Section 19. How, though the Sphere shewed me other mysteries
of Spaceland, I still desired more; and what came of it
When I saw my poor brother led away to imprisonment, I attempted
to leap down into the Council Chamber, desiring to intercede
on his behalf, or at least bid him farewell. But I found that
I had no motion of my own. I absolutely depended on the volition
of my Guide, who said in gloomy tones, "Heed not thy brother;
haply thou shalt have ample time hereafter to condole with him.
Follow me."
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Once more we ascended into space. "Hitherto," said the Sphere,
"I have shewn you naught save Plane Figures and their interiors.
Now I must introduce you to Solids, and reveal to you the plan
upon which they are constructed. Behold this multitude
of moveable square cards. See, I put one on another, not,
as you supposed, Northward of the other, but ON the other.
Now a second, now a third. See, I am building up a Solid
by a multitude of Squares parallel to one another. Now the Solid
is complete, being as high as it is long and broad,
and we call it a Cube."
"Pardon me, my Lord," replied I; "but to my eye the appearance is as
of an Irregular Figure whose inside is laid open to the view;
in other words, methinks I see no Solid, but a Plane such as
we infer in Flatland; only of an Irregularity which betokens
some monstrous criminal, so that the very sight of it is painful
to my eyes."
"True," said the Sphere, "it appears to you a Plane,
because you are not accustomed to light and shade and perspective;
just as in Flatland a Hexagon would appear a Straight Line to one
who has not the Art of Sight Recognition. But in reality
it is a Solid, as you shall learn by the sense of Feeling."
He then introduced me to the Cube, and I found that this
marvellous Being was indeed no Plane, but a Solid; and that he was
endowed with six plane sides and eight terminal points
called solid angles; and I remembered the saying of the Sphere
that just such a Creature as this would be formed by a Square moving,
in Space, parallel to himself: and I rejoiced to think
that so insignificant a Creature as I could in some sense be called
the Progenitor of so illustrious an offspring.
But still I could not fully understand the meaning of what my Teacher
had told me concerning "light" and "shade" and "perspective";
and I did not hesitate to put my difficulties before him.
Were I to give the Sphere's explanation of these matters,
succinct and clear though it was, it would be tedious to an inhabitant
of Space, who knows these things already. Suffice it, that by his
lucid statements, and by changing the position of objects and lights,
and by allowing me to feel the several objects and even his own
sacred Person, he at last made all things clear to me,
so that I could now readily distinguish between a Circle and a Sphere,
a Plane Figure and a Solid.
This was the Climax, the Paradise, of my strange eventful History.
Henceforth I have to relate the story of my miserable Fall: --
most miserable, yet surely most undeserved! For why should the thirst
for knowledge be aroused, only to be disappointed and punished?
My volition shrinks from the painful task of recalling my humiliation;
yet, like a second Prometheus, I will endure this and worse,
if by any means I may arouse in the interiors of Plane and Solid
Humanity a spirit of rebellion against the Conceit which would limit
our Dimensions to Two or Three or any number short of Infinity.
Away then with all personal considerations! Let me continue
to the end, as I began, without further digressions or anticipations,
pursuing the plain path of dispassionate History. The exact facts,
the exact words, -- and they are burnt in upon my brain, --
shall be set down without alteration of an iota; and let my Readers
judge between me and Destiny.
The Sphere would willingly have continued his lessons
by indoctrinating me in the conformation of all regular Solids,
Cylinders, Cones, Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons,
and Spheres: but I ventured to interrupt him. Not that I was
wearied of knowledge. On the contrary, I thirsted for yet deeper
and fuller draughts than he was offering to me.
"Pardon me," said I, "O Thou Whom I must no longer address
as the Perfection of all Beauty; but let me beg thee to vouchsafe
thy servant a sight of thine interior."
SPHERE. My what?
I. Thine interior: thy stomach, thy intestines.
SPHERE. Whence this ill-timed impertinent request? And what
mean you by saying that I am no longer the Perfection of all Beauty?
I. My Lord, your own wisdom has taught me to aspire to One
even more great, more beautiful, and more closely approximate
to Perfection than yourself. As you yourself, superior to all
Flatland forms, combine many Circles in One, so doubtless there is One
above you who combines many Spheres in One Supreme Existence,
surpassing even the Solids of Spaceland. And even as we,
who are now in Space, look down on Flatland and see the insides
of all things, so of a certainty there is yet above us some higher,
purer region, whither thou dost surely purpose to lead me --
O Thou Whom I shall always call, everywhere and in all Dimensions,
my Priest, Philosopher, and Friend -- some yet more spacious Space,
some more dimensionable Dimensionality, from the vantage-ground
of which we shall look down together upon the revealed insides
of Solid things, and where thine own intestines, and those of thy
kindred Spheres, will lie exposed to the view of the poor wandering
exile from Flatland, to whom so much has already been vouchsafed.
SPHERE. Pooh! Stuff! Enough of this trifling! The time is short,
and much remains to be done before you are fit to proclaim the Gospel
of Three Dimensions to your blind benighted countrymen in Flatland.
I. Nay, gracious Teacher, deny me not what I know it is
in thy power to perform. Grant me but one glimpse of thine interior,
and I am satisfied for ever, remaining henceforth thy docile pupil,
thy unemancipable slave, ready to receive all thy teachings
and to feed upon the words that fall from thy lips.
SPHERE. Well, then, to content and silence you, let me say at once,
I would shew you what you wish if I could; but I cannot.
Would you have me turn my stomach inside out to oblige you?
I. But my Lord has shewn me the intestines of all my countrymen
in the Land of Two Dimensions by taking me with him
into the Land of Three. What therefore more easy than now
to take his servant on a second journey into the blessed region
of the Fourth Dimension, where I shall look down with him once more
upon this land of Three Dimensions, and see the inside
of every three-dimensioned house, the secrets of the solid earth,
the treasures of the mines in Spaceland, and the intestines of every
solid living creature, even of the noble and adorable Spheres.
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. 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 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.
I ask therefore, is it, or is it not, the fact, that ere now
your countrymen also have witnessed the descent of Beings
of a higher order than their own, entering closed rooms,
even as your Lordship entered mine, without the opening of doors
or windows, and appearing and vanishing at will? On the reply
to this question I am ready to stake everything. Deny it,
and I am henceforth silent. Only vouchsafe an answer.
SPHERE. (AFTER A PAUSE). It is reported so. But men are divided
in opinion as to the facts. And even granting the facts,
they explain them in different ways. And in any case,
however great may be the number of different explanations,
no one has adopted or suggested the theory of a Fourth Dimension.
Therefore, pray have done with this trifling, and let us return
to business.
I. I was certain of it. I was certain that my anticipations
would be fulfilled. And now have patience with me and answer me yet
one more question, best of Teachers! Those who have thus appeared --
no one knows whence -- and have returned -- no one knows whither --
have they also contracted their sections and vanished somehow into
that more Spacious Space, whither I now entreat you to conduct me?
SPHERE (MOODILY). They have vanished, certainly --
if they ever appeared. But most people say that these visions arose
from the thought -- you will not understand me -- from the brain;
from the perturbed angularity of the Seer.
I. Say they so? Oh, believe them not. Or if it indeed be so,
that this other Space is really Thoughtland, then take me to
that blessed Region where I in Thought shall see the insides
of all solid things. There, before my ravished eye, a Cube,
moving in some altogether new direction, but strictly according
to Analogy, so as to make every particle of his interior pass through
a new kind of Space, with a wake of its own -- shall create
a still more perfect perfection than himself, with sixteen terminal
Extra-solid angles, and Eight solid Cubes for his Perimeter.
And once there, shall we stay our upward course? In that blessed
region of Four Dimensions, shall we linger on the threshold
of the Fifth, and not enter therein? Ah, no! Let us rather resolve
that our ambition shall soar with our corporal ascent. Then,
yielding to our intellectual onset, the gates of the Sixth Dimension
shall fly open; after that a Seventh, and then an Eighth --
How long I should have continued I know not. In vain did the Sphere,
in his voice of thunder, reiterate his command of silence,
and threaten me with the direst penalties if I persisted.
Nothing could stem the flood of my ecstatic aspirations.
Perhaps I was to blame; but indeed I was intoxicated with
the recent draughts of Truth to which he himself had introduced me.
However, the end was not long in coming. My words were cut short
by a crash outside, and a simultaneous crash inside me,
which impelled me through space with a velocity that precluded speech.
Down! down! down! I was rapidly descending; and I knew
that return to Flatland was my doom. One glimpse, one last
and never-to-be-forgotten glimpse I had of that dull
level wilderness -- which was now to become my Universe again --
spread out before my eye. Then a darkness. Then a final,
all-consummating thunder-peal; and, when I came to myself,
I was once more a common creeping Square, in my Study at home,
listening to the Peace-Cry of my approaching Wife.
