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Nectanebo comments on We need new humans, please help - Less Wrong
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Instead of having children as a pseudo-solution to aging and death, wouldn't it make a lot more sense to work on solving those problems much more directly via research or earning-to-give to organizations doing research? From this perspective, having children is actually explicitly wasteful due to this clear opportunity cost of valuable time, money and effort, not to mention also very defeatist.
If you expect anti-aging technology to be so near that no more new humans at all are necessary for civilization to continue, then yes.
Adjusted for the rates of decline of human population if only a subset of the population ceases creating new humans and the time this gives us until we dip past the civilization-sustaining threshold, then yes, there exists a relatively large subset of humans where the equations balance out to the researchers having enough time to develop anti-aging technology before we reach the deadline.
How large is "large", and exactly how much time that represents, and which exact conditions define the subset of humans, are all yet to be determined (if I knew, I'd take over the world and make it happen!), but I'm rather confident that the number of such humans we could affort to put on Deathward duty is significantly higher than you've previously assumed.
(Partially leaning on the knowledge that human brains tend to fart out and underestimate severely when estimating the impact of large numbers like "6 billion", which you seem to have currently placed on the side where it would increase the number of quality-adjusted humans we produce and, thereby, the time we have until humanfall. )