See, I am building up a Solid
by a multitude of Squares parallel to one another. Now the Solid
is complete, being as high as it is long and broad,
and we call it a Cube."
"Pardon me, my Lord," replied I; "but to my eye the appearance is as
of an Irregular Figure whose inside is laid open to the view;
in other words, methinks I see no Solid, but a Plane such as
we infer in Flatland; only of an Irregularity which betokens
some monstrous criminal, so that the very sight of it is painful
to my eyes."
"True," said the Sphere, "it appears to you a Plane,
because you are not accustomed to light and shade and perspective;
just as in Flatland a Hexagon would appear a Straight Line to one
who has not the Art of Sight Recognition. But in reality
it is a Solid, as you shall learn by the sense of Feeling."
He then introduced me to the Cube, and I found that this
marvellous Being was indeed no Plane, but a Solid; and that he was
endowed with six plane sides and eight terminal points
called solid angles; and I remembered the saying of the Sphere
that just such a Creature as this would be formed by a Square moving,
in Space, parallel to himself: and I rejoiced to think
that so insignificant a Creature as I could in some sense be called
the Progenitor of so illustrious an offspring.
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