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Section 13. How I had a Vision of Lineland

Edwin A. Abbott (1838-1926)


"O brave new worlds, that have such people in them!"

Section 13.  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?"



                         My view of Lineland


                              |       |

                              | Myself|

                              |       |

                      My eye  o--------

 Women  A boy       Men        The KING        Men       A boy  Women

+ + + +   -   --- -- -- -- --  (>----<)  -- -- -- -- ---   -   + + + +

                                ^    ^

                              The KING'S eyes

                              much larger than the reality

                              shewing that HIS MAJESTY

                              could see nothing but a point.

"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 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 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."

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This World Wide Web document is a personal research project motivated by the following claim: "Truth is the object of Knowledge of whatever kind; and when we inquire what is meant by Truth, I suppose it is right to answer that Truth means facts and their relations, which stand towards each other pretty much as subjects and predicates in logic. All that exists, as contemplated by the human mind, forms one large system or complex fact, and this of course resolves itself into an indefinite number of particular facts, which, as being portions of a whole, have countless relations of every kind, one towards another." (The Idea of a University, John Henry Newman, 1801-1890)

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