Christian Thomas Kohl The Metaphysical Foundations of Buddhism and Modern Science

qualification not to be analyzed in terms of any things more final than
itself. But an analogous question can be asked, to which Greek thought
was unanimous as to its answer. To what sort of things does the concept
of apply, and in particular what sort of conditions are requisite for its
evocation? The Greek answer to that latter pair of questions was that
beauty belonged to composite things, and that the composition is
beautiful when the many components have obtained in some sense the
proper proportions. This was the Greek doctrine of Harmony, in respect
to which neither Plato nor Aristotle ever waved.
In respect to Harmony, the Greeks made a discovery which is a landmark
in the history of thought. They found out that exact Mathematical
Relationships, as they exist in Geometry and in the numerical proportions
of measurements, are realized in various outstanding examples of
beautiful composition. For instance Archytas discovered that, other
circumstances being equal, the note given out by a stretched string
depends on the length of the string, and that beautiful compositions of
notes correspond to certain simple laws as to the proportional lengths of
the strings. Also they investigated the dependence of the beauty of
architecture upon the preservation of the proper proportions in the
various dimensions. This was an immense discovery, the dependence of
the qualitative elements in the world upon mathematical relations. The
facts had gradually accumulated through thousands of years. The early
Babylonians knew that the qualitative fact of the succession of seasons