I haven’t done a good job at trying to explain my point. Although somewhat different from that point I wished to make, there exists a similar position described in a popular physics book I’ve decided to steal from; better to express something similar to my point well in another’s words than to express my own point too poorly to be understood. To that end:
“Even if we were to commandeer the entire observable Universe and use it as a digital computer, its information storage capacity would still be finite, and it could not even “remember” one irrational number with complete precision…Determinism implies predictability only in the idealized limit of infinite precision…This infinite precision is, as we have seen, impossible…
The universe itself cannot “know” its own workings with absolute precision, and therefore cannot “predict” what will happen next, in every detail…deterministic chaos seems random because we are necessarily ignorant of the ultrafine detail of just a few degrees of freedom, and so is the Universe itself.”
Davies, P., & Gribbin, J. (1992). The Matter Myth. Simon & Schuster.
There are two points important in the above quotes. The first is that any simulation of any physical system that would seek to be so exact that the physical “universe” we experience is that simulation must necessarily be so imprecise that the set of input values which can even in principle be used consists of a set of measure 0 (the rational numbers are infinitely close to one another, but are negligible; almost all numbers are both irrational and non-computable). As infinite precision is necessary to simulate even extremely simple systems in our would-be “simulated” reality, this means that such simulations are impossible.
The second and related point is that even if we consider the actual universe as somehow “computing” future states based upon past states, we are again at a loss (even if we assume classical determinism). The only way this computational universe could take current states and apply the laws of physics to output future states is via something like inherently and intrinsically stochastic probabilities: the universe itself cannot “compute”, predict, or in-principle simulate future states based upon the present state (only the next state).
Of course, the cosmos is fundamentally indeterministic, the laws of physics don’t apply to open systems or the universe (but to isolated, closed systems), and we cannot even conceive of a method whereby any computational system (even one capable of handling infinitely large sets) can precisely simulate fairly simple systems that are ubiquitous in our would-be simulated universe.