Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
and finally underneath this last the bottom layer of the
last of our normal blocks.
Similarly we make the second representative group by
taking the middle courses of our three blocks. The last
is made by taking the three topmost layers. The three
axes in our space before the transverse motion begins
are blue, white, yellow, so we have light green tesseract
faces, and after the motion begins sections transverse to
the red light.
These three blocks represent the appearances as the
tesseract group in its new position passes across our space.
The cubes of contact in this case are those determined by
the three axes in our space, namely, the white, the
yellow, the blue. Hence they are light green.
It follows from this that light green is the interior
cube of the first block of representative cubic faces.
Practice in the manipulations described, with a
realisation in each case of the face or section which
is in our space, is one of the best means of a thorough
comprehension of the subject.
We have to learn how to get any part of these fourdimensional
figures into space, so that we can look at
them. We must first learn to swing a tesseract, and a
group of tesseracts about in any way.
When these operations have been repeated and the
method of arrangement of the set of blocks has become
familiar, it is a good plan to rotate the axes of the normal
cube 1 about a diagonal, and then repeat the whole series
of turnings.
Thus, in the normal position, red goes up, white to the
right, yellow away. Make white go up, yellow to the right,
and red away. Learn the cube in this position by putting
up the set of blocks of the normal cube, over and over
again till it becomes as familiar to you as in the normal
position. Then when this is learned, and the corre-