MATTER', 'SPACE', 'TIME' 233
also followed this path and even postulated an 'absolute space' (emptiness). All of which harks back to the old aristotelianism.
E, N, and A systems have the semantic background of fulness or plenum, although, unfortunately, this background is, as yet, mainly unrealized, not fully utilized; it has not, as yet, generally affected our s.r.
A simple illustration will make the difference clear. Imagine that in one part of a large room we have an open umbrella which we would like to compare with another 'unit' open umbrella. Let us imagine that the room has the air pumped out and also that all other eventual disturbing factors are eliminated. We can move our open 'unit' umbrella from one part of the room to another, and this movement will not considerably distort our 'unit' umbrella. Now let us perform a similar experiment in two houses, separated some distance, during a storm, a storm implying, of course, fulness. Can we transport our 'unit' umbrella through the storm and preserve its shape., in a fulness, without taking the fulness into account? Of course not. We see what serious difference it makes if our theories presuppose 'emptiness' or 'fulness'.
This shows also why the non-euclidean geometries which deal with a plenum are structurally preferable and semantically sounder and more in accord with the structure of the world, than the language of euclidean 'emptiness', to which there is nothing in nature to correspond. Should we wonder that modern linguists (mathematicians) work in the direction of fulness and of fusing geometry with physics. It is obviously the only ching to do. Differential geometry is the foundation of this new outlook, but, even in this geometry, lines could legitimately be transported over great distances. Weyl introduced a semantic improvement of this point of view by assuming that for a differential geometry it is illegitimate to use comparisons at large distances, but that all operations should be between indefinitely near points.1
It should be noticed that scientists, in general, disregard almost completely the verbal and semantic problems explained here, a fact which leads to great and unnecessary confusion, and makes modern works inaccessible to the layman. Take, for instance, the case of the 'curvature of space-time'. Mathematicians use this expression very often and, inside their skins, they know mostly what they are talking about. Millions upon millions of even intelligent readers hear such an expression as the 'curvature of space-time'. Owing to nursery mythology and primitive s.r, 'space' for them is 'emptiness', and so they try to understand the 'curvature of emptiness'. After severe pains, they come to a very true, yet, for them, hopeless, conclusion; namely, that 'curvature of emptiness' is either non-sense or 'beyond them', with the semantic result that either