Checking The Math Behind The Greenhouse Effect

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Supporters of the Homestar legislation say energy-efficient homes would save money and reduce the nation's carbon footprint. Everyone likes saving money, but there's a lot of debate about whether humans are responsible for global warming. That might seem to be a 21st-century political issue, but the matter of greenhouse gases goes back to the 1800s, in the work of French scientist Joseph Fourier. Weekend Edition Math Guy Keith Devlin joins host Scott Simon to give us a little climate-change history.


Supporters of the HOMESTAR legislation say that energy efficient homes would save money and reduce this nation's carbon footprint. People do like saving money, but there's debate about whether humans are responsible for global warming. Now, that might seem to be a 21st century political issue, but the matter of greenhouse gases goes back to the 1800s, in the work of French scientist Joseph Fourier.

WEEKEND EDITIONs Math Guy Keith Devlin is here to give us a little climate change history, from a mathematical point of view. He joins us from Stanford University.

Keith, thanks for being with us.

Professor KEITH DEVLIN (Stanford University): Hi, Scott, nice to be here again.

SIMON: And how did Monsieur Fourier begin to think about this?

Prof. DEVLIN: So, he was thinking about the following rather interesting question. He said: Every day the suns rays strike the Earth's surface and they warm it up, so why doesn't the planet just keep getting hotter and hotter until it's the same temperature as the sun?

Well, the answer, of course, as he realized, was that the heat must be carried out into space. There must be some invisible infrared radiation, we call it today. Well, he used mathematics to calculate that cooling effect. And he got a temperature of the surface of the Earth that was much colder than the Earth really is. So he realized that something must be keeping the heat in.

The only thing that was possible was the atmosphere. So he said the atmosphere keeps the heat in the surface. And he compared it to heating up the air inside a glass box. He didnt actually talk about a greenhouse. He talked about a glass box, and said when you heat up the air in a glass box the heat remains in the box.

SIMON: And what kind of math did he use to make these calculations?

Prof. DEVLIN: Fourier approached the problem by thinking about heat radiation as a radiation process. It's a wave process. So he developed mathematics that allows us to understand the way things radiate through radiation, how they are transmitted through radiation.

Now, he was thinking of heat radiation. But once you have mathematics that studies heat radiation, you can use that same mathematics to study other kinds of radiation. You can apply that mathematics to light waves or to sound waves.

SIMON: So we've known about the greenhouse effect for 150 years.

Prof. DEVLIN: We have - well, almost 200 years. The correct physics was worked out about 150 years ago - in 1862, in fact, by an Irish physicist called John Tyndall. He was doing experiments in his laboratory and he discovered that water vapor and(ph) a particular carbon dioxide dont allow heat to pass through them. That means that if you have any carbon dioxide in the atmosphere, heat is not going to be able to pass through it.

So he gave us the correct explanation of why the atmosphere keeps the heat in. The more carbon dioxide you have in the atmosphere, the less able the heat is to escape and the more the Earth's surface will get warmer and warmer.

SIMON: Well, Keith, thank you very much.

Prof. DEVLIN: Okay. My pleasure, Scott. And try to keep cool.

(Soundbite of laughter)

SIMON: Not a problem this time of year, for the moment. Our Math Guy Keith Devlin out of Stanford.

And this NPR News.

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