Hinton - The Fourth Dimension.pdf

238
THE FOURTH DIMENSION
catalogue cube 2 is rightly placed. Catalogue cube 3 is
just like number 1.
Having these cubes in what we may call their normal
position, proceed to build up the three sets of blocks.
This is easily done in accordance with the colour scheme
on the catalogue cubes.
The first block we already know. Build up the second
block, beginning with a blue corner cube, placing a purple
on it, and so on.
Having these three blocks we have the means of
representing the appearances of a group of eighty-one
tesseracts.
Let us consider a moment what the analogy in the case
of the plane being is.
He has his three sets of nine slabs each. We have our
three sets of twenty-seven cubes each.
Our cubes are like his slabs. As his slabs are not the
things which they represent to him, so our cubes are not
the things they represent to us.
The plane being’s slabs are to him the faces of cubes.
Our cubes then are the faces of tesseracts, the cubes by
which they are in contact with our space.
As each set of slabs in the case of the plane being
might be considered as a sort of tray from which the solid
contents of the cubes came out, so our three blocks of
cubes may be considered as three-space trays, each of
which is the beginning of an inch of the solid contents
of the four-dimensional solids starting from them.
We want now to use the names null, red, white, etc.,
for tesseracts. The cubes we use are only tesseract faces.
Let us denote that fact by calling the cube of null colour,
null face; or, shortly, null f., meaning that it is the face
of a tesseract.
To determine which face it is let us look at the catalogue
cube 1 or the first of the views of the tesseract, which