Suppose a figure of any kind drawn on the plane inhabited by the plane being; all he sees of it are lines and points: and from the number of lines which he can see when he views it from different sides, and from the size of the angle at each point, he determines whether the figure he is considering is a triangle, square, pentagon, etc., etc. He cannot by any possibility see the shape of the figure; we who can do that, do it because we look from another direction. He would say "the only way to get at the inside of a square is to penetrate one of the sides, push it apart, so to say." So we say "you can touch only the surface of a solid: its interior can be reached only by penetrating and pushing apart."
It is well known that clairvoyants can plainly see objects from which they are separated by opaque bodies; and when they are asked to describe how it is they so see, they cannot give any explanation comprehensible to us. They see it, and that is all they can say. Thus a clairvoyant (of course I mean a genuine, and an exceptionally fine clairvoyant) can, on looking at any one's body, see all the interior organs and describe their position, relations, and condition with wonderful accuracy. Must we not conclude this to be by a process similar to that by which we can see and touch a point in the interior of a triangle, without touching or looking through the sides? the simplest of every day operations to us, but one of which no description could give an adequate idea to a plane being.
Suppose a cube is passing through the plane which constitutes the plane being's space: what does he perceive? A square, bounded by the usual four lines and four angles. Suppose this cube to come from our "above" into his plane, and pass through and below it. To him the process would be this: — -a square suddenly appears where before there was none, coming from nowhere in space; it lasts a short time, then disappears as mysteriously as it came. Suppose a cylinder to pass through his plane; he would suddenly see a circle, which after a certain time disappears as the square did. If he saw a point suddenly appear, and then become a minute circle which steadily increased in diameter till it vanished at the time it was the largest, that would mean that a cone had passed through. If the increase in size of the circle was more rapid at first and slower afterward, it would mean a hemisphere; and we might trace in the same way other bodies.
If we have a cylinder around which is traced a spiral line, he would see a circle, around the circumference of which a point revolves, the openness or closeness of the spiral being represented to him by the greater or less speed of the point. A cylinder inscribed with a number of lines would be represented to him by points moving in various ways, at varying rates, about a circle. Some curious features might result from the passage of less regular bodies through the plane. Take a cylinder terminated at each end by a cone; we have a point appearing, then a circle increasing up to a certain size, which persists for a time, then diminishes to a point and disappears. A quite irregular body might give some curious results, as any one can work out at leisure.
Now think what is a human life. We appear in this world, go through various changes in form and place, and then leave this world. Cannot we see an analogy to the last described case? May not the real entity, the true individuality, exist all the time in a higher space of which we know nothing, what we call our life being merely the fleeting appearance produced by its passage through this plane of being, its true existence extending far beyond. When we compare with our ordinary space and space life the space and life of the plane beings, how insignificant and meagre the latter appear; and the difference is not one of degree, of more or less. No conceivable number of square inches will make a cubic inch; no possible extension of a plane being's experience can give him an idea of space: his universe is a thin film; it and its beings are hardly more than mental conceptions, not realities, to us. The squares, triangles, and other surfaces, which to him are the most absolute of realities, to us are but the surfaces bounding the solid bodies, the only true realities.
So to a being in higher space, our entire universe, all space even beyond the remotest stars, is the merest film on the surface of real being; and our solid worlds no realities, merely mental conceptions of the appearances of real entities.
When a cube rests on a plane, the plane being sees a square and nothing else; by turning the cube in different ways he can be made to see the six squares which bound it, but only one at a time; to him they are separate entities, appearing one after another, and with no connection except that of sequence in time and similarity in size. To us they are the six squares bounding the cube, distinct and independent of each other, but with no independent existence apart from the cube, of which they are but the manifestations. So also, individual human beings appear to us as distinct entities, standing separate and isolated; but seen from the standpoint of the higher life, each is merely a manifestation of the one life. Apart from that one life, each is an unreality, a form of illusion, no more an actually existing thing than is the side of the cube apart from the cube. Yet just as the sides of the cube, considered as squares, are distinct and independent, their unity being not identity one with another but with the cube, so to each human being is given his own individual existence, which only he can fill.
This is no mere fancy, no mere analogy; a little study into higher space laws shows that, once granting the existence of more dimensions of space than are perceived by our five senses, then there must certainly be existences, of which all our solid world and its contents are merely partial manifestations, but which existences can be manifested in many other ways, of which we are now totally ignorant. And when we see that our only real being is in a higher one, of which we are but the partial manifestations; that only as our consciousness becomes centred in that higher being has it any real value; that only as we work for the whole has our work any value or permanence; when we once see these things; what more evidence do we need for the fundamental principle of our society, universal human brotherhood?
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