On Understanding, Comprehending and Learning

Our freshmen year math professor told us on the first lecture: in university, you are not going to focus on learning the practical skills — there are trade schools for that — you are going to learn how to learn (meta learning!), because while everything else is going to change during your life, one thing is constant: the ever changing world which requires constant learning to stay relevant.

After 10 years of learning how to learn I want to believe I became decent at it, and one thing I notice that distinguish someone who learns effectively from someone is less so is the stress testing the comprehension, taking things to the limits and drawing the testable hypotheses from the input material. Let me explain.

Say your mentor/professor/instructor (and that’s why learning in person is so valuable-see further) is explaining how X works. You have some background on X, but there is a lot of new information and you are carefully knitting the web of new facts and connections on top of it. How do you make sure you comprehend the new X fully? There are several effective strategies that work great in a combination:

  • Explain it back: using your own words, what’s the idea and its implications? That also helps the instructor to understand where you stand.
  • Take the idea to the limits: if X is true, then at the one extreme, this must be true, on the other — that; X is somewhere in the middle — definitions by limiting. Doing that also allows to check how well does instructor understands the topic-bad instructor won’t be able to articulate clearly the effects and implications once the X is extrapolated beyond the textbook example.
  • Draw testable hypotheses — this a hallmark of good science in general, and is applicable to learning in particular: if X is true, and given A, B and C, we should expect to see Y in such and such situation. Is that so? Extrapolating the X is useful because it allows to test our intuitions as well as finding the failure modes of X. No idea is absolutely perfect, every idea, or a model, has a limitation. By knowing the limits we can better understand the applicability of each idea, and without applications the ideas or knowledge can only give us so much.

Note that the techniques above are so much more easier to do when one has a mentor that can speed up answering the questions, as well as guiding on asking the right questions and drawing interesting hypotheses. That’s why education in person is so valuable and productive, but only when the mentor themselves knows the area and these techniques well.

What's life without a little adventure?

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