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.