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TheOtherDave comments on Timeless Identity - Less Wrong
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I think we have the same model of the situation, but I feel compelled to normalize my probability. A guess as to why:
I can rephrase Mark's question as, "In 10 hours, will you remember having gone to the beach or having bowled?" (Assume the simulation will continue running!) There'll be a you that went bowling and a you that went to the beach, but no single you that did both of those things. Your successive wakings example doesn't have this property.
I suppose I answer 50% to indicate my uncertainty about which future self we're talking about, since there are two possible referents. Maybe this is unhelpful.
Yes, that seems to be what's going on.
That said, normalizing my probability as though there were only going to be one of me at the end of the process doesn't seem at all compelling to me. I don't have any uncertainty about which future self we're talking about -- we're talking about both of them.
Suppose that you and your husband are planning to take the day off tomorrow, and he is planning to go bowling, and you are planning to go to the beach, and I ask the two of you "what's y'all's probability that one of y'all will go bowling, and what's y'all's probability that one of y'all will go to the beach?" It seems the correct answers to those questions will add up to more than 1, even though no one person will experience bowling AND going to the beach. In 10 hours, one of you will will remember having gone to the beach, and one will remember having bowled.
This is utterly unproblematic when we're talking about two people.
In the duplication case, we're still talking about two people, it's just that right now they are both me, so I get to answer for both of them. So, in 10 hours, I (aka "one of me") will remember having gone to the beach. I will also remember having bowled. I will not remember having gone to the beach and having bowled. And my probabilities add up to more than 1.
I recognize that it doesn't seem that way to you, but it really does seem like the obvious way to think about it to me.
I think your description is coherent and describes the same model of reality I have. :)