[pron]

As that paper very first assumption is both unlikely and shows a complete lack of imagination, I think its results are dubious. In addition, I seriously doubt that we hae the math to be able to predict this.

Here is what the paper says:

Let us start with the worst-case scenario (for overpopulation)—physical immortality... Consider a situation, when parents produce less than 2 children on average, so that each next generation is smaller than the previous one... This conclusion does not require any complex calculations and questionable assumptions, but follows directly from the calculus, and the property of infinite geometric series to converge

Well, I beg to differ with the "questionable assumption" part. Why would anyone think that in infinite time, parents will have, on average, less than two children?

And here's the lack of imagination: the whole (cultural) concept of "parents" and family dissolves when there's no death. If you marry at 1000, and stay married to your wife for 5000 years (producing one child), chances are that by the time you're 50000 you've likely forgotten your wife's name, and your only child's too. In fact, you won't even remember that happened (well, maybe you'll remember your first time around, but by your 200th marriage, you won't remember how many children you had with your 37th wife).

Of course, I may be suffering from lack of imagination, and the structure of society will be completely different. The point is that making any assumption on human behavior after such a revolution of much of what makes us human, is preposterous. Immortal humans will behave in ways that we cannot predict, and we therefore cannot predict how the population will grow.

[forloop]

From the paper: 'Even for very long 100-year projection horizon, with the most radical life extension scenario (assuming no aging at all after age 60), the total population increases by 22% only (from 9.1 to 11.0 million).'

That stat is for Sweden—in case anyone wonders where the numbers are from.

Anyway, that's for the next 100 years. In 5000 years one would hope the human race will be multi-planetary. Looking at the time-scale, concern is still misplaced.

[pron]

That number only makes sense of people are unable to reproduce as they age. There is probably no correlation between population growth of mortal humans and immortal humans. They may have 100x more children, and they may have almost none. You can't extrapolate after such a bifurcation in the model.

In 5000 years the human race might be multi-planetary, or extinct. We have absolutely no information to make such predictions or even estimate their likelihood.

[forloop]

Yes. In 5000 or 50000 years there may be a problem with overpopulation—or not.

When someone expresses concern for overpopulation due to life extension, what time span are they referring to? 50000 years? Probably not. Looking at population growth for 100 years as per the model, the conclusion of the paper holds:

> Therefore, the real concerns should be placed not on the threat of catastrophic population consequences (overpopulation), but rather on such potential obstacles to the success of a biomedical war on aging, such as scientific, organizational, and financial limitations.