What is nonlinear science?
Stanislaw Ulam reportedly said (something like) “Calling a science ‘nonlinear’ is like calling zoology ‘the study of non-human animals’. So why do we have a name that appears to be merely a negative? Firstly, linearity is rather special, and no model of a real system is truly linear. Some things are profitably studied as linear approximations to the real models–for example the fact that Hooke’s law, the linear law of elasticity (strain is proportional to stress) is approximately valid for a pendulum of small amplitude implies that its period is approximately independent of amplitude. However, as the amplitude gets large the period gets longer, a fundamental effect of nonlinearity in the pendulum equations (see http://monet.physik.unibas.ch/~elmer/pendulum/upend.htm and [3.10]). (You might protest that quantum mechanics is the fundamental theory and that it is linear! However this is at the expense of infinite dimensionality which is just as bad or worse–and ‘any’ finite dimensional n
Nonlinear science is one of a number of emerging methodological and theoretical constructs that make up what is often called the “science of complexity.” The popular name for this new science is “chaos theory.” The chaos referred to in the theory is not a lack of organization or order but is, instead, a complex state in which apparant randomness of a system is really constrained by a type of order that is nonlinear.
