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Forty Years with Birds and Dogs 

Power Laws--Economics and Complexity

Per Bak in "How Nature Works" pointed out that understanding complex systems requires accounting for fractals and the ubiquity of power law distributions.

Power laws, called 1/f noise, mean there are lots of small events and few large ones and a moderate number of moderate events--like earthquakes. If you plot the frequency vs the size of events, you get a straight line on a log log plot-- frequency is inversely proportional to the power or size of an event. The data are scale free, like fractals, but can breakdown at very small or large values. See Benoit Mandelbrot's "The Misbehavior of Markets." Someone has pointed out that no laws in physics hint at the ubiquity of this observation.

Some interesting examples are the distribution of internet nodes with certain numbers of links, canopy gap size in forests, Zipf's Law--the fraction of cities with so many inhabitants, the frequency of the use of words in English, and economic systems--a realization just now making some waves carrying a touch of hope. Check out the Bibliography in the previous blog.

Since economic systems are certainly complex, they might carry the features--indicators, we've called them--of complex systems, including unpredictability from at least six sources. We'd better get cracking on regulations that protect us against any more unpredictable and "inevitable catastrophes," assumed by power law distributions. We need not stand under the mountain waiting for the avalanche to cut loose again.

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