The Fourth Dimension

by Charles Howard Hinton

Fig. 92.

In speaking of them he would have to denote what part of the respective cube each square represents. Thus, at the beginning he would have null cube orange face, and after the motion had begun he would have null cube ochre section. As he could get the same coloured section whichever way the cube passed through, it would be best for him to call this section white section, meaning that it is transverse to the white axis. These colour-names, of course, are merely used as names, and do not imply in this case that the object is really coloured. Finally, after a minute, as the first cube was passing beyond his plane he would have null cube orange face again.

The same names will hold for each of the other cubes, describing what face or section of them the plane being has before him; and the second wall of cubes will come on, continue, and go out in the same manner. In the area he thus has he can represent any movement which we carry out in the cubes, as long as it does not involve a motion in the direction of the white axis. The relation of parts that succeed one another in the direction of the white axis is realised by him as a consecution of states.

Now, his means of developing his space apprehension lies in this, that that which is represented as a time sequence in one position of the cubes, can become a real co-existence, if something that has a real co-existence becomes a time sequence.

We must suppose the cubes turned round each of the axes, the red line, and the yellow line, then something, which was given as time before, will now be given as the plane creature’s space; something, which was given as space before, will now be given as a time series as the cube is passed through the plane.

The three positions in which the cubes must be studied are the one given above and the two following ones. In each case the original null point which was nearest to us at first is marked by an asterisk. In figs. 93 and 94 the point marked with a star is the same in the cubes and in the plane view.

Fig. 93.
The cube swung round the red line, so that the white line points towards us.

In [fig. 93] the cube is swung round the red line so as to point towards us, and consequently the pink face comes next to the plane. As it passes through there are two varieties of appearance designated by the figures 1 and 2 in the plane. These appearances are named in the figure, and are determined by the order in which the cubes come in the motion of the whole block through the plane.