Imagine that I visit a cloning facility that can flawlessly duplicate a human, memories and all. The techs there put me in a medical gown and sedate me, and a while later I wake up in an empty room. Without any additional information, I have no way to determine if I am the clone or not. I know only that there is another me in the building somewhere, having the exact same thoughts as I am having right now. In fact, I…
This is all basic stuff. Think deeper. You go to sleep every night. When you wake up the next day, how do you know you're the same person as yesterday? What does that mean? Now consider if you didn't have memories of the past. What would make you "you"? The body would be the same but your amnesia would change things, eh? Now what if you knew next week you would lose your memories for sure, but this week you can go on…
(Maybe this whole discussion is less interesting to Buddhists trained in not-self thinking. :)