All the energy from the Sun

As we have seen, Andrew Leonard is a strong supporter of economic growth (and he shares this perspective with many others across the political spectrum). Opponents of a generalized program of economic growth, such as myself, are often concerned about the damage and resulting ecological instability left in the wake of such a program. Some of these opponents are particularly concerned about the possibility of a catastrophic collapse of our economic system, our environment, or both. In Debunking the peak oil apocalypse, Leonard takes these opponents to task for their emphasis on our dependence on fossil fuels, including Peak Oil theory. He emphasizes that we can still shift away from intense consumption of fossil fuels, replacing them with renewable sources of energy. I notice this refrain often, so let's take a look at it, shall we?

Leonard presents a dramatic and potentially reassuring piece of information:

[A]s Alex Farrell, an assistant professor at U.C. Berkeley's Energy and Resources Groups [sic] notes, global solar energy input to the earth, in a given year, is 5,000 times as great as the amount of energy humans consume in a year. There's some room to maneuver there.

Is that right? Well, as of 2008 we use 15 TW of total energy in our society. (Of course, please note that much of that energy is taken from non-renewable sources.) About 122 PW make it from the Sun to the Earth past its atmosphere, which is 122000 / 15 ≅ 8000 times more than what we currently use. That's well within a reasonable range of Dr. Farrell's figure. As Professor Albert Bartlett likes to intone in his deeply important Arithmetic, Population and Energy, “by most measures you'd say that is an enormous remaining reserve!” It is, after all, the Sun.

Now, we certainly can't just will the photovoltaics (solar panels) into place to capture all this energy as electricity. There are some deep challenges including, but not limited to: engineering and manufacturing time and cost (including physical resources and energy for the manufacturing of the PV panels themselves, sometimes referred to as the "embodied energy" of a manufactured item); efficiency of conversion from sunlight into electricity; ground surface area needed to deploy these panels; and the fact that currently, electricity does not directly meet many of our energy needs. For a sobering perspective on how practical such a renewable energy transition actually may be, I strongly encourage you to refer to Dr. David MacKay's book Sustainable Energy – without the hot air.

Let's make a big leap anyway, and say that we can swap out our current fossil fuel usage for renewable energy from the Sun. Now let's introduce economic growth to the picture. I'm sure you took the time to watch and internalize the principles that Professor Bartlett taught in the lecture that I referenced above, so you understand the basics of exponential growth. How many doubling periods would it take for our consumption to increase 8000 times? Well, that's simply log₂8000 ≅ 13, so our energy consumption needs to double 13 times to reach the total available solar input. What's the length of the doubling period? We saw that this is approximately 70/P years, where P is the percentage growth per year. Economists generally preach that something between 3% and 5% growth is necessary. So the doubling period might be between 70/3 years and 70/5 years, for a total time of between 180 and 300 years until we reach the hard ceiling of what the Sun provides.

We can work out the arithmetic in detail, if you want to follow it more closely. We want to find the point in time when the utilization has grown by 8000 times, where the growth is exponential. Here's the general formula for exponential growth:

x(t) = x₀e^rt = x₀e^(P/100)t

Here, x is the quantity at time t, x₀ is the initial quanity, and r is the rate (or, equivalently, the percentage P divided by 100). What we want to know is the time t at which the quantity is 8000 times the initial quantity:

x(t) = 8000x₀ = x₀e^rt = x₀e^(P/100)t

ln 8000 = (P/100)t

(100/P) ln 8000 = t

Then you just plug in the growth rate P to find out how long it will take, given that growth rate. It is an easy exercise to use this same approach to derive the handy mnemonic for the doubling time, given exponential growth at a particular constant growth rate.

Professor Bartlett has a hilarious segment during his lecture. He brings up Dr. Julian Simon and his book The Ultimate Resource, in which Simon writes:

Clearly there is no meaningful limit to this source except the sun's energy. ... But even if our sun were not as vast as it is, there may well be other suns elsewhere.

Dramatic pause. Bartlett:

Simon's right.
There are other suns elsewhere. But now the question is, would you base public policy on the belief that if we ever need another sun, we'll figure out how to go get it and haul it back into the solar system? Now don't laugh; for decades before his death this man was a trusted policy advisor at the very highest levels in Washington, D.C.

When we move back to reality, where the most accessible source of energy is ancient sunlight stored in chemically fossilized form (e.g. oil, coal, and natural gas), we notice that exponential growth consumes that resource with the same extraordinary speed that would bring us in a few hundred years to total utilization of sunlight in the solar energy fantasy world. Even in stretching to promote some compromise between reality and this fantasy world, Leonard raises a warning:

It's not going to be easy, and there may well be depressions and recessions and wars and other calamities to face along the way, but it is also not by definition impossible.

Well, that's comforting.

All the energy from the Sun

Abstract