The new painters have been sharply criticized for their preoccupation with geometry. And yet, geometric figures are the essence of draftsmanship. Geometry, the science that deals with space, its measurement and relationships, has always been the most basic rule of painting.
Until now, the three dimensions of Euclidean geometry sufficed to still the anxiety provoked in the souls of great artists by a sense of the infinite – anxiety that cannot be called scientific, since art and science are two separate domains.
The new painters do not intend to become geometricians, any more than their predecessors did. But it may be said that geometry is to the plastic arts what grammar is to the art of writing. Now today’s scientists have gone beyond the three dimensions of Euclidean geometry. Painters have, therefore, very naturally been led to a preoccupation with those new dimensions of space that are collectively designated, in the language of modern studios, by the term fourth dimension.
Without entering into mathematical explanations pertaining to another field, and confining myself to plastic representation as I see it, I would say that in the plastic arts the fourth dimension is generated by the three known dimensions: it represents the immensity of space eternalized in all directions at a given foment. It is space itself, or the dimension of infinity; it is what gives objects Plasticity. It gives them their just proportion in a given work, where as in Greek ar t, for example, a kind of mechanical rhythm is constantly destroving proportion.
Greek art had a purely human conception of beauty. It took man as the Measure of perfection. The art of the new painters takes the infinite universe a s its ideal, and it is to the fourth dimension alone that we owe this new measure of perfection that allows the artist to give objects the proportions appropriate 10 the degree of plasticity he wishes them to attain. […]
Wishing to attain the proportions of the ideal and not limiting themselves to humanity, the young painters offer us works that are more cerebral than sensual They are moving further and further away from the old art of optical illusions and literal proportions, in order to express the grandeur of metaphysical forms.
Originally published in Les Soirees de Paris, April-May 1912