The greatest ‘divination’ of the ancients was the supremacy which
they assigned to mathematics in all the realms of nature; for in
all of them there is a foundation of mechanics. Even physiology
partakes of figure and number; and Plato is not wrong in
attributing them to the human frame, but in the omission to
observe how little could be explained by them. Thus we may remark
in passing that the most fanciful of ancient philosophies is also
the most nearly verified in fact. The fortunate guess that the
world is a sum of numbers and figures has been the most fruitful
of anticipations. The ‘diatonic’ scale of the Pythagoreans and
Plato suggested to Kepler that the secret of the distances of the
planets from one another was to be found in mathematical
proportions. The doctrine that the heavenly bodies all move in a
circle is known by us to be erroneous; but without such an error
how could the human mind have comprehended the heavens?
Astronomy, even in modern times, has made far greater progress by
the high a priori road than could have been attained by any
other. Yet, strictly speaking—and the remark applies to ancient
physics generally—this high a priori road was based upon a
posteriori grounds. For there were no facts of which the ancients
were so well assured by experience as facts of number. Having
observed that they held good in a few instances, they applied
them everywhere; and in the complexity, of which they were
capable, found the explanation of the equally complex phenomena
of the universe. They seemed to see them in the least things as
well as in the greatest; in atoms, as well as in suns and stars;
in the human body as well as in external nature. And now a
favourite speculation of modern chemistry is the explanation of
qualitative difference by quantitative, which is at present
verified to a certain extent and may hereafter be of far more
universal application. What is this but the atoms of Democritus
and the triangles of Plato? The ancients should not be wholly
deprived of the credit of their guesses because they were unable
to prove them. May they not have had, like the animals, an
instinct of something more than they knew?