“Up to the present time the three dimensions of Euclid have sufficed to express the problems that infinity gives rise to in the souls of great artists.
“Geometry is to the plastic arts what grammar is to the art of the writer.
“Today philosophers do not confine their speculations to the three dimensions of Euclid. Painters, by intention, so to speak, have cause naturally to preoccupy themselves with these new lines of extension which, in the language of modern studios, are classed under the term, fourth dimension.”[38]
Speaking of Cézanne, it is said:
To him a sphere was not always round, a cube always square, or an ellipse always elliptical. Thus the traditional oval of the conventional face disappeared in his portraits, the generally accepted round surfaces of a vase or bowl was represented as flat and dented in spots and the horizontal stability of the horizon was rendered elliptical whenever it so appeared to him.
The general truthfulness of his observations may readily be tested by any one of normal vision who will carefully observe the actual appearance of the surfaces of a round sugar bowl, for example, when placed in the light of a window. It will be found that certain planes are as flat as the table, that others present the appearance of dents and hollows, and the more clearly this is perceived the more grotesque will the object appear as compared with the preconceived image of it established in our minds by the unconscious interaction of the sense of touch and sight.
We know that, scientifically regarded, there is no such thing as a round surface, that what appears to be such is simply the closely adjusted juxtaposition of infinitesimal planes that are each perfectly flat. And the very fact that painters refer to the surface of a figure as planes is indicative of a partial recognition of this basic characteristic of structure. Nevertheless, both artists and laymen persist in speaking of the roundness of a torso, for example, when in reality, if we could disassociate the sense of roundness from the appearance of roundness as did Cézanne, we would find large surfaces of spheroids quite flat. Therein lies the real secret of the art of Cézanne who is the first of realists.