Hinton - The Fourth Dimension.pdf

164
THE FOURTH DIMENSION
natural supposition to make. It is also natural to suppose
that blue added to red makes purple. Orange and blue
can be made to give a brown, by using certain shades and
proportions. And ochre and blue can be made to give a
light brown.
But the scheme of colours is merely used for getting a
definite and realisable set of names and distinctions
visible to the eye. Their naturalness is apparent to any
one in the habit of using colours, and may be assumed to
be justifiable, as the sole purpose is to devise a set of
names which are easy to remember, and which will give
us a set of colours by which diagrams may be made easy
of comprehension. No scientific classification of colours
has been attempted.
Starting, then, with these sixteen colour names, we have
a catalogue of the sixteen tesseracts, which form a fourdimensional
block analogous to the cubic block. But
the cube which we can put in space and look at is not one
of the constituent tesseracts; it is merely the beginning,
the solid face, the side, the aspect, of a tesseract.
We will now proceed to derive a name for each region,
point, edge, plane face, solid and a face of the tesseract.
The system will be clear, if we look at a representation
in the plane of a tesseract with three, and one with four
divisions in its side.
The tesseract made up of three tesseracts each way
corresponds to the cube made up of three cubes each way,
and will give us a complete nomenclature.
In this diagram, fig. 101, 1 represents a cube of 27
cubes, each of which is the beginning of a tesseract.
These cubes are represented only by their lowest squares,
the solid content must be understood. 2 represents the
27 cubes which are the beginnings of the 27 tesseracts
one inch on in the fourth dimension. These tesseracts
are represented as a block of cubes put side by side with