The fourth dimension

CHAPTER IIl

THE SIGNIFICANCE OF A FOURDIMENSIONAL EXISTENCE

HAVING now obtained the conception of a four-dimensional space, and having formed the analogy which, without any further geometrical difficulties, enables us to enquire into its properties, I will refer the reader, whose interest is principally in the mechanical aspect, to Chapters VI. and VII. In the present chapter I will deal with the general significance of the enquiry, and in the next with the historical origin of the idea.

First, with regard to the question of whether there is any evidence that we are really in four-dimensional space, I will go back to the analogy of the plane world.

A being in a plane world could not have any experience of three-dimensional shapes, but he could have an experience of three-dimensional movements.

We have seen that his matter must be supposed to have an extension, though a very small one, in the third dimension. And thus, in the small particles of his matter, three-dimensional movements may well be conceived to take place. Of these movements he would only perceive the resultants. Since all movements of an observable size in the plane world are two-dimensional, he would only perceive the resultants in two dimensions of the small three-dimensional movements. Thus, there would be phenomena which he could not explain by his

15