Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
of cubic faces we have put up—these would last for a
minute, then would come the second block and then the
third. At first we should have a cube of tesseract faces,
each of which would be brown. Directly the movement
began, we should have tesseract sections transverse to the
white line.
There are two more analogous positions in which the
block of tesseracts can be placed. To find the third
position, restore the blocks to the normal arrangement.
Let us make the yellow axis go out into the positive
unknown, and let the blue axis, consequently, come in
running towards us. The yellow ran away, so the blue
will come in running towards us.
Put catalogue cube 1 in its normal position. Take
catalogue cube 7 and place it so that its pink face
coincides with the pink face of cube 1, making also its
red axis coincide with the red axis of 1 and its white
with the white. Moreover, make cube 7 come
towards us from cube 1. Looking at it we see in our
space, red, white, and blue axes. The yellow runs out.
Place catalogue cube 8 in the neighbourhood of
7—observe that every region in 8 has a change in
the direction of yellow from the corresponding region
in 7. This is because it represents what you come
to now in going in the unknown, when the yellow axis
runs out of our space. Finally catalogue cube 9,
which is like number 7, shows the colours of the third
set of tesseracts. Now evidently, starting from the
normal position, to make up our three blocks of tesseract
faces we have to take the near wall from the first block,
the near wall from the second, and then the near wall
from the third block. This gives us the cubic block
formed by the faces of the twenty-seven tesseracts which
are now immediately touching our space.
Following the colour scheme of catalogue cube 8,