One of the impulses behind science is the desire to gain reliable knowledge about the world so that we can control it. There is no denying the extraordinary success of this enterprise, which has given us electrical illumination, television, jet aircraft, antibiotics, computers, artificial pacemakers for the heart -- the list goes on. The principle that underlies these technologies is an orderly and predictable relationship between cause and effect. More often than not the relationship is linear: the illumination from the light bulb changes in direct proportion to the amount the dimmer switch is turned; the power from the jet engines varies directly with the movement of the throttle. But the linear relationship between cause and effect in such processes holds only over a limited range; it always fails if that range is exceeded.
Nonlinearity does not mean that control is not possible. Plenty of nonlinear processes are orderly, predictable, and hence controllable. The pendulum of a grandfather clock follows a well-defined, stable cycle of nonlinear motion. Small extraneous impulses to the pendulum coming from mechanical disturbances of the clock, such as walking past it on a wooden floor, don't knock it from one periodic orbit to another, as would happen in a linear system in which impulses permanently change the motion (i.e., the whole of a linear system is the sum of its parts, which include extraneous perturbations).
The pendulum of a clock always returns to the same stable cycle, a limit cycle, which is determined by the length and mass of the pendulum and the amount of energy added each cycle by the escapement mechanism. We control the period of the cycle simply by altering the length of the pendulum so that the clock can be adjusted to keep accurate time, as long as you remember to wind it up once a week.
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