Hinton - The Fourth Dimension.pdf

180
THE FOURTH DIMENSION
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 b1, b2, b3 and the farther
face of this cube in the blue direction is shown in b4--
a pink face, called pink bl. 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.
Take again the orange face, that determined by the
red and yellow axes; from it goes a brown cube in the
blue direction, for red and yellow and blue are supposed
to make brown. This brown cube is shown in three
sections in the faces b1, b2, b3. In b4 is the opposite
orange face of the brown cube, the face called orange bl.,