The world is simpler than it seems. Approximation and modeling are surprisingly sufficient to understand how it works. And as Samuel Karlin said, “The purpose of models is not to fit the data, but to sharpen the questions.†Two chapters of Mark Buchanan’s book deal with criticality and using simulation as a way to explore that phenomenon.
There exists a point when the tendency toward ordered and disordered states is at equilibrium. This produces a dynamic state, a point of criticality, where new properties arise. This effect is illustrated by relating the history of magnetism research, beginning with Gilbert’s observations about magnets losing their properties at extreme heat. Onsager — who couldn’t master the immense calculations of all individual polarities of magnetic parts — later devised a simulation of a magnet by greatly simplifying the possible states of each atom. This strategy helped explain, even through abstraction, the mechanics of the phenomenon.
The limited rules lead to insights about a system, but they also help dictate the nature of the simulation outcomes. Bak, Tang and Wisenfeld showed apparent self-organization in their sand pile simulation, but the rules the creators embedded in the game (whether intentionally or not) were initially discounted in analysis of the model. Grains dropped one at a time always pause before the next event until the system again reaches a point of stable equilibrium. This turns out to be an important rule since it allows the opposing forces of the system to operate in separate time frames. The simulation breaks down from a complexity standpoint when grains are dropped while the force of the previous impact is still being distributed into the system. Likewise, dimension and the general shape of the component parts in Gilbert’s simulated magnet are important factors and can lead to universality only when different systems of the same geometry share the same critical point.
The book notes the potentially negative impact intervention has on a system by examining forest fires. In nature, fire and growth are forces in opposition that allow self-organization to occur. When American forest rangers made a successful effort to top fires early before they spread, they inadvertently increased the probability that the self-organization would require a catastrophic response to keep the phases in equilibrium. That catastrophe happened in 1988 and gave a name to the impact of such intervention: “The Yellowstone Effect.”
