In this figure the tesseract is shown in five stages distant from our
space: first, zero; second, 1/4 in.; third, 2/4 in.; fourth, 3/4 in.;
fifth, 1 in.; which are called _b_0, _b_1, _b_2, _b_3, _b_4, because
they are sections taken at distances 0, 1, 2, 3, 4 quarter inches along
the blue line. All the regions can be named from the first cube, the
_b_0 cube, as before, simply by remembering that transference along
the b axis gives the addition of blue to the colour of the region in
the ochre, the _b_0 cube. In the final cube _b_4, the colouring of the
original _b_0 cube is repeated. Thus the red line moved along the blue
axis gives a red and blue or purple square. This purple square appears
as the three purple lines in the sections _b_1, _b_2, _b_3, taken at
1/4, 2/4, 3/4 of an inch in the fourth dimension. If the tesseract
moves transverse to our space we have then in this particular region,
first of all a red line which lasts for a moment, secondly a purple
line which takes its place. This purple line lasts for a minute—that
is, all of a minute, except the moment taken by the crossing our space
of the initial and final red line. The purple line having lasted for
this period is succeeded by a red line, which lasts for a moment; then
this goes and the tesseract has passed across our space. The final red
line we call red bl., because it is separated from the initial red
line by a distance along the axis for which we use the colour blue.
Thus a line that lasts represents an area duration; is in this mode
of presentation equivalent to a dimension of space. In the same way
the white line, during the crossing our space by the tesseract, is
succeeded by a light blue line which lasts for the inside of a minute,
and as the tesseract leaves our space, having crossed it, the white bl.
line appears as the final termination.
Take now the pink face. Moved in the blue direction it traces out a
light purple cube. This light purple cube is shown in sections in
_b__{1}, _b__{2}, _b__{3}, and the farther face of this cube in the
blue direction is shown in _b__{4}—a pink face, called pink _b_ because
it is distant from the pink face we began with in the blue direction.
Thus the cube which we colour light purple appears as a lasting square.
The square face itself, the pink face, vanishes instantly the tesseract
begins to move, but the light purple cube appears as a lasting square.
Here also duration is the equivalent of a dimension of space—a lasting
square is a cube. It is useful to connect these diagrams with the views
given in the coloured plate.
Public-domain text, read in full here on John Shaqi.
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