[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. [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 four dimensions. This represents the emancipation of the mind from the tyranny of mere appearances; the turning of consciousness in a new direction. It has therefore a high symbolical significance as typifying that movement away from materialism which is so marked a phenomenon of the times.