The fourth dimension

150 THE FOURTH DIMENSION

solid. Using the addition of white to symbolise the products of this motion this new kind of solid will be light orange or ochre, and it will be bounded on the far side by the final position of the orange square which traced it out, and this final position we suppose to be coloured like the square in its first position, orange with yellow and red boundaries and null corners.”

This product of movement, which it is so easy for us to describe, would be difficult for him to conceive. But this difficulty is connected rather with its totality than with any particular part of it.

Any line, or plane of this, to him higher, solid we could show to him, and put in his sensible world.

We have already seen how the pink square could be put in his world by a turning of the cube about the red line. And any section which we can conceive made of the cube could be exhibited to him. You have simply to turn the cube and push it through, so that the plane of his existence is the plane which cuts out the given section of the cube, then the section would appear to him as a solid. In his world he would see the contour, get to any part of it by digging down into it.

THE PROCESS BY WHICH A PLANE BEING WOULD GAIN A NoTION OF A SOLID.

If we suppose the plane being to have a general idea of the existence of a higher solid—our solid—we must next trace out in detail the method, the discipline, by which he would acquire a working familiarity with our space existence. The process begins with an adequate realisation of a simple solid figure. For this purpose we will suppose eight cubes forming a larger cube, and first we will suppose each cube to be coloured throughout uniformly,