Flatland: A Romance of Many DimensionsAbbott, Edwin Abbott
Science
Flatland: A Romance of Many Dimensions
Abbott, Edwin Abbott
Fourth dimension
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 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 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. If I am wrong, I yield, and will no longer
demand a Fourth Dimension; but, if I am right, my Lord will listen to
reason.
Public-domain text, read in full here on John Shaqi.
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