By now there have been many detailed dissections of everything that is wrong with the treatment of climate in Superfreakonomics , but what has been lost amidst all that extensive discussion is how really simple it would have been to get this stuff right. The problem wasn’t necessarily that you talked to the wrong experts or talked to too few of them. The problem was that you failed to do the most elementary thinking needed to see if what they were saying (or what you thought they were saying) in fact made any sense. If you were stupid, it wouldn’t be so bad to have messed up such elementary reasoning, but I don’t by any means think you are stupid. That makes the failure to do the thinking all the more disappointing. I will take Nathan Myhrvold’s claim about solar cells, which you quoted prominently in your book, as an example.

Myhrvold’s claim in this context is essentially that using solar cells to fight global warming is not a good idea, because solar cells must be dark in order to absorb solar energy. However, only a fraction of that energy is converted into electricity, while the rest simply becomes waste heat that in turn will heat up the atmosphere.

Using nothing more than simple arithmetic, Pierrehumbert then tries to reason his way through such an argument to see if it makes any sense. As expected, it does not. My favorite part of the argument is the graphic that shows how many solar panels would be required to supply the world’s electricity:

That black square in Saudi Arabia certainly doesn’t look like it should make any significant contribution to the planet’s heating, and indeed, Pierrehumbert uses mathematics to argue quite effectively that it wouldn’t.

The letter is worth a read, not just for the strength of Pierrehumber’s argument, but for the simple mathematics that gives his argument such strong support. Levitt offered a meek response in the comments (#47, I believe), which was then quickly rebutted. Since then, all’s been quiet.

Of course, Levitt and Dubner may think that the math is on their side – since I haven’t read the chapter in question, I can’t comment. But the arguments put forth by Pierrehumbert are quite compelling, due in no small part to the simple calculations he performs. There’s no doubt that mathematics can be used both for good and for evil, but Pierrehumbert, like Spider Man, seems to understand that with great power comes great responsibility.

This year’s focus is on Mathematics and Climate. On the homepage you can find links to a variety of articles, most of which focus on the difficulty in coming up with mathematical models that can accurately reflect the complexity of the interconnected world in which we live. This is perhaps best summarized by Professor Pat Kenschaft, who writes the following in her essay, “Climate Change: A Research Opportunity for Mathematics?”:

How do we analyze the dynamics of the atmosphere, the oceans, the solid earth (especially volcanic emissions) and the biosphere (the system of plants, animals, and other living things)? Scientists have studied pieces of these systems, cutting them both conceptually and geographically, but even the pieces are not tractable by current mathematics, and the challenges as we try to understand the interplay of all phenomena involved are far beyond current conceptual and computational capabilities.

This is a theme that comes up in quite a few of the articles related to this year’s focus on the intersection of math and climate. As we begin to demand more from our models, those models will necessarily need to become more sophisticated. This requires mathematicians to create models that not only reflect reality, but are also optimized so that we can obtain results within a reasonable time frame.

There are a host of other articles discussing the interplay between climate and mathematics. Some of the articles cover related topics as well – for example, Professor Margot Garritsen’s article “Mathematics in Energy Production” provides a good example of the essential role mathematics plays in our current methods for procuring gas and oil, and briefly discusses the relationship between math and alternative energies.

With city-sized blocks of ice crumbling off of the Antarctic, there can be little doubt that climate change is happening, even if we don’t understand everything that underlies it. Will mathematics come to our rescue? Don’t worry – if it doesn’t, I’m hopeful that Captain Planet will.