'Our broken sticks' c/o Roger Lewin "Complexity: life at the edge of chaos"

Chapter 4 Explosions and Extinctions

  'Is Stu being led astray? I asked. "There's something called the broken stick model in statistics," said Dave. In this trick, a random number generator "breaks'' a stick a hundred inches long at twenty-five points, and produces twenty-six short sticks. Measure them, count the number that are one inch long, the number two inches long, and so on, and draw a histogram. You get a skewed distribution, toward the short end, just like many natural phenomena, including the distribution of sizes of U.S. cities, for instance. "One thing you have to remember about extinctions is that some species are more likely than others to die out, just because they exist as small, isolated populations,'' explained Dave. "This sort of statistical quirk can skew your results, easily." So, you would be suspicious of anything that looks like a power law? "I would, because it's common, just in the nature of statistics. It may tell you that a system is poised at a critical point, whatever that means, but it may not. In any case, when Stu says that the curve he gets from my data is close to a power law, he knows that there are many other mathematical models that could fit equally well."
  Clearly, there were many reasons to be cautious about drawing the conclusion that global ecosystems are poised at the edge of chaos, using just the extinction data.' p.80.

 

Hodges' model: Axes (structure) and Domains (content)

If we take the axes of Hodges' model, and break them at twenty-five points, I wonder what we end-up (or start) with?

 

Lewin, Roger. (1993) Complexity: life at the edge of chaos. London : Phoenix [Dent, 1993] ISBN: 1857990285.

Previously: 'complexity' : 'system'