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Meaning of Chaos Theory in Science
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Chaos Theory
Since its inception, science relied on predictability and order. The true beauty of science was its uncanny ability to find patterns and regularity in seemingly random systems. For centuries the human mind as easily grasped and mastered the concepts of linearity. Physics illustrated the magnificent order to which the natural world obeyed. If there is a God he is indeed mathematical. Until the 19th century Physics explained the processes of the natural world successfully, for the most part. There were still many facets of the universe that were an enigma to physicists. Mathematicians could indeed illustrate patterns in nature but there were many aspects of Mother Nature that remained a mystery to Physicists and Mathematicians alike. Mathematics is an integral part of physics. It provides an order and a guide to thinking; it shows the relationship between many physical phenomenons. The error in mathematics until that point was linearity. “Clouds are not spheres, mountains are not cones, bark is not smooth, nor does lightning travel in a straight line.” - Benoit Mandlebrot. Was it not beyond reason that a process, which is dictated by that regularity, could master a world that shows almost no predictability whatsoever? A new science and a new kind of mathematics were developed that could show the universe’s idiosyncrasies. This new amalgam of mathematics and physics takes the order of linearity and shows how it relates to the unpredictability of the world around us. It is called Chaos Theory.
The secular definition of chaos can be misleading when the word is used in a scientific context. As defined by Webster’s dictionary chaos is total disorder. That may lead one to believe that chaos theory is indeed the study of total disorder, which it truly is not. In 1986 at a prestigious conference on Chaos another definition for chaos was introduced. It is stochastic behavior occurring in a deterministic set. This definition of chaos was hesitantly brought forth. The scientists, mathematicians and intellectuals present were hesitant to define a concept they did not truly understand yet. They left the scientific community with a rather cryptic and oxymoronic definition of chaos. Deterministic sets behave by precise unbreakable law. Stochastic behavior is the opposite of deterministic it has no finite laws, it is totally dependant upon ch...
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...are self-similar; in that case at higher and higher magnification the fractal image resembles the original.
The stock market is indeed chaotic and also self similar. It is truly random, but shows an orderly trend. It is highly dependant upon initial conditions, but because it is nearly impossible to describe those initial conditions it is impossible to predict the action of the market. Short term trading is random and futile. Long term trading however is not random at all. (Gleick 85) A deterministic order comes from chaos over time.
Chaos Theory has made quite an impact on the modern world. Even in its infancy it has been a powerful tool in shaping popular thought of the natural world. Once dismissed as a theoretical science with no practical application, chaos theory has blossomed into an intricate and beautiful pattern, much like the fractals it deals with. Chaos theory is a complex combination of math and physics, but with its mastery comes a new era in the human understanding of the world around us.
A. A violent order is disorder: and
B. A great disorder is an order.
These two things are one
Wallace Stevens
“Connoisseur of Chaos”
The Scientific Context of the Word Chaos In a scientific context, the word chaos has a slightly different
All of the perceptions of spontaneity are one and the same. It's nature's way. "That is the world, that is the tao, but perhaps that makes us feel afraid. We may ask, "If all that is happening spontaneously, who's in charge? I am not in charge, that is pretty obvious, but I hope there is God or somebody looking after all this" (Watts).
“Chaos theory proves that unpredictability is built into our daily lives.”(Crichton 313). Ian Malcolm’s words resolve the book, Jurassic Park, in a very absolute way. Throughout the book, Malcolm, spoke about chaos theory and his self proclaimed “Malcolm Effect” to explain his reasoning in his predictions. Ian Malcolm had predicted the demise of Jurassic Park even before its opening, as well as its multiple problems and difficulties. Malcolm’s theory is evidenced countless times throughout the story of Jurassic Park; dinosaurs are breeding, dinosaurs are escaping, and systems fail.
Indirectly through out his novel, Camus compares people who rely too much on their logic and rationality, versus those who accept that our world is confusing and unpredictable. Similar to his thinking, in “Crickets, Bats, Cats and Chaos” Lewis Thomas suggests that chaos stimulates the brain and actually suggests that even crickets or cats have thoughts during chaotic or unpredictable situations. Even though I have always seen chaos as a total lack of order, a desperate situation in which an individual loses control, Thomas gave me a new concept for chaos. He says that it emerges when a system is altered by a small change or small uncertainty in its interior; chaos is then the
According to Edward Lorenz (founder of the Chaos Theory) chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. (Lorenz 1995: 187)
... in order to affect the world. Chaos becomes, by the end of the novel, nearly
The development of the Chaos began with a computer and mathematic problems of random data that can calculate and predict patterns that repeat themselves. For example, it picks up the pattern of a person’s heart beat and the pattern of snowflakes hitting the ground. Researchers have found that the patterns may be viewed as “unstable”, “random” and “disorderly” they tend to mimic zig-zags, lightning bolts or electrical currents. This theory has not only been used by physicist, but has also been used by astronomers, mathematicians, biologists, and computer scientists. The Chaos Theory can be applied to predict air turbulence, weather and other underlying parts of nature that is not easily understood (Fiero, p.
Michael Guillen, the author of Five Equations that Changed the World, choose five famous mathematician to describe. Each of these mathematicians came up with a significant formula that deals with Physics. One could argue that others could be added to the list but there is no question that these are certainly all contenders for the top five. The book is divided into five sections, one for each of the mathematicians. Each section then has five parts, the prologue, the Veni, the Vidi, the Vici, and the epilogue. The Veni talks about the scientists as a person and their personal life. The Vidi talks about the history of the subject that the scientist talks about. The Vici talks about how the mathematician came up with their most famous formula.
My infatuation in fractals began freshmen year at Greeley after taking a Seminar with one of the seniors. I’m not sure exactly when simple interest turned to a kind of obsession, but during that lesson something seemed to click. It seemed as if this was the universe’s answer to everything; the mystery was solved, however complex the answer was to understand. I’m still not sure if I was misunderstanding the lesson, or if I had somehow seen it for what it really was; a pattern to describe the way the universe works.
In Heart of Darkness, by Joseph Conrad, the strongest conflict is an internal conflict that is most prominently shown in Marlow and Kurtz. This conflict is the struggle between their image of themselves as civilized human beings and the ease of abandoning their morality once they leave society. This inability has a close resemblance to the chaos theory. This is shown through the contrast of Kurtz as told by others and the actuality of him and through the progression of Marlow's character throughout Heart of Darkness.
Howard, T , Rifkin, J. Entropy: A New world View. 1980. New York: Bantam Books. Print.
...t. The Chaos Game can be applied to create other fractals and shapes, and is a major part of an entirely separate area of study: chaos theory. The fact that the Sierpinski Triangle transcends the boundaries of fractal and number theory proves that it is an important part of mathematics. Perhaps the Sierpinski Triangle still holds secrets that, if discovered, will change the way we think about mathematics forever.
Fractal Geometry The world of mathematics usually tends to be thought of as abstract. Complex and imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an explanation to things. The importance of fractal geometry is that it provides an answer, a comprehension, to nature, the world, and the universe.
Chaos theory has numerous application including helping explain phenomena or helping to predict the future. Chaos theory is applicable in various fields ranging from weather, business to medicine. Chaos theory explains the reason why it is practically improbable to predict the weather with the current technology as well as providing a way for people to find patterns in the chaotic system of stock exchange. It also helps with the running of organisation by showing what sort of condition is needed for a profitable business as well as helping doctors predict when heart failure may occur. Fractals which is a concept of chaos theory also is portrayed in the natural world in examples such as lightning and neurons in the brains. Chaos theory has
Abstractions from nature are one the important element in mathematics. Mathematics is a universal subject that has connections to many different areas including nature. [IMAGE] [IMAGE] Bibliography: 1. http://users.powernet.co.uk/bearsoft/Maths.html 2. http://weblife.bangor.ac.uk/cyfrif/eng/resources/spirals.htm 3.