One possibility: I suggest that with decent schooling, the kids who could start working professionally at 14 can instead be doubling their productivity every year, so there is a benefit to working on building talent directly before trying to extract outputs- exploration vs exploitation.
My public school was beyond good to me, and so I was learning math as fast as I could from the age of 11 to 21, commuting to the local university for my last two years of high school for multivariable calc, diff eq, linear algebra, and discrete math at the university, then taking a mix of undergraduate and graduate math during college. During highschool I also spent some time working at a lab at the university. The time I spent working in the lab was valuable 99% as a learning experience to 1% actually pushing science- the crux of my actual contribution was a single pull request to matplotlib that took months and months to craft, which would take me around a day today. My work in medical imaging that takes years now would take infinity time without 10 years of math classes behind me.
The question then is, is working on real adult goals a better proxy task for learning than the typical gifted highschooler fare of unproductive projects, contests and tests. I’d guess that as proxy goals, contests > self chosen projects >> real productive work >> school assigned projects > tests.
One possibility: I suggest that with decent schooling, the kids who could start working professionally at 14 can instead be doubling their productivity every year, so there is a benefit to working on building talent directly before trying to extract outputs- exploration vs exploitation.
My public school was beyond good to me, and so I was learning math as fast as I could from the age of 11 to 21, commuting to the local university for my last two years of high school for multivariable calc, diff eq, linear algebra, and discrete math at the university, then taking a mix of undergraduate and graduate math during college. During highschool I also spent some time working at a lab at the university. The time I spent working in the lab was valuable 99% as a learning experience to 1% actually pushing science- the crux of my actual contribution was a single pull request to matplotlib that took months and months to craft, which would take me around a day today. My work in medical imaging that takes years now would take infinity time without 10 years of math classes behind me.
The question then is, is working on real adult goals a better proxy task for learning than the typical gifted highschooler fare of unproductive projects, contests and tests. I’d guess that as proxy goals, contests > self chosen projects >> real productive work >> school assigned projects > tests.