I don’t have good evidence. Note that the space of all possible problems is very large; most problems are ones that either all humans could solve trivially, or all humans would fail to solve. You aren’t necessarily going to get a nice clean “window” into the space of all possible problems so that all problems such that c < difficulty(problem) < d are in your window; you might have the situation P(problem is in your view) ~ 1 / difficulty(problem). Suppose that we then define problem difficulty in terms of algorithm runtime or minimal program length, and define educational level as being proportional to the difficulty of problems solvable by a person of that educational level. Suppose that the number of problems in problem-space nps(edu) that someone with education edu can solve is nps(edu) = edu^2. The number of viewable problems that person can solve is only npv(edu) = ( edu^2 / difficulty ) ~ edu, and would appear to us to be linear in the set of problems faced.
So the answer probably depends on what subset of problems we face. I believe that we continually make our society as complex as we can (to improve efficiency) while maintaining specialists in every necessary area who can deal with most of the problems arising in that area.
So it might be that, within an area of expertise (say, metallurgy), you’d find that most competent metallurgists can solve 90% of the set of problems they consider. There aren’t enough unsolvable problems in the space to detect an exponential increase. But most non-metallurgists might be able to solve 2% of them. (Totally made-up figures.)
If we suppose that politics is an area in which practitioners are chosen for their ability to get elected rather than expertise in problem-solving, and that, the subset of problems under consideration being set by the same kind of process as for metallurgy, we might expect that 90% of political problems would be solvable by someone with the right education, but that only 5% can be solved by the typical politician. If we suppose that the 2%-solving politician is only 1 standard deviation below the 5%-solving politician, then, under the theory that number of problems solved increases linearly or less with ability/education/etc, the atypical 90%-solving politician would have to be so many SDs above the 5%-solving politician, that none would exist. So, by contradiction, the relationship must be more than linear.
A weakness with this argument is that I just guessed all the numbers right now.
I don’t have good evidence. Note that the space of all possible problems is very large; most problems are ones that either all humans could solve trivially, or all humans would fail to solve. You aren’t necessarily going to get a nice clean “window” into the space of all possible problems so that all problems such that c < difficulty(problem) < d are in your window; you might have the situation P(problem is in your view) ~ 1 / difficulty(problem). Suppose that we then define problem difficulty in terms of algorithm runtime or minimal program length, and define educational level as being proportional to the difficulty of problems solvable by a person of that educational level. Suppose that the number of problems in problem-space nps(edu) that someone with education edu can solve is nps(edu) = edu^2. The number of viewable problems that person can solve is only npv(edu) = ( edu^2 / difficulty ) ~ edu, and would appear to us to be linear in the set of problems faced.
So the answer probably depends on what subset of problems we face. I believe that we continually make our society as complex as we can (to improve efficiency) while maintaining specialists in every necessary area who can deal with most of the problems arising in that area.
So it might be that, within an area of expertise (say, metallurgy), you’d find that most competent metallurgists can solve 90% of the set of problems they consider. There aren’t enough unsolvable problems in the space to detect an exponential increase. But most non-metallurgists might be able to solve 2% of them. (Totally made-up figures.)
If we suppose that politics is an area in which practitioners are chosen for their ability to get elected rather than expertise in problem-solving, and that, the subset of problems under consideration being set by the same kind of process as for metallurgy, we might expect that 90% of political problems would be solvable by someone with the right education, but that only 5% can be solved by the typical politician. If we suppose that the 2%-solving politician is only 1 standard deviation below the 5%-solving politician, then, under the theory that number of problems solved increases linearly or less with ability/education/etc, the atypical 90%-solving politician would have to be so many SDs above the 5%-solving politician, that none would exist. So, by contradiction, the relationship must be more than linear.
A weakness with this argument is that I just guessed all the numbers right now.