It is equally absurd
and impossible to us if we require the third line to be drawn on
the paper. But we should reply, "If you allow us to leave the
paper or flat surface, then we can solve the problem by simply
drawing the third line through the paper perpendicular to its
surface."
[Illustration with caption: FIG. 2]
Now, to pursue the analogy, suppose that, after we have drawn
three mutually perpendicular lines, some being from another sphere
proposes to us the drawing of a fourth line through the same
point, perpendicular to all three of the lines already there. We
should answer him in the same way that the inhabitants of "flat-
land" answered us: "The problem is impossible. You cannot draw any
such line in space as we understand it." If our visitor conceived
of the fourth dimension, he would reply to us as we replied to the
"flat-land" people: "The problem is absurd and impossible if you
confine your line to space as you understand it. But for me there
is a fourth dimension in space. Draw your line through that
dimension, and the problem will be solved. This is perfectly
simple to me; it is impossible to you solely because your
conceptions do not admit of more than three dimensions.
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