I. My Lord, your assertion is easily put to the test.
You say I have a Third Dimension, which you call "height".
Now, Dimension implies direction and measurement. Do but measure
my "height", or merely indicate to me the direction in which
my "height" extends, and I will become your convert. Otherwise,
your Lordship's own understanding must hold me excused.
STRANGER. (TO HIMSELF.) I can do neither. How shall I
convince him? Surely a plain statement of facts followed by
ocular demonstration ought to suffice. -- Now, Sir; listen to me.
You are living on a Plane. What you style Flatland is
the vast level surface of what I may call a fluid, on, or in,
the top of which you and your countrymen move about,
without rising above it or falling below it.
I am not a plane Figure, but a Solid. You call me a Circle;
but in reality I am not a Circle, but an infinite number of Circles,
of size varying from a Point to a Circle of thirteen inches
in diameter, one placed on the top of the other. When I cut through
your plane as I am now doing, I make in your plane a section
which you, very rightly, call a Circle.
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