Quote by Tournesol
.... Any physical system that has any kind of determinism is going to have 'redundant' variables, precisely because some of its parameters can be predicted from others. But the correct interpretation of this is in terms of determinism, not in terms of things not existing at all in the first place.

Your prior ref to the pendulum was in post 66 where you ask /state:
"Consider, instead, a frictional pendulum. It's total energy decays with time. How can you rewrite that as a decay wrt space (or something..other than an external clock)."
I essentially did this already if I understand you. In the very first post of this thread, if memory serves (not looking at it as I type) I assumed an axample of swing, Amplitude, A, of the form:
A =15 sin(7t) and then inverted it for t = {arcsin(A/15)}/7. or in general terms t = a'(A). This as someone I thanked for doing so, is not fully correct as in general, many observables besides A would be required (For example where the pendulum is on the Earth, B, would be required as gravity is not uniform over all the Earth etc. Thus I readly conceeded that the correct general form is"
t = a'(A,B,C....) and so forth for t = b'(A,B,C,....) etc.
When I eliminate "t" (and it appears that you are now conceeding that I can, at least formally, do this) from all equations describing eveything in the universe, including all changes that occur, you still are objecting that (if I understand you) that effectively "t" is still there because some of the observables (A,B,C,...) correlate well with time. I do not deny this. My only claim is that time need not be used to describe the changes or event sequences that we can observe, and that time itself consequently is not the cause of any change. It is powerless to affect anything. consequently it does not exist, is not observable, is not needed, but is avery convenient parameter in the equations of physics as they are usually written.
Now it appears that you want the example where
A = exp(t)15sin(7t)
OK, but I can not longer explicitly state the inverse, (no longer a simple arcsin) so I am forced to state the inverse in general notation as:
t = a"(A,B,C....) whre the function a" is no longer the arcsin.
So what!
My formal elimination of "t" NEVER DEPENDED UPON THE SPECIFIC FORM OF THE INVERSE FUNCTION.
I must be missing your point. Please explain how making the pendulum decay changes anything.