When I read this, I got the impression that Andy wasn't trying to describe reality as it is... but as it might be. Just a hypothetical thought experiment or something. I'd hate to put words in hir mouth though.... so this is just my impression and my response to that impression.
So... about the issue of continuity of "self" is destroyed every infinitesimal unit of time, I guess I'm kind of thinking about it as a video? A video represented on a computer is just a bunch of static images that are displayed quickly to make it appear as though there is motion. I guess perhaps the same could be said for the situation that Andy is describing. That would imply that there is some sort of overhead that's causing the "motion" to take place. (glancing up, it looks like AnimeKitty had the same thought.)
Andy, it looks like you're drawing parallels between the idea of LastThursdayism and the idea of creating a clone, destroying the former clone, and so on? I suppose I see some similarities (the destruction of one consciousness replaced by another copycat) but there are some issues, with it, as well.... I think. One is a passive mechanism of this world you're hypothesizing about but I think the clone situation is a little more complex. I don't know how the clone is being used, what happens to the original (or former clone, if a train of them are created) and so on. There's actually a funny video on this topic that I'm sure plenty of you have seen:
But conceptually, I can see how you'd draw the parallel between the two scenarios - if we're destroyed and reconstructed every infinitesimal unit of time, there's only the illusion that we're "building" onto previous experiments while, in your world's reality, it's just a new creation with more stuff added to it.
I suppose if you can take anything from it at all, it might be to value yourself a little less because you are never really "you", as you're constantly being replaced with another entity, which might make pseudo-immortality through cloning appear more appealing. :P
Oh, right... so, this thought arose from the topic although it's not the focus (dying every instant) of the thread... but I don't know how to talk about that for a lengthy period of time.
So, your "self" is dying every instant and being replaced but what about the rest of the world? What happens to it? How does the overhead work? What's causing this mechanism to work?