Hinton - The Fourth Dimension.pdf

CHAPTER XIII
REMARKS ON THE FIGURES
AN inspection of above figures will give an answer to
many questions about the tesseract. If we have a
tesseract one inch each way, then it can be represented
as a cube—a cube having white, yellow, red axes, and
from this cube as a beginning, a volume extending into
the fourth dimension. Now suppose the tesseract to pass
transverse to our space, the cube of the red, yellow, white
axes disappears at once, it is indefinitely thin in the
fourth dimension. Its place is occupied by those parts of
the tesseract which lie further away from our space
in the fourth dimension. Each one of these sections
will last only for one moment, but the whole of them
will take up some appreciable time in passing. If we
take the rate of one inch a minute the sections will take
the whole of the minute in their passage across our
space, they will take the whole of the minute except the
moment which the beginning cube and the end cube
occupy in their crossing our space. In each one of the
cubes, the section cubes, we can draw lines in all directions
except in the direction occupied by the blue line, the
fourth dimension; lines in that direction are represented
by the transition from one section cube to another. Thus
to give ourselves an adequate representation of the
tesseract we ought to have a limitless number of section
cubes intermediate between the first bounding cube, the
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