Teachers

My friend Manuel recently commented that he had learned some Theory of Relativity during his degree, and there were plenty of things that still puzzled him. For instance, the Twin Paradox, where one twin travels in space at high speed, then comes back to Earth and finds he’s younger than his brother. It was difficult to reconcile this asymmetry with the rest of what he had been taught about Relativity.

Iván and I countered with the standard justification that the traveling twin had experienced acceleration, and so the symmetry was broken. Manuel was not convinced, and thinking more about it, I agreed with him. I went in search of a convincing explanation, and though I found several books and lectures disappointing, there was a 5-minute video from minutephysics that left me satisfied, and aware that my knowledge is very superficial. There is a course on Relativity in Brilliant that has been written in collaboration with minutephysics, and I think I’m going to take it sometime soon.

When you find a teacher that speaks to you, or a book, it is invaluable. It warrants full focus and appreciation. It is also very personal.

I was reflecting a bit on which teaching works for me, and which doesn’t.

I’ve never responded well to teachers that give “just” what is needed to pass their subject, without a mention to the wider world nor how the subject connects to other subjects. These teachers are efficient like stagecoach horses, but I can’t think of any that have inspired me.

In my engineering degree I had one of these professors for Differential Equations. She was popular with the students because she dictated her lessons, to the point of distinguishing stops from full stops like a primary education teacher, and so we all had very neat class notes. She was soft spoken and had a kind and unpretentious demeanor towards the students, unlike most of the other professors. But her subject was my least favorite mathematical subject in the degree. It was just blah, written down very cleanly.

My favorite math professor in the degree was loathed by most of the students. He would garnish his lectures with side trips connecting what he had just shown us with other areas of mathematics or engineering. It was difficult to take notes in his classes; he jumped around a lot, and when he was on-topic, he was quick and terse. I found his enthusiasm for math relatable, but many of the students would complain about his geekery and his penchant for corduroy pants.

I’ve had some very good teachers. In school there was don Santos, who taught me science when I was 12. He was a tall intimidating man with a goatee and mustache that gave him the air of a stern musketeer. I was always entranced by his classes. This was my first real encounter with science in school, and for the life sciences it would remain my best exposure in school.

At 16 I had don Javier, a recent mathematics graduate who had not been teaching high school long, and who hit us with the full force of mathematical formality to deal with infinity and start us on our road to calculus. I remember in one class he gave us two similar definitions: accumulation point of a sequence of numbers, and limit of a sequence of numbers. At recess I kept going over the definitions in my head. I was dumbfounded and obsessed. Something clicked in my head, and then I saw clearly the difference between the concepts, and where the key distinction was in the definitions. That was a good time.

I’ve had other great teachers. There was don José Antonio, “el Mozún” for high-school physics, who was funny and somewhat thunderous in class, but also a serious, careful teacher. There was “el bicho” who taught our first history class and made me love ancient Greece and Rome. Sadly, the history teachers I had in the rest of my school education made the subject dry and boring.

At Columbia there was Shree Nayar teaching Computer Vision, who was perhaps the best lecturer I’ve seen in action, and Cliff Stein for Algorithms, whose enjoyment in class was contagious (to me at least.)

Some teachers have had a positive impact for non-intellectual reasons. There was Maria José, my language teacher when I was 13, who would make prickly, biting comments on me in front of the class when I started to slide academically, which went on for several months. After I turned around my year, she took me aside and told me she had been particularly stern with me because she knew I was worth it. I thanked her, and to this day I think she did me a great kindness.

Most of the teachers I’ve had have left no significant mark. There have been so many; well over a hundred, I estimated once.

Looking back I think that what I want from teachers, and from learning, is growth. It’s a tall order.