The Chaos theory, sometimes called turbulence, other times 'the theory of nonlinear dynamics', is a complex theory that attempts to explain or define multi-dimensional systems. These multi-dimensional systems range from weather patterns and prediction to the New York stock market trading fluctuations to population growth and if we look deep enough: to our everyday lives.

    The irregular and unpredictable time evolution of many nonlinear systems has been dubbed ‘Chaos’. It’s central characteristic is that the system does not repeat it’s past behavior (even approximately). Despite their lack of regularity, chaotic dynamical systems follow deterministic equations, such as those derived from Newton’s 2^nd law. Edward Lorenz, one of the original "discoverers" or founders of the concept of Chaos, gives us a very interesting example which is often used as to explain the theory, the Butterfly Effect.

    In Australia a butterfly arises from it’s rest place on a flower and flies on to it’s next unknown destination. In order to do this it must flap or move it’s wings. In doing so it creates a small air current or movement. This movement or fluctuation in the air gradually increases, like a that of a wave in the ocean. As this continues to grow, it catches the flow of an ocean current. Ultimately, this air current creates a typhoon and, upon reaching New Guinea, takes numerous lives.

    Of course many would argue that this could never happen. That this is a chain of events that is unrealistic, but how are we to make a definite conclusion? How can this ever be tested, proven or shown to be wrong? While we can not necessarily confirm the destiny of this specific example, we do know that minute changes in an environment do effect the outcome of a system. For example, we all know when we drop a rock (or even a pebble), into a body of water it creates a "ripple" effect. This ripple carries to the edges of this body and reflects back, creating all sorts of distortion (or turbulence) in this previously calm water.

    Lorenz found this out while performing a weather experiment in 1960. He had created a program which, unfortunately, boiled weather down to the barest skeleton. It was the best that could be done in the interest of time, money, and computer access. After every simulated day this program would print a series of numbers which refereed to the changing internal conditions. Although not extremely realistic in the way we think of our world or even a computer simulation of it, Lorenz’s program was ample. Its output of winds and temperatures behaved in a way that seemed very recognizable, in an earthly sort of way. His printouts showed the gradual movements of the west wind, slowly traveling north and then south, again and again. It circled back around in cycles that were predictable, but never exactly same as before.

    One day in the winter of 1961, while comparing data printouts, Lorenz made a decision. Instead of starting the whole trial over from the beginning, he just plugged in the numbers from a midpoint and continued compiling data in this fashion. Little did he know how this simple alteration was about to effect his data. Because this new run should have exactly duplicated the previous information, Lorenz even entered the numbers into the computer himself. Instead, the data changed so rapidly that within a few months, all similarities had disappeared. Upon further investigation, which included checking the vacuum tubes, he realized what had happened. Without real consideration Lorenz had entered ".506", into the computer. The printout he was taking these numbers from actually said ".506127". Obviously what we would consider next to nothing, one part in a thousand, was not inconsequential.

    Sensitivity to initial conditions can be the success or downfall of a system. So what happens as far as human learning and development goes? This sensitivity to all stimulation of a system means that every situation we are involved in effects our whole perspective of the world. Our personality, attitudes, motivation, our whole being are constantly being manipulated by our environment. Not only does this effect adults, but young people are especially susceptible. As psychology demonstrates, children’s personalities are impressionable. Development can be altered when certain activities are, for example, praised or disregarded. What if one time we do not praise a young one, be it consciously or unconsciously, as much as we could? Can this change his/her whole life? It must alter it in some way. But should we really worry about how everything we do is changing everything and everyone around us? Well, it seems like this kind of anxiety could easily drive someone insane. So how does one stay s ane while still being aware of this? Sanity is subjective.

    If Lorenz had not realized what had really happened he could have simply written his mishap off as just "scientific error". Which, for some reason, is a common phrase in the scientific world. So how many other experiments have been skewed or ended, in similar ways? What does this mean about our current knowledge of the world around us and how it works? Should we be skeptical about whether or not so called "facts" are really as concrete as they appear to be or appear to have been proven? Or could it be that our world is changing and the reason something may not be as "on target" or exact as it was, is that the world is constantly changing? Therefore, in the long term, can anything ever really be proven? If this is so, then how can we live our daily lives with the same understanding and confidence? This is life in Chaos.

    Psychologist Philip Zimbardo has a very interesting statement. "An individual responds to reality as it appears subjectively in the individual’s inner world of thoughts and imagination, not as it exists in the objective world." I think this statement sums up Chaos from a humanistic standpoint. Everyone perceives the world differently, yet for some reason, through all this dissimilarity, we have developed common languages, activities, habits, governments and lives. It’s interesting to think of the development of human social interaction in the same Darwinian theory as the physical evolutionary process. Certain attitudes and customs that were, and in some cases still are, considered polite, are now considered unneeded or even offensive. For example in South Africa is it considered polite to burp at the table, it is a sign of a meal that was enjoyed.

    The really interesting thing about Chaos is the way a pattern that seems random, can create such beauty. Fractals are a very fascinating and somewhat melodious way to see Chaos as more than just a theory[see last pages]. Fractals are special kinds of graphic images, pictures (created using computers), which capture a fantastic and delicate structure underlying complexity. The natural world is filled with numerous examples of this. Why flowers are certain colors. Why animals have developed certain skills or over other traits. Why landscapes have developed their hills and valleys.

    Just because someone has never told a lie does not mean that they will not in the future. Science is constantly being reevaluated and changed. A procedure that, just a few years or months ago, was routine for a diagnosis, may not be used anymore because it was found to have harmful side effects. The same thing is happening to other more applicable cases in everyday life.

    In the Hill district of Pittsburgh, there is a high crime rate. We are going to take this as a fact, even though since the last time someone has experienced this first hand, it may have changed. What is fact then? In Chaos there seems to be only one way to tell, by definite experience. By this is it meant that only I can tell what is real or not? No, only what I trust (i.e. what I see and understand) can I consider to be real.

    I see an article in a paper I understand to be non-bias, about a situation in Pittsburgh. I have learned, from my experience, that I can trust what it says because of my past agreement with their stories, or can I? Chaos also teaches us that we can not trust anything for any lengthy period of time (with out reevaluating it), since the world is constantly changing and re-modifying itself. How does this effect us as far as relationships are concerned?

    Can we "really" trust the ones we love? Many would like to hope so. Yes, we can trust them, but we must never forget that (just like the world around us) we, too, are constantly changing, as are our loved ones.

    Does this mean that walking though the Hill district is dangerous? Why? Because previously there has been case after case showing us or pointing us in the direction that "bad" things happen in this area? Somehow this sounds like a superstition, is it the actual ground that the Hill district lays on, or the people who live there? If it is the people, then would they do the same thing if they were in another area? Chaos shows us that the near future is somewhat predictable, therefore, since a crime has occurred within the last week, it would be safe assume that it will happened again. But why? If no crimes have been committed in a year would that mean that the Hill is safe now? Can an area that used to be crime ridden, ever become safe?

    If a gun is brandished and never used, then it becomes somewhat routine to a person. Does that mean that every time a gun is pulled it will not be used? From experience, be it personal or otherwise, we can disagree. A situation involving a gun is exactly the kind of chaos that is everyday life. Many people simply blow off this by saying that it will never happen to them. But we can not predict the long-term future, therefore how can that statement be finite?

    Chaos is where mathematicians, physicists, biologists, economists, and chemists all have something in common. Irregularity. Irregularity that seems surprisingly regular when observed closely. James Gleick says in his book, appropriately entitled CHAOS, "Where Chaos begins, classical science stops." So how can this theory explain the world around us so well?

    When we understand Chaos, we look at things from a different angle. Since we can not predict the long-term future, why try? It would seem all we can do is continue our lives without attempting to predict life so much. To live in the now, while remembering that the future is only predictable in the short term. Not forgetting the future, just remembering that it is not definite/chaotic (depending on your perspective). We never know how close death is, be it accidental or intentional.

    The Chaos theory is less of an explanation or reason that a certain event or circumstance will happen, as much as it is a justification for why something did occur. Christia Vidal, a French scientist, who co-wrote the book Order within Chaos, has a very interesting statement related to this. "What the [Chaos] theory does not at all specify is the set of circumstances which must be united for a given sequence of events ending in chaos to occur. The Theory does not define, at least not yet, the prerequisites for chaotic behavior". Then how can this theory be so influential in our world? It would seem that the direction of systems is never to be predicted. This understanding of unpredictability in everyday life is Chaos. It is not the "answer to all", but merely a way to believe we understand it all. By using a term that is applicable to everything, we feel more at ease with our changing environment. Much like the order of this paper, Chaos is seen in an infinite array of examples.

    David Ruelle, author of Chance and Chaos, has a way to apply Chaos directly to life. "I suggest that you now engage in a noble and fulfilling enterprise: creating life." All the ‘randomness’ that creates your child (gene combinations, cell mutation, character traits, etc) is Chaos. Therefore your child is a direct result of Chaos. A living, breathing, piece of you, that is Chaos.

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Gleick, James. CHAOS. Harrisonburg, Va: Viking Penguin Inc., 1987.

Baker, Gregory L., and Jerry P. Gollub. Chaotic dynamics: an introduction. Cambridge: ScotPrint Ltd. Musselburgh, 1990.

Berge, Pierre, Yves Pomeau, and Christian Vidal (translated by Laurette Tuckerman). Order Within Chaos. France: Hermann and John Wiley & Sons, Inc., 1988.

Ruelle, David. Chance and Chaos. Princeton NJ: PrincetonUniversity Press, 1991.

Zimbardo, Philip G., and Ann L. Weber. Psychology. New York, NY: R. R. Donnelley & Sons Company, 1994.

Barnsley, Micheal F. (editor). Chaotic Dynamics and Fractals. San Diego, CA: Academic Press, Inc., 1986.

Tompson, J. M. T., and H.B. Stewart. Nonlinear Dynamic and Chaos. Great Britain: John Wiley & Sons, Inc., 1987.