Secondly, you’re right about conditioning on the last split. The original and last clone each think that they have a 50% chance of being the original and everyone knows that they aren’t.
Given this, it’s tough making sense of the problem posed in the original post. Maybe the question isn’t asking about the probability of the original knowing that they are the original at the end, but the chance of someone who thinks they might be the original (including those with false memories) turning out to be the original. Of course it is hard to define exactly what time we are asking about since some of these memories are false. It seems like we need to define some kind of virtual time for it to even make sense. But once this is surmounted, it should be 1/n.
Again, I should be clear, this is one part of anthropics where my ideas are less developed. I think this post will have to be edited once I have a more comprehensive theory.
Firstly, what’s 0-.5-.5 mean?
Secondly, you’re right about conditioning on the last split. The original and last clone each think that they have a 50% chance of being the original and everyone knows that they aren’t.
Given this, it’s tough making sense of the problem posed in the original post. Maybe the question isn’t asking about the probability of the original knowing that they are the original at the end, but the chance of someone who thinks they might be the original (including those with false memories) turning out to be the original. Of course it is hard to define exactly what time we are asking about since some of these memories are false. It seems like we need to define some kind of virtual time for it to even make sense. But once this is surmounted, it should be 1/n.
Again, I should be clear, this is one part of anthropics where my ideas are less developed. I think this post will have to be edited once I have a more comprehensive theory.