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.” [1]
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.
Notes:
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.
Atanu Dey : Life is a Random Draw 
Nice one Atanu,
I am pretty sure you delivered a likeable lecture and made it interesting and assimilable. I have learnt more while reading during the course of the employment than in School and College. I have learnt many concepts from many different sources. In fact to this day I feel uncomfortable and uneasy when I dont recall the basic axioms and principles in Mathematics and Physics. I instantly feel I am unfit for what I get paid for. The reason I forgot them at the first place was some third rate dis-interested teachers in a fourth rate Govt School first introduced me to these subjects and they had no incentive of making it appealing and ever-lasting to the dumbest guy in the class aka me and they immediately jumped to solving some problem sets by trying to fit values in a formula and eureka.. I have l cleared the exams with 95% in Physics in my 12th standard but beleive me I have begun to admire wave-particle thoery now better after coming acrosss the a video on double-slit experiment for the first time in over a decade and a half of last trying to absorb it. It fact the lectures in youtube by Prof. Walter Levin would make anyone instantly love physics. I must admit despite being a merit scholar for the marks I scored, I knew almost nothing. We are all as good as our teachers at School made us.
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On simplicity:
Do you mean that all natural laws are simple in some sense? That the number of bits required to describe a natural law is always some small number? It’s an attractive idea, but why would we assume this? In science, we try to find the simplest explanation that fits the phenomena. But the simplest explanation needn’t actually be simple…
On the cost of energy:
Q3: I’d say it has been going up. Of course the canonical answer is it has been going down, but that usually ignores the human cost (Iraqi lives, for example) and the environmental cost.
Q4: Current sources of energy will keep increasing in cost. If we discover a new way towards cheap energy then it will definitely go down. But if we don’t then it won’t. So the question is really asking, will there be a major technological breakthrough? It’s hard to predict such things…
On different representations of physical laws:
Isn’t it a little like we’re using different languages to describe the same things? Is it nature that’s doing this, or us?
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Richard Feynman was a great teacher, but also good at pulling your feet. His insightful comments are meant for really intelligent readers, and sometimes I am not sure if he wrote/ said them with his tongue firmly in his cheek.
About energy:
1) The costs were high initially, then they fell with better technology and discovery of more/ larger fields. However, in the last 20 years the costs (human, capital, environmental) have gone up again.
2) Energy will get costlier, since supply will certainly shrink and will be out-stripped by demand from a growing economy. No new fields have been discovered of size to offset the demand growth. No new technology has been invented to offset it either.
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China races ahead of the US – and India too? – in drive to go solar.
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WUXI, China — President Obama wants to make the United States “the world’s leading exporter of renewable energy,” but in his seven months in office, it is China that has stepped on the gas in an effort to become the dominant player in green energy — especially in solar power, and even in the United States.
Chinese companies have already played a leading role in pushing down the price of solar panels by almost half over the last year. Shi Zhengrong, the chief executive and founder of China’s biggest solar panel manufacturer, Suntech Power Holdings, said in an interview here that Suntech, to build market share, is selling solar panels on the American market for less than the cost of the materials, assembly and shipping.
Backed by lavish government support, the Chinese are preparing to build plants to assemble their products in the United States to bypass protectionist legislation. As Japanese automakers did decades ago, Chinese solar companies are encouraging their United States executives to join industry trade groups to tamp down anti-Chinese sentiment before it takes root.
The Obama administration is determined to help the American industry. The energy and Treasury departments announced this month that they would give $2.3 billion in tax credits to clean energy equipment manufacturers. But even in the solar industry, many worry that Western companies may have fragile prospects when competing with Chinese companies that have cheap loans, electricity and labor, paying recent college graduates in engineering $7,000 a year.
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Rest here: http://www.nytimes.com/2009/08/25/business/energy-environment/25solar.html?em
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Dear Atanu-da,
While you take your break from Berkeley, give the man (Feynman)some orange juice…..and have some yourself. Very refreshing!
Cheers
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