Hinton - The Fourth Dimension.pdf

188
THE FOURTH DIMENSION
whatever cubic view we take of them we can say exactly
what sides of the tesseracts we are handling, and how
they touch each other.*
Thus, for instance, if we have the sixteen tesseracts
shown below, we can ask how does null touch blue.
In the arrangement given in fig. 111 we have the axes
white, red, yellow, in space, blue running in the fourth
dimension. Hence we have the ochre cubes as bases.
Imagine now the tesseractic group to pass transverse to
our space—we have first of all null ochre cube, white
Yellow
axis
Red
axis
x
Light yellow hidden
A.b0
Yellow
direction
White
axis
Fig. 111.
Red
direction
White
direction
Light green hidden
B.b1
ochre cube, etc.; these instantly vanish, and we get the
section shown in the middle cube in fig. 103, and finally,
just when the tesseract block has moved one inch transverse
to our space, we have null ochre cube, and then
immediately afterwards the ochre cube of blue comes in.
Hence the tesseract null touches the tesseract blue by its
ochre cube, which is in contact, each and every point
of it, with the ochre cube of blue.
How does null touch white, we may ask? Looking at
the beginning A, fig. 111, where we have the ochre
* At this point the reader will find it advantageous, if he has the
models, to go through the manipulations described in Appendix I.