r/Fitness does a weekly "Moronic Monday", a judgment-free thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. I thought this seemed like a useful thing to have here - after all, the concepts discussed on LessWrong are probably at least a little harder to grasp than those of weightlifting. Plus, I have a few stupid questions of my own, so it doesn't seem unreasonable that other people might as well.
A' doesn't become A'' by catching up to him, he becomes A'' when he uses his time machine to jump back 3 hours.
There would be three babies for 6 hours, but then the youngest two would use their time machines and disappear into the past.
A'' doesn't cease to exist. A' "ceases to exist" because his time machine sends him back into the past to become A''.
Oh! Alright, thank you. :) So if you go back and do something one hour in the past, then the loop closes an hour later, when the other version of yourself goes back for the same reasons you did, and now once again you are the only "you" at this moment in time. It's not A' that continues on with life leaving A'' off the hook, it is A'' who moves on while A' must go back. That makes much more sense.
Edit: This means it is always the oldest Harry that we see, right? The one with all the extra waiting around included in his age? Since all the other Harries are stuck in a six hour loop.