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Imagine this: you’ve “dated” 600 people in San Fransisco without having typed a word to any of them. Instead, a busy little bot has completed the mindless ‘getting-to-know-you’ chatter on your behalf, and has told you which people you should actually get off the couch to meet.
The memes are becoming real. 
~~Altered Carbon has a lot of the same weird issues. although I enjoyed it, it kinda handwaves over them~~
EDIT: I don't remember well enough, I think the problems are fundamental to transfer of consciousness and fwiw you have to make some choices to bridge those contradictions. I'll have to re-read it to articulate it, so I'm striking it.
I feel like the addressed it pretty head on. Every copy of you is equally you. That is the materialist explanation we would expect.
I've only read the first book, I should re-read it but I remember having some problems with the way the backups worked. good story though
Kinda. Once your brain is copied to a chip yeah. After that once it is just a pattern of data then it is just as continuous as you perceive it to be.
Yeah i'm not sure if "losing continuity of consciousness means you died" is a cultural thing that can change or what. Bc people do lose continuity all the time when they black out, go under for surgery, get concussed, and so forth. Subjectively when you come to you feel like you're the same person and continuity is maintained, and people don't perceive themselves to have died. But is the mind that boots up after surgery the same mind that was shut down? It gives me the willies.
Or sleep. It can't really be avoided.