Hinton - The Fourth Dimension.pdf

APPENDIX I: THE MODELS 239
can be used instead of the models. It has three axes,
red, white, yellow, in our space. Hence the cube determined
by these axes is the face of the tesseract which we
now have before us. It is the ochre face. It is enough,
however, simply to say null f., red f. for the cubes which
we use.
To impress this in your mind, imagine that tesseracts
do actually run from each cube. Then, when you move the
cubes about, you move the tesseracts about with them.
You move the face but the tesseract follows with it, as the
cube follows when its face is shifted in a plane.
The cube null in the normal position is the cube which
has in it the red, yellow, white axes. It is the face
having these, but wanting the blue. In this way you can
define which face it is you are handling. I will write an
“f.” after the name of each tesseract just as the plane
being might call each of his slabs null slab, yellow slab,
etc., to denote that they were representations.
We have then in the first block of twenty-seven cubes,
the following—null f., red f., null f., going up; white f., null
f., lying to the right, and so on. Starting from the null
point and travelling up one inch we are in the null region,
the same for the away and the right-hand directions.
And if we were to travel in the fourth dimension for an
inch we should still be in a null region. The tesseract
stretches equally all four ways. Hence the appearance we
have in this first block would do equally well if the
tesseract block were to move across our space for a certain
distance. For anything less than an inch of their transverse
motion we would still have the same appearance.
You must notice, however, that we should not have null
face after the motion had begun.
When the tesseract, null for instance, had moved ever
so little we should not have a face of null but a section of
null in our space. Hence, when we think of the motion