springs, to name but one o
by doubleunplussed 4y ago
Periodic functions like sin(x) are the solutions to differential equations like dy/dx = -y that describe for example, oscillations of springs, to name but one of an extremely large number of dynamical systems that behave this way.
- omrjml 4y agoOf course sine can appear in the solution for dynamical systems but the function itself is not dynamical. When evaluating sin(x) you do not need to know about the previous state.
- zmgsabst 4y agoThat is true, the problem is with the conclusion you drew from that fact: > So it should not be approximated in that way. We can’t conclude a dynamic approximation is a bad approach based purely on the fact the underlying function isn’t dynamic. The function might nevertheless be easily approximated via dynamics — as in the case of predicting sine from seeing the recent history.
- freemint 4y agosin(x) only arises as solution in second order systems. So d^2x/dt^2 = -x
- doubleunplussed 4y agoSorry, you're absolutely correct. Brain fart. The equation I wrote actually is for an exponential, whoops.