I don’t think asymptotic reasoning is really the right tool for the job here.
We *know* things level off eventually because of physical limits (https://en.wikipedia.org/wiki/Limits_of_computation).
But fast takeoff is about how fast we go from where we are now to (e.g.) a superintelligence with a decisive strategic advantage (DSA). DSA probably doesn’t require something near the physical limits of computation.
I don’t think asymptotic reasoning is really the right tool for the job here.
We *know* things level off eventually because of physical limits (https://en.wikipedia.org/wiki/Limits_of_computation).
But fast takeoff is about how fast we go from where we are now to (e.g.) a superintelligence with a decisive strategic advantage (DSA). DSA probably doesn’t require something near the physical limits of computation.