Exponential growth: From optimism to absurdity

In the last article, I made the claim that economic growth is necessarily finite, and that an economic system that requires continuous growth is, over the long term, impossible. This is obvious; unchecked growth with finite resources is impossible. It is instructive, nevertheless, to quantify this. What does, say, 2.5% annual growth mean in tangible terms? And, more importantly, how close are we to hitting- or overshooting- the limits?

Just how much can the economy grow?

Consider, for a moment, annual growth of 2.5%. That sounds pretty mediocre when you're talking about your retirement savings, but it's on the optimistic side for the complete economies of the developed nations. At 2.5% growth, our rates of consumption of energy and resources would, after a decade, be 30% higher than at present. They'll have expanded to 11.8 times their current values after a century. Imagine the USA filled with 3.7 billion people, extracting, consuming and throwing away a dozen times as much stuff as it currently does. It is difficult to believe it is possible.

Surely, though, slower growth will be more sustainable? Such thinking would be fallacious; slowing the rate of growth only changes the timelines without changing the fundamental problem. Even a miserable 1% annual growth, considered by politicians and businesspeople to be just barely out of recession territory, gives a 10.5% increase after a decade. A century of this still brings a 2.7-fold increase in production and consumption; after 246 years, we're at the same 11.8x increase as previously. Cutting growth to "AAAH Recession!!!" levels, permanently, only bought us another century and a half.

A substantial fraction of the world is currently aspiring to growth rates around 10%. That's a 2.8-fold increase every decade; a century of 10% growth would grow the economy to 13,780 times its present size. Clearly, such rapid growth is only possible for very short terms, and then only when the starting point is awfully close to zero.

Taking the argument to a plausible and yet completely absurd limit, let us suppose that we want our industrialized society to endure for a thousand years. This is less than a blink of an eye in geological time, and several ancient civilizationss endured far longer. A millennium of 2.5% growth is a 52,949,930,180-fold increase. That kind of growth in the resource sector would have us strip-mining the crust of Earth-sized planets to bare rock at the rate of eight planets per second(1). In the energy sector, a millennium of 2.5% growth would require us to have figured out how to harness 0.25% of the total output of the Sun, with only a bit over 200 years remaining in which to build a Dyson sphere that would collect every last watt of the Sun's output for our use.

Closer Limits

The preceding examples are, evidently, not our real limits. Other factors will get in the way long before we'd consider strip-mining planets by the millions.

In the next few articles, we will look at these factors (energy, arable land, population, resources) in more detail. In some cases, we have a bit of room to breathe; in others, we've already overshot critical turning points. The energy sector's up first. Stay tuned.


(1) Assuming that, averaged over all mineral resources of interest, we have 200 years of total resources remaining at current extraction rates before there is simply no interesting metal left anywhere we could conceivably get to it. This is of course a huge approximation, but a 100-fold increase in this estimate only takes us from "planets per second" to a similarly absurd "planets per minute". And, of course, any society that can use this much material this quickly is likely chopping up the whole planet, not just picking the good stuff out of the crust.

(2)Total solar output is 3.846x1026 W. Total worldwide primary energy production is 5.553x1020 J/year, or 1.761x1013 W.



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