We imagine three lines at right angles to each other to extend indefinitely out into space, and we think of ourselves as being situated at the point of intersection of these three straight lines. If anything moves in the universe outside ourselves we can resolve this motion into three components, each of which is to be measured along one of the axes of our system of co-ordinates. But any motion whatever in the universe outside ourselves can be represented equally well by supposing that the origin of the system of co-ordinates has been changed; that is, by supposing that we have changed our position relative to the rest of the universe. Therefore motion outside ourselves is not to be distinguished from a contrary motion of our own body--a statement of the “principle of relativity”--except that any change outside ourselves may be distinguished from that compensatory change in the position of our body which _appears_ to be the same thing, by the absence of the intuition that we have expended a certain quantity of energy in producing the change. Conscious motion of our own body is something _absolute_; all other motion is relative. So far we have been speaking of our crude bodily motion, but a very little consideration will show that our knowledge of space attained by scientific measurements depends just as much on our intuition of our bodily activity, and its direction; the measurement of a stellar parallax, or that of the meridian altitude of the sun, for instance, by astronomical instruments, involves bodily exertion, though of a refined kind. Three-dimensional space, that is _our_ space, therefore represents the manner of our activity, just as convex two-dimensional space represents the manner of the activity of the Infusorian, and one-dimensional space would represent the manner of activity of an animal which was compelled to live in a tube, the sides of which it fitted closely, so that it could move only in one direction--up and down. A parasite, living attached to some fixed object, and the movements of which were represented only by the growth of its tissues, could not form any idea of space; and the “higher” forms of geometry, that is, space of four or more dimensions, present no clear notion to our minds, even although we regard the operations included in mathematics of this kind as pure symbolism, because we cannot relate this imaginary space to any form of bodily exertion. Geometry, then, represents the manner in which our bodily exertion cuts up the homogeneous medium in which we live.