It would be weird after a trillion years when your human life was just a tiny sliver of your whole life.
I can't handle that thought any more or less than the thought that I'll die - As a cartoon dog said, I just distract myself with pointless stuff, it seems to work.
Not to get too esoteric, but at some point a trillion years is meaningless. Nothing really matters or doesn't matter - it's how you want to look at it. And distracting yourself with pointless stuff is totally valid. In fact, it's probably what we're all doing in one way or the other.