Like Question 1 and traditional probability problems, Question 3′s events reflect different possible worlds, different outcomes of the room-assigning experiment. Question 2′s supposed events reflect different locations of the self in the same possible world, i.e. different centred worlds.
Controversial anthropic probability problems occur only when the latter type is used. So there is good reason to think this distinction is significant.
Hmm. I don’t think you require the framework of centered possible worlds for question 2. Nothing is stopping us to perceive the situations as different possible worlds, not different places in the same world. There are hundred independent elementary outcomes (I am in room X for X up to 100). So we can define probability space and satisfy the conditions of Kolmogorov’s Axioms.
On the other hand, consider classic Sleeping Beauty. Heads and Monday, Tails and Tuesday, Tails and Tuesday are not three independent outcomes (the last two are casually connected), so normal probability theory is not applicable and people are trying to do the shenanigans with centered possible worlds.
Can you point out the difference why Tails and Monday, Tails and Tuesday are casually connected while the 100 people created by the incubator are not, by independent outcomes instead?
Nothing is stopping us to perceive the situations as different possible worlds, not different places in the same world.
All this post is trying to argue is statement like this requires some justification. Even if the justification is a mere stipulation, it should be at least recognized as an additional assumption. Given that anthropic problems often lead to controversial paradoxes, it is prudent to examine every assumption we make in solving them.
Can you point out the difference why Tails and Monday, Tails and Tuesday are casually connected while the 100 people created by the incubator are not, by independent outcomes instead?
Sure. Tails and Tuesday always happens after Tails and Monday with the same person. While each of a hundred people are created only in one room. Here I’ve shown how this is a big deal.
There is a general problem with applying probability theory to moments in time due to it’s conectedness. We can in principle design an experiment to make this conectedness irrelevant. But SB isn’t that because it simultaneously tries to track random sampled results of a coin toss and non random sampled days. When we fix the day we can meaningfully talk about P(Heads|Monday) and P(Tails|Monday). When we fix the outcome of the coin toss we can meaningfully talk about P(Monday|Heads) and P(Monday|Tails). But as soon as we try to combine them together… well then we have to talk about “centered possible words” for which we do not actually have proper mathematical framework, which means we are just unlawfully making things up.
Given that anthropic problems often lead to controversial paradoxes, it is prudent to examine every assumption we make in solving them.
Totally agree with this point. I just believe that I’ve already found the source of these paradoxes and it has to do with wrongly applying probability theory and not with whether the problem is anthropic or not. But yeah, I can be missing something here and it’s important to be prudent with such things.
Doesn’t example 3 show that one and two are actually the same? What difference does it make whether you start inside or outside the room?
Like Question 1 and traditional probability problems, Question 3′s events reflect different possible worlds, different outcomes of the room-assigning experiment. Question 2′s supposed events reflect different locations of the self in the same possible world, i.e. different centred worlds.
Controversial anthropic probability problems occur only when the latter type is used. So there is good reason to think this distinction is significant.
Hmm. I don’t think you require the framework of centered possible worlds for question 2. Nothing is stopping us to perceive the situations as different possible worlds, not different places in the same world. There are hundred independent elementary outcomes (I am in room X for X up to 100). So we can define probability space and satisfy the conditions of Kolmogorov’s Axioms.
On the other hand, consider classic Sleeping Beauty. Heads and Monday, Tails and Tuesday, Tails and Tuesday are not three independent outcomes (the last two are casually connected), so normal probability theory is not applicable and people are trying to do the shenanigans with centered possible worlds.
Can you point out the difference why Tails and Monday, Tails and Tuesday are casually connected while the 100 people created by the incubator are not, by independent outcomes instead?
All this post is trying to argue is statement like this requires some justification. Even if the justification is a mere stipulation, it should be at least recognized as an additional assumption. Given that anthropic problems often lead to controversial paradoxes, it is prudent to examine every assumption we make in solving them.
Sure. Tails and Tuesday always happens after Tails and Monday with the same person. While each of a hundred people are created only in one room. Here I’ve shown how this is a big deal.
There is a general problem with applying probability theory to moments in time due to it’s conectedness. We can in principle design an experiment to make this conectedness irrelevant. But SB isn’t that because it simultaneously tries to track random sampled results of a coin toss and non random sampled days. When we fix the day we can meaningfully talk about P(Heads|Monday) and P(Tails|Monday). When we fix the outcome of the coin toss we can meaningfully talk about P(Monday|Heads) and P(Monday|Tails). But as soon as we try to combine them together… well then we have to talk about “centered possible words” for which we do not actually have proper mathematical framework, which means we are just unlawfully making things up.
Totally agree with this point. I just believe that I’ve already found the source of these paradoxes and it has to do with wrongly applying probability theory and not with whether the problem is anthropic or not. But yeah, I can be missing something here and it’s important to be prudent with such things.