23 July 2011

Doing the Math on Infinite Growth, It Doesn't Add Up


Since the beginning of the Industrial Revolution, we have seen an impressive and sustained growth in the scale of energy consumption by human civilization. Plotting data from the Energy Information Agency on U.S. energy use since 1650 (1635-1945, 1949-2009, including wood, biomass, fossil fuels, hydro, nuclear, etc.) shows a remarkably steady growth trajectory, characterized by an annual growth rate of 2.9% (see figure). It is important to understand the future trajectory of energy growth because governments and organizations everywhere make assumptions based on the expectation that the growth trend will continue as it has for centuries—and a look at the figure suggests that this is a perfectly reasonable assumption.
Figure 1. Total U.S. Energy consumption in all forms since 1650. The vertical scale is logarithmic, so that an exponential curve resulting from a constant growth rate appears as a straight line. The red line corresponds to an annual growth rate of 2.9%. Data source: EIA.
Growth has become such a mainstay of our existence that we take its continuation as a given. Growth brings many positive benefits, such as cars, television, air travel, and iGadgets. Quality of life improves, health care improves, and, aside from a proliferation of passwords to remember, life tends to become more convenient over time. Growth also brings with it a promise of the future, giving reason to invest in future development in anticipation of a return on the investment. Growth is then the basis for interest rates, loans, and the finance industry.
Because growth has been with us for "countless" generations—meaning that everyone we ever met or our grandparents ever met has experienced it—growth is central to our narrative of who we are and what we do. We therefore have a difficult time imagining a different trajectory.
At this point you may realize that our sun is not the only star in the galaxy. The Milky Way galaxy hosts about 100 billion stars. Lots of energy just spewing into space, there for the taking. Recall that each factor of ten takes us 100 years down the road. One-hundred billion is eleven factors of ten, so 1100 additional years. Thus in about 2500 years from now, we would be using a large galaxy's worth of energy. We know in some detail what humans were doing 2500 years ago. I think I can safely say that I know what we won't be doing 2500 years hence.
Figure 2. Global power demand under sustained 2.3% growth on a logarithmic plot. In 275, 345, and 400 years, we demand all the sunlight hitting land and then the earth as a whole, assuming 20%, 100%, and 100% conversion efficiencies, respectively. In 1350 years, we use as much power as the sun generates. In 2450 years, we use as much as all hundred-billion stars in the Milky Way galaxy. Vertical notes provide historical perspective on how distant these benchmarks are in the context of civilization.
We can explore more exactly the thermodynamic limits to the problem. Earth absorbs abundant energy from the sun—far in excess of our current societal enterprise. The Earth gets rid of its energy by radiating into space, mostly at infrared wavelengths. No other paths are available for heat disposal. The absorption and emission are in near-perfect balance, in fact. If they were not, Earth would slowly heat up or cool down. Indeed, we have diminished the ability of infrared radiation to escape, leading to global warming. Even so, we are still in balance to within less than the 1% level. Because radiated power scales as the fourth power of temperature (when expressed in absolute terms, like Kelvin), we can compute the equilibrium temperature of Earth's surface given additional loading from societal enterprise.
Figure 3. Earth surface temperature given steady 2.3% energy growth, assuming some source other than sunlight is employed to provide our energy needs and that its use transpires on the surface of the planet. Even a dream source like fusion makes for unbearable conditions in a few hundred years if growth continues. Note that the vertical scale is logarithmic.
Once we appreciate that physical growth must one day cease (or reverse), we can come to realize that all economic growth must similarly end. This last point may be hard to swallow, given our ability to innovate, improve efficiency, etc. But this topic will be put off for another post.


More: http://feedproxy.google.com/~r/theoildrum/~3/3vlM3HdLgz4/8155

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