Chaos and Order

Chaos and order K. Lee Lerner scholar.harvard.edu/kleelerner kleelerner@alumni.harvard.edu This article is part of a series of essays identifying and explaining theories essential to understanding modern scientific thought. This is a DRAFT COPY of an article that appeared in World of Physics and other STEM references (print and online) books published by Thomson Gale or Cnegage Gale. The content of this article was subsequently revised and published in Scientific Thought: In Context, edited by Brenda Wilmoth Lerner and K. Lee Lerner, and published in two volumes by Thomson Gale (now Cengage Gale) in 2010. Chaos and order, as used in chaos theory, are terms used to describe conditions of complex systems in which, out of seemingly random, disordered (aperiodic) processes, there arise processes that are deterministic and predictable. Accordingly, despite its name, chaos theory attempts to identify and quantify order in apparently unpredictable systems. Along with quantum and relativity theories, chaos theory, with its inclusive concepts of chaos and order, is widely regarded as one of the great intellectual leaps of the twentieth century. The modern physical concepts of chaos and order, however, actually trace their roots to classical mechanical concepts introduced in English physicist Sir Isaac Newton's 1686 work, Philosophy Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). It was Newton, one of the inventors of calculus, who revolutionized astronomy and physics by showing that the behavior of all bodies (celestial and terrestrial) was governed by the same laws of , motion which could be expressed as differential equations. These differential equations relate the rates of change of physical quantities to the values of those quantities themselves. Such calculated predictability of physical phenomena led to the concept of a mechanistic, clockwork , universe that operated according to deterministic laws. The idea that the universe operated in strict accord with physical laws was profoundly influential on science, philosophy, and theology. Most physical models are devoted to the understanding of simple systems. For example, kinetic molecular theories often rely on concepts related to a ball bouncing in a box. Using easily quantifiable behavior of such simple systems, theorists often attempt to project the behavior of more complex systems, such as the collision and , dynamics of hundreds of balls bouncing in a box. It was long thought by physicists that, with regard to these types of models, the complexity of a system simply veiled an underlying fundamental simplicity. According to classical deterministic concepts, the accurate analysis and prediction of complex systems, like the determination of the , momentum of a particular ball among hundreds of other balls bouncing and colliding in a box, could be calculated if the initial or starting conditions were accurately known. The fact that itís usually impossible to predict the exact condition or behavior of a system (especially considering that such interactions or measurements of a system must also alter the system itself) is explained away as the result of a lack of knowledge regarding starting conditions or a lack of calculating vigor (e.g., inadequate computing power). Used together, the terms chaos and order fundamentally describe conditions related to the thermodynamic concept of , entropy. Entropy is a measure of thermodynamics , equilibrium used to explain irreversibility in physical and chemical processes. The second law of , thermodynamics specifies that in an isolated system, increasing entropy corresponds to changes in the system over time and that entropy tends toward (a statistical mechanical concept of) maximization. The , second law of thermodynamics dictates that in natural processes, without work being done on a system, there is a movement from order to disorder. According to the laws of thermodynamics, in all natural processes there is a tendency for movement from the ordered state to a more chaotic (disordered) state. Conversely, according to some chaos theory models, chaotic, unpredictable, and , irreversible processes may evolve into or produce ordered states. The study of such mathematical irregularities involving chaos and order remained a relatively unnoticed corner of advanced mathematics until the advent of the digital computer. In 1956, Edward Lorenz, a professor of , meteorology at the Massachusetts Institute of Technology was using 12 recursive equations to simulate basic atmospheric phenomena. Lorenz came to the conclusion that his set of differential equations displayed a sensitive dependence on initial conditions, a sensitivity of the same type that French mathematician Jules-Henri Poincaré had discovered for the Newtonian equations when those equations were applied to celestial dynamics. Lorenz, however, gave this phenomenon a new and highly appealing name, the Butterfly Effect, suggesting that, in the extreme, the flapping of a butterfly's wings in Kansas might be responsible for a monsoon in India a month later. Precise definitions of chaos and order are hotly debated among physicists. The terms themselves presuppose definitions for entropy, complexity, and irreversibility that are anything but well settled in the modern physics community. Regardless, physicists generally agree that the discovery of underlying order, instead of complete randomness, in seemingly chaotic systems is perfectly consistent with the proper application of the laws of thermodynamics. ==Content Redacted== I am the original author of this title and its original publication is noted below my byline. Regardless, publisher's copyright restrictions apply to this content. To remain sensitive to those restrictions. only brief "fair use" selected passages of this work are published herein. Please also note that derivative copies of this work have been licensed to a number of academic resources (both books and online) over the years. Some of these derivatives have been updated by editors of those respective resources and my participation in such updating, while often the case, should not be assumed. Unlicensed or pirated copies of passages from this article may also exist in open online resources. If you have a scholarly interest in reading a complete copy of this work in its original form, please send a request to kleelerner@alumni.harvard.edu or along with a brief note outlining your current affiliation, interest, intended use, and any related questions. I will respond as soon as possible. Cheers, K. Lee Lerner. ================= _______________________ "Recognized for his use of language, accuracy, and balanced presentation, K. Lee Lerner's portfolio covering science and global issues has garnered respected writing, book and media awards. His dossier spans every continent, includes two global circumnavigations, and features coverage from areas suffering civil war, violent protests, drought, famine, and disease outbreaks. That experience, built on a scholarly foundation in science, allows his evidence-based writing to bring clarity to chaotic and complex issues. Contributing editor of more than 40 academic books and writer and/or producer for more than two dozen major media projects, for more than three decades — across print, broadcast media, and digital platforms -- Lerner's 'Taking Bearings,' essays have ranged across the human intellectual enterprise. He has served on the board of advisors for the venerable American Men and Women of Science since 2003 and his Academia site (https://harvard.academia.edu/kleelerner)consistently ranks among those most frequently accessed by students, scholars, and decision makers from around the world." — National Press Club biography. 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