I read an item in one of the scientific web sites to the effect living forever is impossible. The basis was a survey of the age of death of the very oldest, and while lifetimes have been getting longer, this maximum age has not. Therefore no matter how good medical care and so on get, there is a maximum age.
While I agree living forever is impossible, this evidence draws the wrong conclusion. We age for some unknown complex of reasons, but each species seems to have a different and evolving maximum age, and there is no reason for that not to apply to us. There are biological reasons we age and die, and each species reflects these in accordance to its lifestyle and the normal age of death from disease or predation. That humans overcome these would remove the biological reason for aging and dying, and we would expect maximum lifetimes to slowly increase -- but on evolutionary terms this would require thousands or millions of years, not the short time of the observations.
The important thing here is that the fact that maximum age varies from species to species tells us it is not inherent but evolved, and that therefore there ought to be ways to interfere with it.
The reason living forever is impossible is simple -- one may never die but at the same time one has never reached infinite age. One may be a million or billion or gazillion years old, but never infinite.
One day the earth will become uninhabitable, a little later the solar system. Humans will of course know it is coming and we presume will have the ability to go elsewhere. Even orbiting a red dwarf, long-lived as they are, would someday have to come to an end.
There is reason to think, though, that space-time has unlimited low-entropy energy available -- this is after all how our present universe got its energy. Just separate the positive and the negative keeping the total at zero. So humanity could go on.
Back to nearer to us in time, what might a society where there is no aging and presumably very few if any deaths (technology would also steadily improve safety) be like? One can imagine frightening scenarios -- say a Stalin was in power and would live on and on -- and other messes, but one can also imagine things being pretty nice. Remove death and you also remove a lot of human angst.
Don't worry about overpopulation. That particular worry is trivial. If it came to it children would stop happening, but I think more likely humanity would expand. It's a big universe.
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