Flatland: A Romance of Many Dimensions
their wont, in strict accordance with precedent, the highest Circles of
the realm were meeting in solemn conclave, as they had met on the first
hour of the first day of the year 1000, and also on the first hour of
the first day of the year 0.
The minutes of the previous meetings were now read by one whom I at
once recognized as my brother, a perfectly Symmetrical Square, and the
Chief Clerk of the High Council. It was found recorded on each
occasion that: "Whereas the States had been troubled by divers
ill-intentioned persons pretending to have received revelations from
another World, and professing to produce demonstrations whereby they
had instigated to frenzy both themselves and others, it had been for
this cause unanimously resolved by the Grand Council that on the first
day of each millenary, special injunctions be sent to the Prefects in
the several districts of Flatland, to make strict search for such
misguided persons, and without formality of mathematical examination,
to destroy all such as were Isosceles of any degree, to scourge and
imprison any regular Triangle, to cause any Square or Pentagon to be
sent to the district Asylum, and to arrest any one of higher rank,
sending him straightway to the Capital to be examined and judged by the
Council."
"You hear your fate," said the Sphere to me, while the Council was
passing for the third time the formal resolution. "Death or
imprisonment awaits the Apostle of the Gospel of Three Dimensions."
"Not so," replied I, "the matter is now so clear to me, the nature of
real space so palpable, that methinks I could make a child understand
it. Permit me but to descend at this moment and enlighten them." "Not
yet," said my Guide, "the time will come for that. Meantime I must
perform my mission. Stay thou there in thy place." Saying these
words, he leaped with great dexterity into the sea (if I may so call
it) of Flatland, right in the midst of the ring of Counsellors. "I
come," cried he, "to proclaim that there is a land of Three Dimensions."
I could see many of the younger Counsellors start back in manifest
horror, as the Sphere's circular section widened before them. But on a
sign from the presiding Circle--who shewed not the slightest alarm or
surprise--six Isosceles of a low type from six different quarters
rushed upon the Sphere. "We have him," they cried; "No; yes; we have
him still! he's going! he's gone!"
"My Lords," said the President to the Junior Circles of the Council,
"there is not the slightest need for surprise; the secret archives, to
which I alone have access, tell me that a similar occurrence happened
on the last two millennial commencements. You will, of course, say
nothing of these trifles outside the Cabinet."
Raising his voice, he now summoned the guards. "Arrest the policemen;
gag them. You know your duty." After he had consigned to their fate
the wretched policemen--ill-fated and unwilling witnesses of a
State-secret which they were not to be permitted to reveal--he again
addressed the Counsellors. "My Lords, the business of the Council
being concluded, I have only to wish you a happy New Year." Before
departing, he expressed, at some length, to the Clerk, my excellent but
most unfortunate brother, his sincere regret that, in accordance with
precedent and for the sake of secrecy, he must condemn him to perpetual
imprisonment, but added his satisfaction that, unless some mention were
made by him of that day's incident, his life would be spared.
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