Physics > Economics?

Here’s an interesting contention, from the blog of physicist Tom Murphy:

At that 2.3% [GDP] growth rate, we would be using energy at a rate corresponding to the total solar input striking Earth in a little over 400 years. We would consume something comparable to the entire sun in 1400 years from now. By 2500 years, we would use energy at the rate of the entire Milky Way galaxy—100 billion stars! I think you can see the absurdity of continued energy growth. 2500 years is not that long, from a historical perspective. We know what we were doing 2500 years ago. I think I know what we’re not going to be doing 2500 years hence.

Dr. Murphy, in the form of an embellished true dialogue between himself and an economist, proposes that the laws of thermodynamics constrain (or should constrain) a basic assumption of economic theory–that future economic growth is indefinite. Dr. Murphy’s concern is the production of excess heat through energy generation. He argues, in brief, that:

  1. All energy we use produces excess heat, most of which cannot be radiated into space.
  2. We can improve the heat efficiency of energy generation (e.g. power plants) only up to a ceiling, perhaps two or three times more efficient than current power plants.
  3. Similarly, we can improve the heat efficiency of energy consumption (e.g. light bulbs, computers) only up to a ceiling.
  4. Therefore, we can only produce a finite amount of energy and gain a finite amount of work before we heat the Earth to inhospitable temperatures (e.g. the temperature of boiling, or of the surface of the sun).
  5. Energy is a limiting factor for economic growth. That is, it must always represent at least a minimum fraction of total economic activity (he suggests, for the sake of argument, 1% of GDP).
  6. Therefore, given a finite amount of energy, GDP growth is also limited to a finite cap.
  7. Given certain assumptions about efficiency, we can project that the surface temperature of the Earth will reach 100 degrees Celsius within 400 years.
  8. Since extreme heating would cause untold economic problems, we can reasonably assume that within the coming centuries, economic growth will slow and finally halt.

As Dr. Murphy observes, it’s trivial (though, I believe, ingenious) to demonstrate that growth (in the sense of increasing production and operation of physical objects) is limited as long as we’re limited to planet of finite size. However, his estimate that we may rub up against this limit within a few centuries are suspect to me. I believe the limit is much, much more distant, for several reasons:

  • Computational efficiency is advancing in lockstep with Moore’s law. Feynman calculated that we still have many orders of magnitude of energy efficiency potential even with conventional semiconductor processing. With future technology like quantum computing, could we not achieve many more orders of magnitude beyond that? And since computing is probably the most important terrestrial energy need of the future, those gains should translate to very long-term sustainable improvement in overall energy efficiency.
  • The minimum ratio of energy to GDP may be extremely large, approaching infinite. If energy’s share of the economy plummets, regulations and anti-trust controls (or outright nationalization) should still prevent an individual or entity from imposing catastrophic market distortions. We witness this routinely in scarce goods (like rare earth metals) that are important to wide swaths of the economy. And these tend to be geographically specific. Energy is not, and should thus be even easier to regulate.
  • The ceiling on thermodynamic efficiency of energy generation may be much higher than Dr. Murphy supposes. Efficiency gains are asymptotic to 100%, but that also means heat loss is asymptotic to zero. Why can’t we imagine a fusion plant, or some entirely different technology, climbing toward the asymptote indefinitely?

There is also the problem of defining “growth”. As Dr. Murphy acknowledges, “Under a model in which GDP is fixed—under conditions of stable energy, stable population, steady-state economy: if we accumulate knowledge, improve the quality of life, and thus create an unambiguously more desirable world within which to live, doesn’t this constitute a form of economic growth?”

But I think I’m burying the lede here. What’s most provocative about Dr. Murphy’s dialogue is the notion that physics has something to say about economics. Even introducing psychology and sociology to the study of economics was hard enough. Now the hard sciences, too?

We typically assume that whether or not physics, chemistry, and biology can fully explain complex phenomena like human decision-making and social organization, we lack sufficient information or processing power to make such explanations accurate or practical. There’s such a wide gap between predicting the behavior of a molecule and predicting the outcome of an election that it would be crazy even to try. Instead, we seek statistical or inductive methods to help comprehend those phenomena which defy basic scientific analysis.

Yet here is an example of those methods colliding head-on. Regardless of the economic merits of Dr. Murphy’s argument, his novel observation that thermodynamics ultimately limit economic growth seems indisputable. True, the constraint he posits is only relevant at the fringe of economics–most economists aren’t concerned with long-term macro prediction so much as with historical analysis and short-term prediction. Still, the thermodynamic limit conflicts explicitly with the perpetual-growth assumption of conventional economics. That’s pretty nifty.

Where else do the hard sciences challenge social scientific postulates?

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