The first paragraph is a pretty good introduction. It makes the reader think about their own feelings on immortality; is it the same? Is it different? How so? I read it and I go "Yeah, I can relate to this." If the reader can relate somewhat to the story, it'll hook them better.
The second paragraph intrigues me. I'm curious as to what happens next. I'm sure others would feel the same way.
As others might have said, first paragraph is meh, but the last part is pretty interesting. I would take out the first part, or if you really want it, put it as some sort of intro or summary or something but shorter and more to the point.
I have to agree with `saintartaud. What's the story? I'd drop us into that, first. If the first paragraph is coming from a narrator we've invested in and care about, it wouldn't feel so much like an essay. But at the beginning, we don't even know who the narrator is.
I'm guilty of writing little "lectures" like these myself. As I've had pointed out to me, they often don't add much to the story. Sometimes, they can even insult or offend your reader. (See ^neurotype's comment). I'm not saying this one doesn't add anything. It's hard to tell without having the full story. But, working this deeper into the story might be something to consider.
Thanks! I'm actually considering typing up two or three different opening "pages" in different styles to see what flows and sets the theme best. Maybe I'll post those and see what people think then! I'll see if I can chop this "lecture" off and save it for later then.
I think the best feedback you're going to get will come from someone who has read the entire manuscript. At the very least, provide the entire first chapter. It's difficult to give proper feedback on just an opening with no other context.
Part of a good opening is how well it leads into what follows.