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The population problem cannot be solved in a technical way, any more than can the problem of winning the game of tick-tack-toe.
Population, as Malthus said, naturally tends to grow "geometrically," or, as we would now say, exponentially.
In a finite world this means that the per-capita share of the world's goods must decrease. A fair defense can be put forward for the view that the world is infinite or that we do not know that it is not.
But, in terms of the practical problems that we must face in the next few generations with the foreseeable technology, it is clear that we will greatly increase human misery if we do not, during the immediate future, assume that the world available to the terrestrial human population is finite.  A finite world can support only a finite population; therefore, population growth must eventually equal zero.
Because of previous failures in prophecy, it takes courage to assert that a desired technical solution is not possible.
(I can also, of course, openly abandon the game -- refuse to play it.
They think that farming the seas or developing new strains of wheat will solve the problem -- technologically.
I try to show here that the solution they seek cannot be found.
How it is conventionally conceived needs some comment.
It is fair to say that most people who anguish over the population problem are trying to find a way to avoid the evils of overpopulation without relinquishing any of the privileges they now enjoy.
(The case of perpetual wide fluctuations above and below zero is a trivial variant that need not be discussed.) When this condition is met, what will be the situation of mankind? It is not mathematically possible to maximize for two (or more) variables at the same time.