The reason for this is first, our love for, and understanding of, the concrete and personal:  it is the world-aspect and not the world-order which interests us; and second, the inadequacies of current forms of art expression to render our sense of the eternal secret heart of things as it presents itself to our young eyes.  Confronted with this difficulty, we have shirked it, and our ambition has shrunk to the portrayal of those aspects which shuffle our poverty out of sight.  It is not a poverty of technique—­we are dexterous enough; nor is it a poverty of invention—­we are clever enough; it is the poverty of the spiritual bankrupt trying to divert attention by a prodigal display of the smallest of small change.

Reference is made here only to the arts of space; the arts of time—­music, poetry, and the (written) drama—­employing vehicles more flexible, have been more fortunate, though they too suffer in some degree from worshipping, instead of the god of order, the god of chance.

The corrective of this is a return to first principles:  principles so fundamental that they suffer no change, however new and various their illustrations.  These principles are embodied in number, and one might almost say nowhere else in such perfection.  Mathematics is not the dry and deadly thing that our teaching of it and the uses we put it to have made it seem.  Mathematics is the handwriting on the human consciousness of the very Spirit of Life itself.  Others before Pythagoras discovered this, and it is the discovery which awaits us too.

To indicate the way in which mathematics might be made to yield the elements of a new aesthetic is beyond the province of this essay, being beyond the compass of its author, but he makes bold to take a single phase:  ornament, and to deal with it from this point of view.

The ornament now in common use has been gathered from 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.]