But if we could discover that we live in the matrix or at the whim of some deity, it would mean that that fact had some effect on the world. Even a tiny non-zero effect could be amplified, like you explained, to have gigantic repercussions.
However, I was only really thinking of fundamentally unknowable things. That is, my argument is basically (in mathy notation) `∀x: ¬disoverable(x) → ¬matters(x)`. That is, if you can know x, I've said nothing about it. All I'm saying is that if you cannot discover something to be true, it cannot have any effect on you.
The contrapositive is also very important: `∀x: matters(x) → disoverable(x)`. That is, if something could have an effect (like your examples) then it has to be discoverable.
Since your main premise is that disoverable(x) is true--e.g. we can somehow find this out--my statement does not apply (or, rather, thanks to the way implication works, it's true regardless of what effect x does or does not have).
Now, if we fundamentally can't prove whether we're living in a simulation or not, somebody could still convince the human population that we are and cause the same effects you're mentioning. However, the beautiful thing here is that this could happen regardless of whether we actually are in a simulation or not (since the premise is that we can't tell), so the truth of the fact doesn't actually matter.
However, I was only really thinking of fundamentally unknowable things. That is, my argument is basically (in mathy notation) `∀x: ¬disoverable(x) → ¬matters(x)`. That is, if you can know x, I've said nothing about it. All I'm saying is that if you cannot discover something to be true, it cannot have any effect on you.
The contrapositive is also very important: `∀x: matters(x) → disoverable(x)`. That is, if something could have an effect (like your examples) then it has to be discoverable.
Since your main premise is that disoverable(x) is true--e.g. we can somehow find this out--my statement does not apply (or, rather, thanks to the way implication works, it's true regardless of what effect x does or does not have).
Now, if we fundamentally can't prove whether we're living in a simulation or not, somebody could still convince the human population that we are and cause the same effects you're mentioning. However, the beautiful thing here is that this could happen regardless of whether we actually are in a simulation or not (since the premise is that we can't tell), so the truth of the fact doesn't actually matter.