While technically and economically true, global fertility rates except in parts of Africa, the Middle East, and Asia are cratering. Income, community cohesiveness, and leisure time of the non-ultrarich need to substantially improve to encourage larger families.

This is not a contradiction as these are multiple variables. The most important variable is the size of population able to participate in knowledge production.

Naturally higher the population size, higher the size of population able to participate in knowledge production. This creates a positive feedback loop on the population growth.

Downside of this is that every gain that would allow better living is eaten up by the population growth (there is actually name for this - Malthusian trap). Downside of this is that the size of knowledge producing population stays relatively constant in relation to the total population size.

There is another feedback loop, three actually. If households restrain the number of offspring in return of better education of the offspring then three things happen. First the size of knowledge producing population starts to grow independent of total population growth, total population growth will stagnate or decrease and amount of personal wealth will increase (surplus of resource growth is divided among fewer people).

This is also why Western world is rich, large parts of Asia is getting rich and Africa and India are staying poor.

Naturally there is a huge downside in the negative feedback loop on the population growth as eventually it will start hurting the total amount of knowledge production. It would be better if these two feedback loops would balance each other out.

Income seems to negatively correlate with fertility on a worldwide basis.

It's not necessarily an either-or situation. Increased population can enable increased technological sophistication and increased technological sophistication can in turn enable an even larger population. This can be a self-reinforcing process. Anyway, I think your referencing the rgeen revolution which happened in the last hundred years while the GP is referencing the rise of agriculture.

There's also the (English) agricultural revolution.

And the rise of logistics and world trade in general. Bigger markets mean more productivity from specialisation, even if the underlying technology doesn't change. See eg the ancient Roman economy. https://acoup.blog/2022/08/26/collections-why-no-roman-indus... is a good introduction.

It's a feedback loop.

More precisely, many things are roughly modelable as differential equations where aggregate rate of change depends on an amount present.

In that language, I would say that we are dealing with a multi-dimensional differential equation.