In Foerster’s paper, he links the increase in productivity linearly with the increase in population. But Scott has also proposed that the rate of innovation is slowing down, due to a logarithmic increase of productivity from population. So maybe Foerster’s model is still valid, and 1960 is only the year where we exhausted the almost linear part of progress (the “low hanging fruits”).
Perhaps nowadays we combine the exponential growth of population from population with the logarithmic increase in productivity, to get the linear economic growth we see.
This would still lead to something explosive if I understand it correctly,, since dx/dt=xlogx is solved by x=exp(const×exp(t)). Double exponential growth doesn’t diverge in finite time, but it’s still very fast and inconsistent with the graph in the post.
In Foerster’s paper, he links the increase in productivity linearly with the increase in population. But Scott has also proposed that the rate of innovation is slowing down, due to a logarithmic increase of productivity from population. So maybe Foerster’s model is still valid, and 1960 is only the year where we exhausted the almost linear part of progress (the “low hanging fruits”).
Perhaps nowadays we combine the exponential growth of population from population with the logarithmic increase in productivity, to get the linear economic growth we see.
This would still lead to something explosive if I understand it correctly,, since dx/dt=xlogx is solved by x=exp(const×exp(t)). Double exponential growth doesn’t diverge in finite time, but it’s still very fast and inconsistent with the graph in the post.