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Comment by Allen Myers

Part of the population-environment debate in recent issues of Â鶹´«Ã½ has focused on Paul Erlich's formula I=PAT. This attempts to relate environmental impact to population, average levels of affluence or consumption and technology.

At least some of the participants in the discussion have referred to this formula as "scientific". It seems important for clarity to understand in what senses this description is or isn't true.

Some may simply mean that the ideas summarised by Erlich in this formula are supported by scientific research. In that case, one can ask them to specify the research they have in mind, and the discussion can proceed to what this research shows and its meaning for the overall debate.

However, the mathematical appearance of the formula, as well as the manner of argument of others of its proponents (particularly when it is stated that PAT means population "multiplied by" affluence "multiplied by" technology), implies that they have something more in mind when they refer to it as "scientific".

The suggestion is that I=PAT has a status superior to other arguments because it quantifies environmental impact, that it is scientific — and therefore essentially unchallengeable without a major reworking of scientific knowledge — in the same way that the formula for the kinetic energy of a moving object, k =

.5J243I>1

55IJ0>/

.5I>2

55I>mv2

, is scientific.

What is it, precisely, that makes k =

.5J243I>1

55IJ0>/

.5I>2

55I>mv2

scientific? Not its truth — although, so far as we know, it is true. The key thing is that the formula is testable, at least potentially.

The formula k =

.5J243I>1

55J0I>/

.5I>2

55I>mv2

makes a definite statement whose validity can be checked: the kinetic energy of a moving object, measured in joules, is equal to half the object's mass at rest, measured in kilograms, multiplied by the square of its velocity, measured in metres per second. The kinetic energy of objects of varying mass, moving at varying speeds, can be measured to determine whether the equation really holds true; if

situations are discovered in which it does not, then the formula has to be modified or abandoned.

Suppose that the formula k =

.5J243I>1

55IJ0>/

.5I>2

55I>mv2

had not yet been discovered by modern physics. In a discussion about kinetic energy, someone might then advance the proposition, "The kinetic energy of an object is determined by its mass and velocity". The statement is (as we know) true, but it would not be testable because it states nothing about a measurable relationship between energy, mass and velocity — for example, whether energy increases in the same or opposite direction as its two determinants.

As we looked into kinetic energy more deeply, we might arrive at a further statement: "Kinetic energy at any velocity is directly proportional to rest mass". This would be a scientific formulation, although not as complete as k =

.5J243I>1

55IJ0>/

.5I>2

55I>mv2

: we could test it by measuring the energy of different masses as they moved at the same velocity to find out if, whenever we repeated the test, energies were in fact proportional to mass.

Does the formula I=PAT have this sort of testability? No, it lacks it for several reasons.

To be checkable, a statement about environmental impact in general needs to provide a common measure for specific impacts (just as it needs to be possible to express all kinetic energies in joules). The formula doesn't do this.

For example, in situation Y, PAT coincides with an environmental impact of 1 tonne of stratospheric ozone destroyed and 2 tonnes of topsoil lost. In situation Z, a different PAT destroys 2 tonnes of ozone and 1 tonne of topsoil. In which situation is I greater? The formula doesn't give us any means to answer that question, so there is no way that I=PAT can be confirmed or disproved by scientific observation.

The same objection applies to the other variables in the equation. How is the affluence of a particular situation to be measured? By monetary income or some other standard? If the former, is it average income, median income or perhaps either of those combined with the shape of the income distribution curve? Similarly with technology: how do you add microcomputers, jet aircraft, nitrogen fertilisers and so on to arrive at a figure for the technological level?

Population, at least, might seem to be fairly simple: people are people, and all you have to do is count them. But even here, we

have to ask the proponents of I=PAT to be more precise — is P only a matter of numbers, or should we also take account of things like the age distribution of this population, or where (city or bush) it lives?

It's clear, then, that I=PAT is not a scientific formula. Rather, it is a shorthand way of expressing the idea, "Environmental impact is determined by population, the population's level of affluence and the technology used to produce that affluence, and each of these three factors is of equal importance".

The fact that it is not a scientific formula does not, of course, mean that this statement is untrue. It does mean that its proponents have yet to prove their case, and that they have not put it in a form in which proof is a mere matter of mathematics.