which by the clash of innate
antagonisms developed into a knowable universe (see above, pp. 12, 16).
But one can easily imagine that once the idea of Number became
associated with that of the knowable in things, a wide field of
detailed development and experiment, so to speak, in the arcana of
nature, seemed to be opened. Every arithmetical or geometrical theorem
became in this view another window giving light into the secret heart
of things. Number became a kind of god, a revealer; and the philosophy
of number a kind of religion or mystery. And this is why the {26}
second grade of disciples were called Mathematicians; mathematics was
the essential preparation for and initiation into philosophy.

Whether that which truly exists was actually identical with Number or
Numbers, or whether it was something different from Number, but had a
certain relation to Number; whether if there were such a relation, this
was merely a relation of analogy or of conformability, or whether
Number were something actually embodied in that which truly
exists--these were speculative questions which were variously answered
by various teachers, and which probably interested the later more than
the earlier leaders of the school.

[56]

A further question arose: Assuming that ultimately the elements of
knowable existence are but two, the One or Definite, and the Manifold
or Indefinite, it was argued by some that there must be some third or
higher principle governing the relations of these; there must be some
law or harmony which shall render their intelligible union [57]
possible. This principle of union was God, ever-living, ever One,
eternal, immovable, self-identical. [58] This was the supreme reality,
the Odd-Even or Many in One, One in Many, in whom was gathered up, as
in an eternal harmony, all the contrarieties of lower [61] existence.
Through the interchange and intergrowth of these contrarieties God
realises Himself; the {27} universe in its evolution is the
self-picturing of God. [62] God is diffused as the seminal principle
throughout [68] the universe; He is the Soul of the world, and the
world itself is God in process. The world, therefore, is in a sense a
living creature. At its heart and circumference are purest fire;
between these circle the sun, the moon, and the five planets, whose
ordered movements, as of seven chords, produce an eternal music, the
'Music of the Spheres.' Earth, too, like the planets, is a celestial