And the necessity of a conducting circuit for a current is exactly that which we should expect if it were a four-dimensional vortex. According to Maxwell every current forms a closed circuit, and this, from the four-dimensional point of view, is the same as saying a vortex must have its ends on a boundary of the fluid.
Thus, on the hypothesis of a fourth dimension, the rotation of the fluid ether would give the phenomenon of an electric current. We must suppose the ether to be full of movement, for the more we examine into the conditions which prevail in the obscurity of the minute, the more we find that an unceasing and perpetual motion reigns. Thus we may say that the conception of the fourth dimension means that there must be a phenomenon which presents the characteristics of electricity.
We know now that light is an electro-magnetic action, and that so far from being a special and isolated phenomenon this electric action is universal in the realm of the minute. Hence, may we not conclude that, so far from the fourth dimension being remote and far away, being a thing of symbolic import, a term for the explanation of dubious facts by a more obscure theory, it is really the most important fact within our knowledge. Our three-dimensional world is superficial. These processes, which really lie at the basis of all phenomena of matter, escape our observation by their minuteness, but reveal to our intellect an amplitude of motion surpassing any that we can see. In such shapes and motions there is a realm of the utmost intellectual beauty, and one to which our symbolic methods apply with a better grace than they do to those of three dimensions.
CHAPTER VIII
THE USE OF FOUR DIMENSIONS IN THOUGHT
Having held before ourselves this outline of a conjecture of the world as four-dimensional, having roughly thrown together those facts of movement which we can see apply to our actual experience, let us pass to another branch of our subject.
The engineer uses drawings, graphical constructions, in a variety of manners. He has, for instance, diagrams which represent the expansion of steam, the efficiency of his valves. These exist alongside the actual plans of his machines. They are not the pictures of anything really existing, but enable him to think about the relations which exist in his mechanisms.
And so, besides showing us the actual existence of that world which lies beneath the one of visible movements, four-dimensional space enables us to make ideal constructions which serve to represent the relations of things, and throw what would otherwise be obscure into a definite and suggestive form.
From amidst the great variety of instances which lies before me I will select two, one dealing with a subject of slight intrinsic interest, which however gives within a limited field a striking example of the method of drawing conclusions and the use of higher space figures.[1]
[1] It is suggestive also in another respect, because it shows very clearly that in our processes of thought there are in play faculties other than logical; in it the origin of the idea which proves to be justified is drawn from the consideration of symmetry, a branch of the beautiful.
The other instance is chosen on account of the bearing it has on our fundamental conceptions. In it I try to discover the real meaning of Kant’s theory of experience.