Читать книгу A Theory of the Mechanism of Survival: The Fourth Dimension and Its Applications онлайн

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We have already seen that a cube laid on a flat surface will present to a plane being, in that surface, the appearance of a square. It is also clear that if it is pushed through the surface it will continue to present the same appearance until it has passed right through, when it will suddenly vanish away.

He would be unconscious of any movement on the part of the cube unless there was some difference between the first and last sections which he perceived.

If, for instance, the bottom face was red and the top face blue he would be conscious of a colour change on the part of the square which he perceived. It would start by being red and would pass through various shades of purple till, just before its final disappearance, it would be pure blue. But now suppose that it was pressed through his surface not "normally" but corner wise as indicated in Fig. 6—that is to say with one of its corners leading and one of its diagonals vertical. The plane being would then see quite a different set of figures. First would be a point; this would grow into a triangle which would increase in size until it reached a certain maximum when it would begin to develope three new sides at its corners which would grow, at the expense of the original sides, until a regular hexagon was produced when the reverse process would set in and the hexagon gradually change back into a triangle which in turn would dwindle away and disappear. It is easy to work out what would happen in the case of other solids, e.g., Sphere, Cone, Tetrahedron, etc. All such changes would appear very mysterious to the plane being if he had formed no conception of three-dimensional space or the shapes of bodies therein.