Nope. cf. the under-determination of evidence by theory.
> So accurately modelling the past is certainly very informative for the future.
Nope. cf. we don't have infinite measures on infinite events in the past.
Consider that any given measure of an event, say M(E) is really a measure of a near infinite number of causes, say C1...n. Now, how many independent measures of these do we have? A handful.
so we really have, M(E|Controlling(Handful C1..n)))
do we want to model that?!? No.. that's insane. That's superstition. That's what all of science stands against.
Here's what we do: we build models not fit to any data. We build models that can generate the data we observe, but we build them by familiarity with reality *NOT* with the measures M.
How do we do that? Many ways, but the body is a key component of the answer. We have practically certain causal models of the body.
ConceptCup = MySensoryMotorActions(RealCups)
I_Touch = MySensoryMotorActions(Me)
P(I_Touch_Cup|Cup_Exists, ConceptCut) ~= 1
P(I_Touch_Cup|-Cup_Exists, ConceptCup) ~= 0
by iterating through such sensory-motor actions we can find concepts which produce these discrete splits. We call these concepts 'objects'. And from these we assemble models of reality whose shadow is our measures.We handle the cup, and by handling the cup can imagine the cup, and by imagine the cup can generate measures of the cup.
You cannot reverse from a shadow of a vase to the clay vase itself: there are an infinite number, given abribtarily infinite parameters. The task is to find the right parameterisation; not to suppose that any given one has one solution (it doesnt, so a fool's hope anyway).
Such a condition is just a formalisation of supersition: my model is decided by the data; my parameterisation is 'free'. My model of the world is cooincidence.
Indeed, the truth is, in a sense, only a single parameter.