Sphere. But where is this land of Four Dimensions?
I. I know not: but doubtless my Teacher knows.
Sphere. Not I. There is no such land. The very idea of it is
utterly inconceivable.
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.
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