[Illustration: PLATE XII. IMAGINARY COMPOSITION. THE BALCONY]
[Illustration: Figure 9.]
Suppose, for example, that we attempt to deal decoratively which such simple figures as the three lowest Platonic solids—the tetrahedron, the hexahedron, and the octahedron. [Figure 12.] Their projection on a plane yields a rhythmical division of space, because of their inherent symmetry. These projections would correspond to the network of lines seen in looking through a glass paperweight of the given shape, the lines being formed by the joining of the several faces. Figure 13 represents ornamental bands developed in this manner. The dodecahedron and icosahedron, having more faces, yield more intricate patterns, and there is no limit to the variety of interesting designs obtainable by these direct and simple means.
[Illustration: Figure 10.]
If the author has been successful thus far in his exposition, it 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.
[Illustration: Figure 12.]
[Illustration: Figure 13.]