This graph shows frequency of earthquakes versus intensity. Note that intensity is a log scale, so if you go from a 6 to 7 on the Richter scale you're moving up by about an order of magnitude in terms of the severity of the quake. This relationship is very typical of the behavior of complex systems. It means that more intense earthquakes are rarer than less intense ones -- that's the good news -- but the frequency falls off much more slowly than the danger of the quakes increase. That means that if you consider the total impact of all earthquakes, a disproportionate amount of the punch is concentrated at the right end of the curve.
Notwithstanding our best efforts at prediction, from time to time the world presents us with nasty surprises. Freak events of this kind present a dilemma to policymakers. It would be paranoid to assume that the worst will always happen. Yet, perhaps paradoxically, it is reasonably foreseeable that non-reasonably foreseeable events will occur from time to time. A planning process that ignores this reality will work satisfactorily nearly all of the time, but when failures do occur they may be catastrophic. The overwhelming majority of the Lincoln family=s theater outings went smoothly, but Mrs. Lincoln doubtless took little comfort from this observation.
Environmental regulation has grappled with this problem for several decades. This essay assesses those efforts in light of the developing theory of dynamic systems, sometimes called complexity theory or chaos theory. One lesson of complexity theory involves the peculiar statistical behavior of complex systems. Even people who have never heard of a bell curve (a/k/a normal distribution) have an intuitive sense of its properties, with most events bunched near the average and extreme outcomes fading away quickly. If the average cat weights ten pounds, we can expect that most cats will be within a few pounds of the average, and we can safely disregard the possibility of a two-hundred pound tabby. But complex systems are often characterized by a different kind of statistical distribution called a power law. If cats’ weights were subject to a power law, we would find that the vast majority of cats were tiny or even microscopic, but that thousand-pound house cats would cross our paths now and then. Under a power law, the possibility of freak outcomes (a one-ton Siamese) weighs heavily in the analysis, often more heavily than the far more numerous routine outcomes (the tiny micro-cats). The harmless kittens that litter your path would be much less of an issue than the enraged saber-tooth you you might encounter once in a lifetime. Indeed, a power-law probability distribution makes it somewhat misleading to even talk about the attypical, given the huge range of possibilities.
Ecological thought has moved away from the idea of equilibrium toward a more dynamic vision, as Fred Bosselman and Dan Tarlock have explained:
[E]cology is following physics as it owes much to chaos theory. Non-equilibrium ecology rejects the vision of a balance of nature. Change and instability are the new constants. . . . Ecosystems are patches or collections of conditions that exist for finite periods of time. The accelerating interaction between humans and the natural environment makes it impossible to return to an ideal state of nature. At best, ecosystems can be managed rather than restored or preserved, and management will consist of series of calculated risky experiments.Rather than following the familiar normal distribution, the bell curve, outcomes in complex systems often follow what are called power laws -- that is, the frequency of an event is often given by its magnitude taken to a fixed negative exponent. A classic example is given by earthquakes. Other examples include the size of extinction events, the number of species present in a habitat, or the size of the Nth smallest species (meaning that almost all species are rare but a few have very large populations).
What all of this adds up to is that the world behaves less “normally” than we would expect. We are lulled into complacency by a host of small events, assuming that larger events will be on the same scale. We get used to hurricanes as an annual, almost routine event in parts of the country. Then Katrina comes along.
We need to adjust our planning to deal with a chaotic world. Systems that are designed for the routine or the slightly surprise will not hold us in good stead when the catastrophic happens. Katrina provides us an example of this, which we should not forget – but which we are likely to forget over time, unless we take steps to build long-term institutions based on this insight.
We're only beginning to figure out how to construct such institutions. In the next few postings, I'll be discussing some modest steps forward that we could take with FEMA, the Army Corps of Engineers, and other government agencies.