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.
[Illustration: 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.
With regard to these squares severally, however, different names must
be used, determined by their relations in the block.
Thus, in fig. 93, when the cube first rests against the plane the null
cube is in contact by its pink face; as the block passes through we get
an ochre section of the null cube, but this is better called a yellow
section, as it is made by a plane perpendicular to the yellow line.
When the null cube has passed through the plane, as it is leaving it,
we get again a pink face.
[Illustration: Fig. 94. The cube swung round yellow line, with red line
running from left to right, and white line running down.]
The same series of changes take place with the cube appearances which
follow on those of the null cube. In this motion the yellow cube
follows on the null cube, and the square marked yellow in 2 in the
plane will be first “yellow pink face,” then “yellow yellow section,”
then “yellow pink face.”
Public-domain text, read in full here on John Shaqi.
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