In a recent blog, I talked about the concept of an energy cycle. At the time, I wanted to draw attention to an analogous concept by Stuart Kaufmann's called "autocatalytic sets". I didn't have time to expand upon this concept so left it out. Fortunately, I've noticed that Stuart Kaufmann has recently published a paper in Scientific American that saves me the effort of explaining some of his thinking. It is called The Evolving Web of Future Wealth (May 9, 2008). Here is a passage in that article that I found particularly interesting:

The web of complements to a good forms a mutually self-reinforcing and cross-reinforcing subnetwork that enhances its own economic growth. For example, with the car came its complements, among them gasoline, paved roads, motels, fast food restaurants and suburbia. In turn suburbia gave rise to an enormous number of consumers of automobiles, gasoline, paved roads and so on. We might call such mutual cross-enhancement "collectively autocatalytic," in that each component helps create the economic environment and market for the others and all mutually benefit. In economic terms, we might call them collective webs of mutually positive "externalities" between complementary technologies. Such collectively autocatalytic webs of complements can drive enormous wealth production, provide a very large investment incentive and massively promote the evolution of future wealth possibilities.

What I have gotten out of this article so far is what I was looking for; namely, the idea that the shift from a fossil-fuel based economy to a green-economy might involve a phase transition rather than an incremental adjustment. According to a "Buttons And Thread" model, you start with a cluster of green businesses denoted by buttons, and as you increase the links between the buttons, denoted by threads, you will reach a phase transition region at a ratio of 1 thread to every two buttons, or a 0.5 ratio. In practical terms, what this might mean is that U.S. policy and investment should be directed at "linking up" green businesses in a strategic way in order to create wealth and hasten a "phase transition" to the green economy in under 10 years as Al Gore aggressively suggests we should aim for.

It is important to note that the "Buttons And Thread" model is easily formalized using random graph theory and that the concept of a "phase transition" in this model denotes the idea that the connectivity ratio changes rapidly from 0.5 to 1.0 once you surpass a threshold ratio of threads to buttons of 0.5. Whereas before the 0.5 ratio you could lift up a button and only pick up a couple of other thread-connected buttons, after the 0.5 point you can increasingly lift a cluster of buttons connected to the button you are trying to pick up. The change between sparse connectivity and dense connectivity is not an incremental change, but rather has the mathematical character of a phase transition.

A useful vocabulary that includes "collectively autocatalytic", "autocalytic sets", "catalytic closure", "reaction networks" and more has been developed by Stuart Kaufmann in his books:

1. At Home in the Universe: The Search for the Laws of Self-Organization and Complexity (Oxford University Press, 1996)
2. Reinventing the Sacred: A New View of Science, Reason, and Religion (Basic Books, New York; May 2008)

I'm currently reading the first book while on vacation. I've had it for awhile but decided to read it once I noticed he had published a new book. Stuart Kaufmann is a wonderful writer and thinker.