Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
plane being would represent three-dimensional space, only
one of the catalogue cubes and one of the three blocks is
needed.
APPLICATION TO THE STEP FROM PLANE TO SOLID.
Look at fig. 1 of the view of the tesseract, or, what
comes to the same thing, take catalogue cube No. 1 and
place it before you with the red line running up, the
white line running to the right, the yellow line running
away. The three dimensions of space are then marked
out by these lines or axes. Now take a piece of cardboard,
or a book, and place it so that it forms a wall
extending up and down, not opposite to you, but running
away parallel to the wall of the room on your
left hand.
Placing the catalogue cube against this wall we see
that it comes into contact with it by the red and yellow
lines, and by the included orange face.
In the plane being’s world the aspect he has of the
cube would be a square surrounded by red and yellow
lines with grey points.
Now, keeping the red line fixed, turn the cube about it
so that the yellow line goes out to the right, and the
white line comes into contact with the plane.
In this case a different aspect is presented to the plane
being, a square, namely, surrounded by red and white
lines, and grey points. You should particularly notice
that when the yellow line goes out, at right angles to the
plane, and the white comes in, the latter does not run in
the same sense that the yellow did.
From the fixed grey point at the base of the red line
the yellow line ran away from you. The white line now
runs towards you. This turning at right angles makes
the line which was out of the plane before, come into it