<U>An Introduction To Chaos</U>
Many people believe that twentieth century science will be remebered for three main theories: quantum mechanics, relativity, and chaos. Chaos theory is a blanketing theory that covers all aspects of sciece, hence, it shows up everywhere in the world today: mathematics, physics, biology, finance, and even music. Where classical sciences end, chaos is only beggining.
The term chaos theory is used widely to describe an emerging scientific discipline whose boundries are not clearly defined. The terms complexity theory and complex systems theory provide a better description of the subject matter, but the term chaos theory will be used throughout this document as it is more widely accepted.
Chaos theory is a developing scientific discipline which is focused on the study of nonlinear systems. To uderstand chaos theory, you must first have a grasp upon its roots: systems and the term nonlinear.
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Prior to the devolepment of chaos theory, the majority of scientific study involved attempting to understand the world using linear models. Beginning with the work of Sir Isaac Newton, physics has been the has provided the processes for modeling nature, and the mathematics associated with them have been in a linear nature. Afterwards, when a study resulted in strange answers, when a prediction usually held, but not this one time, the failure was blamed on experimental error, otherwise know as noise.
After research into complex systems, we now know that noise is actually important information about the experiment. When noise is inserted into the graph results, the graph no longer appears as a straight line, nor are its points predictable. At one time, this noise was referred to as the chaos in the experiment. The process of studying the noise in an experiment is one of the major parts of the chaos theory.
Another important word which has been used repeatedly is complex. What is the determining factor making one system more complex than another? The complexity of a 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 the system's results, the more complex the system is considered to be. The most complex system example is the weather (e.a. or finance), which can only be modeled with an exact duplicate of itself.
keyowrds:
chaos theory
complex systems
self-organizing system
http://library.thinkquest.org/3493/noframes/chaos.html