When I was a student, learning resources were far and few between. There was your teacher, and the textbook. Some students also joined private coaching classes but I never did that. So if the teacher was good, life became much easier. When I was in the Nowrosjee Wadia College in Pune, we had a teacher called Prof. H. D. Moogat. His lectures were like rock concerts. Students from other colleges used to flock to his lectures, sitting in windows or standing. Not a single place was empty. We had to be there early to reserve a seat. His subject? Mathematics!! Generations of students including me owe him a mountain of gratitude for making maths understandable.
You cannot expect such gifted teachers for every subject; that would be impractical. However, today’s technology offers many alternatives. For me, one of the greatest learning resources in the past decade has been YouTube. I have learned so much from watching YouTube videos on every topic under the sun – from finance and evolution to how to open a bottle with tight cap (hold it under hot water for 30 seconds, causing the metal cap to exapnd). And the education continues.
One of the great advantages of YouTube is you can find many lectures on the same topic by different professors. And this is the key to my hack to understand a difficult topic.
Let me explain. Imagine you want to understand a difficult topic. You start by watching a lecture on YouTube. If the topic is difficult, somewhere along the line, you will not understand a point. This is a crucial moment. Earlier, I used to get stuck at this point. What I should have done and now regularly do, is to acknowledge that this point is obscure, but not to lose the thread of the lecture. This takes some practice, but if you persist, at the end of the lecture you can say, “okay, I have understood points 1, 2, and 4 but I have not understood point 3 and hence it’s not clear to me how point 5 follows from point 3.” This is great. Now you know exactly what you don’t understand. At this point, you may want to write down the core concept.
Now comes the hack. And I must underline the fact that this was not possible when I was a student. You watch a lecture on YouTube on the same topic by a different professor.
Believe me, this works wonders. Different professors have different teaching styles, they emphasize different topics. So when you watch a second lecture, this professor may explain points 3 and 5 well but may be a bit vague on points 1, 2 and 4. But you have already understood those from the previous lecture. So in effect, watching the two lectures, you have understood all the five important points on the topic.
I want to illustrate this method by an example. However, the example is rather technical so those not interested can skip to the next section. My apologies for that.
Topological insulators
Recently, I became interested in topological insulators. The main property of topological insulators is easy to understand. These are special materials that are insulators on the inside but perfect conductors on the edges or on the surface depending on whether it’s a 2D material or a 3D material.
Why do these materials behave in this way? This is the tricky part mainly because it involves a branch of mathematics called topology that is famous for being difficult to understand.
When I listened to the first lecture, I understood the basic definition of a topological insulator. I also understood that it’s closely related to the quantum hall effect. I did not understand
- What does it mean when you say that two surfaces are topologically same?
- How does that affect the electrical behavior of the topological insulators?
- Why do the electrons have a one way street at the edges which make for a perfect conductor?
So I listened to a different lecture and I understood that when a surface can be transformed into another without breaking it, it means that the two surfaces are topologically same. So a coffee cup can be transformed into a donut without breaking the hole. Another lecture made me understand that the electronic states of a topological insulator behave like a topographical geometrical surface and that is characterized by a TKNN number. Finally, I understood that electrons flow only in one direction because of the time-reversal symmetry and spin-orbit coupling.
I liked this lecture by Prof. Charles Kane where he showed this scary looking equation that describes the topological insulator and he said, “It’s not difficult, it’s just more advanced… And it’s okay if you don’t get it.”
Finally, I had to decide how deep I want to go into the topic because there is always more to learn.
Seeking clarity
To summarize, it may take more than one tries to understand a complex topic. If you don’t understand it the first time, it is very important to know exactly which points are unclear so that when you listen to a second lecture, you will know where to focus. The gaps in your knowledge are a key to a better understanding of the topic.
