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randallsquared comments on Justifiable Erroneous Scientific Pessimism - Less Wrong
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There is no a priori reason, of course. We can imagine a world in which brains were highly efficient and people looked more like elephants, in which one could revolutionize physics every year or so but it takes a decade to push out a calf.
Yet, the world we actually live in doesn't look like that. A woman can (and historically, many have) spend her life in the kitchen making no such technological contributions but having 10 kids. (In fact, one of my great-grandmothers did just that.) It was not China or India which launched the Scientific and Industrial Revolutions.
That's not even required, though. What we're looking for (blade-size-wise) is whether a million additional people produce enough innovation to support more than a million additional people, and even if innovators are one in a thousand, it's not clear which way that swings in general.
Sure, it's just an example which does not seem to be impossible but where the blade of innovation is clearly bigger than the blade of population growth. But the basic empirical point remains the same: the world does not look like one where population growth drives innovation in a virtuous spiral or anything remotely close to that*.
* except, per Miller's final reply, in the very wealthiest countries post-demographic-transition where reproduction is sub-replacement and growth maybe even net negative like Japan and South Korea are approaching, then in these exceptional countries some more population growth may maximize innovation growth and increase rather than decrease per capita income.