Sunday, November 25, 2012
Chaos Theory and Butterfly Effect
Chaos theory is the study of nonlinear dynamics, in which seemingly random events are actually predictable from simple deterministic equations.
In other words, the deterministic nature of these systems does not make them predictable.
This behavior is known as deterministic chaos, or simply chaos.
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions, where a small change at one place in a deterministic nonlinear system can result in large differences to a later state. The name of the effect, coined by Edward Lorenz, is derived from the theoretical example of a hurricane's formation being contingent on whether or not a distant butterfly had flapped its wings several weeks before.
Although the butterfly effect may appear to be an esoteric and unlikely behavior, it is exhibited by very simple systems: for example, a ball placed at the crest of a hill may roll into any of several valleys depending on, among other things, slight differences in initial position.
A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction, positive feedback leads to a self-amplifying chain of events.
Chain reactions are one way in which systems which are in thermodynamic non-equilibrium can release energy or increase entropy in order to reach a state of higher entropy. For example, a system may not be able to reach a lower energy state by releasing energy into the environment, because it is hindered in some way from taking the path that will result in the energy release. If a reaction results in a small energy release making way for more energy releases in an expanding chain, then the system will typically collapse explosively until much or all of the stored energy has been released.
A metaphor for chain reactions is thus a snowball causing larger snowfall until finally an avalanche results ("snowball effect"). This is a result of stored gravitational potential energy seeking a path of release over friction.
Can be roughly grouped into three types:
A positive, unexpected benefit (usually referred to as luck, serendipity or a windfall).
A negative, unexpected detriment occurring in addition to the desired effect of the policy (e.g., while irrigation schemes provide people with water for agriculture, they can increase waterborne diseases that have devastating health effects, such as schistosomiasis).
A perverse effect contrary to what was originally intended (when an intended solution makes a problem worse), such as when a policy has a perverse incentive that causes actions opposite to what was intended.
Possible causes of unintended consequences include the world's inherent complexity (parts of a system responding to changes in the environment), perverse incentives, human stupidity, self-deception, failure to account for human nature or other cognitive or emotional biases.
As a sub-component of complexity (in the scientific sense), the chaotic nature of the universe—and especially its quality of having small, apparently insignificant changes with far-reaching effects (e.g., the butterfly effect)—applies.
Robert K. Merton listed five possible causes of unanticipated consequences
Ignorance (It is impossible to anticipate everything, thereby leading to incomplete analysis)
Error (Incorrect analysis of the problem or following habits that worked in the past but may not apply to the current situation)
Immediate interest, which may override long-term interests
Basic values may require or prohibit certain actions even if the long-term result might be unfavorable (these long-term consequences may eventually cause changes in basic values)
Self-defeating prophecy (Fear of some consequence drives people to find solutions before the problem occurs, thus the non-occurrence of the problem is not anticipated.)
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