Dr Faustus of Modern Physics - Department of Speech, Music and ...

42 CHAPTER 8. WELLPOSED VS ILLPOSED
8.2 Causality as Wellposedness
The most basic principle of science may be viewed to be causality, that a
certain cause has a certain effect, or that a certain effect results from a
certain cause. Causality has an essential time aspect in the sense that an
effect has to come after a cause. By causality predictions can be made: If
the cause is known an effect can be predicted to occur at a later time.
Causality is directly connected to wellposedness: If an arbitrarily small
cause can have a substantial effect, that is if the model is illposed, then
causality is lost in the sense that the cause of an effect is no longer known,
that is the coupling cause-effect is lost.
Figure 8.1: Riding a unicycle is like balancing an inverted pendulum: An
illposed problem.
8.3 Pendulum: Wellposed and Illposed
The motion of a pendulum of a clock is wellposed with a period which is
not sensitive to perturbations. This is why a pendulum can be used to keep
track of time.
On the other hand, the motion of an inverted pendulum is illposed if the
pendulum reaches the top position with small velocity, in which case a small
perturbation may change the direction of the motion. The illposedness is
expressed as the difficulty of balancing an inverted pedndulum.