“I occasionally run into people who say something like, “There’s a theoretical limit on how much you can deduce about the outside world, given a finite amount of sensory data.” Yes. There is. The theoretical limit is that every time you see 1 additional bit, it cannot be expected to eliminate more than half of the remaining hypotheses (half the remaining probability mass, rather). And that a redundant message cannot convey more information than the compressed version of itself. Nor can a bit convey any information about a quantity with which it has correlation exactly zero across the probable worlds you imagine. But nothing I’ve depicted this human civilization doing even begins to approach the theoretical limits set by the formalism of Solomonoff induction. It doesn’t approach the picture you could get if you could search through every single computable hypothesis, weighted by their simplicity, and do Bayesian updates on all of them.” (Eliezer Yudkowsky, Rationality)

Related to Solomonoff Induction, Limits of Knowability