On Learning

When you truly understand something, you can express it at any level of detail while maintaining coherence. The master can provide the one-sentence version, the paragraph version, and the chapter version, all of which tell the same story at different resolutions. The novice can only repeat what they've memorized at one resolution.

— Shane Parrish, Brain Food, "Different Resolutions" (Farnam Street, September 7, 2025)

I have started using this as a test, mostly on myself. If I can only give one version of an idea — the version I first heard, or the version I once wrote down — I do not understand it yet. I have memorised a path through it, not the ground it covers.

Teaching makes this hard to hide. A student asks the same question in three ways, and each way needs a different answer: the quick one at the door, the longer one in office hours, the full one on the board. When I know the material, the three answers agree. When I do not, they quietly contradict each other, and a good student notices before I do.

Research works the same way. The abstract, the introduction, and the paper are the one-sentence, one-paragraph, and one-chapter versions of a single claim. If they do not line up, the problem is rarely the writing. It is that I have not finished understanding what I found.