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Why are you assuming that S[n+1] takes S[n] as an input, rather than being completely unaffected by S[n]? If different states would be independent, if there we
by danbruc 6y ago
Why are you assuming that S[n+1] takes S[n] as an input, rather than being completely unaffected by S[n]?
If different states would be independent, if there were not even statistical relations, it would just be a sequence of random states. It would not even really make any sense to say that S[n] evolved into S[n + 1].
Is n here a discretization of time or a "meta-time" that captures state progression?
I did not want to imply any discretization, I just could not come up with a better notation. Proper mathematical treatment would probably use some index set with some kind of order defined on it. This would probably also overcome the linearity of state evolution implied by my notation.
And I used n intentionally to not imply time so that time can be emergent. On the other hand the entire idea of the state of the universe evolving is very heavily influenced by our experience with things changing over time. So I am actually less worried about the details of the independent variable, whether it is time or true-time, how many dimensions it has, or what not. I think the real problem is that the entire idea of state evolution might be wrong, maybe there is no state or no evolution and our brains are just not capable of imagining the way the universe actually works
On the other hand we have quite a few very general results like Turing-completeness, incompleteness theorems, uniqueness of the reals, and whatnot. And all this is built on top of rather simple axioms of logic without assuming much so it seems not that easy that we are totally missing some fundamental structure that we are not only unable to imagine but where we also lack the necessary logical or mathematical tools to even describe them. But it surly might be that there is a third option besides x is true and x is not true that humans are incapable of understanding and therefore our logic and everything build on top of it is missing.