on,
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. 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 accordin