The Undiscovered Country and the Final Frontier

Tom Murphy at his Do the Math blog recounts a conversation between an "Exponential Economist" and himself, a "Finite Physicist" (ht Marginal Revolution). Murphy's basic point is this:

Earth’s physical resources—particularly energy—are limited and may prohibit continued growth within centuries, or possibly much shorter depending on the choices we make.

As the discussion continues, Murphy settles on something of an upper limit to growth at around 400 years, which roughly corresponds to two limits. First, in about 400 years the waste heat from our energy use will be so great as to raise the average temperature of Earth to the boiling point. Second, in about 400 years, the energy we use will reach the "total solar input striking Earth."

There are a few specific problems with his argument that need to be countered.

I) The economist in Murphy's discussion says that economic growth is not equivalent to energy growth, and that growth in both GDP and utility can continue even if energy use stagnates. Murphy hand-waves this away by insisting that energy underpins the entire economy and that it will drag down the rest of the economy when it stagnates. Robin Hanson at Overcoming Bias and the commenter Vaniver on Hanson's post both raise direct critiques of Murphy's point. Vaniver points out that even with a constant quantity of energy, the price and therefore percentage of real GDP of energy can continue to rise. Hanson shows mathematically that even if one economic factor is held constant, the economy can continue growing as long as any other factor continues to grow. Hanson agrees that exponential economic growth will eventually cease, but only because he expects "diminishing returns to everything," not just energy or other physical resources.

II) Both of Murphy's above limits rest critically on the assumption that the discussion remains "grounded to Earth," that there is no "exodus to space, colonizing planets, living the Star Trek life, etc." When the economist for whatever reason accepts this assumption, Murphy says he sighed in relief that he wasn't dealing with "a space cadet." Indeed, in a previous blog entry, Murphy had derided the idea that we'll leave Earth as "escapism." You can read his full argument for why we won't go into space at the above link, but it basically amounts to two ideas: space is really, really big ("You just won't believe how vastly, hugely, mindbogglingly big it is," as Douglas Adams would say), and all the good stuff is here on Earth, so why would we even want to leave?

In other words, if we never leave Earth, we'll be doomed to economic stagnation; but we'll never choose to leave Earth, because there's no reason to. Well call me a space cadet, but the counterargument is obvious. If the only way to achieve economic growth is to go into space, why would we ever stay on Earth? Indeed, the more we find ourselves constrained by Murphy's energy limits, the more we will want to go to space and the more resources the market will make available to do so.

His two constraints on energy are easily overcome by a space-based civilization. First, the waste heat of energy use is far easier to get rid of in the depths of space than in Earth's atmosphere; here, the bigness of space works to our advantage. Waste heat is only a constraint if we stay on Earth, which no doubt is why Murphy is so keen to stay on Earth in the first place. Second, there's no reason at all to think that a space-based civilization would be limited to the amount of energy in the sunlight that strikes Earth. The total energy output of the sun is about 2.2 billion times the amount that hits Earth. Even if we don't leave the solar system, and even if we don't become any more energy-efficient than we are right now, that would give us quite a few centuries of extra growth. Even modest gains in energy efficiency will add millennia of extra growth before we hit the limit, and non-solar sources of energy will extend that even further.

Murphy might counter that the space age is over; we once went to the moon but haven't been back for decades, and now even the shuttle will never take flight again. This, of course, ignores the continuing advances being made by other countries and even private organizations, at a time when the only real economic value in space comes from tourism and national bragging rights. By the time Murphy's constraints begin to come into play, there's no reason to think that we'll still be constrained to Earth. A few centuries from now, we could easily be more of a space-based species than a planet-based one, especially once you consider likely advances in genetics and cybernetics that will help us adapt to life in space.

III) In contradiction to Cowen's and Hanson's summaries, Murphy's point is not that exponential growth will stop, but that all growth will stop. He doesn't say our limited resources may prohibit exponential growth, but rather, they "may prohibit continued growth." His epilogue makes it clear that he foresees "a model in which GDP is fixed—under conditions of stable energy, stable population, steady-state economy."

Other commenters on Hanson's post suggested that space only provides linear expansion opportunities, and that we would eventually outpace the speed of light if we grew exponentially. Once our civilization becomes large enough, this is true. If the speed of light is as fundamental a constraint as physicists believe, we will eventually run up against it. But once we've extended our growth limit to the speed of light itself, I think it's fair to say that Murphy's limit of "centuries, or possibly much shorter" has been soundly defeated. Moreover, growth even at some fraction of the speed of light is still growth! We're not going to hit that "steady-state economy" until the accelerating expansion of space pushes all other galaxies beyond the edge of the visible universe in a trillion years or so. Maybe I'm just short-sighted, but that's far enough in the future that it's not gonna keep me up at night.

(Translated from Trek-ese, the title of this post is, of course, The Future and Space.)