Created: April 05, 2020
Modified: April 05, 2020
Modified: April 05, 2020
teaching at the critical point
This page is from my personal notes, and has not been specifically reviewed for public consumption. It might be incomplete, wrong, outdated, or stupid. Caveat lector.- As a researcher, I wonder if there's a 'critical point' of growing an idea when it's important to be teaching it, whether formally or just by talking to people.
- That critical point is basically, when you first have the idea, or at least, when you first have it in a way that you can formulate to other people. (so, a good first step for a new idea is always to try to formulate it in a clear and communicable way).
- When the idea is fresh in your mind, it hasn't become 'frozen solid' (or at least annealed to low temperature).
- When you explain it to someone else, they will ask questions. If the questions end up shooting down the idea, it's good to have learned this early. If they don't
- Engaging in this fashion forces you to construct an interactive proof, which is a powerful framework. (I want to be able to say something like: optimizing over interactive proof systems makes more sense than optimizing over proofs? I'm not sure if there's a technical sense in which this could be true. I guess an interactive proof that a problem is solvable is a black-box algorithm to find the solution, and optimizing over those is powerful. Anyway certainly having an interactive prover---and conversely, being able to function as a verifier---is a very powerful tool since you can convince people of things you would otherwise never have been able to convince them of)
- The social motivation will make you curious about your own idea. If there are questions you don't have good answers to, you'll want to find good answers to them so that you look smart the next time you explain the idea.
- You might also genuinely learn something or get new ideas from your interlocuter, but even if you don't, it's still well worth it.
- The opposite of teaching ideas when you first have them, is not (for most people) to keep developing the idea internally until it's perfect. Most people, including most great researchers, don't have the level of self-discipline to work for so long on something that no one else cares about. And regardless, if your idea is going to matter, it needs to be built of communicable blocks (see: Mochizuki's 'proof' of the abc conjecture). The only way to make that happen is to communicate it early and often.