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    Chaos Theory

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    letlight

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    Join date : 2014-04-15

    Chaos Theory

    Post by letlight on Tue Apr 22, 2014 4:59 pm

    Chaos theory is a field of study in mathematics, with applications in several disciplines including meteorology, physics, engineering, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions—a paradigm popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as follows:

    Chaos: When the present determines the future, but the approximate present does not approximately determine the future.
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    DaniFooFani

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    Re: Chaos Theory

    Post by DaniFooFani on Fri Apr 25, 2014 9:46 am

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    DaniFooFani

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    Join date : 2014-04-22

    Re: Chaos Theory

    Post by DaniFooFani on Fri Apr 25, 2014 10:22 am

    I WANTED to post an cool little article I read, but APPARENTLY I can't until my 7 day droog forum anniversary. From skonieczna @ wordpress.com:

    "...Chaos Theory is a dark horse of contemporary science. Two hundred years ago it would be unthinkable – Newtonian perfectly organized world-view, with its deliciously logical mechanics, was too strong to allow any serious benefit of a doubt. A hundred years ago Einstein’s genius abolished the rule of determinism, reductionism and objective knowledge in science – his contribution was so revolutionary and complex that it hasn’t been fully digested yet; practically, one can easy predict, that our 21st century would be a completely different fairy-tale if it wasn’t for that one man and his theories…

    The ‘scandal’ of Chaos in science had started to develop in maths (with regular experiments being conducted in 1920s onwards), then had been followed by physics, chemistry and biology – where scientists observed irregularities, even randomness in the dynamics of systems considered as ‘ordered’ by the traditional views. From various chemical reactions in micro and macro-cosmos to weather and climate – universe has started to display itself as – in fact – infinite chaos, rather than the absolute order, as humankind was keen to believe for ages.

    In natural world, there have always existed structures and phenomena, which proved to be impossible to describe by traditional Euclidean geometry or Newtonian dynamics… Mountains ranges, clouds, coastlines, crystals, lightning, blood vessels - boundless, captivatingly beautiful, unpredictable in its evolution though fairly self-similar, they generate themselves forever expanding accordingly to the rules, which cannot be completely captured or explained, simply because they’re no definite rules… Epitomes of Life per se – the face of Nature in its most primordial, creative and self-sustaining structure… These are FRACTALS – children of the organized chaos of the Universe. Yet “chaos” here doesn’t simply mean ‘anarchy’ but ‘a higher order’ – out of confusion and complexity life emerges as a functioning organism, it may be unpredictable and extremely sensitive to any stimulants – yet – it displays that innate tendency to form into patterns and structures – it fosters and commands order despite of all forces that act against it.

    Fragmented, ‘broken’, complex, inexhaustible – this is the ‘fractal’ theory of existence (transplanting scientific concepts on the philosophical field). One of those very few examples where the nature of the human thought and the nature of the physical world interweave so closely and creatively.

    Focusing on the creativity- ‘fractal’ world-view belongs to the oldest, most pre-thought, deeply spiritual as the example from the ancient “Book of Kells” (above) shows. There are many symbols and primitive art images created by ancient civilizations, which show their intuitive reading of nature as fragmented, ‘fractured’.

    Picasso’s portrait of A. Vollard (above), just like many cubists works from its analytical period picture the fractal vision of reality – looks like art preceded science in its practical applications of the Chaos and Fractal Theory (though calling it with different names)… In many abstract and abstract expressionist works, from P. Klee and J. Pollock to postmodern works (look above -work from the “Fractal Gallery”), often digitally generated one can easily noticed how that chaotic, ‘broken’, non-linear (as opposed to ‘classical’ ordered) representation of reality prevails presenting itself with innovative spirit, confidence and haunting beauty."
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    Maximus

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    Re: Chaos Theory

    Post by Maximus on Tue Apr 29, 2014 12:42 pm


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