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 population growth is stopped and prevented in the future.
And food production following an O(2^n) curve is highly improbable, the best we can imho do is something polynomial or linear.
That's why Malthuus might have been a little wrong back then, but basic mathematics or computer science knowledge instantly proves him right, just not back then, because humanity got lucky.
> The problem with that refutation is, population growth is O(2^n)
WTF, no it isn’t. Human population increased exponentially for a period of time while we adjusted to lower infant mortality but fertility rates quickly altered to account for the new situation. Humans aren’t rabbits, we don’t give birth in large litters and we can reason about and control the number of children we have. As the last few places on earth finish their journey through industrialization we’re going to see population stabilize and then decline. Set a reminder for 2050 when we’ll all be panicking about there not being enough young people to fund our social security.
Moore's law was famously exponential, until it wasn't, because there are physical limits. Grain per hectare made some noticeable jumps, but no growth or even negative growth due to organics. Limit now is probably what the ecosystem will bear, and that is something linear or constant.
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.
And food production following an O(2^n) curve is highly improbable, the best we can imho do is something polynomial or linear.
That's why Malthuus might have been a little wrong back then, but basic mathematics or computer science knowledge instantly proves him right, just not back then, because humanity got lucky.