High g-factor can get you to the top 25% or even top 10% of the population in an awful lot areas all by itself. If only 5% of the population has ever formally studied and practiced chess strategy, then 95th percentile g-factor may be enough to hit 90th percentile of chess skill without any formal study at all (though the exact numbers depend on correlation of g-factor with formal study). Problem is, g-factor only counts once; we don’t want to double-count it by saying e.g. “assume top 10% in physics and philosophy are independent”.
Specialist expertise is mostly strongly anticorrelated. Most people pick one specialized career path, and even the people who “generalize” don’t usually tackle more than 2 or 3 areas at a deep level—our lives are not that long.
Put those two together, and it means that above-average-but-below-expert skill levels mostly won’t compound, but expert skill levels in multiple fields can yield a lot more bits than the independence calculation suggests—e.g. if almost nobody studies both topology and anthropology.
I do think the “how many bits does this get me?” approach is a useful way to think about it, but I’m not yet sure what set of assumptions is reasonable for quantification.
Two gotchas to bear in mind there:
High g-factor can get you to the top 25% or even top 10% of the population in an awful lot areas all by itself. If only 5% of the population has ever formally studied and practiced chess strategy, then 95th percentile g-factor may be enough to hit 90th percentile of chess skill without any formal study at all (though the exact numbers depend on correlation of g-factor with formal study). Problem is, g-factor only counts once; we don’t want to double-count it by saying e.g. “assume top 10% in physics and philosophy are independent”.
Specialist expertise is mostly strongly anticorrelated. Most people pick one specialized career path, and even the people who “generalize” don’t usually tackle more than 2 or 3 areas at a deep level—our lives are not that long.
Put those two together, and it means that above-average-but-below-expert skill levels mostly won’t compound, but expert skill levels in multiple fields can yield a lot more bits than the independence calculation suggests—e.g. if almost nobody studies both topology and anthropology.
I do think the “how many bits does this get me?” approach is a useful way to think about it, but I’m not yet sure what set of assumptions is reasonable for quantification.