How I Vainly Tried to Explain the Nature of Flatland

Thinking that it was time to bring down the Monarch from his raptures to
the level of common sense, I determined to endeavour to open up to him
some glimpses of the truth, that is to say of the nature of things in
Flatland. So I began thus: "How does your Royal Highness distinguish the
shapes and positions of his subjects? I for my part noticed by the sense
of sight, before I entered your Kingdom, that some of your people are
Lines and others Points, and that some of the Lines are larger⁠---"

"You speak of an impossibility," interrupted the King; "you must have
seen a vision; for to detect the difference between a Line and a Point
by the sense of sight is, as everyone knows, in the nature of things,
impossible; but it can be detected by the sense of hearing, and by the
same means my shape can be exactly ascertained. Behold me⁠---I am a Line,
the longest in Lineland, over six inches of Space⁠---"

"Of Length," I ventured to suggest.

"Fool," said he, "Space is Length. Interrupt me again, and I have done."

I apologized; but he continued scornfully, "Since you are impervious to
argument, you shall hear with your ears how by means of my two voices I
reveal my shape to my wives, who are at this moment six thousand miles
seventy yards two feet eight inches away, the one to the North, the
other to the South. Listen, I call to them."

He chirruped, and then complacently continued: "My wives, at this moment
receiving the sound of one of my voices, closely followed by the other,
and perceiving that the latter reaches them after an interval in which
sound can traverse 6.457 inches, infer that one of my mouths is 6.457
inches further from them than the other, and accordingly know my shape
to be 6.457 inches. But you will of course understand that my wives do
not make this calculation every time they hear my two voices. They made
it, once for all, before we were married. But they could make it at
any time. And in the same way I can estimate the shape of any of my male
subjects by the sense of sound."

"But how," said I, "if a man feigns a woman's voice with one of his two
voices, or so disguises his Southern voice that it cannot be recognized
as the echo of the Northern? May not such deceptions cause great
inconvenience? And have you no means of checking frauds of this kind by
commanding your neighbouring subjects to feel one another?" This of
course was a very stupid question, for feeling could not have answered
the purpose; but I asked with the view of irritating the Monarch, and I
succeeded perfectly.

"What!" cried he in horror, "explain your meaning."

"Feel, touch, come into contact," I replied.

"If you mean by feeling," said the King, "approaching so close as to
leave no space between two individuals, know, stranger, that this
offence is punishable in my dominions by death. And the reason is
obvious. The frail form of a woman, being liable to be shattered by such
an approximation, must be preserved by the State; but since women cannot
be distinguished by the sense of sight from men, the law ordains
universally that neither man nor woman shall be approached so closely as
to destroy the interval between the approximator and the approximated.

"And indeed what possible purpose would be served by this illegal and
unnatural excess of approximation which you call touching, when all
the ends of so brutal and coarse a process are attained at once more
easily and more exactly by the sense of hearing? As to your suggested
danger of deception, it is nonexistent: for the voice, being the essence
of one's being, cannot be thus changed at will. But come, suppose that I
had the power of passing through solid things, so that I could penetrate
my subjects, one after another, even to the number of a billion,
verifying the size and distance of each by the sense of feeling: how
much time and energy would be wasted in this clumsy and inaccurate
method! Whereas now, in one moment of audition, I take as it were the
census and statistics, local, corporeal, mental and spiritual, of every
living being in Lineland. Hark, only hark!"

So saying he paused and listened, as if in an ecstasy, to a sound which
seemed to me no better than a tiny chirping from an innumerable
multitude of lilliputian grasshoppers.

"Truly," replied I, "your sense of hearing serves you in good stead, and
fills up many of your deficiencies. But permit me to point out that your
life in Lineland must be deplorably dull. To see nothing but a Point!
Not even to be able to contemplate a Straight Line! Nay, not even to
know what a Straight Line is! To see, yet be cut off from those Linear
prospects which are vouchsafed to us in Flatland! Better surely to have
no sense of sight at all than to see so little! I grant you I have not
your discriminative faculty of hearing; for the concert of all Lineland
which gives you such intense pleasure, is to me no better than a
multitudinous twittering or chirping. But at least I can discern, by
sight, a Line from a Point. And let me prove it. Just before I came into
your kingdom, I saw you dancing from left to right, and then from right
to left, with seven men and a woman in your immediate proximity on the
left, and eight men and two women on your right. Is not this correct?"

"It is correct," said the King, "so far as the numbers and sexes are
concerned, though I know not what you mean by 'right' and 'left,' But I
deny that you saw these things. For how could you see the Line, that is
to say the inside, of any man? But you must have heard these things, and
then dreamed that you saw them. And let me ask what you mean by those
words 'left' and 'right,' I suppose it is your way of saying Northward
and Southward."

"Not so," replied I; "besides your motion of Northward and Southward,
there is another motion which I call from right to left."

King. Exhibit to me, if you please, this motion from left to right.

I. Nay, that I cannot do, unless you could step out of your Line
altogether.

King. Out of my Line? Do you mean out of the world? Out of Space?

I. Well, yes. Out of your world. Out of your Space. For your
Space is not the true Space. True Space is a Plane; but your Space is
only a Line.

King. If you cannot indicate this motion from left to right by
yourself moving in it, then I beg you to describe it to me in words.

I. If you cannot tell your right side from your left, I fear that no
words of mine can make my meaning clear to you. But surely you cannot be
ignorant of so simple a distinction.

King. I do not in the least understand you.

I. Alas! How shall I make it clear? When you move straight on, does
it not sometimes occur to you that you could move in some other way,
turning your eye round so as to look in the direction towards which your
side is now fronting? In other words, instead of always moving in the
direction of one of your extremities, do you never feel a desire to move
in the direction, so to speak, of your side?

King. Never. And what do you mean? How can a man's inside "front" in
any direction? Or how can a man move in the direction of his inside?

I. Well then, since words cannot explain the matter, I will try
deeds, and will move gradually out of Lineland in the direction which I
desire to indicate to you.

At the word I began to move my body out of Lineland. As long as any part
of me remained in his dominion and in his view, the King kept
exclaiming, "I see you, I see you still; you are not moving." But when I
had at last moved myself out of his Line, he cried in his shrillest
voice, "She is vanished; she is dead."

"I am not dead," replied I; "I am simply out of Lineland, that is to
say, out of the Straight Line which you call Space, and in the true
Space, where I can see things as they are. And at this moment I can see
your Line, or side⁠---or inside as you are pleased to call it; and I can
see also the men and women on the North and South of you, whom I will
now enumerate, describing their order, their size, and the interval
between each."

When I had done this at great length, I cried triumphantly, "Does that
at last convince you?" And, with that, I once more entered Lineland,
taking up the same position as before.

But the Monarch replied, "If you were a man of sense⁠---though, as you
appear to have only one voice I have little doubt you are not a man but
a woman⁠---but, if you had a particle of sense, you would listen to
reason. You ask me to believe that there is another Line besides that
which my senses indicate, and another motion besides that of which I am
daily conscious. I, in return, ask you to describe in words or indicate
by motion that other Line of which you speak. Instead of moving, you
merely exercise some magic art of vanishing and returning to sight; and
instead of any lucid description of your new world, you simply tell me
the numbers and sizes of some forty of my retinue, facts known to any
child in my capital. Can anything be more irrational or audacious?
Acknowledge your folly or depart from my dominions."

Furious at his perversity, and especially indignant that he professed to
be ignorant of my sex, I retorted in no measured terms, "Besotted being!
You think yourself the perfection of existence, while you are in reality
the most imperfect and imbecile. You profess to see, whereas you can see
nothing but a Point! You plume yourself on inferring the existence of a
Straight Line; but I can see Straight Lines, and infer the existence
of Angles, Triangles, Squares, Pentagons, Hexagons, and even Circles.
Why waste more words? Suffice it that I am the completion of your
incomplete self. You are a Line, but I am a Line of Lines, called in my
country a Square: and even I, infinitely superior though I am to you, am
of little account among the great nobles of Flatland, whence I have come
to visit you, in the hope of enlightening your ignorance."

Hearing these words the King advanced towards me with a menacing cry as
if to pierce me through the diagonal; and in that same moment there
arose from myriads of his subjects a multitudinous war-cry, increasing
in vehemence till at last methought it rivalled the roar of an army of a
hundred thousand Isosceles, and the artillery of a thousand Pentagons.
Spellbound and motionless, I could neither speak nor move to avert the
impending destruction; and still the noise grew louder, and the King
came closer, when I awoke to find the breakfast-bell recalling me to the
realities of Flatland.