Chaos Theory: A Brief History and Its Applications to Arcadia

Chaos Theory



Fractal Game!


Where chaos begins, classical science stops."
James Gleick
"The century's third great revolution in physical sciences."
Gleick

Chaos Theory:
The study of complex nonlinear dynamic systems and forever changing complex systems based on mathematical concepts of recursion. Known as the irregular side of science- its discontinuities and erratic sides. Deals with connection between different types of irregularity.

IMAGE OF FRACTAL"The chaos theory predicts that complex nonlinear systems are inherently unpredictable- but, at the same time, chaos theory also insures that often, the way to express such an unpredictable system lies not in exact equations, but in representation of the behavior of a system- in plots of strange attractors or in fractals." Gleick

Chaos is not about disorder! The word chaos stands for the very essence of order!

History:

The chaos theory, first discovered by Edward Lorenz in the 1960's, essentially states that simple systems may actually produce complex behavior. On the other hand, it has also been proven that complex systems actually have a simple underlying order. Fractals are an important part of chaos, exemplifying the beauty and symmetrical magic of the chaos theory. Fractals in geometry may be the single most perfect way to express the chaos theory and its principles. Although at first one may think "chaos" is unpredictable and random, in actuality, chaos is the very essence of order. Although chaos deals with the erratic side of science and math, it produces a concrete order in every seemingly random iteration or problem.

Relation to Arcadia:

As Valentine explains to Hannah on page 47, " The unpredictable and predetermined unfold together to make everything the way it is. It's how nature creates itself, on every scale, the snowflake and the snowstorm." They argue about the possibilities of chaos as they attempt to figure out what Thomasina was really on to in her discoveries. They soon realize she had gotten a grip on the concept of iterated algorithms during her experiment with the leaf and its relation to fractal geometry. At this point in the play, the reader becomes aware of Thomasina's brilliance. She has already begun to study and understand the complex concept of the chaos theory. This also links the two time periods of the play together when Valentine is expressing his knowledge of the topic. The characters of the present learn that Thomasina was already onto this subject at her extremely young age.

The chaos theory is also present throughout the play during discussions of Valentine's grouse project. He speaks of the importance of iterated algorithms in calculating the grouse population in a given year. In the situation of determining the growth of a certain species over a period of time, x is the number of animals and y is the result. The equation summarizes the effect of the environment on the number of animals each year and their fluctuations in population.

Arcadia's explanation of noise also relates to the chaos theory. When working on the grouse project, Valentine refers to noise as the impracticalities and unpredictable variables of the equation. He refers to the extremely small factors in nature that, in result, come to have a major impact on the outcome. Thank you for visiting the "Chaos in Arcadia" web page!!!!

An outstanding site for the examination of these mathematical concepts and their relation to the play is Chaos, Fractals and Arcadia which you may link by clicking the title. If you are interested in a more in depth discussion and every day life application of chaos theory, you might want to visit this page


Page by Jessica Lind and Annie Casey

Bibliography:

Gleick, James. Chaos. Penguin Books, 1987.

Briggs and Peat. Turbulent Mirror. Harper and Row, 1989.

Fied and Golbitsky. Symmetry in Chaos. Oxford University Press, 1992.



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