But thou, whence intrudest thou into my realm of Lineland?” Receiving
this abrupt reply, I begged pardon if I had in any way startled or
molested his Royal Highness; and describing myself as a stranger I
besought the King to give me some account of his dominions. But I had the
greatest possible difficulty in obtaining any information on points that
really interested me; for the Monarch could not refrain from constantly
assuming that whatever was familiar to him must also be known to me and
that I was simulating ignorance in jest. However, by persevering
questions I elicited the following facts:
It seemed that this poor ignorant Monarch—as he called himself—was
persuaded that the Straight Line which he called his Kingdom, and in
which he passed his existence, constituted the whole of the world, and
indeed the whole of Space. Not being able either to move or to see, save
in his Straight Line, he had no conception of anything out of it. Though
he had heard my voice when I first addressed him, the sounds had come to
him in a manner so contrary to his experience that he had made no answer,
“seeing no man,” as he expressed it, “and hearing a voice as it were from
my own intestines.” Until the moment when I placed my mouth in his World,
he had neither seen me, nor heard anything except confused sounds beating
against what I called his side, but what he called his _inside_ or
_stomach_; nor had he even now the least conception of the region from
which I had come. Outside his World, or Line, all was a blank to him;
nay, not even a blank, for a blank implies Space; say, rather, all was
non-existent.
His subjects—of whom the small Lines were Men and the Points Women—were
all alike confined in motion and eye-sight to that single Straight Line,
which was their World. It need scarcely be added that the whole of their
horizon was limited to a Point; nor could any one ever see anything but a
Point. Man, woman, child, thing—each was a Point to the eye of a
Linelander. Only by the sound of the voice could sex or age be
distinguished. Moreover, as each individual occupied the whole of the
narrow path, so to speak, which constituted his Universe, and no one
could move to the right or left to make way for passers by, it followed
that no Linelander could ever pass another. Once neighbours, always
neighbours. Neighbourhood with them was like marriage with us. Neighbours
remained neighbours till death did them part.
Such a life, with all vision limited to a Point, and all motion to a
Straight Line, seemed to me inexpressibly dreary; and I was surprised to
note the vivacity and cheerfulness of the King. Wondering whether it was
possible, amid circumstances so unfavourable to domestic relations, to
enjoy the pleasures of conjugal union, I hesitated for some time to
question his Royal Highness on so delicate a subject; but at last I
plunged into it by abruptly inquiring as to the health of his family. “My
wives and children,” he replied, “are well and happy.”
Staggered at this answer—for in the immediate proximity of the Monarch
(as I had noted in my dream before I entered Lineland) there were none
but Men—I ventured to reply, “Pardon me, but I cannot imagine how your
Royal Highness can at any time either see or approach their Majesties,
when there are at least half a dozen intervening individuals, whom you
can neither see through, nor pass by? Is it possible that in Lineland
proximity is not necessary for marriage and for the generation of
children?”
“How can you ask so absurd a question?” replied the Monarch. “If it were
indeed as you suggest, the Universe would soon be depopulated. No, no;
neighbourhood is needless for the union of hearts; and the birth of
children is too important a matter to have been allowed to depend upon
such an accident as proximity. You cannot be ignorant of this. Yet since
you are pleased to affect ignorance, I will instruct you as if you were
the veriest baby in Lineland. Know, then, that marriages are consummated
by means of the faculty of sound and the sense of hearing.
“You are of course aware that every Man has two mouths or voices—as well
as two eyes—a bass at one and a tenor at the other of his extremities. I
should not mention this, but that I have been unable to distinguish your
tenor in the course of our conversation.” I replied that I had but one
voice, and that I had not been aware that His Royal Highness had two.
“That confirms my impression,” said the King, “that you are not a Man,
but a feminine Monstrosity with a bass voice and an utterly uneducated
ear. But to continue.
“Nature herself having ordained that every Man should wed two wives——”
“Why two?” asked I. “You carry your affected simplicity too far,” he
cried. “How can there be a completely harmonious union without the
combination of the Four in One, viz. the Bass and Tenor of the Man and
the Soprano and Contralto of the two Women?” “But supposing,” said I,
“that a man should prefer one wife or three?” “It is impossible,” he
said; “it is as inconceivable as that two and one should make five, or
that the human eye should see a Straight Line.” I would have interrupted
him; but he proceeded as follows:
“Once in the middle of each week a Law of Nature compels us to move to
and fro with a rhythmic motion of more than usual violence, which
continues for the time you would take to count a hundred and one. In the
midst of this choral dance, at the fifty-first pulsation, the inhabitants
of the Universe pause in full career, and each individual sends forth his
richest, fullest, sweetest strain. It is in this decisive moment that all
our marriages are made. So exquisite is the adaptation of Bass to Treble,
of Tenor to Contralto, that oftentimes the Loved Ones, though twenty
thousand leagues away, recognise at once the responsive note of their
destined Lover; and, penetrating the paltry obstacles of distance, Love
unites the three. The marriage in that instant consummated results in a
threefold Male and Female offspring which takes its place in Lineland.”
“What! Always threefold?” said I. “Must one wife then always have twins?”
“Bass-voiced Monstrosity! yes,” replied the King. “How else could the
balance of the Sexes be maintained, if two girls were not born for every
boy? Would you ignore the very Alphabet of Nature?” He ceased, speechless
for fury; and some time elapsed before I could induce him to resume his
narrative.
“You will not, of course, suppose that every bachelor among us finds his
mates at the first wooing in this universal Marriage Chorus. On the
contrary, the process is by most of us many times repeated. Few are the
hearts whose happy lot it is at once to recognise in each other’s voices
the partner intended for them by Providence, and to fly into a reciprocal
and perfectly harmonious embrace. With most of us the courtship is of
long duration. The Wooer’s voices may perhaps accord with one of the
future wives, but not with both; or not, at first, with either; or the
Soprano and Contralto may not quite harmonise. In such cases Nature has
provided that every weekly Chorus shall bring the three Lovers into
closer harmony. Each trial of voice, each fresh discovery of discord,
almost imperceptibly induces the less perfect to modify his or her vocal
utterance so as to approximate to the more perfect. And after many trials
and many approximations, the result is at last achieved. There comes a
day at last, when, while the wonted Marriage Chorus goes forth from
universal Lineland, the three far-off Lovers suddenly find themselves in
exact harmony, and, before they are aware, the wedded Triplet is rapt
vocally into a duplicate embrace; and Nature rejoices over one more
marriage and over three more births.”
§ 14.—_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 every one 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 apologised; 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 recognised
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 Man, 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 non-existent: 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, corporal, 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 to 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 my 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 also see 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.”
[Illustration: ]
When I had done this at great length, I cried triumphantly, “Does this 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.
Spell-bound 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.
§ 15.—_Concerning a Stranger from Spaceland._
From dreams I proceed to facts.
It was the last day of the 1999th year of our era. The pattering of the
rain had long ago announced nightfall; and I was sitting[3] in the
company of my wife, musing on the events of the past and the prospects of
the coming year, the coming century, the coming Millennium.
My four Sons and two orphan Grandchildren had retired to their several
apartments; and my Wife alone remained with me to see the old Millennium
out and the new one in.
I was rapt in thought, pondering in my mind some words that had casually
issued from the mouth of my youngest Grandson, a most promising young
Hexagon of unusual brilliancy and perfect angularity. His uncles and I
had been giving him his usual practical lesson in Sight Recognition,
turning ourselves upon our centres, now rapidly, now more slowly, and
questioning him as to our positions; and his answers had been so
satisfactory that I had been induced to reward him by giving him a few
hints on Arithmetic, as applied to Geometry.
Taking nine Squares, each an inch every way, I had put them together so
as to make one large Square, with a side of three inches, and I had hence
proved to my little Grandson that—though it was impossible for us to
_see_ the inside of the Square—yet we might ascertain the number of
square inches in a Square by simply squaring the number of inches in the
side: “and thus,” said I, “we know that 3², or 9, represents the number
of square inches in a Square whose side is 3 inches long.”
The little Hexagon meditated on this awhile and then said to me: “But you
have been teaching me to raise numbers to the third power; I suppose 3³
must mean something in Geometry; what does it mean?” “Nothing at all,”
replied I, “not at least in Geometry; for Geometry has only Two
Dimensions.” And then I began to show the boy how a Point by moving
through a length of three inches makes a Line of three inches, which may
be represented by 3; and how a Line of three inches, moving parallel to
itself through a length of three inches, makes a Square of three inches
every way, which may be represented by 3².
Upon this, my Grandson, again returning to his former suggestion, took me
up rather suddenly and exclaimed, “Well, then, if a Point by moving three
inches, makes a Line of three inches represented by 3; and if a straight
Line of three inches, moving parallel to itself, makes a Square of three
inches every way, represented by 3²; it must be that a Square of three
inches every way, moving somehow parallel to itself (but I don’t see how)
must make a Something else (but I don’t see what) of three inches every
way—and this must be represented by 3³.”
“Go to bed,” said I, a little ruffled by his interruption; “if you would
talk less nonsense, you would remember more sense.”
So my Grandson had disappeared in disgrace; and there I sat by my Wife’s
side, endeavouring to form a retrospect of the year 1999 and of the
possibilities of the year 2000, but not quite able to shake off the
thoughts suggested by the prattle of my bright little Hexagon. Only a few
sands now remained in the half-hour glass. Rousing myself from my reverie
I turned the glass Northward for the last time in the old Millennium; and
in the act, I exclaimed aloud, “The boy is a fool.”
Straightway I became conscious of a Presence in the room, and a chilling
breath thrilled through my very being. “He is no such thing,” cried my
Wife, “and you are breaking the Commandments in thus dishonouring your
own Grandson.” But I took no notice of her. Looking round in every
direction I could see nothing; yet still I _felt_ a Presence, and
shivered as the cold whisper came again. I started up. “What is the
matter?” said my Wife, “there is no draught; what are you looking for?
There is nothing.” There was nothing; and I resumed my seat, again
exclaiming, “The boy is a fool, I say; 3³ can have no meaning in
Geometry.” At once there came a distinctly audible reply, “The boy is not
a fool; and 3³ has an obvious Geometrical meaning.”
My Wife as well as myself heard the words, although she did not
understand their meaning, and both of us sprang forward in the direction
of the sound. What was our horror when we saw before us a Figure! At the
first glance it appeared to be a Woman, seen sideways; but a moment’s
observation shewed me that the extremities passed into dimness too
rapidly to represent one of the Female Sex; and I should have thought it
a Circle, only that it seemed to change its size in a manner impossible
for a Circle or for any Regular Figure of which I had had experience.
But my Wife had not my experience, nor the coolness necessary to note
these characteristics. With the usual hastiness and unreasoning jealousy
of her Sex, she flew at once to the conclusion that a Woman had entered
the house through some small aperture. “How comes this person here?” she
exclaimed, “you promised me, my dear, that there should be no ventilators
in our new house.” “Nor are there any,” said I; “but what makes you think
that the stranger is a Woman? I see by my power of Sight Recognition——”
“Oh, I have no patience with your Sight Recognition,” replied she,
“‘Feeling is believing’ and ‘A Straight Line to the touch is worth a
Circle to the sight’”—two Proverbs, very common with the Frailer Sex in
Flatland.
“Well,” said I, for I was afraid of irritating her, “if it must be so,
demand an introduction.” Assuming her most gracious manner, my Wife
advanced towards the Stranger, “Permit me, Madam, to feel and be felt
by——” then, suddenly recoiling, “Oh! it is not a Woman, and there are no
angles either, not a trace of one. Can it be that I have so misbehaved to
a perfect Circle?”
“I am indeed, in a certain sense a Circle,” replied the Voice, “and a
more perfect Circle than any in Flatland; but to speak more accurately, I
am many Circles in one.” Then he added more mildly, “I have a message,
dear Madam, to your husband, which I must not deliver in your presence;
and, if you would suffer us to retire for a few minutes——” But my Wife
would not listen to the proposal that our august Visitor should so
incommode himself, and assuring the Circle that the hour for her own
retirement had long passed, with many reiterated apologies for her recent
indiscretion, she at last retreated to her apartment.
I glanced at the half-hour glass. The last sands had fallen. The second
Millennium had begun.
§ 16.—_How the Stranger vainly endeavoured to reveal to me in words the
mysteries of Spaceland._