__GOTTA RESIST__

Linear relationships are easy to think about: the more the merrier. Linear
equations are solvable, which makes them suitable for textbooks. Linear
systems have an important modular virtue: you can take them apart, and put
them together again - the pieces add up. Nonlinear systems generally cannot
be solved and cannot be added together. In fluid systems and mechanical
systems, the nonlinear terms tend to be the features that people want to
leave out when they try to get a good, simple understanding. Friction, for
example. Without friction a simple linear equation expresses the amount
of energy you need to accelerate a hockey puck. With friction the relationship
gets complicated, because the amount of energy changes depending on how
fast the puck is moving. Nonlinearity means that the act of playing the
game has a way of changing the rules. You cannot assign a constant importance
to friction, because its importance depends on speed. Speed, in turn, depends
on friction. That twisted changeability makes nonlinearity hard to calculate,
but it also creates rich kinds of behavior that never occur in linear systems.
In fluid dynamics, everything boils down to one canonical equation, the
Navier-Stokes equation. It is a miracle of brevity, relating a fluid's velocity,
pressure, density, and viscosity, but it happens to be nonlinear. So the
nature of those relationships often becomes impossible to pin down. Analyzing
the behavior of nonlinear equation like the Navier-Stokes equation is like
walking through a maze whose walls rearrange themselves with each step you
take…

*-- James Gleick in Chaos: Making a New Science, © 1987, pp. 23-24 *