But, just as there WAS the realm of Flatland,
though that poor puny Lineland Monarch could neither turn to left
nor right to discern it, and just as there WAS close at hand,
and touching my frame, the land of Three Dimensions,
though I, blind senseless wretch, had no power to touch it,
no eye in my interior to discern it, so of a surety there is
a Fourth Dimension, which my Lord perceives with the inner eye
of thought. And that it must exist my Lord himself has taught me.
Or can he have forgotten what he himself imparted to his servant?
In One Dimension, did not a moving Point produce a Line
with TWO terminal points?
In Two Dimensions, did not a moving Line produce a Square
with FOUR terminal points?
In Three Dimensions, did not a moving Square produce --
did not this eye of mine behold it -- that blessed Being, a Cube,
with EIGHT terminal points?
And in Four Dimensions shall not a moving Cube -- alas, for Analogy,
and alas for the Progress of Truth, if it be not so -- shall not,
I say, the motion of a divine Cube result in a still more divine
Organization with SIXTEEN terminal points?
Behold the infallible confirmation of the Series, 2, 4, 8, 16:
is not this a Geometrical Progression? Is not this -- if I might
quote my Lord's own words -- "strictly according to Analogy"?
Again, was I not taught by my Lord that as in a Line there are
TWO bounding Points, and in a Square there are FOUR
bounding Lines, so in a Cube there must be SIX bounding Squares?
Behold once more the confirming Series, 2, 4, 6: is not this
an Arithmetical Progression? And consequently does it not
of necessity follow that the more divine offspring of the divine Cube
in the Land of Four Dimensions, must have 8 bounding Cubes:
and is not this also, as my Lord has taught me to believe,
"strictly according to Analogy"?
O, my Lord, my Lord, behold, I cast myself in faith upon conjecture,
not knowing the facts; and I appeal to your Lordship to confirm
or deny my logical anticipations.
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