inclined to attach no importance to it, seemed, itself, to be something
wonderful. Here in Geometry and Arithmetic, here was order and harmony
unsurpassed and unsurpassable. What wonder then that Pythagoras concluded
that the solution of the mighty riddle of the Universe was contained in
the mysteries of Geometry? What wonder that he read mystic meanings into
the laws of Arithmetic, and believed Number to be the explanation and
origin of all that is?"[1]


[1] _A Mathematical Theory of Spirit_ (1912), pp. 64-65.


No doubt the Pythagorean theory suffers from a defect similar
to that of the Kabalistic doctrine, which, starting from the fact
that all words are composed of letters, representing the primary
sounds of language, maintained that all the things represented
by these words were created by God by means of the twenty-two letters
of the Hebrew alphabet. But at the same time the Pythagorean
theory certainly embodies a considerable element of truth.
Modern science demonstrates nothing more clearly than the importance
of numerical relationships. Indeed, "the history of science shows us
the gradual transformation of crude facts of experience into increasingly
exact generalisations by the application to them of mathematics.
The enormous advances that have been made in recent years in
physics and chemistry are very largely due to mathematical methods
of interpreting and co-ordinating facts experimentally revealed,
whereby further experiments have been suggested, the results of
which have themselves been mathematically interpreted. Both physics
and chemistry, especially the former, are now highly mathematical.
In the biological sciences and especially in psychology it is true