It comes up nine times out of ten that I talk to an Environmental Studies student. IPAT. (Environmental) Impact = Population * Affluence * Technology. It’s introduced in Environmental Studies 101 at Greenback, and at pretty much every other campus that has an ES program. If Environmental Studies has a mantra, it’s IPAT. It gets drummed into students’ heads, course after course. It sticks like glue. And it’s not helpful.

It’s not helpful in the manner that all oversimplified mantras are unhelpful – the mantra supplants the more complex truth of which it was meant to be a reminder. I don’t fault Environmental Studies faculty – most of them are quite conscientious about saying that IPAT is just shorthand. Most of them emphasize that the equation is calculable (if not particularly meaningful) only on small homogeneous populations. But those subtleties don’t stick. The mantra sticks. Impact = Population * Affluence * Technology. In an educational system which values universal truths, that means all population, all technology, worldwide.

If you take the equation – simple multiplication – at face value, you can only make it work by jiggering the units. Population (in people) times affluence (in dollars of GDP per capita) times technology (umm . . . that must be environmental impact per dollar of GDP) equals environmental impact. But while that equation works, it doesn’t work well. It doesn’t tell us anything. It begs the question of the nature of environmental impact and its relation to something called GDP. By invoking the doubly-synthetic unit of “environmental impact per dollar of GDP”, we’ve created a tautology. And why GDP? Wouldn’t the calculation work out equally well if we made it “population times affluence (pounds of dog food per capita) times technology (environmental impact per pound of dog food) = environmental impact”?

The simple fact is that stating the IPAT equation as a simple multiplication has a certain conceptual validity, but no arithmetic significance. The combination of terms is potentially meaningful, but the multiplication isn’t. It would be more appropriate to say that I = f(P,A,T) [impact is an undefined function of three exogenous variables – population, affluence and technology] than to imply that the interaction of those variables resembles simple multiplication.

I have a lot of concerns about the IPAT mantra, and choice of arithmetic operators is definitely the most picayune. But in several ways those multiplication signs are emblematic of my broader concerns with the IPAT equation. And the way we educate Environmental Studies majors. And the way we educate students in general. But that’s another post. Indeed, a whole series of other posts.