# The Theory Of Chaos Essay Research Paper — страница 2

movement until they find a condition under which they are in balance. A group of stones which do not touch one another are not a system, because there is no interaction. A system can be modeled. Which means another system which supposedly replicates the behavior ofthe original system can be created. Theoretically, one can take a second group of stones which are the same weight, shape, and density of the first group, pile them in the same way as the first group, and predict that they will fall into a new configuration that is the same as the first group. Or a mathematical representation can be made of the stones through application of Newton’s law of gravity, to predict how future piles of the same type – and of different types of stones – will interact. Mathematical modeling is the key, but not the only modeling process used for systems. The word nonlinear has to do with understanding mathematical models used to describe systems. Before the growth of interest in nonlinear systems, most models were analyzed as though they were linear systems meaning that when the mathematical formulas representing the behavior of the systems were put into a graph form, the results looked like a straight line. Newton used calculus as a mathematical method for showing change in systems within the context of straight lines. And statistics is a process of converting what is usually nonlinear data into a linear format for analysis. Linear systems are the classic scientific system and have been used for hundreds of years, they are not complex, and they are easy to work with because they are very predictable. For example, you would consider a factory a linear system. If more inventory is added to the factory, or more employees are hired, it would stand to reason that more pieces produced by the factory by a significant amount. By changing what goes into a system we should be able to tell what comes out of it. But as any factory manager knows, factories don’t actually work that way. If the amount of people, the inventory, or whatever other variable is changed in the factory you would get widely differing results on a day to day basis from what was predicted. That is because a factory is a complex nonlinear system, like most systems found in nature. When most natural systems are modeled, their mathematical representations do not produce straight lines on graphs, and that the system outputs are extremely difficult to predict. Before the chaos theory was developed, most scientists studied nature and other random things using linear systems. Starting with the work of Sir Isaac Newton, physics has provided a process for modeling nature, and the mathematical equations associated with it have all been linear. When a study resulted in strange answers, when a prediction usually came true but not this one time, the failure was blamed on experimental error or noise. Now, with the advent of the Chaos theory and research into complex systems theory, we know that the “noise” actually was important information about the experiment. When noise is added to the graph results, the results are no longer a straight line, and are not predictable. This noise is what was originally referred to as the chaos in the experiment. Since studying this noise, this chaos, was one of the first concerns of those studying complex systems theory, Glieck originally named the discipline Chaos Theory. Another word that is vital to understanding the Complexity theory is complex. What makes us determine which system is more complex then another? There are many discussions of this question. In Exploring Complexity, Nobel Laureate Ilya Prigogine explains that the complexity of the system is defined by the complexity of the model necessary to effectively predict the behavior of the system. The more the model must look like the actual system to predict system results, the more complex the system is considered to be. The most complex system example is the weather, which, as demonstrated by Edward Lorenz, can only be effectively modeled with an exact duplicate of itself. One example of a simple system to model is to calculate the time it takes for a train to go from city A to city B if it travels at a given speed. To predict the time we need only to know the speed that the train is traveling (in mph) and the distance (in miles). The simple formula would be mph/m, which is a simple system. But the pile of stones, which appears to be a simple system, is actually very complex. If we want to predict which stone will end up at which place in the pile then you would have to know very detailed information about the stones, including their weights, shapes, and starting location of each stone to make an

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