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Abbott, Edwin Abbott, 1838-1926

"Flatland: a romance of many dimensions"

--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, or in, the top of which you and your
countrymen move about, without rising above 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. For even a Sphere--which is my proper name in my own
country--if he manifest himself at all to an inhabitant of Flatland--
must needs manifest himself as a Circle.
Do you not remember--for I, who see all things, discerned last
night the phantasmal vision of Lineland written upon your brain--
do you not remember, I say, how when you entered the realm of Lineland,
you were compelled to manifest yourself to the King, not as a Square,
but as a Line, because that Linear Realm had not Dimensions enough
to represent the whole of you, but only a slice or section of you?
In precisely the same way, your country of Two Dimensions is not spacious
enough to represent me, a being of Three, but can only exhibit a slice
or section of me, which is what you call a Circle.


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