Number is the tune to which all things move, and as it were make music; it is in the pulses of the blood no less than in the starred curtain of the sky. It is a necessary concomitant alike of the sharp bargain, the chemical experiment, and the fine frenzy of the poet. Music is number made audible; architecture is number made visible; nature geometrizes not alone in her crystals, but in her most intricate arabesques.

If number be indeed the universal solvent of all forms, sounds, motions, may we not make of it the basis of a new æsthetic—a loom on which to weave patterns the like of which the world has never seen? To attempt such a thing—to base art on mathematics—argues (some one is sure to say) an entire misconception of the nature and function of art. "Art is a fountain of spontaneous emotion"—what, therefore, can it have in common with the proverbially driest, least spontaneous preoccupation of the human mind? But the above definition concludes with the assertion that this emotion reaches the soul "through various channels." The transit can be effected only through some sensuous element, some language (in the largest sense), and into this the element of number and form must inevitably enter—mathematics is "there" and cannot be thought or argued away.

[Illustration: PLATE XI. IMAGINARY COMPOSITION: THE PORTAL]

But to make mathematics, and not the emotion which it expresses, the important thing, is not this to fall into the time-worn heresy of art for art's sake, that is, art for form's sake—art for the sake of mathematics? To this objection there is an answer, and as this answer contains the crux of the whole matter, embraces the proposition by which this thesis must stand or fall, it must be full and clear.

What is it, in the last analysis, that all art which is not purely personal and episodical strives to express? Is it not the world-order?—the very thing that religion, philosophy, science, strive according to their different natures and methods to express? The perception of the world-order by the artist arouses an emotion to which he can give vent only in terms of number; but number is itself the most abstract expression of the world order. The form and content of art are therefore not different, but the same. A deep sense of this probably inspired Pater's famous saying that all art aspires toward the condition of music; for music, from its very nature, is the world-order uttered in terms of number, in a sense and to a degree not attained by any other art.

This is not mere verbal juggling. We have suffered so long from an art-phase which exalts the personal, as opposed to the cosmic, that we have lost sight of the fact that the great arts of antiquity, preceding the Renaissance, insisted on the cosmic, or impersonal aspect, and on this alone, just as does Oriental art, even today. The secret essence, the archetypal idea of the subject is the preoccupation of the Oriental artist, as it was of the Egyptian, and of the Greek. We of the West today seek as eagerly to fix the accidental and ephemeral aspect—the shadow of a particular cloud upon a particular landscape; the smile on the face of a specific person, in a recognizable room, at a particular moment of time. Of symbolic art, of universal emotion expressing itself in terms which are universal, we have very little to show.

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 æsthetic 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.