How to understand anything
When I was hopelessly stuck in solving a problem, sometimes I would give up and go for a short walk outside. Somehow after clearing my head and not thinking about the problem for awhile, I would return to my seat and it would seem easier. In Junior College, when I was trying to derive a complex algebraic formula, I would often do so in a relaxed state, like lying on a sofa and often fall asleep while thinking of it. Turns out Thomas Edison and Salvador Dali, a surrealist artist, used a similar technique to tackle hard problems, which I describe more below. Here are some other ‘hacks’ I did to understand or master things:
- I tried to read everything I could find on the topic. Textbooks in the syllabus, extra textbooks, my own notes, notes from other professors, slides online on slideshare, books written by the textbook authors, blogs, youtube videos. Basically, I immersed in the topic and saw the same idea being represented by different experts and it gave me useful perspective. A nice side effect: I end up falling in love with the subject at the end of the term.
- “There are no dumb questions.” Actually, there are. But I would still take every opportunity in class to ask a question. When I think my question is stupid I’d try to ask my professor during breaks or after class. One thing I learnt was if I did not understand something, someone else in class probably doesn’t as well; hence I was doing a favour for him/her when I asked my question. I would also email my professors. They probably hated me because I would email them a few times in the same day. One thing I noticed while composing emails was that the act of writing an email often times cleared my thought process and sometimes I would understand the concept merely by articulating it.
- Testing myself. I would make sure my understanding of something is poked at and tested rigourously. The easiest way would be through practice questions, the harder way would be through covering my notes and explaining concepts to myself, and checking back immediately if I understood and remembered what was taught. An extension of that would be to think of how the professor may test me on the concept and pushing the boundaries of what I know and not know.
- Advanced flashcarding. I used this to acquire deep understanding of the subject without spending too much time revising.
I only know so much. Here are some tips that other people have used to understand.
- Moving in between ‘diffuse’ and ‘focused’ modes of thinking: Thomas Edison would relax on a chair hold ball bearings in his hand while thinking vaguely about a scientific problem. As his mind drifted away and he went from a ‘focused’ to ‘diffused’ mode of thinking, he would drift asleep, dropping the ball bearings and rousing himself. He would wake up with the ideas generated from the diffused mode thinking and solve the problem. The key is to toggle between those two modes to allow learning to take place at a faster pace. Source: Coursera — Learning to learn.
- Analogies/Metaphors — Metaphors give the mind a shortcut to understanding something by modifying what you already know. Hence the mind does not have to start from scratch. It works with whatever framework you have already. Source: Scott H Young
- Visualisation. Drawing things help. Putting frameworks, diagrams into your learning helps to consolidate thinking. I recommend this book by Dan Roam, where he talks about how any problem can be visualised. After reading it, it gave me the confidence to imagine any concept/problem into a drawing. Also, watch this video from Scott Young
- Be like Richard Feynman pt1: Richard Feynman, a famous physicist once tried to create a freshman college lecture for an advanced physics theorem to challenge his understanding of it. When he couldn’t, he realised he did not truly understand it. The lesson is if you cannot explain it in layman terms to someone, you do not really understand it. Source.
- Be like Richard Feynman pt2: They found these words on Richard Feynman’s blackboard at the time of his death, “What I cannot create, I do not understand”. When he was a professor, he would challenge the math department that he could understand any concept that they could explain to him and tell them if it was right or wrong. He did so by visualising in his mind what the math guys described to him. By doing so, he would be able to know what was true or false. In his book, he explained how he did it: “Actually there was a certain genius quality to my guesses. I had a scheme, which I still use today when somebody is explaining something I am trying to understand: I keep coming up with examples. For instance, the mathematicians would come in with a terrific theorem, and they are all excited. As they are telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball) — disjoint (two balls). Then the balls turn colours, grow hairs, or whatever, in my head as they put more conditions on. Finally they state theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say “false!”.”
“Everything he read to me he would translate as best as he could into some reality. […] But I learned from my father to translate: everything I read I try to figure out what it really means. What it’s really saying”. This captures the essence of understanding to me.