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By so doing he may erect for himself a veritable Jacob's ladder, "Pitched between Heaven and Charing Cross." He should accustom himself to ascend it, step by step, dimension by dimension. Then he will learn to trust Emerson's dictum, "Nature geometrizes," even in regions where the senses fail him, and the mind alone leads on. Much profitable amusement is to be gained by such exercises as follow.
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?
Guided by what seems to be a law; guided, at any rate, by the knowledge that there are laws; that "God geometrizes," as Plato says: that which is within flows outward upon a design; that life precipitates itself through human affairs as it does through the forms of the crystals; that there is nothing more haphazard about the sequence of empires and civilizations, than there is about the unfolding of petals of a flower.
'God geometrizes, it used to be said; and it was believed that Euclid's elements literally reproduced his geometrizing. There is an eternal and unchangeable 'reason'; and its voice was supposed to reverberate in Barbara and Celarent.