> I'm stating that the math involved is a model but it isn't ever going to be identical to the thing being modeled.
I don't know what "identical" means in this context. Either a mathematical model can capture all of the information in the system, or it can't. We know that we can reproduce a function on a long enough timeline just by observing its outputs via Solomonoff Induction.
The only escape hatch here is if reality has incomputable features. There's no evidence of this at this time. That's why it's confusing that you would go from "we have persistent hard problems" to "mathematical models can't exactly correspond to reality".
I don't know what "identical" means in this context. Either a mathematical model can capture all of the information in the system, or it can't. We know that we can reproduce a function on a long enough timeline just by observing its outputs via Solomonoff Induction.
The only escape hatch here is if reality has incomputable features. There's no evidence of this at this time. That's why it's confusing that you would go from "we have persistent hard problems" to "mathematical models can't exactly correspond to reality".