That that’s the philosophical stuff. However, there’s no known way to prove it, so I don’t care! Newton’s flaming laser sword!
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It does however say that there should be more continuety between a nap’s beginning and end over a backup’s creation and activation…
Also, if you activated such a backup while being “active” inside the computer, wouldn’t that count as a clone with memories extending as far back to you creating that backup (while for the original you, years might’ve passed)?