Wednesday, June 3, 2020

Chaos Theory



 

From Wikipedia

Chaos theory is a branch of mathematics focusing on the study of chaos—states of dynamical systems whose apparently-random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions.[1][2] Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnectedness, constant feedback loops, repetition, self-similarity, fractals, and self-organization.[3] The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions).[4] A metaphor for this behavior is that a butterfly flapping its wings in China can cause a hurricane in Texas [5].

Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.[6] This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution[7] and is fully determined by their initial conditions, with no random elements involved.[8] In other words, the deterministic nature of these systems does not make them predictable.[9][10] This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as:[11]
Chaos: When the present determines the future, but the approximate present does not approximately determine the future.

Whether in personal confrontation or concerning city wide conflagration

The strongest answer is not always overwhelming force.

 

A portion of our training ought to include being aware of small events that can yield greater results.
 

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