should be sufficiently plain that from the inexhaustible well of
mathematics fresh beauty may be drawn. But what of its significance?
Ornament must _mean something_; it must have some relation to the
dominant ideation of the day; it must express the psychological mood.

What is the psychological mood? Ours is an age of transition; we live
in a changing world. On the one hand we witness the breaking up of
many an old thought crystal, on the other we feel the pressure of
those forces which shall create the new. What is nature's first
visible creative act? The formation of a geometrical crystal. The
artist should take this hint, and organize geometry into a new
ornamental mode; by so doing he will prove himself to be in relation
to the _anima mundi_. It is only by the establishment of such a
relation that new beauty comes to birth in the world.

[Illustration: Figure 11.]

Ornament in its primitive manifestations is geometrical rather than
naturalistic. This is in a manner strange, that the abstract and
metaphysical thing should precede the concrete and sensuous. It would
be natural to suppose that man would first imitate the things which
surround him, but the most cursory acquaintance with primitive art
shows that he is much more apt to crudely geometrize. Now it is
not necessary to assume that we are to revert to the conditions of
savagery in order to believe that in this matter of a sound æsthetic
we must begin where art has always begun--with number and geometry.
Nevertheless there is a subtly ironic view which one is justified in
holding in regard to quite obvious aspects of American life, in the
light of which that life appears to have rather more in common with
savagery than with culture.