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How Though The Sphere Shewed Me Other Mysteries Of Spaceland I Still Desire More And What Came Of It






Part of: OTHER WORLDS
From: Flatland

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."

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 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 the 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 reform. 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 of Spaceland, and the
intestines of every solid living creature, even 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 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 at 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 Six 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.





Next: How The Sphere Encouraged Me In A Vision

Previous: How I Came To Spaceland And What I Saw There



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