If we should be immortal -- truly invincible, for example through a medium that is indestructible or as information that is easily stored and copied and thus disposable -- then what goals could we have? I wonder then if there would be anything to do?

From HP:MoR, Chapter 39, Pretending to be Wise, Pt. 1:

"I have lived a hundred and ten years," the old wizard said quietly (taking his beard out of the bowl, and jiggling it to shake out the color). "I have seen and done a great many things, too many of which I wish I had never seen or done. And yet I do not regret being alive, for watching my students grow is a joy that has not begun to wear on me. But I would not wish to live so long that it does! What would you do with eternity, Harry?"

Harry took a deep breath. "Meet all the interesting people in the world, read all the good books and then write something even better, celebrate my first grandchild's tenth birthday party on the Moon, celebrate my first great-great-great grandchild's hundredth birthday party around the Rings of Saturn, learn the deepest and final rules of Nature, understand the nature of consciousness, find out why anything exists in the first place, visit other stars, discover aliens, create aliens, rendezvous with everyone for a party on the other side of the Milky Way once we've explored the whole thing, meet up with everyone else who was born on Old Earth to watch the Sun finally go out, and I used to worry about finding a way to escape this universe before it ran out of negentropy but I'm a lot more hopeful now that I've discovered the so-called laws of physics are just optional guidelines."