Does it even matter that one gets remembered by a few more centuries (if mankind's lucky) before we destroy ourselves (or ultimately by the Sun boiling the planet) rather than after one's grandchildren or so die?
Depends what the possible futures you're envisioning are. If some crazy hive-mind/brain-upload/matrioshka brain/turn the universe into computronium future happens, what you do now could influence part of the course of that.
I don't get the 'either we destroy ourselves, or the sun explodes'. If we don't destroy ourselves now, there's no way humans just stick around in the solar system till the sun explodes- at one point, some civilisation will invent brain uploading or general AI or something, and then they'll go and eat the Galaxy. It's either that or total extinction. I can't envision a very likely future where humans survive for Billions of years as-is.
Either way, the universe will undergo heat death. So on very long timescales nothing will be left. Also, we don't have
"billions" of years on the planet, more like 1 billion tops. Life on Earth is on its final stretch.
Yes, as much as anything matters. Quoting the titular Angel: "if nothing we do matters, then all that matters is what we do".
We ourselves create meaning in our lives, and our doing so is subject to memetics, like most everything else. I would argue that the desire to do acts that affect others and be remembered through them is a pretty clear leader in this memetic race.
I don't get the 'either we destroy ourselves, or the sun explodes'. If we don't destroy ourselves now, there's no way humans just stick around in the solar system till the sun explodes- at one point, some civilisation will invent brain uploading or general AI or something, and then they'll go and eat the Galaxy. It's either that or total extinction. I can't envision a very likely future where humans survive for Billions of years as-is.