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Eliezer, why no mention of the no-cloning theorem?
Indeed. It is disappointing to see this buried at the bottom of the page. I don't think the no-cloning and no-teleportation theorems have any serious implications for Eliezer's arguments for life extension (although, it might have some implications for how he anticipates being recovered later). But, it does have some implications for the ideas about identity presented here. Here is the relevant text:
Are you under the impression that one of these bodies is constructed out of the original atoms—that it has some kind of physical continuity the other does not possess? But there is no such thing as a particular atom, so the original-ness or new-ness of the person can't depend on the original-ness or new-ness of the atoms.
In fact, having read the entire QM sequence, I am not under the impression that I am made out of atoms at all! I am an ever-decohering configuration of amplitude distributions. Furthermore since I know my configuration can never be decomposed and transmitted via classical means, I also know that the scanner/teleporter so-defined can't possibly exist.
Now, if you want to talk about entangling my body at point A, with some matter at point B, and via some additional information transmitted via normal channels, move me from point A to point B that way - now we have something to talk about. But the original proposition, of a teleporter which can move me from point A to point B, but can also, with some minor tweaking, be turned into a scanner which would "merely" create a copy of me at point A, is an absurdity. It is impossible to copy the configuration that makes up "me". The original classical teleporter kills the people who use it, because the configuration of amplitude constructed at point B can't possibly match, even in principle the one destroyed at point A.