Knowledge, esp. math knowledge. It is difficult to measure the amount as well as the benefit, but it feels like one additional year of math education (which builds upon previous math knowledge) allows to modell (and thus understand in depth) significally more phenomena and structures than the previous years.
The question may be how valuable this ability is. I get the impression that it significantly simplifies understanding conrete practival domains (which can be modelled by the math in question).
it feels like one additional year of math education (which builds upon previous math knowledge) allows to modell (and thus understand in depth) significally more phenomena and structures than the previous years.
Since math professors don’t look like bodhisattvas, I rather suspect there is a turnover point when the marginal utility starts to decrease.
Generally speaking, when you start learning an unfamiliar skill the first steps have close to zero marginal utility and only when you can actually achieve something does your utility increase. Once you achieve competence, however, I doubt that your marginal utility will continue to increase.
Knowledge, esp. math knowledge. It is difficult to measure the amount as well as the benefit, but it feels like one additional year of math education (which builds upon previous math knowledge) allows to modell (and thus understand in depth) significally more phenomena and structures than the previous years.
The question may be how valuable this ability is. I get the impression that it significantly simplifies understanding conrete practival domains (which can be modelled by the math in question).
This is related to the more general education comment.
Since math professors don’t look like bodhisattvas, I rather suspect there is a turnover point when the marginal utility starts to decrease.
Generally speaking, when you start learning an unfamiliar skill the first steps have close to zero marginal utility and only when you can actually achieve something does your utility increase. Once you achieve competence, however, I doubt that your marginal utility will continue to increase.
I fully agree. But there’s probably a turning point for any kind of increasing marginal utility.
Probably, though in many cases it will be constrained by available resources first.