John Schwartz and the New York Times gave us an unusually thoughtful piece of journalism last Saturday: No Easy Way To Restrict Construction In Risky Areas. Several cases are examined: Oso Landslide, Sandy, Katrina and more.
This is largely an issue of the transfer, avoidance, reduction, or acceptance of risk. Very closely related are attitudes toward contingency.
The Oso landslide is a specific case where “complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or punctuations of all sizes.” Other dynamical systems include seismic networks, volcanoes, ocean currents and I would include the electrical grid and significant concentrations (populations) of almost anything.
In a seminal 1995 paper Per Bak and Maya Paczuski outline two very different explanations of the same “punctuation” event:
A Historian Describes a Sandslide.
On December 16, 1994, a grain of sand landed at the site with coordinates [14, 17] on the pile. Adding to the grains of sand already accumulated at this site, this addition caused a toppling of that site, spilling over to the neighboring sites. Unfortunately, one of these sites [14, 18] happened to be near an instability so that the toppling caused this site to topple also. This toppling destabilized sites [14, 19] and [15, 18] and eventually led to the collapse of a large part of the pile. “Clearly, the event was contingent on several factors. First, had the initial grain of sand fallen elsewhere, nothing dramatic would have happened. Also, if the configuration at position [14, 19] had been slightly different, the sandslide would have stopped sooner, without devastating consequences. While we can give an accurate and complete account of what actually happened, we are at a loss to explain how these many accidental features could possibly have conspired to produce an event of such magnitude. The event was contingent upon many separate, freak occurrences and could clearly have been prevented. Furthermore, we are baffled by the fact that even though sand had been added to the system for a longtime, only minor events had occurred before the devastating collapse, and we had every right to expect the system to be stable. Clearly, the event was a freak one caused by very unusual and unfortunate circumstances in an otherwise stable system that appeared to be in balance. Precautions should and could be taken to prevent such events in the future.
A Physicist Describes a Sandslide
During a long transient period, the pile evolved to a critical state with avalanches of all sizes. We were able to make a rough identification of the toppling rule and to construct a computer model of the phenomenon. Actually, the particular rule that we use is not very important. In any case, we do not have sufficient information about the details of the system to be able to make long-term predictions. “Nevertheless, our model exhibits some general features of the sandpile. We monitored how many avalanches of each size occurred, after the addition of a single grain to the pile. We made a histogram (Fig. 2), and found that the distribution of events where a total of s sites topple obeys a power law, P(s)- s-T. Thus, if one waits long enough, one is bound to see events that are as large as one has the patience to wait for. We ran our simulations (the tape of evolution) several times. Eliminating the particular grain of sand that caused a particular avalanche only made the system produce large avalanches somewhere else at different times. Changing the rules slightly — for instance, by planting snow screens here and there — does not have any effect on the general pattern.
Avalanches are an unavoidable and intrinsic part of the sandpile dynamics. “Actually, I’m not interested in the specific details of the event which Prof. Historian is so excited about and gives such a vivid account of. What the professor sees as a string of freak events appearing accidentally and mysteriously by an apparent act of God and leading to a catastrophe is simply a manifestation of the criticality of the system. History has prepared the sandpile in a state that is far from equilibrium, and the matrix through which the avalanche propagates is predisposed to accommodate events of large sizes. The complex dynamics which is observed in the ‘historical science,’ where the outcome appears contingent on many different, specific events, represents the dynamics of self-organized critical systems.
Historical narrative is inclined toward an understanding of reality where human intention, rationality and will can assert control. Bak and Paczuski point toward the possibility of domains beyond our power, though certainly deserving our attention and respect.