"The chemist, in describing some mineral, may present all its attributes, color mass, density, volume, molecular construction, and its properties exhibited in relation to heat, light, sound, and electric waves, and the resulting conception will not be mathematical. On the other hand, in describing its form as cubical, he relies upon the purely mathematical abstraction involved in the definition of a cube, which includes that of the mathematical plane, which involves the geometric line, which, in turn, resolves into an assemblage of points. Not one of these conceptions finds its realization in physical phenomena, but at best an approximation. The types conceived by the mind remain, however, definite and unchangeable. The idea of the ultimate element, the "point," best illustrates the nature of these abstractions, and involves the first difficulty that lies in the way of the understanding. The point is defined as having but one positive attribute, and that is, position in space. ...The mathematical point cannot be realized by this process, for the resulting principle is this: all material things are indefinitely divisible, and, no matter how small, possess magnitude and occupy space. The negative of this thought is the point, which does not have magnitude, but position only. It is a negative thought concept, a mathematical abstraction..."