I should have been more clear about the role I believe experiences play. What matters to me is not just a person's concrete memories of experiences, but their unique personality that has been built up by a combination of those experiences, genetics, and a hefty dose of randomness.
In the "accidental clone" scenario, I wouldn't just be losing memories of a few minutes of experiences; I'd also be losing whatever delta to my personality the discarded clone went through in those minutes. However, in most cases I wouldn't care because that delta would be miniscule. As I mentioned, a potential problematic case is if I suddenly had a eureka moment in those few minutes that single-handedly changed my personality, but that's pretty unlikely.
With Abby and Brittany Hensel, on the other hand, they've had three decades to build up unique personalities, so despite sharing many of the same experiences they're definitely different people. (Plus, there are various sources of divergence between their experiences. For example, each of them will remember a different subset of their experiences, and in any argument between the two of them, each of them would experience being on a different side of the argument.)
Similarly, "I live on" and "my child live on" are very different things; a parent and child don't even share most of the same experiences, let alone personality.
> Then why don't you suicide right now, if continuity of experience is that casually irrelevant to you and all you need is a belief that some other body in the universe shares the same ideas you do? There are a lot of people on the planet right now, are you not convinced that someone, somewhere, shares enough of the important ideas with you already? Why not? Is your memory of a dentist's visit in third grade, or your particular grandmother's generic apple pie really that special?
I'm a special snowflake… just like everybody else. [ed:] I'm not important, but I'm unique; nobody is exactly like me.
Do I make the world much better with my existence? Not really. Hopefully I make it a little better; hopefully I don't make it worse; but I'm only one person and not a particularly famous one.
But I still want to live, and I want other people who are alive to keep living. Not as a means to some end, but as an ingrained human desire.
Yet I choose to interpret "I" as "my special-snowflakeness", as opposed to tying it to some physical object [ed: or continuity or linearity of experience, which I think are largely violated already when I fall asleep or lose memories]. An exact copy of me is the same special snowflake, at least at first, progressively diverging as the two copies start to have different experiences.