If I’m forked, I expect to continue my experience as either the original or the copy with a probability of 1⁄2 -- whatever that means.
Apologies if this is tangential to your point, but this is incorrect, which might be causing confusion. Say that the term ‘shokwave’ represents the algorithm that represents my personal identity, plus all my subjective experiences. Say also that ‘+o’ represents the subjective experience of emerging from the forking event as the original, and ‘+c’ represents the subjective experience of emerging from the forking event as the copy.
We can see that it would be an error for ‘shokwave’ to expect to become ‘shokwave+o’ with pr 0.5 and ‘shokwave+c’ with pr 0.5. Both the original and the copy are ‘shokwave’ in every sense—by definition. Therefore, conditional on the forking event working as expected with pr 1, ‘shokwave’ should expect to become ‘shokwave+o’ with pr 1 and also should expect to become ‘shokwave+c’ with pr 1.
That might seem a little strange, that ‘shokwave’ expects two mutually exclusive events both with pr 1. After all, ‘shokwave+o’ is obviously not ‘shokwave+c’, so they must be exclusive? That’s where our intuitions go wrong. The definition of our forking event is that both ‘shokwave+o’ and ‘shokwave+c’ are ‘shokwave’, so the two events aren’t exclusive.
I think the 0.5 probability is correct, if we’re talking about frequency of particular experiences. (Of course, that’s not always what we’re talking about, as in the Sleeping Beauty non-paradox, but in a situation like this, where there’s no decision contingent on your probability estimate and you immediately know the outcome, presumably you mainly just want to know how much any given experience should surprise you.) If we assume that the duplication process is instantaneous and non-destructive, then, at the moment the duplication takes place, you know that there will soon be twice as many agents with a mind-state identical to yours, and that 50% of them will subjectively experience what feels like suddenly teleporting (to wherever the duplicator is constructing the copy).
Apologies if this is tangential to your point, but this is incorrect, which might be causing confusion. Say that the term ‘shokwave’ represents the algorithm that represents my personal identity, plus all my subjective experiences. Say also that ‘+o’ represents the subjective experience of emerging from the forking event as the original, and ‘+c’ represents the subjective experience of emerging from the forking event as the copy.
We can see that it would be an error for ‘shokwave’ to expect to become ‘shokwave+o’ with pr 0.5 and ‘shokwave+c’ with pr 0.5. Both the original and the copy are ‘shokwave’ in every sense—by definition. Therefore, conditional on the forking event working as expected with pr 1, ‘shokwave’ should expect to become ‘shokwave+o’ with pr 1 and also should expect to become ‘shokwave+c’ with pr 1.
That might seem a little strange, that ‘shokwave’ expects two mutually exclusive events both with pr 1. After all, ‘shokwave+o’ is obviously not ‘shokwave+c’, so they must be exclusive? That’s where our intuitions go wrong. The definition of our forking event is that both ‘shokwave+o’ and ‘shokwave+c’ are ‘shokwave’, so the two events aren’t exclusive.
I think the 0.5 probability is correct, if we’re talking about frequency of particular experiences. (Of course, that’s not always what we’re talking about, as in the Sleeping Beauty non-paradox, but in a situation like this, where there’s no decision contingent on your probability estimate and you immediately know the outcome, presumably you mainly just want to know how much any given experience should surprise you.) If we assume that the duplication process is instantaneous and non-destructive, then, at the moment the duplication takes place, you know that there will soon be twice as many agents with a mind-state identical to yours, and that 50% of them will subjectively experience what feels like suddenly teleporting (to wherever the duplicator is constructing the copy).