Okay. So, we agree that your prior says that there’s a 1/N chance that you are unkillable by Russian Roulette for stupid reasons, and you never get any evidence against this. And let’s say this is independent of how much Russian Roulette one plays, except insofar as you have to stop if you die.
Let’s take a second to sincerely hold this prior. We aren’t just writing down some small number because we aren’t allowed to write zero; we actually think that in the infinite multiverse, for every N agents (disregarding those unkillable for non-stupid reasons), there’s one who will always survive Russian Roulette for stupid reasons. We really think these people are walking around the multiverse.
So now let K be the base-5/6 log of 1/N. If N people each attempt to play K games of Russian Roulette (i.e. keep playing until they’ve played K games or are dead), one will survive by luck, one will survive because they’re unkillable, and the rest will die (rounding away the off-by-one error).
If N^2 people across the multiverse attempt to play 2K games of Russian Roulette, N of them will survive for stupid reasons, one of them will survive by luck, and the rest will die. Picture that set of N immortals and one lucky mortal, and remember how colossal a number N must be. Are the people in that set wrong to think they’re probably immortals? I don’t think they are.
I have thought about this before posting, and I’m not sure I really believe in the infinite multiverse. I’m not even sure if I believe in the possibility of being an individual exception for some other sort of possibility. But I don’t think just asserting that without some deeper explanation is really a solution either. We can’t just assign zero probability willy-nilly.
Okay. So, we agree that your prior says that there’s a 1/N chance that you are unkillable by Russian Roulette for stupid reasons, and you never get any evidence against this. And let’s say this is independent of how much Russian Roulette one plays, except insofar as you have to stop if you die.
Let’s take a second to sincerely hold this prior. We aren’t just writing down some small number because we aren’t allowed to write zero; we actually think that in the infinite multiverse, for every N agents (disregarding those unkillable for non-stupid reasons), there’s one who will always survive Russian Roulette for stupid reasons. We really think these people are walking around the multiverse.
So now let K be the base-5/6 log of 1/N. If N people each attempt to play K games of Russian Roulette (i.e. keep playing until they’ve played K games or are dead), one will survive by luck, one will survive because they’re unkillable, and the rest will die (rounding away the off-by-one error).
If N^2 people across the multiverse attempt to play 2K games of Russian Roulette, N of them will survive for stupid reasons, one of them will survive by luck, and the rest will die. Picture that set of N immortals and one lucky mortal, and remember how colossal a number N must be. Are the people in that set wrong to think they’re probably immortals? I don’t think they are.
I have thought about this before posting, and I’m not sure I really believe in the infinite multiverse. I’m not even sure if I believe in the possibility of being an individual exception for some other sort of possibility. But I don’t think just asserting that without some deeper explanation is really a solution either. We can’t just assign zero probability willy-nilly.