If number be indeed the universal solvent of all forms, sounds, motions, may we not make of it the basis of a new aesthetic—­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.