I go through life unnoticed most of the time. When I have died, I don't care if I'm remembered or not.

People probably forget faster now than before, with so many distractions. They barely pay attention to the living, so much less the dead. In my case, since I won't even leave any descendants, I doubt that anyone will mention my existence two generations from now.
But just because something is improbable doesn't mean it's impossible. So, it's possible that the children of my closest nephews and nieces might start looking through photos and see me there, and perhaps say something... Then, if I can observe them from "beyond the grave," I'd like them to at least say a couple of good things, such as: The few people who knew her trusted her; she was a reliable person; or she was someone who focused on finding solutions rather than getting stuck in problems.
A couple of things like that are more than just ego matters. From my perspective, they can perhaps help inspire others or simply highlight the good qualities in them, even if they're dead, it can evoke positive vibes; that's contagious and positive.
On the other hand, I know that remembering the bad things about others can even fill us with resentment and hatred. I experience this personally when I think of my grandmother. She's dead, and I doubt she's affected by what I think of her. Perhaps she's even reincarnated into someone completely different—who knows? However, every time I remember her negative traits, which are really the only references I have of her, I'm the one who's affected. So I wouldn't want to be the cause of bad feelings in someone if I'm already dead. I'd rather not be remembered at all.

In general, when I am dead, I don't dream of being remembered, admired, or missed; it's fine if it's as if I never existed. Surely my soul will be occupied with more transcendental matters, I hope. Or perhaps dying is similar to when we sleep. Right in the moment of sleep, we don't want to be remembered; we don't really want anything. We simply rest and are completely unaware of what's happening outside our closed eyes.
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