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Larissa de Lima's avatar

This connects to something I've been thinking about since your last post. In my math olympiad days, we talked about the concept of "mathematical maturity" (or "maturing")

First level is simply remembering a proof. You can reproduce it, even talk about it convincingly, so its the interactional expertise. Then there's the level where you can re-enact it: you're not relying on memory but on understanding the mechanics well enough to reconstruct it. You're not faking it, but the subjective experience can still feel like you're an automaton.

Then there's this more elusive level, where universal truths about the subject start becoming clear. This is what "maturing" then means. You can extrapolate the theory, you "really get it." I think there's yet a level beyond that, where you see the structure of the representation itself and can go beyond it. That's where creativity lives. Feels like contributory can be at either of these two levels, depending on the contribution.

What strikes me is how long it can take to "mature," how slow the process is. There are concepts where I didn't really feel subjectively that I "got it" until decades later. And so many more that I never "got."

There's a a Quanta profile of Fields Medalist June Huh https://www.quantamagazine.org/june-huh-high-school-dropout-wins-the-fields-medal-20220705/ that also touches on this. His collaborator describes him as "very slow," so slow you'd think he couldn't pass a qualifying exam, but he was learning simple things in a deeper way that later proved essential.

It also makes me think of how hard it is to teach that the last mile of autonomous driving, while any 18 year old can pick it up in just a few months. The 18 year old, of course, has spent 18 years building a model of the physical world. Is there something to the slowness that scale cannot replicate?

Ben Recht's avatar

I should have known you were also a member of the Harry Collins Superfan Club.

There's so much discourse in academia about AI eliminating the need for graduate students, but through the lens of Collins' interactional expertise, you see the PIs of big science--whose work devolves into management, grant-writing, and self-promotion--are even more automatable.

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