Didn’t he say that he mentioned the time-turner because it disproves the simulation hypothesis? It would also guarantee that nobody would simulate it.
He seems to have figured out how to simulate it later, but that requires simulating everything, and there’s no guarantee that there will even be a reality with a stable time loop, unless you have the infinite number of realities necessary to allow connectedness, in which case you can’t possibly simulate all the possibilities.
Actually, there is a guarantee that there will be a stable time loop. Look up the Novicov Consistency Principal some time. And I think that was to stop people speculating that magic was being provided by the Matrix Lords, although sadly it doesn’t. I was referring to the corridor tiled with pentagons (although it never actually says they were regular pentagons) and the spiral staircase that lifts you by rotating.
The Novicov Consistency Principal relies on the Kakutani fixed-point theorem, which relies on convexness, which implies connectedness, which implies an infinite number of realities.
I admit I’ve never seen a proof of the Novikov Consistency Principle. I know that’s how I’d prove something like that, and I know I could easily come up with a case of time travel with no possible stable time loop of I’m given a discrete space, a non-compact space, etc.
Sorry, I cannot find a link, but feel free to ask what does not make sense. As for the stable time loop, I’m not sure that it is always possible to find, given that you apparently want to fix both initial and final conditions of a hyperbolic PDE, unless I misunderstand what is involved in constructing such a loop.
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?
I can think of ways to simulate those quite easily. It does involve cheating with the environment, but not really cheating with any minds. Mostly the same kinds of tricks mentioned in Eliezers “that’d it take to make me belive 2+2=3” article.
Like, for example, deforming the tiling pattern constantly so that it was always the right type of angles and side lengths where the eyes were looking, and stopping the motion detection from going of on those changes. Or have the stairs tile exactly, just snap people on them up in exact increments of tiles, and again doing clever things with the way motion is detected in the eye.
The pentagons are doable, if you’re willing to cheat, but the spiral staircase is harder; spiral staircases appear to lift things but actually don’t. What would an optical illusion that was true be like? How do you build Penrose steps in 3d?
Didn’t he say that he mentioned the time-turner because it disproves the simulation hypothesis? It would also guarantee that nobody would simulate it.
He seems to have figured out how to simulate it later, but that requires simulating everything, and there’s no guarantee that there will even be a reality with a stable time loop, unless you have the infinite number of realities necessary to allow connectedness, in which case you can’t possibly simulate all the possibilities.
Actually, there is a guarantee that there will be a stable time loop. Look up the Novicov Consistency Principal some time. And I think that was to stop people speculating that magic was being provided by the Matrix Lords, although sadly it doesn’t. I was referring to the corridor tiled with pentagons (although it never actually says they were regular pentagons) and the spiral staircase that lifts you by rotating.
The Novicov Consistency Principal relies on the Kakutani fixed-point theorem, which relies on convexness, which implies connectedness, which implies an infinite number of realities.
It does not.
I admit I’ve never seen a proof of the Novikov Consistency Principle. I know that’s how I’d prove something like that, and I know I could easily come up with a case of time travel with no possible stable time loop of I’m given a discrete space, a non-compact space, etc.
What does it rely on?
Solely on the uniqueness of the metric in GR.
Do you have a link to a better explanation?
Also, can you explain how this could be used to find a stable time loop?
Sorry, I cannot find a link, but feel free to ask what does not make sense. As for the stable time loop, I’m not sure that it is always possible to find, given that you apparently want to fix both initial and final conditions of a hyperbolic PDE, unless I misunderstand what is involved in constructing such a loop.
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?
I can think of ways to simulate those quite easily. It does involve cheating with the environment, but not really cheating with any minds. Mostly the same kinds of tricks mentioned in Eliezers “that’d it take to make me belive 2+2=3” article.
Like, for example, deforming the tiling pattern constantly so that it was always the right type of angles and side lengths where the eyes were looking, and stopping the motion detection from going of on those changes. Or have the stairs tile exactly, just snap people on them up in exact increments of tiles, and again doing clever things with the way motion is detected in the eye.
The pentagons are doable, if you’re willing to cheat, but the spiral staircase is harder; spiral staircases appear to lift things but actually don’t. What would an optical illusion that was true be like? How do you build Penrose steps in 3d?
Inception sort of almost pulled it of.
Nah, that scene only works from the right angle.