I think your prediction of superexponential growth isn’t really about “superexponential” growth, but instead of there being an outright discontinuity where the time-horizons go from a finite value to infinity. I guess this is “superexponential” in a certain loose sense, but not in the same sense as ex2 is superexponential.
I don’t think this can be modeled via extrapolating straight lines on graphs / quantitative models of empirically observed external behavior / “on-paradigm” analyses.
I’m confused by this. A hyperbolic function 1/(t_c−t) goes to infinity in finite time. It’s a typical example of what I’m talking about when I talk about “superexponential growth” (because variations on it are a pretty good theoretical and empirical fit to growth dynamics with increasing returns). You can certainly use past data points of a hyperbolic function to extrapolate and make predictions about when it will go to infinity.
I don’t see why time horizons couldn’t be a superexponential function like that.
(In the economic growth case, it doesn’t actually go all the way to infinity, because eventually there’s too little science left to discover and/or too little resources left to expand into. Still a useful model up until that point.)
I’m confused by this. A hyperbolic function 1/(t_c−t) goes to infinity in finite time. It’s a typical example of what I’m talking about when I talk about “superexponential growth” (because variations on it are a pretty good theoretical and empirical fit to growth dynamics with increasing returns). You can certainly use past data points of a hyperbolic function to extrapolate and make predictions about when it will go to infinity.
I don’t see why time horizons couldn’t be a superexponential function like that.
(In the economic growth case, it doesn’t actually go all the way to infinity, because eventually there’s too little science left to discover and/or too little resources left to expand into. Still a useful model up until that point.)