How I Had a Vision of Lineland

It was the last day but one of the 1999th year of our era, and the first
day of the Long Vacation. Having amused myself till a late hour with my
favourite recreation of geometry, I had retired to rest with an unsolved
problem in my mind. In the night I had a dream.

I saw before me a vast multitude of small Straight Lines (which I
naturally assumed to be women) interspersed with other beings still
smaller and of the nature of lustrous points⁠---all moving to and fro in
one and the same Straight Line, and, as nearly as I could judge, with
the same velocity.

A noise of confused, multitudinous chirping or twittering issued from
them at intervals as long as they were moving; but sometimes they ceased
from motion, and then all was silence.

Approaching one of the largest of what I thought to be women, I accosted
her, but received no answer. A second and a third appeal on my part were
equally ineffectual. Losing patience at what appeared to me intolerable
rudeness, I brought my mouth into a position full in front of her mouth
so as to intercept her motion, and loudly repeated my question, "Woman,
what signifies this concourse, and this strange and confused chirping,
and this monotonous motion to and fro in one and the same Straight
Line?"

"I am no woman," replied the small Line. "I am the Monarch of the world.
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 nonexistent.

His subjects⁠---of whom the small Lines were men and the Points
women⁠---were all alike confined in motion and eyesight 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 anyone 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 having herself 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, recognize 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 recognize 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 harmonize. 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 awake, the wedded
triplet is rapt vocally into a duplicate embrace; and Nature rejoices
over one more marriage and over three more births."