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Abbott, Edwin Abbott, 1838-1926

"Flatland: a romance of many dimensions (Illustrated)"


I. Not inconceivable, my Lord, to me, and therefore still less
inconceivable to my Master. Nay, I despair not that, even here,
in this region of Three Dimensions, your Lordship's art
may make the Fourth Dimension visible to me; just as in the Land
of Two Dimensions my Teacher's skill would fain have opened the eyes
of his blind servant to the invisible presence of a Third Dimension,
though I saw it not.
Let me recall the past. Was I not taught below that when I saw a Line
and inferred a Plane, I in reality saw a Third unrecognized Dimension,
not the same as brightness, called "height"? And does it not now
follow that, in this region, when I see a Plane and infer a Solid,
I really see a Fourth unrecognized Dimension, not the same as colour,
but existent, though infinitesimal and incapable of measurement?
And besides this, there is the Argument from Analogy of Figures.
SPHERE. Analogy! Nonsense: what analogy?
I. Your Lordship tempts his servant to see whether he remembers
the revelations imparted to him. Trifle not with me, my Lord;
I crave, I thirst, for more knowledge. Doubtless we cannot SEE
that other higher Spaceland now, because we we have no eye
in our stomachs.


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