Some context first:
First, there is this result that extends Gödel's incompleteness which states (among other things) that given the set $S$ of all true statements, the probability that a statement $s\in S$ is indecidable is closer to $1$ as the complexity of $s$ increases, ultimately that probability tends to $1$ as the complexity tends to $\infty$. (Complexity in the sense of Kolmogorov).
Second, there is this idea that the complexity (Kolmogorov again) of the universe changes as the universe evolve. When it was small and super-dense and very homogeneic, its complexity was quite small. Right now its complexity is much higher. And when the universe will "die" (because of a big crunch or because of expansion), its complexity will be small again.
Here are my questions:
- Can the universe be thought as some kind of logical system that is affected by Gödel's incompleteness ?
- If so, is it correct to think that what is possible right now (including our ability to think and elaborate theories) is limited by the complexity of the universe ?
- Are there some "hidden" truth in the universe that cannot be captured by reason (right now) but maybe later the universe will become complex enough to unveil these truths ?
- Conversely, is it possible that at some point, when the universe will become less complex, some well known and established truth will become unfatomable ?