The fourth dimension

236 THE FOURTH DIMENSION

familiarity with our cube. Turn the catalogue cube (or imagine the coloured figure turned) so that the red line runs up, the yellow line out to the right, and the white line towards you. Then turn the block of cubes to occupy a similar position.

The block has now a different wall in contact with the plane. Its appearance to a plane being will not be the same as before. He has, however, enough slabs to represent this new set of appearances. But he must remodel his former arrangement of them.

He must take a null, a red, and a null slab from the first of his sets of slabs, then a white, a pink, and a white from the second, and then a null, a red, and a null from the third set of slabs.

He takes the first column from the first set, the first column from the second set, and the first column from the third set.

To represent the half-way-through appearance, which is as if a very thin slice were cut out half way through the block, he must take the second column of each of his sets of slabs, and to represent the final appearance, the third column of each set.

Now turn the catalogue cube back to the normal position, and also the block of cubes.

There is another turning—a turning about the yellow line, in which the white axis comes below the support.

You cannot break through the surface of the table, so you must imagine the old support to be raised. Then the top of the block of cubes in its new position is at the level at which the base of it was before.

Now representing the appearance on the plane, we must draw a horizontal line to represent the old base. The line should be drawn three inches high on the cardboard.

Below this the representative slabs can be arranged.

It is easy to see what they are. The old arrangements