And yet Dumbledore doesn’t treat such a statement as information about the future when using his Time-Turner, which suggests that maybe the 6-hour limit is something you can think your way around.
Or that it works like magic does which seems to be not very careful about pesky things like rigorous notions of what constitutes information in the same way that brooms can work off what amounts to pseudo-Aristotelian physics.
I figured that the two were equivalent. If we find something that magic does not consider information (but we do), we can use it to receive information from an arbitrarily far future.
For example, suppose that magic does not consider merely “Does a timeturned person show up at time T at this location or not” to be information, and we want to know if the world ends in the next 10 years.
Four people with time-turners agree to the following scheme (using Unbreakable Vows if necessary):
If, at 12:01 AM on March 14th, 2025, the world has not ended, Alice goes back 6 hours using a Time-Turner.
If, at 6:01 PM on March 13th, 2025, Bob sees Alice appear out of nowhere, he goes back 6 hours using a Time-Turner.
If, at 12:01 PM on March 13th, 2025, Carol sees Bob appear out of nowhere, he goes back 6 hours using a Time-Turner.
If, at 6:01 AM on March 13th, 2025, Dan sees Carol appear out of nowhere, he goes back 6 hours using a Time-Turner.
If, at 12:01 AM on March 13th, 2025, Alice sees Dan appear out of nowhere, he goes back 6 hours using a Time-Turner.
...
Also, they make sure that in case of anything not world-ending, they will have a substitute available so that the chain will not break.
After agreeing to this, if Alice sees Dan appear out of nowhere at 12:01 AM tomorrow, then they know that the world has not ended. If not, then something sufficiently bad to cause the chain to break must have happened in the next 10 years. (Either way, they must continue to implement the plan for as long as possible.)
Using further chains of Time-Turners, we can use our favorite unbounded binary search scheme to narrow down a more precise date for the world ending.
(Edit: actually, we can probably improve the resolution simply by using the Time-Turners at a different specified time depending on circumstances.)
I think this is taking “6 hour limit” way too literally, when by far the simplest explanation is that time turners can protect you against Time’s tendency towards simplicity for 6 hours or so, but if you try to chain that, it becomes overwhelmingly computationally simpler (and therefore more likely) for the intention to set up such a chain to result in the death of everyone involved, than for the chain to work as designed.
I agree that the scheme I propose would fail under many interpretations of how time travel works.
I disagree that we know enough to say that Time has a tendency towards computational simplicity, or that Time-Turners protect you from it, or for that matter that a Time-Turner chain is any more likely to short-circuit in some bizarre accident than a regular use of Time-Turners.
The simplest explanation I can think of under which my scheme might not work is actually the 6-hour buffer model. In that case, I expect no time travel would occur at all, so we’d want to design the scheme in such a way that (a) this is a clean way to fail and (b) this is not a failure case we expect short of either the world ending or the scheme not working.
And yet Dumbledore doesn’t treat such a statement as information about the future when using his Time-Turner, which suggests that maybe the 6-hour limit is something you can think your way around.
Or that it works like magic does which seems to be not very careful about pesky things like rigorous notions of what constitutes information in the same way that brooms can work off what amounts to pseudo-Aristotelian physics.
I figured that the two were equivalent. If we find something that magic does not consider information (but we do), we can use it to receive information from an arbitrarily far future.
For example, suppose that magic does not consider merely “Does a timeturned person show up at time T at this location or not” to be information, and we want to know if the world ends in the next 10 years.
Four people with time-turners agree to the following scheme (using Unbreakable Vows if necessary):
If, at 12:01 AM on March 14th, 2025, the world has not ended, Alice goes back 6 hours using a Time-Turner.
If, at 6:01 PM on March 13th, 2025, Bob sees Alice appear out of nowhere, he goes back 6 hours using a Time-Turner.
If, at 12:01 PM on March 13th, 2025, Carol sees Bob appear out of nowhere, he goes back 6 hours using a Time-Turner.
If, at 6:01 AM on March 13th, 2025, Dan sees Carol appear out of nowhere, he goes back 6 hours using a Time-Turner.
If, at 12:01 AM on March 13th, 2025, Alice sees Dan appear out of nowhere, he goes back 6 hours using a Time-Turner.
...
Also, they make sure that in case of anything not world-ending, they will have a substitute available so that the chain will not break.
After agreeing to this, if Alice sees Dan appear out of nowhere at 12:01 AM tomorrow, then they know that the world has not ended. If not, then something sufficiently bad to cause the chain to break must have happened in the next 10 years. (Either way, they must continue to implement the plan for as long as possible.)
Using further chains of Time-Turners, we can use our favorite unbounded binary search scheme to narrow down a more precise date for the world ending.
(Edit: actually, we can probably improve the resolution simply by using the Time-Turners at a different specified time depending on circumstances.)
I think this is taking “6 hour limit” way too literally, when by far the simplest explanation is that time turners can protect you against Time’s tendency towards simplicity for 6 hours or so, but if you try to chain that, it becomes overwhelmingly computationally simpler (and therefore more likely) for the intention to set up such a chain to result in the death of everyone involved, than for the chain to work as designed.
I agree that the scheme I propose would fail under many interpretations of how time travel works.
I disagree that we know enough to say that Time has a tendency towards computational simplicity, or that Time-Turners protect you from it, or for that matter that a Time-Turner chain is any more likely to short-circuit in some bizarre accident than a regular use of Time-Turners.
The simplest explanation I can think of under which my scheme might not work is actually the 6-hour buffer model. In that case, I expect no time travel would occur at all, so we’d want to design the scheme in such a way that (a) this is a clean way to fail and (b) this is not a failure case we expect short of either the world ending or the scheme not working.