What is the Fascinating World of Chaos Theory?

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Chaos theory explores how small changes in initial conditions can lead to vastly different outcomes, exemplified by weather forecasting. It focuses on deterministic systems rather than random effects, characterized by a positive Lyapunov exponent indicating exponential divergence. This theory is significant both mathematically and philosophically, as it illustrates how complex phenomena can arise from simple rules. The discussion highlights that chaos theory has become mainstream, with recommendations for accessible literature, such as Gleick's book, to better understand its concepts. Overall, chaos theory provides valuable insights into the unpredictability of certain systems.
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what is the chaos theory all about??
 
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Chaos! To be more specific, processes where very small changes in input give wildly different outputs. Weather forecasting more than a day or so in advance is a typical example.
 
For clarification, deterministic systems with great sensitivity in initial conditions. Random effects don't count. Mathematically defined as a positive lyapunov exponent - showing an exponential divergence in initial conditions. Philosophically significant as a way complex effects may be explained in terms of simple ones.

This doesn't really belong here. Chaos is pretty mainstream these days.
 
try finding Gleick's book, its very interesting stuff, nothing too math heavy, but gives a good introduction to what chaos theory is about and how it developed.
 
I think it's easist first to watch a short vidio clip I find these videos very relaxing to watch .. I got to thinking is this being done in the most efficient way? The sand has to be suspended in the water to move it to the outlet ... The faster the water , the more turbulance and the sand stays suspended, so it seems to me the rule of thumb is the hose be aimed towards the outlet at all times .. Many times the workers hit the sand directly which will greatly reduce the water...

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