Learning takes a long time

by JonahSinick 4y31st May 201536 comments


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 thereinso 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.