Hinton - The Fourth Dimension.pdf

NOMENCLATURE AND ANALOGIES 145
opposite sense to that in which the red line ran before.
Now if we use i, j, k, for the three space directions,
i left to right, j from near away, k from below up; then,
using the colour names for the axes, we have that first
of all white runs i, yellow runs j, red runs k; then after
Null Yellow
White
White
Yellow
first appearance
Fig. 89.
Orange
Red
Pink
x
Null y. Null White Null
Yellow
the first turning round the k axis, white runs negative j,
yellow runs i, red runs k; thus we have the table:—
i j k
1st position white yellow red
2nd position yellow white— red
3rd position red yellow white—
Here white with a negative sign after it in the column
under j means that white runs in the negative sense of
the j direction.
We may express the fact in the following way:—
In the plane there is room for two axes while the body
has three. Therefore in the plane we can represent any
two. If we want to keep the axis that goes in the
unknown dimension always running in the positive
sense, then the axis which originally ran in the unknown
dimension (the white axis) must come in the negative