Schrödinger's wave-mechanics is not a physical theory, but a dodge — and a very good dodge too. - Arthur Eddington

The external world of physics has thus become a world of shadows. In removing our illusions we have removed the substance, for indeed we have seen that substance is one of the greatest of our illusions.

Phys. I know that it is often a help to represent pressure and volume as height and width on paper; and so geometry may have applications to the theory of gases. But is it not going rather far to say that geometry can deal directly with these things and is not necessarily concerned with lengths in space? Math. No. Geometry is nowadays largely analytical, so that in form as well as in effect, it deals with variables of an unknown nature. … It is literally true that I do not want to know the significance of the variables x, y, z, t that I am discussing. … Phys. Yours is a strange subject. You told us at the beginning that you are not concerned as to whether your propositions are true, and now you tell us you do not even care to know what you are talking about.
Math. That is an excellent description of Pure Mathematics, which has already been given by an eminent mathematician <nowiki>[</nowiki>Bertrand Russell<nowiki>]</nowiki>.

To the pure geometer the radius of curvature is an incidental characteristic — like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.