Self-Organizing Criticality

Self-Organizing Criticality

Self-organized criticality (SOC) is a property of nonlinear dynamical systems that have a critical point as an attractor, meaning the system endogenously organizes itself into a critical state.1 Phenomena that are a product of SOC exhibit a power law distribution in the frequency of their occurrence. This phenomenon of self-organized criticality has been identified in many different systems from earthquakes to fluctuations within financial markets, to ecological evolution to outbreaks of epidemics and the occurrence of solar flares. Self-organized criticality is typically illustrated with reference to what is called the sandpile model, developed by researcher Pear Bac. The sandpile model was the first model to exhibit self-organized critical behavior, where the system endogenously moves towards its critical (phase transition) point.

Sandpile Model

The sandpile model is taken from the empirical observation that when we drop small grains (of something like sand) on top of each other they will build up into a pile with occasional grains running off, one or two at a time, in proportion to the rate at which we are dropping them, this is the linear equilibrium state to the system’s development, grains of sand are held on the pile by its low incline and the friction from other grains that have already built up (this is the attractor). But at some critical point the pile of sand has built up to such an extent that the incline on the side has reached a critical level, by dropping just one additional grain of sand we can cause a cascading avalanche, a positive feedback as each new grain of sand that cascades down destabilizes the system more which will feedback to effect more grains to slide off. The sandpile phenomenon is a classical example of nonlinear change, here we can note the prolonged period for which the system was held in a stable equilibrium and the very short period of rapid nonlinear change, this is also an illustration of the idea of punctuated equilibrium; prolonged periods of stability and then rapid phase transitions characteristic of nonlinear change. The avalanche is a product of positive feedback the more grains that are falling the more likely they will display additional grains that will then augment the size of the pile and so on a positive feedback loop leading to an avalanche. Thus these self-organized systems like the sand pile are nonlinear in that a small perturbation to the system can have a very negligible effect or it can have a radically disproportionate one where a single grain inputted can cause an entire avalanche, we do not know when it will either.

Power Laws

The size of the avalanche and the number of times it occurs represents a power law distribution, meaning there will very many, very small slides and very flew very large slides, this power law distribution that is a common feature within nonlinear systems allows for events that are statistically virtually impossible within linear system, these very large events are called “black swan” events. Many phenomena exhibit this power law distribution including stock market crashes. Some stock market crashes are so large that they would be virtually impossible given a normal distribution, and this is coming from the positive feedback, of herd behavior in this case.

Self-Organization

To illustrate the self-organizing dimension to SOC we could think about the tragedy of the commons as an example of SOC within social systems. Where out of local events – that is to say by everyone acting in their own rational self-interest, using the commons as much as possible – this will drive the whole system to a critical state where we get the overuse of the commons and global collapse. The point being that this collapse was the attractor to that system. Thus we can say that it is the way that the local rules are setup that creates the destructive global outcome.

Systems Innovation

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