It's not technogically impossible - one day. Not today.
Even still; imagine a world like that? We're overpopulated as it is. Most people need to die - and an estimated 99.98% of the human population could not psychologically handle immortality. That can only be a rough estimate, of course, I'd hate to see the efforts someone must go through to clarify it, considering the state of the world. Seems a believeable number, though.
Me, I can handle immortality, and it's no secret my life's work is to achieve that. I may do that - no guarantee, slim chance, but still, I'll try. But I can do it - my mindset and conceptual grasp are the right frame. I feel no sense of loss at the passing of others, years are insignificant, and, of course, I am nothing like anybody else. So, again, I can.
But other people? Science fiction writers, even, have pointed out the likeliehood of decay and extreme overpopulation by masses perverting natural order. Most living things simply must die.
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Oh, well, fancy that! Isn't that neat, eh?