If I duplicate the state of a paused algorithm and then immediately unpause both of them, even if I did it with no time in between, I can't claim that the secon

If I duplicate the state of a paused algorithm and then immediately unpause both of them, even if I did it with no time in between, I can't claim that the second one is the first one. If the algorithm makes up some "mind", a new one is created - and there is a new person. My point is basically that I will not magically look through someone else's eyes, even if the someone is my copy.