[Illustration: Figure 12.]

[Illustration: Figure 13.]

The submersion of scholarship by athletics in our colleges is a case
in point, the contest of muscles exciting much more interest and
enthusiasm than any contest of wits. We persist in the savage habit of
devouring the corpses of slain animals long after the necessity for it
is past, and some even murder innocent wild creatures, giving to their
ferocity the name of sport. Our women bedeck themselves with furs and
feathers, the fruit of mercenary and systematic slaughter; we perform
orgiastic dances to the music of horns and drums and cymbals--in
short, we have the savage psychology without its vital religious
instinct and its sure decorative sense for color and form.

But this is of course true only of the surface and sunlit shadows of
the great democratic tide. Its depths conceal every kind of subtlety
and sophistication, high endeavour, and a response to beauty and
wisdom of a sort far removed from the amoeba stage of development
above sketched. Of this latter stage the simple figures of Euclidian
plane and solid geometry--figures which any child can understand--are
the appropriate symbols, but for that other more developed state of
consciousness--less apparent but more important--these will not do.
Something more sophisticated and recondite must be sought for if we
are to have an ornamental mode capable of expressing not only the
simplicity but the complexity of present-day psychology. This need not
be sought for outside the field of geometry, but within it, and by
an extension of the methods already described. There is an altogether
modern development of the science of mathematics: the geometry of