Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
Take models 4, 5, 6. Place 4, or suppose No. 4 of the
tesseract views place, with its orange face coincident with
the orange face of 1, red line to red line, and yellow line
to yellow line, with the blue line pointing to the left.
Then remove cube 1 and we have the tesseract face
which comes in when the white axis runs in the positive
unknown, and the blue axis comes into our space.
Now place catalogue cube 5 in some position, it does
not matter which, say to the left; and place it so that
there is a correspondence of colour corresponding to the
colour of the line that runs out of space. The line that
runs out of space is white, hence, every part of this
cube 5 should differ from the corresponding part of 4 by
an alteration in the direction of white.
Thus we have white points in 5 corresponding to the
null points in 4. We have a pink line corresponding to
a red line, a light yellow line corresponding to a yellow
line, an ochre face corresponding to an orange face. This
cube section is completely named in Chapter XI. Finally
cube 6 is a replica of 4.
These catalogue cubes will enable us to set up our
models of the block of tesseracts.
First of all for the set of tesseracts, which beginning
in our space reach out one inch in the unknown, we have
the pattern of catalogue cube 4.
We see that we can build up a block of twenty-seven
tesseract faces after the colour scheme of cube 4, by
taking the left-hand wall of block 1, then the left-hand
wall of block 2, and finally that of block 3. We take,
that is, the first three walls of our previous arrangement
to form the first cubic block of this new one.
This will represent the cubic faces by which the group
of tesseracts in its new position touches our space.
We have running up, null f., red f., null f. In the next
vertical line, on the side remote from us, we have yellow f.,