Geometric Space and Perceptual Space.—It is often said the images of external objects are localized in space, even that they can not be formed except on this condition. It is also said that this space, which serves thus as a ready prepared frame for our sensations and our representations, is identical with that of the geometers, of which it possesses all the properties.
To all the good minds who think thus, the preceding statement must have appeared quite extraordinary. But let us see whether they are not subject to an illusion that a more profound analysis would dissipate.
What, first of all, are the properties of space, properly so called? I mean of that space which is the object of geometry and which I shall call geometric space.
The following are some of the most essential:
2º It is infinite;
3º It has three dimensions;
4º It is homogeneous, that is to say, all its points are identical one with another;
5º It is isotropic, that is to say, all the straights which pass through the same point are identical one with another.
Compare it now to the frame of our representations and our sensations, which I may call perceptual space.