But if you had done such arduous research as, say, reading the Wikipedia page for the NCP, you would see that a sum over histories using only non-paradoxical timelines apparently works. Not that I really understand that in more than a superficial way, but it sure as hell sounds like an answer to your point.
There are only guaranteed to be non-paradoxical timelines if you have an infinite number of realities, which is what I was saying from the beginning.
You could look for all the timelines that are within delta of being a paradox. I think the shadowing theorem guarantees that, for small enough delta, this is epsilon-close to a non-paradoxical history. I don’t think it tells you what delta is, and I don’t think it’s guaranteed that every non-paradoxical history will be shadowed. This would mean that you’re not randomly picking the choice of history. More importantly, it might be that none of the non-paradoxical histories are shadowed, and you’ll have no idea what to look at.
Do random samples until you find enough, then. It wouldn’t be perfect, but it should be close enough that you wouldn’t notice with enough computing power, right?
Couldn’t it be approximated?
The theorem doesn’t tell you how to find a fixed point. It only tells you that one exists.
But if you had done such arduous research as, say, reading the Wikipedia page for the NCP, you would see that a sum over histories using only non-paradoxical timelines apparently works. Not that I really understand that in more than a superficial way, but it sure as hell sounds like an answer to your point.
There are only guaranteed to be non-paradoxical timelines if you have an infinite number of realities, which is what I was saying from the beginning.
You could look for all the timelines that are within delta of being a paradox. I think the shadowing theorem guarantees that, for small enough delta, this is epsilon-close to a non-paradoxical history. I don’t think it tells you what delta is, and I don’t think it’s guaranteed that every non-paradoxical history will be shadowed. This would mean that you’re not randomly picking the choice of history. More importantly, it might be that none of the non-paradoxical histories are shadowed, and you’ll have no idea what to look at.
Do random samples until you find enough, then. It wouldn’t be perfect, but it should be close enough that you wouldn’t notice with enough computing power, right?