So your issue is that a copy of you is not you? And you would treat star trek-like transporter beams as murder?
Nothing so melodramatic, but I wouldn't use them. UNLESS they were in fact manipulating my wave function directly somehow causing my amplitude to increase in one place and decrease in another. Probably not what the screenplay writers had in mind, though.
But you are OK with a gradual replacement of your brain, just not with a complete one?
Maybe even a complete one eventually. If the vast majority of my cognition has migrated to the synthetic regions, it may not seem as much of a loss when parts of the biological brain break down and have to be replaced. Hard to speak on behalf of my future self with only what I know now. This is speculation.
How fast would the parts need to be replaced to preserve this "experience of continuity"?
This is an empirical question that could be answered if/when it becomes possible perform for real the thought experiment I described (the second one, with the blank brain being attached to the existing brain).
Basically, what I am unclear on is whether your issue is continuity of experience or cloning.
Continuity. I'm not opposed to non-destructive copies of me, but I don't see them as inherently beneficial to me either.
In June 2012, Robin Hanson wrote a post promoting plastination as a superior to cryopreservation as an approach to preserving people for later uploading. His post included a paragraph which said:
This left me with the impression that the chances of the average cryopreserved person today of being later revived aren't great, even when you conditionalize on no existential catastrophe. More recently, I did a systematic read-through of the sequences for the first time (about a month 1/2 ago), and Eliezer's post You Only Live Twice convinced me to finally sign up for cryonics for three reasons:
I don't find that terribly encouraging. So now I'm back to being pessimistic about current cryopreservation techniques (though I'm still signing up for cryonics because the cost is low enough even given my current estimate of my chances). But I'd very much be curious to know if anyone knows what, say, Nick Bostrom or Anders Sandberg think about the issue. Anyone?
Edit: I'm aware of estimates given by LessWrong folks in the census of the chances of revival, but I don't know how much of that is people taking things like existential risk into account. There are lots of different ways you could arrive at a ~10% chance of revival overall:
is one way. But:
is a very similar conclusion from very different premises. Gwern has more on this sort of reasoning in Plastination versus cryonics, but I don't know who most of the people he links to are so I'm not sure whether to trust them. He does link to a breakdown of probabilities by Robin, but I don't fully understand the way Robin is breaking the issue down.