I think there are two easy ways to get hyperbolic growth:
As long as there is free energy in the environment, without any technological change you can grow like f′(x)=f(x). Then if there is any technological progress that can be driven by your expanding physical civilization, then you get f′(x)=f(x)1+α, where α depends on how fast the returns to technology diminish.
Even without physical growth, if you have sufficiently good returns to technology (as we observe for historical technologies, if you treat doubling food as doubling output, or for modern information technology) then you end up with a similar functional form.
That would feel more like “plausible guess” if we didn’t have any historical data, but given that historical growth has in fact accelerated a huge amount it seems like a solid best guess to me. There’s been a bunch of debate about whether the historical data implies something kind of like this kind of functional form, or merely implies some kind of dramatic acceleration and is consistent with this functional form. But either way, it seems like the good bet is further dramatic acceleration if we either start returning energy capture to output (via AI) or start getting overall technological progress that is similar to existing rates of progress in computer hardware and software (via AI).
I think there are two easy ways to get hyperbolic growth:
As long as there is free energy in the environment, without any technological change you can grow like f′(x)=f(x). Then if there is any technological progress that can be driven by your expanding physical civilization, then you get f′(x)=f(x)1+α, where α depends on how fast the returns to technology diminish.
Even without physical growth, if you have sufficiently good returns to technology (as we observe for historical technologies, if you treat doubling food as doubling output, or for modern information technology) then you end up with a similar functional form.
That would feel more like “plausible guess” if we didn’t have any historical data, but given that historical growth has in fact accelerated a huge amount it seems like a solid best guess to me. There’s been a bunch of debate about whether the historical data implies something kind of like this kind of functional form, or merely implies some kind of dramatic acceleration and is consistent with this functional form. But either way, it seems like the good bet is further dramatic acceleration if we either start returning energy capture to output (via AI) or start getting overall technological progress that is similar to existing rates of progress in computer hardware and software (via AI).