I believe that a mathematical, quantitative understanding can be really valuable as we try to gain some understanding of the environmental challenges ahead. After all, many of these challenges amount to questions of

*scale* - the "how big is my footprint?" issue - and such a question is a quantitative one.

That doesn't mean, though, that

*every* mathematical formula that can be introduced into an environmental discussion necessarily contributes to improved understanding. Some strike me more as attempts to harness the prestige of mathematics as a rhetorical device. Among these questionable formulas is the so-called "IPAT" equation

I=P*A*T

which purports to describe human environmental Impact (I) as the product of Population (P), Affluence (A) (defined as GDP per capita), and Technology (T) (defined as environmental impact per unit of GDP). Related is the "Kaya equation" which expresses carbon dioxide emissions as the product of four quantities: the carbon content of energy, the energy intensity of the economy, the GDP per capita, and population.

These equations are tautologies - they are true by definition of the quantities involved. But one often sees them invoked in arguments such as the following: "The IPAT equation shows that to reduce overall human impact, we have to stabilize the population, end our question for greater affluence, and develop improved technologies. If we don't take care of *all* of these, we are in trouble. The mathematics proves it!"

I don't think the policy recommendations are necessarily bad, but *mathematics* doesn't add anything to the reasoning process involved in getting there. To illustrate, let be develop a new equation of my own - the "ILUV" equation

I = L*U*V

Here I is human impact, as before, L is the average number of Lectures in mathematics per year delivered in an average university, U is the number of Universities, and V is the aVerage environmental impact per lecture in mathematics. This equation is just as much a tautology as the previous one. But it would be fatuous to use it to argue that "The ILUV equation shows that we have to reduce the number of mathematics lectures, shutter universities, and...."

Since the one equation is *mathematically* just as valid as the other one, the difference that makes one argument at least plausible and the other one stupid is not found in the mathematics. Instead, it is found in the way in which the IPAT analysis (perhaps) corresponds to real structural features of the world we inhabit (principalities and powers?) and the ILUV analysis obviously does not. And the extent to which an analysis really corresponds to the structure of the world is a disputable, political (even theological) question. Throwing around some tenth grade algebra won't allow us to dodge the real work here.

(For anyone who wants to explore these ideas further, it would be interesting to read about the dispute about Samuel Huntingdon's election to the National Academy of Sciences.

This web page might get you started...)

Image from Flickr user Marty Coleman, licensed under Creative Commons.