Flatland(弗莱特兰)

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Flatland

by Edwin A. Abbott 1884

Flatland

PART 1

THIS WORLD

SECTION 1 Of the Nature of Flatland

I call our world Flatland, not because we call it so, but to make its

nature clearer to you, my happy readers, who are privileged to live in

Space.

Imagine a vast sheet of paper on which straight Lines, Triangles,

Squares, Pentagons, Hexagons, and other figures, instead of remaining

fixed in their places, move freely about, on or in the surface, but without

the power of rising above or sinking below it, very much like shadows--

only hard with luminous edges--and you will then have a pretty correct

notion of my country and countrymen. Alas, a few years ago, I should

have said "my universe:" but now my mind has been opened to higher

views of things. In such a country, you will perceive at once that it is

impossible that there should be anything of what you call a "solid" kind;

but I dare say you will suppose that we could at least distinguish by sight

the Triangles, Squares, and other figures, moving about as I have

described them. On the contrary, we could see nothing of the kind, not at

least so as to distinguish one figure from another. Nothing was visible, nor

could be visible, to us, except Straight Lines; and the necessity of this I

will speedily demonstrate.

Place a penny on the middle of one of your tables in Space; and

leaning over it, look down upon it. It will appear a circle.

But now, drawing back to the edge of the table, gradually lower your

eye (thus bringing yourself more and more into the condition of the

inhabitants of Flatland), and you will find the penny becoming more and

more oval to your view, and at last when you have placed your eye exactly

on the edge of the table (so that you are, as it were, actually a Flatlander)

Flatland

the penny will then have ceased to appear oval at all, and will have

become, so far as you can see, a straight line.

The same thing would happen if you were to treat in the same way a

Triangle, or a Square, or any other figure cut out from pasteboard. As soon

as you look at it with your eye on the edge of the table, you will find that it

ceases to appear to you as a figure, and that it becomes in appearance a

straight line. Take for example an equilateral Triangle--who represents

with us a Tradesman of the respectable class. Figure 1 represents the

Tradesman as you would see him while you were bending over him from

above; figures 2 and 3 represent the Tradesman, as you would see him if

your eye were close to the level, or all but on the level of the table; and if

your eye were quite on the level of the table (and that is how we see him

in Flatland) you would see nothing but a straight line.

When I was in Spaceland I heard that your sailors have very similar

experiences while they traverse your seas and discern some distant island

or coast lying on the horizon. The far-off land may have bays, forelands,

angles in and out to any number and extent; yet at a distance you see none

of these (unless indeed your sun shines bright upon them revealing the

projections and retirements by means of light and shade), nothing but a

grey unbroken line upon the water.

Well, that is just what we see when one of our triangular or other

acquaintances comes towards us in Flatland. As there is neither sun with

us, nor any light of such a kind as to make shadows, we have none of the

helps to the sight that you have in Spaceland. If our friend comes closer to

us we see his line becomes larger; if he leaves us it becomes smaller; but

still he looks like a straight line; be he a Triangle, Square, Pentagon,

Hexagon, Circle, what you will-- a straight Line he looks and nothing else.

You may perhaps ask how under these disadvantagous circumstances

we are able to distinguish our friends from one another: but the answer to

this very natural question will be more fitly and easily given when I come

to describe the inhabitants of Flatland. For the present let me defer this

subject, and say a word or two about the climate and houses in our

country.

Flatland

SECTION 2 Of the Climate and Houses in

Flatland

As with you, so also with us, there are four points of the compass

North, South, East, and West.

There being no sun nor other heavenly bodies, it is impossible for us to

determine the North in the usual way; but we have a method of our own.

By a Law of Nature with us, there is a constant attraction to the South; and,

although in temperate climates this is very slight-- so that even a Woman

in reasonable health can journey several furlongs northward without much

difficulty-- yet the hampering effort of the southward attraction is quite

sufficient to serve as a compass in most parts of our earth. Moreover, the

rain (which falls at stated intervals) coming always from the North, is an

additional assistance; and in the towns we have the guidance of the houses,

which of course have their side-walls running for the most part North and

South, so that the roofs may keep off the rain from the North. In the

country, where there are no houses, the trunks of the trees serve as some

sort of guide. Altogether, we have not so much difficulty as might be

expected in determining our bearings.

Yet in our more temperate regions, in which the southward attraction is

hardly felt, walking sometimes in a perfectly desolate plain where there

have been no houses nor trees to guide me, I have been occasionally

compelled to remain stationary for hours together, waiting till the rain

came before continuing my journey. On the weak and aged, and especially

on delicate Females, the force of attraction tells much more heavily than

on the robust of the Male Sex, so that it is a point of breeding, if you meet

a Lady on the street, always to give her the North side of the way--by no

means an easy thing to do always at short notice when you are in rude

health and in a climate where it is difficult to tell your North from your

South.

Windows there are none in our houses: for the light comes to us alike

Flatland

in our homes and out of them, by day and by night, equally at all times and

in all places, whence we know not. It was in old days, with our learned

men, an interesting and oft-investigate question, "What is the origin of

light?" and the solution of it has been repeatedly attempted, with no other

result than to crowd our lunatic asylums with the would-be solvers. Hence,

after fruitless attempts to suppress such investigations indirectly by

making them liable to a heavy tax, the Legislature, in comparatively recent

times, absolutely prohibited them. I--alas, I alone in Flatland--know now

only too well the true solution of this mysterious problem; but my

knowledge cannot be made intelligible to a single one of my countrymen;

and I am mocked at --I, the sole possessor of the truths of Space and of the

theory of the introduction of Light from the world of three Dimensions--as

if I were the maddest of the mad! But a truce to these painful digressions:

let me return to our homes.

The most common form for the construction of a house is five-sided or

pentagonal, as in the annexed figure. The two Northern sides RO, OF,

constitute the roof, and for the most part have no doors; on the East is a

small door for the Women; on the West a much larger one for the Men; the

South side or floor is usually doorless.

Square and triangular houses are not allowed, and for this reason. The

angles of a Square (and still more those of an equilateral Triangle,) being

much more pointed than those of a Pentagon, and the lines of inanimate

objects (such as houses) being dimmer than the lines of Men and Women,

it follows that there is no little danger lest the points of a square of

triangular house residence might do serious injury to an inconsiderate or

perhaps absentminded traveller suddenly running against them: and

therefore, as early as the eleventh century of our era, triangular houses

were universally forbidden by Law, the only exceptions being

fortifications, powder-magazines, barracks, and other state buildings,

which is not desirable that the general public should approach without

circumspection.

At this period, square houses were still everywhere permitted, though

discouraged by a special tax. But, about three centuries afterwards, the

Flatland

Law decided that in all towns containing a population above ten thousand,

the angle of a Pentagon was the smallest house-angle that could be

allowed consistently with the public safety. The good sense of the

community has seconded the efforts of the Legislature; and now, even in

the country, the pentagonal construction has superseded every other. It is

only now and then in some very remote and backward agricultural district

that an antiquarian may still discover a square house.

SECTION 3 Concerning the Inhabitants of

Flatland

The greatest length or breadth of a full grown inhabitant of Flatland

may be estimated at about eleven of your inches. Twelve inches may be

regarded as a maximum.

Our Women are Straight Lines.

Our Soldiers and Lowest Class of Workmen are Triangles with two

equal sides, each about eleven inches long, and a base or third side so

short (often not exceeding half an inch) that they form at their vertices a

very sharp and formidable angle. Indeed when their bases are of the most

degraded type (not more than the eighth part of an inch in size), they can

hardly be distinguished from Straight lines or Women; so extremely

pointed are their vertices. With us, as with you, these Triangles are

distinguished from others by being called Isosceles; and by this name I

shall refer to them in the following pages.

Our Middle Class consists of Equilateral or Equal-Sided Triangles.

Our Professional Men and Gentlemen are Squares (to which class I

myself belong) and Five-Sided Figures or Pentagons.

Next above these come the Nobility, of whom there are several degrees,

beginning at Six-Sided Figures, or Hexagons, and from thence rising in

the number of their sides till they receive the honourable title of Polygonal,

or many-Sided. Finally when the number of the sides becomes so

numerous, and the sides themselves so small, that the figure cannot be

Flatland

distinguished from a circle, he is included in the Circular or Priestly order;

and this is the highest class of all.

It is a Law of Nature with us that a male child shall have one more

side than his father, so that each generation shall rise (as a rule) one step in

the scale of development and nobility. Thus the son of a Square is a

Pentagon; the son of a Pentagon, a Hexagon; and so on.

But this rule applies not always to the Tradesman, and still less often

to the Soldiers, and to the Workmen; who indeed can hardly be said to

deserve the name of human Figures, since they have not all their sides

equal. With them therefore the Law of Nature does not hold; and the son

of an Isosceles (i.e. a Triangle with two sides equal) remains Isosceles still.

Nevertheless, all hope is not such out, even from the Isosceles, that his

posterity may ultimately rise above his degraded condition. For, after a

long series of military successes, or diligent and skillful labours, it is

generally found that the more intelligent among the Artisan and Soldier

classes manifest a slight increase of their third side or base, and a

shrinkage of the two other sides. Intermarriages (arranged by the Priests)

between the sons and daughters of these more intellectual members of the

lower classes generally result in an offspring approximating still more to

the type of the Equal-Sided Triangle.

Rarely--in proportion to the vast numbers of Isosceles births-- is a

genuine and certifiable Equal-Sided Triangle produced from Isosceles

parents (footnote 1). Such a birth requires, as its antecedents, not only a

series of carefully arranged intermarriages, but also a long-continued

exercise of frugality and self-control on the part of the would-be ancestors

of the coming Equilateral, and a patient, systematic, and continuous

development of the Isosceles intellect through many generations.

The birth of a True Equilateral Triangle from Isosceles parents is the

subject of rejoicing in our country for many furlongs round. After a strict

examination conducted by the Sanitary and Social Board, the infant, if

certified as Regular, is with solemn ceremonial admitted into the class of

Equilaterals. He is then immediately taken from his proud yet sorrowing

parents and adopted by some childless Equilateral, who is bound by oath

Flatland

never to permit the child henceforth to enter his former home or so much

as to look upon his relations again, for fear lest the freshly developed

organism may, by force of unconscious imitation, fall back again into his

hereditary level.

The occasional emergence of an Equilateral from the ranks of his serf-

born ancestors is welcomed, not only by the poor serfs themselves, as a

gleam of light and hope shed upon the monotonous squalor of their

existence, but also by the Aristocracy at large; for all the higher classes are

well aware that these rare phenomena, while they do little or nothing to

vulgarize their own privileges, serve as almost useful barrier against

revolution from below.

Had the acute-angled rabble been all, without exception, absolutely

destitute of hope and of ambition, they might have found leaders in some

of their many seditious outbreaks, so able as to render their superior

numbers and strength too much even for the wisdom of the Circles. But a

wise ordinance of Nature has decreed that in proportion as the working-

classes increase in intelligence, knowledge, and all virtue, in that same

proportion their acute angle (which makes them physically terrible) shall

increase also and approximate to their comparatively harmless angle of the

Equilateral Triangle. Thus, in the most brutal and formidable off the

soldier class-- creatures almost on a level with women in their lack of

intelligence-- it is found that, as they wax in the mental ability necessary

to employ their tremendous penetrating power to advantage, so do they

wane in the power of penetration itself.

How admirable is the Law of Compensation! And how perfect a proof

of the natural fitness and, I may almost say, the divine origin of the

aristocratic constitution of the States of Flatland! By a judicious use of this

Law of Nature, the Polygons and Circles are almost always able to stifle

sedition in its very cradle, taking advantage of the irrepressible and

boundless hopefulness of the human mind. Art also comes to the aid of

Law and Order. It is generally found possible--by a little artificial

compression or expansion on the part of the State physicians--to make

some of the more intelligent leaders of a rebellion perfectly Regular, and

Flatland

to admit them at once into the privileged classes; a much larger number,

who are still below the standard, allured by the prospect of being

ultimately ennobled, are induced to enter the State Hospitals, where they

are kept in honourable confinement for life; one or two alone of the most

obstinate, foolish, and hopelessly irregular are led to execution.

Then the wretched rabble of the Isosceles, planless and leaderless, are

ether transfixed without resistance by the small body of their brethren

whom the Chief Circle keeps in pay for emergencies of this kind; or else

more often, by means of jealousies and suspicious skillfully fomented

among them by the Circular party, they are stirred to mutual warfare, and

perish by one another's angles. No less than one hundred and twenty

rebellions are recorded in our annals, besides minor outbreaks numbered

at two hundred and thirty-five; and they have all ended thus.

Footnote 1. "What need of a certificate?" a Spaceland critic may ask:

"Is not the procreation of a Square Son a certificate from Nature herself,

proving the Equal-sidedness of the Father?" I reply that no Lady of any

position will mary an uncertified Triangle. Square offspring has sometimes

resulted from a slightly Irregular Triangle; but in almost every such case

the Irregularity of the first generation is visited on the third; which either

fails to attain the Pentagonal rank, or relapses to the Triangular.

SECTION 4 Concerning the Women

If our highly pointed Triangles of the Soldier class are formidable, it

may be readily inferred that far more formidable are our Women. For, if a

Soldier is a wedge, a Woman is a needle; being, so to speak, ALL point, at

least at the two extremities. Add to this the power of making herself

practically invisible at will, and you will perceive that a Female, in

Flatland, is a creature by no means to be trifled with.

But here, perhaps, some of my younger Readers may ask HOW a

woman in Flatland can make herself invisible. This ought, I think, to be

apparent without any explanation. However, a few words will make it

Flatland

clear to the most unreflecting.

Place a needle on the table. Then, with your eye on the level of the

table, look at it side-ways, and you see the whole length of it; but look at it

end-ways, and you see nothing but a point, it has become practically

invisible. Just so is it with one of our Women. When her side is turned

towards us, we see her as a straight line; when the end containing her eye

or mouth--for with us these two organs are identical--is the part that meets

our eye, then we see nothing but a highly lustrous point; but when the

back is presented to our view, then--being only sub-lustrous, and, indeed,

almost as dim as an inanimate object--her hinder extremity serves her as a

kind of Invisible Cap.

The dangers to which we are exposed from our Women must now be

manifest to the meanest capacity of Spaceland. If even the angle of a

respectable Triangle in the middle class is not without its dangers; if to run

against a Working Man involves a gash; if collision with an Officer of the

military class necessitates a serious wound; if a mere touch from the

vertex of a Private Soldier brings with it danger of death; --what can it be

to run against a woman, except absolute and immediate destruction? And

when a Woman is invisible, or visible only as a dim sub-lustrous point,

how difficult must it be, even for the most cautious, always to avoid

collision!

Many are the enactments made at different times in the different States

of Flatland, in order to minimize this peril; and in the Southern and less

temperate climates, where the force of gravitation is greater, and human

beings more liable to casual and involuntary motions, the Laws

concerning Women are naturally much more stringent. But a general view

of the Code may be obtained from the following summary:--

1. Every house shall have one entrance on the Eastern side, for the use

of Females only; by which all females shall enter "in a becoming and

respectful manner" (footnote 1) and not by the Men's or Western door.

2. No Female shall walk in any public place without continually

keeping up her Peace-cry, under penalty of death.

3. Any Female, duly certified to be suffering from St. Vitus's Dance,

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Flatland1FlatlandbyEdwinA.Abbott1884Flatland2PART1THISWORLDSECTION1OftheNatureofFlatlandIcallourworldFlatland,notbecausewecallitso,buttomakeitsnatureclearertoyou,myhappyreaders,whoareprivilegedtoliveinSpace.ImagineavastsheetofpaperonwhichstraightLines,Triangles,Squares,Pentagons,Hexagons,andotherfig...

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