s consist of discrete particles, and are hence measurable
in numerical terms. But modern science is also obliged to postulate an
ether behind these atoms, an ether which is wholly continuous, and hence
transcends the domain of number.(1) It is true that, in quite recent
times, a certain school of thought has argued that the ether is
also atomic in constitution--that all things, indeed, have a grained
structure, even forces being made up of a large number of quantums
or indivisible units of force. But this view has not gained general
acceptance, and it seems to necessitate the postulation of an ether
beyond the ether, filling the interspaces between its atoms, to obviate
the difficulty of conceiving of action at a distance.

(1) Cf. chap. iii., "On Nature as the Embodiment of Number," of my _A
Mathematical Theory of Spirit_, to which reference has already been
made.

According to BERGSON, life--the reality that can only be lived, not
understood--is absolutely continuous (_i.e_. not amenable to numerical
treatment). It is because life is absolutely continuous that we cannot,
he says, understand it; for reason acts discontinuously, grasping only,
so to speak, a cinematographic view of life, made up of an immense
number of instantaneous glimpses. All that passes between the glimpses
is lost, and so the true whole, reason can never synthesise from that
which it possesses. On the other hand, one might also argue--extending,
in a way, the teaching of the physical sciences of the period between
the postulation of DALTON'S atomic theory and the discovery of the
significance of the ether of space--that reality is essentially
discontinuous, our idea that it is continuous being a mere illusion
arising from the coarseness of our senses. That might provide a complete
vindication of the Pythagorean view; but a better vindication, if not
of that theory, at any rate of PYTHAGORAS' philosophical attitude,
is forthcoming, I think, in the fact that modern mathematics has
transcended the shackles of number, and has enlarged her kingdom, so as
to include quantities other than numerical. PYTHAGORAS, had he been
born in these latter centuries, would surely have rejoiced in this,
enlargement, whereby the continuous as well as the discontinuous is
brought, if not under the rule of number, under the rule of mathematics
indeed.

PYTHAGORAS' foremost achievement in mathematics I have already
mentioned. Another notable piece of work in the sa