Now stretch your imagination a little, and conceive
a Square in Flatland, moving parallel to itself upward.
I. What? Northward?
SPHERE. No, not Northward; upward; out of Flatland altogether.
If it moved Northward, the Southern points in the Square would have to
move through the positions previously occupied by the Northern points.
But that is not my meaning.
I mean that every Point in you -- for you are a Square and will serve
the purpose of my illustration -- every Point in you, that is to say
in what you call your inside, is to pass upwards through Space
in such a way that no Point shall pass through the position
previously occupied by any other Point; but each Point shall describe
a straight Line of its own. This is all in accordance with Analogy;
surely it must be clear to you.
Restraining my impatience -- for I was now under a strong temptation
to rush blindly at my Visitor and to precipitate him into Space,
or out of Flatland, anywhere, so that I could get rid of him --
I replied: --
"And what may be the nature of the Figure which I am to shape out
by this motion which you are pleased to denote by the word 'upward'?
I presume it is describable in the language of Flatland.
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