All information is probabilistic, Bayesian. Two scenarios, A & B, may have identical effects, but if the relevant probability ratios are different, then observing this effect can still give you information. If Amelia Bones tells Dumbledore that she’s come from six hours in the future, then his objective Bayesian probability (given the information that he possesses) that she’ll survive the next six hours goes up, even though it doesn’t rise to 100%. And all information is like this; objective Bayesian probability is never quite 100%.
I think that we can take it for granted that Dumbledore is not a rational Bayesian. (Nobody is perfectly, but Dumbledore is not even close.) Arguments about a perfect Bayesian tell us what information is present, not what any particular person will actually believe.
But if time turners work based on what information enters the actual beliefs of actual people, rather than on what information is theoretically present, then that makes a big difference. If scenarios A & B are indistinguishable, that wouldn’t matter; what would matter is which scenario Dumbledore believes is happening.
If time turners work at the level of the information available through fundamental physics, then it will be impossible to have more than six hours in any overlapping chain of time turners, even ones on opposite sides of the world whose users never communicate in a human way. But probably, they work on something much more like what people actually believe. So your question is actually a very pertinent one.
Elsewhere I note that it is not likely that time-turners would use information-theoretic meanings of ‘information’ to prevent paradoxes.
I think it’s most likely that time-turners simply cannot create causal chains where the effect precedes the cause by more than six hours. (Is it exactly one-hour increments? Which ‘hour’ exactly, is it- 1/24th of a mean solar day, or is it 33093474372000 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom at rest and 0K?)
it is not likely that time-turners would use information-theoretic meanings of ‘information’ to prevent paradoxes
Ultimately, I agree. The characters say that you can’t send information back more than six hours, but that’s because of the limits of their understanding. Otherwise things are too rigid. But this thread is basically premised on taking the characters’ understanding at face value.
it’s most likely that time-turners simply cannot create causal chains where the effect precedes the cause by more than six hours
If you’re using an information-theoretic definition of ‘causal chain’, then this is no different!
In discussions here (ETA: meaning, in the Less Wrong community), I mostly take it for granted that people have adopted the Bayesian perspective promoted in Eliezer’s sequences. I think that one can make a pretty good argument (although mathematical rigour is too much to ask for) that receiving information through one’s senses can never be enough to justify absolute certainty about anything external. But I’d rather not try to make it here (ETA: meaning, in this discussion thread).
All information is probabilistic, Bayesian. Two scenarios, A & B, may have identical effects, but if the relevant probability ratios are different, then observing this effect can still give you information. If Amelia Bones tells Dumbledore that she’s come from six hours in the future, then his objective Bayesian probability (given the information that he possesses) that she’ll survive the next six hours goes up, even though it doesn’t rise to 100%. And all information is like this; objective Bayesian probability is never quite 100%.
Does Dumbledore use Bayesian reasoning, or is there perhaps something about which he is completely certain?
I think that we can take it for granted that Dumbledore is not a rational Bayesian. (Nobody is perfectly, but Dumbledore is not even close.) Arguments about a perfect Bayesian tell us what information is present, not what any particular person will actually believe.
But if time turners work based on what information enters the actual beliefs of actual people, rather than on what information is theoretically present, then that makes a big difference. If scenarios A & B are indistinguishable, that wouldn’t matter; what would matter is which scenario Dumbledore believes is happening.
If time turners work at the level of the information available through fundamental physics, then it will be impossible to have more than six hours in any overlapping chain of time turners, even ones on opposite sides of the world whose users never communicate in a human way. But probably, they work on something much more like what people actually believe. So your question is actually a very pertinent one.
Elsewhere I note that it is not likely that time-turners would use information-theoretic meanings of ‘information’ to prevent paradoxes.
I think it’s most likely that time-turners simply cannot create causal chains where the effect precedes the cause by more than six hours. (Is it exactly one-hour increments? Which ‘hour’ exactly, is it- 1/24th of a mean solar day, or is it 33093474372000 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom at rest and 0K?)
Ultimately, I agree. The characters say that you can’t send information back more than six hours, but that’s because of the limits of their understanding. Otherwise things are too rigid. But this thread is basically premised on taking the characters’ understanding at face value.
If you’re using an information-theoretic definition of ‘causal chain’, then this is no different!
I can’t believe that we’re using the phrase “information-theoretic definition of ‘causal chain’” in a discussion about magic...
Although !Harry probably would, if he was willing to try further experimentation.
Is there a rigorous argument for this, or is this just a very powerful way of modeling the world?
In discussions here (ETA: meaning, in the Less Wrong community), I mostly take it for granted that people have adopted the Bayesian perspective promoted in Eliezer’s sequences. I think that one can make a pretty good argument (although mathematical rigour is too much to ask for) that receiving information through one’s senses can never be enough to justify absolute certainty about anything external. But I’d rather not try to make it here (ETA: meaning, in this discussion thread).
It’s more that Bayesian Analysis is a technique you can apply on anything, and under certain conditions is useful.