ion 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 that mathematical
methods are, as yet, not so largely employed. But these sciences are far
less highly developed, far less exact and systematic, that is to say,
far less scientific, at present, than is either physics or chemistry.
However, the application of statistical methods promises good results,
and there are not wanting generalisations already arrived at which
are expressible mathematically; Weber's Law in psychology, and the law
concerning the arrangement of the leaves about the stems of plants in
biology, may be instanced as cases in point."(1)

(1) Quoted from a lecture by the present writer on "The Law of
Correspondences Mathematically Considered," delivered before The
Theological and Philosophical Society on 26th April 1912, and published
in _Morning Light_, vol. xxxv (1912), p. 434 _et seq_.

The Pythagorean doctrine of the Cosmos, in its most reasonable form,
however, is confronted with one great difficulty which it seems
incapable of overcoming, namely, that of continuity. Modern science,
with its atomic theories of matter and electricity, does, indeed, show
us that the apparent continuity of material things is spurious, that all
material thing