The Politics of the Exponential Function

The ignorance of simple math may very well kill us.

This is the premise of a lecture given by Dr. Albert Bartlett, a retired Professor of Physics from the Univ. of Colorado in Boulder (text, as well as streaming video and audio, can be found here -- highly recommended). The problem, he argues, is a complete ignorance and/or blindness to what exponential growth really means:

Legend has it that the game of chess was invented by a mathematician who worked for a king. The king was very pleased. He said, “I want to reward you.” The mathematician said “My needs are modest. Please take my new chess board and on the first square, place one grain of wheat. On the next square, double the one to make two. On the next square, double the two to make four. Just keep doubling till you've doubled for every square, that will be an adequate payment.” We can guess the king thought, “This foolish man. I was ready to give him a real reward; all he asked for was just a few grains of wheat.”

But let's see what is involved in this. We know there are eight grains on the fourth square. I can get this number, eight, by multiplying three twos together. It's 2x2x2, it's one 2 less than the number of the square. Now that continues in each case. So on the last square, I’d find the number of grains by multiplying 63 twos together.

Now let’s look at the way the totals build up. When we add one grain on the first square, the total on the board is one. We add two grains, that makes a total of three. We put on four grains, now the total is seven. Seven is a grain less than eight, it's a grain less than three twos multiplied together. Fifteen is a grain less than four twos multiplied together. That continues in each case, so when we’re done, the total number of grains will be one grain less than the number I get multiplying 64 twos together. My question is, how much wheat is that?

You know, would that be a nice pile here in the room? Would it fill the building? Would it cover the county to a depth of two meters? How much wheat are we talking about?

The answer is, it's roughly 400 times the 1990 worldwide harvest of wheat. That could be more wheat than humans have harvested in the entire history of the earth. You say, “How did you get such a big number?” and the answer is, it was simple. We just started with one grain, but we let the number grow steadily till it had doubled a mere 63 times.

Now there's something else that’s very important: the growth in any doubling time is greater than the total of all the preceding growth. For example, when I put eight grains on the 4th square, the eight is larger than the total of seven that were already there. I put 32 grains on the 6th square. The 32 is larger than the total of 31 that were already there. Every time the growing quantity doubles, it takes more than all you’d used in all the proceeding growth.

Bartlett then uses the logic of exponential arithmetic to lay out what is wrong with with seemingly innocuous notion that we must always be growing in order to be productive. His analysis of the problem is about as good as you're going to find. Introductory, funny, engaging, and downright chilling when he applies this soberly to our consumptive appetite for energy. In short, his mathematical gaze is to the point: not only is our energy consumption unsustainable (we all know that, right?), but the tipping point is actually right upon us, almost certainly within twenty years. The behooves us to ask, he warns: what will your world look like after the demise of cheap energy?

His only major misstep, in my opinion, is his overriding focus on overpopulation. I don't know. Maybe I'm going to ridiculed for this, but I think this is a potentially very dangerous red herring. Certainly as it is traditionally argued -- and even as Bartlett does here. There is, of course, the mathematical and geographical problem of overpopulation, which will surely lead to a catastrophe. A finite area, such as a city, a state, a nation, or a globe, cannot sustain unending growth. I do not argue that. What Bartlett does, however, and what I find most people do who talk about overpopulation (esp. in the global sense), be they conservative or liberal, is speak fully in the abstract about the problem w/ no real vision of a true solution. What is the typical solution? Namely, education -- be it the conservative vision of abstinence, or the liberal vision of unbridled birth control (or, if they're more "radical," reversing patriarchal hierarchies). Maybe tax cuts for people who stop having kids after one or two. Few, of course, will argue for a mandated systemization of abortion. Even fewer will apply a dark vision that genocide, war, and famine will do our job for us, so perhaps we should leave places like Africa to their own devices.

The problem with this perspective, near as I can tell, is that it assumes a certain equality that simply isn't there. It assumes that we are all individually complicit in such a global problem as overpopulation, in equal measure. Of course, that this perspective results in the Third World getting the stink eye is quite natural, as their populations are exploding far beyond that of the First World, and as such they're clearly not doing their part in this worldwide effort to be smart with Mother Earth. This, though, seems a little convenient.

What is so pernicious about this logic is that the very problem damned by the First World, we who search for the solution overpopulation frantically, is, in fact, caused by the steady march of First World growth. The very thing that now defines the First World! In spite of his absolutely vital critique of this growth, even Bartlett ignores the fact that this philosophy of growth is engrained in the very functioning of the First World. I.e., growth is built into the system in such a way that reality no longer matters -- otherwise, would the fact that advanced western economies are built on debt and credit, the buying and selling of debt unbacked by tangible resources, make sense? There is, I would argue, absolutely no means of reforming capitalism with a little humanitarianism here, and and some compassion there. Our incremental progress that late-capitalism was to bring, at this point, is running perilously close to the end of the cheap and ample resources that brought the First World to its present heights in the first place.

The deficiency of Bartlett's math is that it, near as I can tell, cannot show the socio-economic reality that where there is constant growth, there is also an inevitable decline, in the form of those who do not own the land that produces the goods that churn the wheel of progress. These, rather, are given a different criteria by which to judge their success, versus that of the rest of the world -- their standard of living is judged by comparing it to those who are just as poor or poorer, in such a way that we can justify paying them what amounts to scraps in terms of a First World criteria, because 'it's more than they'd normally get, so they really should be happy.'

And then we have the First World solution to the overpopulation of the very places that it effectively renders, and arguably keeps, poor. (Okay, yes, I realize that China is getting richer; as is India. And while one could argue that this is not likely filtering down to the lowest levels of either society, I would argue that the effects of this growth is built on an ecological and energy-depleting timebomb that extends to the budding middle class of these countries a new kind of poverty, namely, a uniquely modern myopic vision of reality that threatens the very livelihoods that have moved them beyond the slums, and inevitably their lives even to the budding middle-class of these countries. So goes the metaphorical cocktease taking place in emergent economies: the extraordinarily hot virgin (capital) with an inexplicable and incurable venereal disease.) This, despite the fact that where there is poverty, there is typically a population increase -- be it in Africa, or be it in Everwhere Ghetto, USA; as poverty decreases, so does the birth rate -- be it in western Europe or Everywhere Suburb, USA. Where there is poverty, education falls, women's rights decrease, and contraception is less available. We know that social conditions have a tremendous impact on population growth, and yet it is officially a non-starter when one questions the relationship of late-capitalism (which, I say again, is fundamentally indistinguishable from the inexcusably ignorant -- willfully ignorant -- object of Bartlett's dead-on critique). Instead, we mistake the symptom for the disease.

That Bartlett shrinks away from this, to something so abstract as warning us about overpopulation, when the the real problem itself is staring him, us, you & me, square in the face, is telling. It is telling of the disconnect between what we actually know and what we believe to be true.