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turchin comments on Identity map - Less Wrong
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I'm reading Robin Hanson's Age of Em right now, and some of his analysis of mind emulations might help here. He explains that emulations have the ability to copy themselves into other ems that will from the moment of copying onward have different experiences and therefore act and think differently. That is to say, even if you are aware of many copies of yourself existing in other worlds, they are effectively different people from the moment of copying onward. The fact remains that you are the one that will experience the pain and have to live with that memory and without a leg.
Maybe the identity question can be approached with some sort of continuity of experience argument. Even if minds can be copied easily, you can trace an individual identity by what they have experienced and will experience. Many copies may share past experiences, but their experiences will diverge at the point of copying, from which point you can refer to them as separate identities.
There is a problem with idea of continuity as a nature of identity, as some people suggested different meaning of it:
"Informational continuity" is when I remember in the moment N+1 my state of consciousness in the moment N. The problem: Every morning when I suddenly get up I have discontinuity in my memory stream as I loose memory of my dreams. Am I dead every morning?
Causal continuity. The main question here is continuity of what - of element of stream of conscuisness which creates next element in the next moment even if they are not remembered (so here arise difference with informational continuity idea), or causal continuity of underlying mechanism of brain. The main problem here will be that I will be not able (probably) feel if my causal stream was stopped and when restarted. (or i could feel it as one moment blackout which i will not remember?)