This chapter looks at the works of a group called the Dynamic Systems Collective,a small group of physicist that formed in 1977. As a group, they sought ways of connecting theory and experiment. One of thequestions they pondered was could unpredictability itself bemeasured? They found the answer in a Russian concept, the Lyapunov exponent. This number provided a measure of topological quantities that corresponded to unpredictability. The Lyapunov exponent provided a way to measure conflicting effects of a system in phase space. It had the ability to provide a view of properties in a systemthat lead to stability ad instability. All, exponent, which were greater than zero, meant there would be stretching, and all exponents less than zero meant there would becontraction in the system. A Lyapunov exponent of zero meant the system was at some sort of equilibrium.
The Lyapunov exponent is
defined as: After learning about this exponent, the Dynamic Systems Collective group related the exponent to other important properties. They looked at the Information theory and its relation to entropy. This came Second law of Thermodynamics, which states that entropy, or disorder, is constantly increasing. For example, if you divided a tub of water, with barriers, in half and filled one half of the tub with ink and the other half with water, and lifted the barrier, the two liquids would start to mix. However, the mixing will never reverse itself, because it continues to drift towards disorder. To evaluate the level of mixing at a particular point in time would require knowledge of the Information theory, which involves quantifying information. With the information theory, results are measured in bits, as opposed to digits or letters. A bit is either zero or one. The Dynamic Systems Collective was able
I found it very interesting how the information theory could be used to quantify and relay none numerical situations in ways that many people can comprehend.
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