ilya_prigogine_isabelle_stengers_alvin_tofflerbookfi-org

73 THE IDENTIFICATION OF THE REAL
evolving, interactive multiplicity thus resisted its reduction to
a timeless and universal scheme.
There were other indications pointing in the same direction.
We have mentioned that trajectories correspond to deterministic
laws; once an initial state is given, the dynamic laws of motion
permit the calculation of trajectories at each point in the
future or the past. However, a trajectory may become intrinsically
indeterminate at certain singular points. For instance, a
rigid pendulum may display two qualitatively different types of
behavior-it may either oscillate or swing around its points of
suspension. If the initial push is just enough to bring it into a
vertical position with zero velocity, the direction in which it
will fall, and therefore the nature of its motion, are indeterminate.
An infinitesimal perturbation would be enough to set it
rotating or oscillating. (This problem of the "instability" of
motion will be discussed fully in Chapter IX.)
It is significant that Maxwell had already stressed the importance
of these singular points. After describing the explosion
of gun cotton, he goes on to say:
In all such cases there is one common circumstancethe
system has a quantity of potential energy, which is
capable of being transformed into motion, but which cannot
begin to be so transformed till the system has reached
a certain configuration, to attain which requires an expenditure
of work, which in certain cases may be infinitesimally
small, and in general bears no definite proportion to the
energy developed in consequence thereof. For example,
the rock loosed by frost and balanced on a singular point
of the mountain-side, the little spark which kindles the
great forest, the little word which sets the world a fighting,
the little scruple which prevents a man from doing his
will, the little spore which blights all the potatoes, the
little gemmule which makes us philosophers or idiots.
Every existence above a certain rank has its singular
points: the higher the rank, the more of them. At these
points, influences whose physical magnitude is too small
to be taken account of by a finite being, may produce
results of the greatest importance. All great results produced
by human endeavour depend on taking advantage
of these singular states when they occur. I4