An introduction to mathematics, by A. N. Whitehead.

METHODS OF APPLICATION 31
clear and distinct in his mind, and realizing
their importance and their relevance to the
fall of an apple and the motions of the planets,
he hit upon the law of gravitation and proved
it to be the formula always satisfied in these
various motions.
The vital point in the application of mathematical formula is to have clear ideas and a
correct estimate of their relevance to the
phenomena under observation. No less than
ourselves, our remote ancestors were impressed with the importance of natural
phenomena and with the desirability of taking
energetic measures to regulate the sequence
of events. Under the influence of irrelevant
ideas they executed elaborate religious ceremonies to aid the birth of the new moon, and
performed sacrifices to save the sun during
the crisis of an eclipse. There is no reason to
believe that they were more stupid than we
are. But at that epoch there had not been
opportunity for the slow accumulation of
clear and relevant ideas.
The sort of way in which physical sciences
grow into a form capable of treatment by
mathematical methods is illustrated by the
history of the gradual growth of the science
of electromagnetism. Thunderstorms are
events on a grand scale, arousing terror in
tnen and even animals. From the earliest
times they must have been objects of wild