h an extraneous utility to attach him to a subject that
has an inherent cogency and charm. Ideas, like other things, have
pleasure in propagation, and even when allowance is made for birth-pangs
and an occasional miscarriage, their native fertility will always
continue to assert itself. The more ideal and frictionless the movement
of thought is, the more perfect must be the physiological engine that
sustains it. The momentum of that silent and secluded growth carries the
mind, with a sense of pure disembodied vision, through the logical
labyrinth; but the momentum is vital, for the truth itself does not
move.

[Sidenote: Its moral value is therefore contingent.]

Whether the airy phantoms thus brought into being are valued and
preserved by the world is an ulterior point of policy which the pregnant
mathematician does not need to consider in bringing to light the
legitimate burden of his thoughts. But were mathematics incapable of
application, did nature and experience, for instance, illustrate nothing
but Parmenides' Being or Hegel's Logic, the dialectical cogency which
mathematics would of course retain would not give this science a very
high place in the Life of Reason. Mathematics would be an amusement, and
though apparently innocent, like a game of patience, it might even turn
out to be a wasteful and foolish exercise for the mind; because to
deepen habits and cultivate pleasures irrelevant to other interests is a
way of alienating ourselves from our general happiness. Distinction and
a curious charm there may well be in such a pursuit, but this quality is
perhaps traceable to affinities and associations with other more
substantial interests, or is due to the ingenious temper it denotes,
which touches that of the wit or magician. Mathematics, if it were
nothing more than a pleasure, might conceivably become a vice. Those
addicted to it might be indulging an atavistic taste at the expense of
their humanity. It would then be in the position now occupied by
mythology and mysticism. Even as it is, mathematicians share with
musicians a certain partiality in their characters and mental
development. Masters in one abstract subject, they may remain children
in the world; exquisite manipulators of the ideal, they may be erratic
and clumsy in their earthly ways. Immense as are the uses and wide the
applications of mathematics, its texture is too thin and inhuman to
employ the whole mind or render it harmonious. It is a scien