Yet he could not make these two triangles coincide. Now this impossibility of bringing together two things which he felt were really alike was the sign to him of his limitation; and by reflecting on the similar appearance which would present itself to a being limited to a straight line—by thinking of two systems of points which were really identical, and which he could make coincide, but which a line being could not make coincide, he would be led to conclude that he in his turn was subject to a limitation. Now is there any object which we know which, considered as a whole consisting of parts, is exactly like another whole, the two having all their parts similarly arranged, so as to form in themselves two identical systems, and yet the one incapable of being made to coincide with the other, even in thought? Let us look at our two hands. They are (except for accidental variations) exactly alike. And yet they cannot be made to coincide. And here, if we reflect on it, is the sign to us that we are limited in our notions of space—that we are really in a four-dimensional world. Watching a ship as it recedes from the shore we see that it becomes hull down before it vanishes, and know that the earth is round. And no less certainly do our two hands, in their curious likeness and yet difference, afford to us a perpetual proof of our limitation, and indicate a larger world. This sign really tells us more than the mere fact of our limitation: it tells us where to look for the possibility of four-dimensional movements. It tells us that movements of any degree of magnitude relative to us are not possible in the fourth dimension. It tells us to look for four-dimensional movements in the minute particles of matter, not in the movements of masses of about our own size. The task before us is difficult. We have to make up from the outside what the appearances of a higher space existence are to us in our space, and then we have to look at the facts of nature and see if they correspond to these appearances. Let us take a few isolated points and look at them patiently. To a being standing on the rim of a plane world a straight line absolutely shuts out the prospect before him. If the straight line is infinite it cuts his world in two; he can never hope to get beyond it. It is to him what an infinite plane would be to us, stretching impassably in front of us, cutting us off from all that lies on the other side. But we know that a point can move round this line. It can revolve round it by going out of the plane, and coming down again into the plane on the other side of the line. This movement would be inconceivable to a plane being; for he can only conceive it possible to get to the other side of the line by going to the end of it and coming back along the other side of the line.