13 
Ill 
The new artists have been violently reproached for their geo 
metric preoccupations. And yet, geometric figures are the 
essence of drawing. Geometry, the science which has for its 
scope space, its measurement and its relations, has been from time 
immemorial the rule even of painting. 
Up till now, the three dimensions of the euclidean geometry 
have sufficed for the solicitude which the sentiment of the infinite 
arouses in the soul of great artists. 
The new painters do not propose, any more than did the old, 
to be geometricians. But, it may be said that geometry is to the 
plastic arts what grammar is to the art of the writer. Today 
scholars no longer hold to the three dimensions of the euclidean 
geometries. The painters have been led quite naturally and, so 
to speak, by intuition, to preoccupy themselvess with possible 
new measures of space, which, in the language of modern studios 
has been designated briefly and altogether by the term the fourth 
dimension. 
The fourth dimension as it is presented to the understanding 
from the plastic point of view would be engendered by the three 
known dimensions; it would show the immensity of space eter 
nalized in every direction at a given moment. It is space itself, 
the dimension of the infinite: it is this which endows objects with 
their plasticity. It gives them the proportions which they merit 
as a part of the whole, whereas, in Greek art, for example, a 
somewhat mechanical rhythm unceasingly destroys the propor 
tions. 
Greek art had a purely human conception of beauty. It took 
man as the standard of perfection. The art of the new painters 
takes the infinite universe as the ideal, and it is this ideal that 
necessitates a new measure of perfection, which permits the artist 
to give to the object proportions which conform to the degree of 
plasticity to which he desired to bring it. 
Nietszche divined the possibility of such an art: “O divine 
Dionysius, why dost thou pull my ears?” Ariadne demands of