Does training scale linearly? Does it take just twice as much time to get someone to 4 bits (top 3% in world, one in every school class) and from 4 to 8 bits (one in 1000)?
This is a good point. The exponential → linear argument is mainly for independent skills: if they’re uncorrelated in the population then they should multiply for selection; if they’re independently trained then they should add for training. (And note that these are not quite the same notion of “independent”, although they’re probably related.) It’s potentially different if we’re thinking about going from 90th to 95th percentile vs 50th to 75th percentile on one axis.
(I’ll talk about the other two points in response to Gunnar’s comment.)
This is a good point. The exponential → linear argument is mainly for independent skills: if they’re uncorrelated in the population then they should multiply for selection; if they’re independently trained then they should add for training. (And note that these are not quite the same notion of “independent”, although they’re probably related.) It’s potentially different if we’re thinking about going from 90th to 95th percentile vs 50th to 75th percentile on one axis.
(I’ll talk about the other two points in response to Gunnar’s comment.)