Earlier quoted context omitted.
The problem with that refutation is, population growth is O(2^n), available space is O(1) and available food is limited by available space and energy. Maybe there will be advances in science, increasing food production. However, to keep up with O(2^n) we need to double food production in constant time intervals, around 40 years. Otherwise, there will be overpopulation. There is no escaping it, except if exponential p…
> And food production following an O(2^n) curve is highly improbable, the best we can imho do is something polynomial or linear. Why? All technology has so far outpaced population growth.
The reason why I think a polynomial is the best we can do is that some very special processes generate exponential behaviour, mostly stuff that is self-replicating. I don't see those in technology. Technology doesn't reproduce all by itself, it needs to be invented, financed, etc. Those are limits that force it subexponential.