CHAPTER VI
THE HIGHER WORLD
It is indeed strange, the manner in which we must begin to think about the higher world.
Those simplest objects analogous to those which are about us on every side in our daily experience such as a door, a table, a wheel are remote and uncognisable in the world of four dimensions, while the abstract ideas of rotation, stress and strain, elasticity into which analysis resolves the familiar elements of our daily experience are transferable and applicable with no difficulty whatever. Thus we are in the unwonted position of being obliged to construct the daily and habitual experience of a four-dimensional being, from a knowledge of the abstract theories of the space, the matter, the motion of it; instead of, as in our case, passing to the abstract theories from the richness of sensible things.
What would a wheel be in four dimensions? What the shafting for the transmission of power which a four-dimensional being would use.
The four-dimensional wheel, and the four-dimensional shafting are what will occupy us for these few pages. And it is no futile or insignificant enquiry. For in the attempt to penetrate into the nature of the higher, to grasp within our ken that which transcends all analogies, because what we know are merely partial views of it, the purely material and physical path affords a means of approach pursuing which we are in less likelihood of error than if we use the more frequently trodden path of framing conceptions which in their elevation and beauty seem to us ideally perfect.
For where we are concerned with our own thoughts, the development of our own ideals, we are as it were on a curve, moving at any moment in a direction of tangency. Whither we go, what we set up and exalt as perfect, represents not the true trend of the curve, but our own direction at the present—a tendency conditioned by the past, and by a vital energy of motion essential but only true when perpetually modified. That eternal corrector of our aspirations and ideals, the material universe draws sublimely away from the simplest things we can touch or handle to the infinite depths of starry space, in one and all uninfluenced by what we think or feel, presenting unmoved fact to which, think it good or think it evil, we can but conform, yet out of all that impassivity with a reference to something beyond our individual hopes and fears supporting us and giving us our being.
And to this great being we come with the question: “You, too, what is your higher?”
Or to put it in a form which will leave our conclusions in the shape of no barren formula, and attacking the problem on its most assailable side: “What is the wheel and the shafting of the four-dimensional mechanic?”
In entering on this enquiry we must make a plan of procedure. The method which I shall adopt is to trace out the steps of reasoning by which a being confined to movement in a two-dimensional world could arrive at a conception of our turning and rotation, and then to apply an analogous process to the consideration of the higher movements. The plane being must be imagined as no abstract figure, but as a real body possessing all three dimensions. His limitation to a plane must be the result of physical conditions.
We will therefore think of him as of a figure cut out of paper placed on a smooth plane. Sliding over this plane, and coming into contact with other figures equally thin as he in the third dimension, he will apprehend them only by their edges. To him they will be completely bounded by lines. A “solid” body will be to him a two-dimensional extent, the interior of which can only be reached by penetrating through the bounding lines.