# The Theory Of Chaos Essay Research Paper — страница 3

accurate prediction. If there is a minor difference between the shape of one stone in the model and the shape of the original stone, the modeled results will be very different. The system is very complex, thus making prediction very difficult.. The generator of unpredictability in complex systems is what Lorenz calls “sensitivity to initial conditions” or “the butterfly effect.” The concept means that with a complex, nonlinear system, a tiny difference in starting position can lead to greatly varied results. For example, in a difficult pool shot a tiny error in aim causes a slight change in the balls path. However, with each ball it collides with, the ball strays farther and farther from the intended path. Lorenz once said that “if a butterfly is flapping its wings in Argentina and we cannot take that action into account in our weather prediction, then we will fail to predict a thunderstorm over our home town two weeks from now because of this dynamic.”(Lorenz, 1987) The general rule for complex systems is that one cannot create a model that will accurately predict outcomes but one can create models that simulate the processes that the system will go through to create the models. This realization is impacting many activities in business and other industries. For instance, it raises considerable questions relating to the real value of creating organizational visions and mission statements as currently practices. Like physics, the Chaos theory provides a foundation for the study of all other scientific disciplines. It is a variety of methods for incorporating nonlinear dynamics into the study of science. Attempts to change the discipline and make it a separate form of science have been strongly resisted. The work represents a reunification of the sciences for many in the scientific community. One of Lorenz’s best accomplishments supporting the Chaos Theory was the Lorenz Attractor. The Lorenz Attractor is based on three differential equations, three constants, and three initial conditions. The attractor represents the behavior of gas at any given time, and its condition at any given time depends upon its condition at a previous time. If the initial conditions are changed by even a tiny amount, checking the attractor at a later time will show numbers totally different. This is because small differences will reproduce themselves recursively until numbers are entirely unlike the original system with the original initial conditions. But, the plot of the attractor, or the overall behavior of the system will be the same. A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had any secret for us, we could still know the situation approximately. If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon has been predicted, that it is governed by the laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible…” (Poincare, 1973) The Complexity theory has developed from mathematics, biology, and chemistry, but mostly from physics and particularly thermodynamics, the study of turbulence leading to the understanding of self-organizing systems and system states (equilibrium, near equilibrium, the edge of chaos, and chaos). “The concept of entropy is actually the physicists application of the concept of evolution to physical systems. The greater the entropy of a system, the more highly evolved is the system.”( Prigogine, 1974) The Complexity theory is also having a major impact on quantum physics and attempts to reconcile the chaos of quantum physics with the predictability of Newton’s universe. With complexity theory, the distinctions between the different disciplines of sciences are disappearing. For example, fractal research is now used for biological studies. But there is a question as to whether the current research and academic funding will support this move to interdisciplinary research. Complexity is already affecting many aspects of our lives and has a great impacts on all sciences. It is answering previously unsolvable problems in cosmology and quantum mechanics. The understanding of heart arrhythmias and brain functioning

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