Nonlinear dynamics describes systems in which the forces acting on those systems do not increase linearly with quantities such as position, mass or velocity. It also describes systems which exhibit a "sensitive dependence on their initial conditions." This expression was first coined in the 1960s by the meteorologist Edward Lorenz, who was working on weather prediction models. He realized that a weather parameter curve would diverge from the original input curve if the starting points of the two curves were infinitesimally different. This behavior is now referred to as the butterfly effect, i.e. small changes in initial conditions may lead to qualitatively and quantitatively different long-term behavior. It led Lorenz to conclude that it was impossible to predict the weather accurately because many parameters can cause slight changes to a weather system at one time thus causing the later behavior of the meteorological system to...