Richard Feynman wrote that he was mystified by the different ways — ways that bear no resemblance to each other — in which a fundamental law of physics can be described. He conjectured that perhaps it was because the fundamental laws are simple. “Perhaps a thing is simple if you can describe it fully in several different ways without immediately knowing that you are describing the same thing.” 
I have been thinking about that in the context of teaching and learning. Teaching at Berkeley got over last week and I will be heading back to India in a couple of days. I am going to miss being here. But I will not dwell on this now. Let me get back to teaching and learning.
I believe that all disciplines have at their foundation a set of simple ideas. Each idea is simple in itself but the ways in which a set of simple ideas interact and combine to give rise to complex phenomena makes it difficult to discern their simplicity. We observe the complex phenomenon, not a simple idea in isolation.
Teaching a course on economic development is instructive. I attempted to bring together a small set of ideas that form the foundation for the study of economic growth and development. The set is small and compact. (Perhaps development is a compact set. Or perhaps not.)
I entertained the idea of using a textbook. But I could not find one that suited my purpose. Eventually I decided on putting the course content together from a variety of sources. I used the notes from a few of the lectures by Prof Alain de Janvry. He teaches the course during the regular Fall term. Prof de Janvry had given me permission to use all his lecture notes but I felt that in the Summer term, it would not be possible to do them. Prof Bardhan had suggested Debraj Ray’s book on development but I found it inadequate.
Eventually, I got together a good set of reference material — not surprisingly quite a bit of it from the web. Most of the references are there on the Econ171 course blog.
We had one midterm and one final exam for the course. Both were take-home exams. I hate exams but I would any day take an exam instead of having to write one. Writing a good exam is much harder than doing well in an exam. Writing take-home exams is harder still. But with a bit of hard work (something that I am not accustomed to), I was able to write two exams which I think were pretty good, even if I say so myself. Actually, many of the students felt the exams were good. One of these days I will discuss the exams.
Here’s a bit from an assignment:
Energy use and economic growth are correlated. This could imply that energy availability could be a potential barrier to economic growth. If the real price of energy were to increase in the long run, it would be seriously bad news for developing economies.
Question 3: What has been the long-term trend in the real price of energy in the world on average? Has the real price gone up or gone down? Give an intuitively plausible explanation.
Question 4. Do you expect the real price of energy to go up or go down in the long run? (Let’s define anything beyond 25 years as the long run.) Explain why.
These questions are very simple but tricky. Perhaps the readers of this blog would like to give it a shot.
Anyway, I have to run right now. So I will continue this post later.
1. Here’s what Feynman said in a lecture:
The fact that electrodynamics can be written in so many ways – the differential equations of Maxwell, various minimum principles with fields, minimum principles without fields, all different kinds of ways, was something I knew, but I have never understood. It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but, with a little mathematical fiddling you can show the relationship.
An example of that is the Schrödinger equation and the Heisenberg formulation of quantum mechanics. I don’t know why this is – it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn’t look at all like the way you said it before. I don’t know what the reason for this is. I think it is somehow a representation of the simplicity of nature.
A thing like the inverse square law is just right to be represented by the solution of Poisson’s equation, which, therefore, is a very different way to say the same thing that doesn’t look at all like the way you said it before. I don’t know what it means, that nature chooses these curious forms, but maybe that is a way of defining simplicity. Perhaps a thing is simple if you can describe it fully in several different ways without immediately knowing that you are describing the same thing.