The Stream of Consciousness Revisited

A couple years back, I wrote about one of the philosophical questions I have about life. Suppose strong AI (I'm fascinated with AI.) were achieved as a computer program living on my computer, and I were to start its life on my terminal. The same questions I brought up about humans earlier would apply to the AI program. If I send the program a ^C and then start the program back up again, is it going to be the same being, the same stream of consciousness?

The thought occurred to me today that it might not matter whether or not it is the same stream of consciousness. As each instant passes, the old being is left behind. It's gone forever. I am a new person with each moment. Even with this thinking, though, I think I've reached another unanswerable question: Why does my existence seem so coherent? This is one of those that makes my brain hurt, like trying to think of how long eternity is...

With each moment that I am aware, I am confident that I will still be aware in the next instant. Time slips by, and I hardly take notice. But if you were to knock me out, clone me, copy my memories over to the clone, then wake both me and my clone up in different rooms, my clone wouldn't even be aware of the fact that he didn't exist previously.