I want to express this problem in practical terms. Please tell me if I am misunderstanding anything.
The original sleeping beauty problem can be carried out like this: wake up beauty once, then toss a coin. If it turns out to be Tails wake her up again with a memory wipe.
The exponential version can be carried out just like the original. Except after waking her up the second time, toss another coin. If Tails, wake her up 2 more times. After which toss another coin. If tails, wake her up 4 more times. Then 8, 16, etc. If we get Heads in any iteration the experiment stops without any additional awakenings or tosses. (All the coin toss could be carried out at the very beginning of the experiment too, just like the original problem.)
When woken up in the experiment, ask beauty: what is the probability that there are/will be, say, 3 Tails in total? Halfers would say it’s simply (1/2)^(3+1) because no new information. SIA supporters could not give any answer since they would consider all possible numbers of Tails equal-probable up to infinity.
I think it is a valid problem for SIA. But doubt this will change the mind of SIA supporters.
My position on anthropics is treating the first-person perspective (indexical like I or Now) like inherently understood primitive concepts, Not assuming them as random samples from some reference class. This means rejecting self-locating probabilities like “now is the 5th day”, which are used in calculating the probability of k in SIA reasoning.
Long answer, there is a difference between the current moment defined by the first-person perspective versus an objectively defined moment. This is the same as the difference between the first-person versus the physical person. The whole “Is ‘I exist’ meaningful evidence” debate is caused by mixing the two meanings and randomly switching their use in reasoning.
I suppose your question is asking “If I check the calendar now (as the current moment), what is the probability it will show 5.” Then there is no way to assign a probability to it.
If you define the moment some other way. E.g. “checking the calendar on a randomly selected awakening in the experiment, ” then of course there is a probability.
Regarding the first-person perspective as a random sample is the assumption I argue against. But that is something both SSA and SIA endorses. Which allows them to assign values to self-locating probabilities. For the above two questions, SSA and SIA will consider them the same question. They however would argue what is the correct selection process.
I want to express this problem in practical terms. Please tell me if I am misunderstanding anything.
The original sleeping beauty problem can be carried out like this: wake up beauty once, then toss a coin. If it turns out to be Tails wake her up again with a memory wipe.
The exponential version can be carried out just like the original. Except after waking her up the second time, toss another coin. If Tails, wake her up 2 more times. After which toss another coin. If tails, wake her up 4 more times. Then 8, 16, etc. If we get Heads in any iteration the experiment stops without any additional awakenings or tosses. (All the coin toss could be carried out at the very beginning of the experiment too, just like the original problem.)
When woken up in the experiment, ask beauty: what is the probability that there are/will be, say, 3 Tails in total? Halfers would say it’s simply (1/2)^(3+1) because no new information. SIA supporters could not give any answer since they would consider all possible numbers of Tails equal-probable up to infinity.
I think it is a valid problem for SIA. But doubt this will change the mind of SIA supporters.
My position on anthropics is treating the first-person perspective (indexical like I or Now) like inherently understood primitive concepts, Not assuming them as random samples from some reference class. This means rejecting self-locating probabilities like “now is the 5th day”, which are used in calculating the probability of k in SIA reasoning.
How is this different from “if I show you a calendar, it will have a 5 on it”, or is that also rejected?
Short answer, also rejected.
Long answer, there is a difference between the current moment defined by the first-person perspective versus an objectively defined moment. This is the same as the difference between the first-person versus the physical person. The whole “Is ‘I exist’ meaningful evidence” debate is caused by mixing the two meanings and randomly switching their use in reasoning.
I suppose your question is asking “If I check the calendar now (as the current moment), what is the probability it will show 5.” Then there is no way to assign a probability to it.
If you define the moment some other way. E.g. “checking the calendar on a randomly selected awakening in the experiment, ” then of course there is a probability.
Regarding the first-person perspective as a random sample is the assumption I argue against. But that is something both SSA and SIA endorses. Which allows them to assign values to self-locating probabilities. For the above two questions, SSA and SIA will consider them the same question. They however would argue what is the correct selection process.