rom the dust-bin
of the ages. What ornamental _motif_ of any universality, worth, or
importance is less than a hundred years old? We continue to use the
honeysuckle, the acanthus, the fret, the egg and dart, not because
they are appropriate to any use we put them to, but because they are
beautiful _per se_. Why are they beautiful? It is not because they
are highly conventionalized representations of natural forms which
are themselves beautiful, but because they express cosmic truths. The
honeysuckle and the acanthus leaf, for example, express the idea
of successive impulses, mounting, attaining a maximum, and
descending--expanding from some focus of force in the manner universal
throughout nature. Science recognizes in the spiral an archetypal
form, whether found in a whirlpool or in a nebula. A fret is a series
of highly conventionalized spirals: translate it from angular to
curved and we have the wave-band; isolate it and we have the volute.
Egg and dart are phallic emblems, female and male; or, if you prefer,
as ellipse and straight line, they are symbols of finite existence
contrasted with infinity. [Figure 1.]

[Illustration: Figure 1.]

Suppose that we determine to divest ourselves of these and other
precious inheritances, not because they have lost their beauty and
meaning, but rather on account of their manifold associations with a
past which the war makes suddenly more remote than slow centuries have
done; suppose that we determine to supplant these symbols with others
no less charged with beauty and meaning, but more directly drawn from
the inexhaustible well of mathematical truth--how shall we set to
work?

We need not _set_ to work, because we have done that already, we are
always doing it, unknowingly, and without knowing the reason why. All
ornamentalists are subjective mathematicians--an amazing statement,
perhaps, but one susceptible of confirmation in countless amusing
ways, of which two will be shown.

[Illustration: Figure 2.]

Consider first your calendar--your calendar whose commonplace face,
having yielded you information as to pay day, due day, and holiday,
you obliterate at the end of each month without a qualm, oblivious to
the fact that were your interests less sordid and personal it would
speak to you of that order which pervades the universe; would make you
realize something of the music of the spheres. For on that familiar
checkerboard of the days are numerical arrangements which are