The fourth dimension

8 THE FOURTH DIMENSION

Let the reader imagine himself, as he looks along the plane, fig. 4, to become more and more identified with the thin body on it, till he finally looks along parallel to the surface of the plane earth, and up and down, losing the sense of the direction which stretches right and left. This direction will be an unknown dimension to him.

Our space conceptions are so intimately connected with those which we derive from the existence of gravitation that it is difficult to realise the condition of a plane being, without picturing him as in material surroundings with a definite direction of up and down. Hence the necessity of our somewhat elaborate scheme of representation, which, when its import has been grasped, can be dispensed with for the simpler one of a thin object slipping over a smooth surface, which lies in front of us.

It is obvious that we must suppose some means by which the plane being is kept in contact with the surface on which he slips. The simplest supposition to make is that there is a transverse gravity, which keeps him to the plane. This gravity must be thought of as different to the attraction exercised by his matter, and as unperceived by him.

At this stage of our enquiry I do not wish to enter into the question of how a plane being could arrive at a knowledge of the third dimension, but simply to investigate his plane consciousness.

It is obvious that the existence of a plane being must be very limited. A straight line standing up from the surface of his earth affords a bar to his progress. An object like a wheel which rotates round an axis would be unknown to him, for there is no conceivable way in which he can get to the centre without going through the circumference. He would have spinning disks, but could not get to the centre of them. The plane being can represent the motion from any one point of his space