On Learning Outside Institutions

I spent large chunks of the past few years reading math and physics textbooks outside college. Here are some of my thoughts.

1. When you’re learning outside of an institution, it’s hard to tell if you’re progressing. There are no exams, promotions, or users to tell you that you’re progressing. But ever so rarely, you get little signals that you’re actually learning things. For example, when talking with graduate students, I can teach them things that they don’t know about. Or when I went to a grad class today, I knew most of the material being taught. I’m learning something!

2. When reading a textbook, since there are no tests to give you feedback, I naturally use “what page number I’m on” as a way to measure my progress. This is bad! It disincentivizes doing exercises and looking back on old chapters that you don’t remember.

The worst might be that it disincentivizes play: asking questions like “what if this assumption didn’t hold?”, or graphing functions on desmos, or trying to get deep intuition for why something is true. It’s during these moments of play that I feel I am learning the most. But there is always this voice in the back of my head that says “move on to the next chapter!”

3. Getting a tutor was one of the best investments I made. I have a document with a list of questions that I share with my tutor before we meet. Having this document gives me permission to ask questions. It unlocks my curiosity!

4. A tutor also helped with discipline — I need to finish the chapter before meeting with them and will say no to invitations if I haven’t finished.

5. One of my friends says he wants to be able to solve every single undergrad physics problem. Another says she wants to be able to derive every single important result in physics. Having these maxims in the back of your head when learning is interesting! They might be one way to get around the bad incentives of page number progression.

6. There’s a difference between reading a text and studying a text. When I read a novel, I read it. But I don’t read a physics textbook, I study it.

This change in wording gives me permission to take my time and ask questions. I find the term studying describes what I do when reading a textbook better than reading.

7. Learning programming outside school was much easier than reading math/physics textbooks. I can program all day but can barely read 60 minutes of a textbook without getting distracted. Why is that? One hypothesis is that software has near instant feedback loops — I read something in documentation and can test it immediately. On the other hand, it takes me ~8 hours to read a textbook chapter before I start doing exercises. And even longer until I apply what I learned.

8. The best hack to learning outside an institution is to read synchronously with a friend.

Thanks Marley Xiong (opens in a new tab), Santi Aranguri (opens in a new tab), and Stephen Fay (opens in a new tab) for your comments!