Learning takes a long time

I re­cently re­al­ized that I had greatly un­der­es­ti­mated the in­fer­en­tial dis­tance be­tween most of my read­ers and my­self. Think­ing it over, I re­al­ize that the bulk of the differ­ence comes from a differ­ence in per­spec­tives on how long it takes to learn sub­stan­tive things.

Peo­ple of­ten tell me that they’re bad at math. I some­times re­spond by say­ing that they didn’t spend enough time on it to know one way or the other. I av­er­aged ~25+ hours a week think­ing about math when I was 16 and 17, for a to­tal of ~2,500+ hours. I needed to im­merse my­self in the math to be­come very good at it, in the same way that I would need to live in French speak­ing coun­try to get very good at French. If my math­e­mat­i­cal ac­tivity had been re­stricted ex­clu­sively to course­work, I never would have be­come a good math­e­mat­i­cian.

Math grad stu­dents who want to learn alge­braic ge­om­e­try of­ten spend spend two years go­ing through Hartshorne’s dense and ob­scure text­book. it’s not un­com­mon for stu­dents to learn in­ter­est­ing ap­pli­ca­tions only af­ter hav­ing gone through it. I find this prac­tice grotesque, and I don’t en­dorse it. I bring it up only to ex­plain where I’m com­ing from. With the Hartshorne rit­ual as a stan­dard prac­tice, it’s felt to me like a very solid achieve­ment to pre­sent sub­stan­tive ma­te­rial that read­ers can un­der­stand af­ter only ~10 hours of read­ing and re­flect­ing deeply.

It was so salient to me that one can’t hope to be­come in­tel­lec­tu­ally so­phis­ti­cated with­out en­gag­ing in such ac­tivity on a reg­u­lar ba­sis that it didn’t oc­cur to me that it might not be ob­vi­ous ev­ery­one. I missed the fact that most of my read­ers aren’t in the habit of spend­ing ~10 hours care­fully read­ing a dense ar­ti­cle and grap­pling with the ideas therein, so that even though I felt like I was mak­ing things ac­cessible, I was still in the wrong bal­l­park al­to­gether.

Think­ing it over, I’m be­mused by the irony of the situ­a­tion. Even as I was ex­as­per­ated by some read­ers’ ap­par­ent dis­in­cli­na­tion to read ar­ti­cles very care­fully and think about them deeply, I was blind to the fact that I was failing be­cause I hadn’t put thou­sands of hours into learn­ing how to com­mu­ni­cate to a gen­eral au­di­ence. See­ing how large my blindspot was made me re­al­ize “Oh… just as I had no idea how much time I need to put into de­vel­op­ing my com­mu­ni­ca­tion abil­ities to reach my read­ers, some of my read­ers who ap­peared to me to be trol­ling prob­a­bly just had no way of know­ing of how much time it takes to learn re­ally deep things.”

The tens of thou­sands of hours that I put into de­vel­op­ing in­tel­lec­tu­ally didn’t feel like a slog – it was fas­ci­nat­ing. It was the same for all of the deep­est thinkers who I know. If you haven’t had this ex­pe­rience, and you’re open to it, you’re in for a won­der­ful treat.