Population, consumption, and rectangles

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Can elementary geometry explain environmental problems? Actually, no.

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Can elementary geometry explain environmental problems? Actually, no.

When an article in National Geographic said that the biggest environmental problem isn’t population growth but the way humans in rich countries get and spend energy, John Feeney of Global Population Speak Out posted this comment:

“So, per capita consumption. As someone pointed out recently, that’s like saying, ‘The biggest contributor to the area of a rectangle is not length. It’s width.’”

Feeney was so proud of this witticism that he posted it twice on the National Geographic website, then bragged about it in his blog.

Paul Ehrlich of Population Bomb fame used the same analogy in a talk he gave in Australia last year:

“Population and consumption are no more separable in producing environmental damage than the length and width of a rectangle can be separated in producing its area — both are equally important.”

Robert Engelmann of Worldwatch Institute says the same thing:

“Did someone just remark that these impacts don’t stem from our population, but from our consumption? … It’s as though a geometry text were to propound the axiom that it is not length that determines the area of a rectangle, but width.”

And when Joe Romm published an article by Simon Butler and me in his excellent Climate Progress blog, someone named Tom King promptly commented:

“It seems hard to figure out whether the problem is caused more by individual consumption, or the overall population. Similarly, its hard to figure out if the area of a rectangle is more influenced by its length or its width.”

I don’t know who said it first, but the rectangle analogy is apparently the latest fad in populationist discourse, a clever riposte to be whipped out whenever anyone questions neomalthusian orthodoxy.

And just like Malthus’s 200-year-old attempt to explain poverty by comparing the “geometric” increase of population to the “arithmetic” increase of food, this analogy simply doesn’t work. It’s bad social analysis, and it’s bad arithmetic.

To start with, Width and Height are independent variables. You can measure them separately —  changing one doesn’t affect the other. But you can’t determine “Per Capita Consumption” unless you already know how many people there are – change the population and per capita consumption must change. Multiplying them together produces a meaningless result.

More seriously, the rectangle analogy incorrectly assumes that there are just two variables, population and individual consumption. In the real world, the production, extraction and destruction operations of corporations and military operations generate far more pollution than all individual “consumers” put together. So if you must use a geometrical analogy, it will require some complex multi-dimensional hyper-shape.

But even if we ignore the need for far more than two dimensions, and the fact that individual behavior is a small part of the problem, the rectangle comparison just doesn’t work.

Height and Width are measured in units such as centimeters or inches. Every unit is exactly the same as every other unit, so reducing the Height or Width by any amount will reduce Area proportionately. Cut the number of centimeters of either dimension in half, and the area will be reduced by 50%. It doesn’t matter which centimeters you remove — every one has exactly the same impact.

That isn’t true of people, by a long shot. There are huge differences of wealth, class, gender, occupation, geography and more. A few people cause a lot of pollution, most cause very little.

As Stephen Pacala of the Princeton Environmental Institute has pointed out, the three billion poorest people in the world “emit essentially nothing.” So if every one of the three billion poorest people disappeared today, reducing the “population dimension” by 43%, total Environmental Damage would be essentially unchanged.

On the other hand, a  few thousand billionaires, politicians and generals make daily decisions that cause massive pollution and environmental destruction. Eliminating that tiny minority’s power would make a huge difference.

The rectangle analogy is just the latest in a long line of populationist attempts to reduce poverty, hunger, pollution, and climate change to simple math.

Like all its predecessors, this one sounds good, but explains nothing. Let’s add it to the  “False Population Analogies” file, and move on.


More from my notebook … 


  • You lost me right at the start. I get the length x width = area. Easy peasy. Now population x per capita consumption are two different attributes which apparently equal “environmental damage” when multiplied. Hmm who says? Where’s the proof? What is “environmental damage”? CO2? Acidification of soil? Of sea? Potholes in the road? What is it measured in and what does it depict? In short that second rectangle isn’t a rectangular relationship at all and is a false assumption. In short that second rectangle is bullsh1t. End of.

  • This “rectangles” metaphor is just another repackaging of the per capita fallacy — the mathematical tautology that says, for example, that total GHG emissions = population × per capita emissions, as if this were some kind of brilliant insight. But since per capita emissions are calculated in the first place as total emissions ÷ population, the brilliant insight becomes:

    total emissions = population × total emissions ÷ population

    which simplifies to: total emissions = total emissions!