If we look at our two hands we see this clearly, though the two hands are a complicated case of a very common fact of shape. Now, there is one way in which the right hand and the left hand may practically be brought into likeness. If we take the right-hand glove and the left-hand glove, they will not fit any more than the right hand will coincide with the left hand. But if we turn one glove inside out, then it will fit. Now, to suppose the same thing done with the solid hand as is done with the glove when it is turned inside out, we must suppose it, so to speak, pulled through itself. If the hand were inside the glove all the time the glove was being turned inside out, then, if such an operation were possible, the right hand would be turned into an exact model of the left hand. Such an operation is impossible. But curiously enough there is a precisely similar operation which, if it were possible, would, in a plane, turn the one triangle in Fig. 2 into the exact copy of the other. [Illustration] Look at the triangle in Fig. 2, A B C, and imagine the point A to move into the interior of the triangle and to pass through it, carrying after it the parts of the lines A B and A C to which it is attached, we should have finally a triangle A B C, which was quite like the other of the two triangles A′ B′ C′ in Fig. 2. Thus we know the operation which produces the result of the “pulling through” is not an impossible one when the plane-being is concerned. Then may it not be that there is a way in which the results of the impossible operation of pulling a hand through could be performed? The question is an open one. Our feeling of it being impossible to produce this result in any way, may be because it really is impossible, or it may be a useful bit of information about ourselves. Now at this point my special work comes in. If there be really a four-dimensional world, and we are limited to a space or three-dimensional view, then either we are absolutely three-dimensional with no experience at all or capacity of apprehending four-dimensional facts, or we may be, as far as our outward experience goes, so limited; but we may really be four-dimensional beings whose consciousness is by certain undetermined conditions limited to a section of the real space. Thus we may really be like the plane-beings mentioned above, or we may be in such a condition that our perceptions, not ourselves, are so limited. The question is one which calls for experiment. We know that if we take an animal, such as a dog or cat, we can by careful training, and by using rewards and punishment, make them act in a certain way, in certain defined cases, in accordance with justice; we can produce the mechanical action. But the feeling of justice will not be aroused; it will be but a mere outward conformity. But a human being, if so trained, and seeing others so acting, gets a feeling of justice.