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Edwin Abbot: Flatland (IW); personally, I have fo
The Internet Wiretap Electronic Edition of FLATLAND
A Public Domain Text
Instantiated by [email protected].com in November 1990
The Internet Wiretap, of Cupertino, California
[email protected]
F L A T L A N D
A Romance of Many Dimensions
With Illustrations
by the Author, A SQUARE
(EDWIN A. ABBOTT)
"Fie, fie how franticly I square my talk!"
[Fifth Edition, Revised]
* * *
To
The Inhabitance of SPACE IN GENERAL
And H.C. IN PARTICULAR
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of THREE DIMENSIONS
Having been previously conversant
With ONLY TWO
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE or EVEN SIX Dimensions
Thereby contributing
To the Enlargment of THE IMAGINATION
And the possible Development
Of that most and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY
* * *
PREFACE TO THE
SECOND AND REVISED
EDITION, 1884.
BY THE EDITOR
If my poor Flatland friend retained the vigour of mind which he
enjoyed when he began to compose these Memoirs, I should not now need
to represent him in this preface, in which he desires, fully, to
return his thanks to his readers and critics in Spaceland, whose
appreciation has, with unexpected celerity, required a second edition
of this work; secondly, to apologize for certain errors and misprints
(for which, however, he is not entirely responsible); and, thirdly, to
explain on or two misconceptions. But he is not the Square he once
was. Years of inprisonment, and the still heavier burden of general
incredulity and mockery, have combined with the thoughts and notions,
and much also of the terminology, which he acquired during his short
stay in spaceland. He has, therefore, requested me to reply in his
behalf to two special objections, one of an intellectual, the other of
a moral nature.
The first objection is, that a Flatlander, seeing a Line, sees
something that must be _thick_ to the eye as well as _long_ to the eye
(otherwise it would not be visible, if it had not some thickness); and
consequently he ought (it is argued) to acknowledge that his
countrymen are not only long and broad, but also (though doubtless to
a very slight degree) _thick_ or _high._ This objection is plausible,
and, to Spacelanders, almost irresistible, so that, I confess, when I
first heard it, I knew not what to reply. But my poor old friend's
answer appears to me completely to meet it.
"I admit," said he -- when I mentioned to him this objection -- "I
admit the truth of your critic's facts, but I deny his conclusions.
It is true that we have really in Flatland a Third unrecognized
Dimension called 'height,' just as it also is true that you have
really in Spaceland a Fourth unrecognized Dimension, called by no name
at present, but which I will call 'extra-height.' But we can no more
take cognizance of our 'height' than you can of your 'extra-height.'
Even I -- who have been in Spaceland, and have had the privilege of
understanding for twenty-four hours the meaning of 'height' -- even I
cannot now comprehend it, nor realize it by the sense of sight or by
any process of reason; I can but apprehend it by faith.
"The reason is obvious. Dimension implied direction, implies
measurement, implies the more and the less. Now, all our lines are
_equally_ and _infinitesimally_ thick (or high, whichever you like);
consequently, there is nothing in them to lead our minds to the
conception of that Dimension. No 'delicate micrometer' -- as has been
suggested by one too hasty Spaceland critic -- would in the least
avail us; for we should not know _what to measure, nor in what
direction._ When we see a Line, we see something that is long and
_bright; brightness,_ as well as length, is necessary to the existence
of a Line; if the brightness vanishes, the Line is extinguished.
Hence, all my Flatland friends -- when I talk to them about the
unrecognized Dimension which is somehow visible in a Line -- say, 'Ah,
you mean _brightness_': and when I reply, 'No, I mean a real
Dimension,' they at once retort, 'Then measure it, or tell us in what
direction it extends'; and this silences me, for I can do neither.
Only yesterday, when the Chief Circle (in other words our High Priest)
came to inspect the State Prison and paid me his seventh annual visit,
and when for the seventh time he put me the question, 'Was I any
better?' I tried to prove to him that he was 'high,' as well as long
and broad, although he did not know it. But what was his reply? 'You
say I am "high"; measure my "high-ness" and I will believe you.' What
could I do? How could I meet his challenge? I was crushed; and he
left the room triumphant.
"Does this still seem strange to you? Then put yourself in a
similar position. Suppose a person of the Fourth Dimension,
condescending to visit you, were to say, 'Whenever you open your eyes,
you see a Plane (which is of Two Dimensions) and you _infer_ a Solid
(which is of Three); but in reality you also see (though you do not
recognize) a Fourth Dimension, which is not colour nor brightness nor
anything of the kind, but a true Dimension, although I cannot point
out to you its direction, nor can you posssibly measure it.' What
would you say to such a visitor? Would not you have him locked up?
Well, that is my fate: and it is as natural for us Flatlanders to
lock up a Square for preaching the Third Dimension, as it is for you
Spacelanders to lock up a Cube for preaching the Fourth. Alas, how
strong a family likeness runs through blind and persecuting humanity
in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes -- we
are all liable to the same errors, all alike the Slavers of our
respective Dimensional prejudices, as one of our Spaceland poets has
said --
'One touch of Nature makes all worlds akin.'" (footnote 1)
On this point the defence of the Square seems to me to be
impregnable. I wish I could say that his answer to the second (or
moral) objection was equally clear and cogent. It has been objected
that he is a woman-hater; and as this objection has been vehemently
urged by those whom Nature's decree has constituted the somewhat
larger half of the Spaceland race, I should like to remove it, so far
as I can honestly do so. But the Square is so unaccustomed to the use
of the moral terminology of Spaceland that I should be doing him an
injustice if I were literally to transcribe his defence against this
charge. Acting, therefore, as his interpreter and summarizer, I
gather that in the course of an imprisonment of seven years he has
himself modified his own personal views, both as regards Women and as
regards the Isosceles or Lower Classes. Personally, he now inclines
to the opinion of the Sphere (see page 86) that the Straight Lines are
in many important respects superior to the Circles. But, writing as a
Historian, he has identified himself (perhaps too closely) with the
views generally adopted by Flatland, and (as he has been informed)
even by Spaceland, Historians; in whose pages (until very recent
times) the destinies of Women and of the masses of mankind have seldom
been deemed worthy of mention and never of careful consideration.
In a still more obscure passage he now desires to disavow the
Circular or aristocratic tendencies with which some critics have
naturally credited him. While doing justice to the intellectual power
with which a few Circles have for many generations maintained their
supremacy over immense multitudes of their countrymen, he believes
that the facts of Flatland, speaking for themselves without comment on
his part, declare that Revolutions cannot always be suppressed by
slaughter, and that Nature, in sentencing the Circles to infecundity,
has condemned them to ultimate failure -- "and herein," he says, "I
see a fulfilment of the great Law of all worlds, that while the wisdom
of Man thinks it is working one thing, the wisdom of Nature constrains
it to work another, and quite a different and far better thing." For
the rest, he begs his readers not to suppose that every minute detail
in the daily life of Flatland must needs correspond to some other
detail in Spaceland; and yet he hopes that, taken as a whole, his work
may prove suggestive as well as amusing, to those Spacelanders of
moderate and modestminds who -- speaking of that which is of the
highest importance, but lies beyond experience -- decline to say on
the one hand, "This can never be," and on the other hand, "It must
needs be precisely thus, and we know all about it."
----------
Footnote 1. The Author desires me to add, that the misconceptions of
some of his critics on this matter has induced him to insert (on pp.
74 and 92) in his dialogue with the Sphere, certain remarks which have
a bearing on the point in question and which he had previously omitted
as being tedious and unnecessary.
* * *
FLATLAND
PART 1
THIS WORLD
SECTION 1. -- Of the Nature of Flatland
I call our world Flatland, not because we cal 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, drawling 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) 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 disadvantages 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.
* * *
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 assistiance;
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 ont he 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 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 fo 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 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 themselve so small, that the
figure cannot be 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 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
amost 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 juidicious
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 generall 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 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 somethimes 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 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, fits, chronic cold accompanied by violent sneezing, or any
disease necessitating involuntary motions, shall be instantly
destroyed.
In some of the States there is an additional Law forbidding
Females, under penalty of death, from walking or standing in any
public place without moving their backs constantly from right to left
so as to indicate their presence to those behind them; other oblige a
Woman, when travelling, to be followed by one of her sons, or
servants, or by her husband; others confine Women altogether in their
houses except during the religious festivals. But it has bbeen found
by the wisest of our Circles or Statesmen that the multiplication of
restrictions on Females tends not only to the debilitation and
diminution of the race, but also to the increase of domestic murders
to such an extent that a State loses more than it gains by a too
prohibitive Code.
For whenever the temper of the Women is thus exasperated by
confinement at home or hampering regulations abroad, they are apt to
vent their spleen upon their husbands and children; and in the less
temperate climates the whole male population of a village has been
sometimes destroyed in one or two hours of a simultaneous female
outbreak. Hence the Three Laws, mentioned above, suffice for the
better regulated States, and may be accepted as a rough
exemplification of our Female Code.
After all, our principal safeguard is found, not in Legislature,
but in the interests of the Women themselves. For, although they can
inflict instantaneous death by a retrograde movement, yet unless they
can at once disengage their stinging extremity from the struggling
body of their vectim, their own frail bodies are liable to be
shattered.
The power of Fashion is also on our side. I pointed out that in
some less civilized States no female is suffered to stand in any
public place without swaying her back from right to left. This
practice has been universal among ladies of any pretensions to
breeding in all well-governed States, as far back as the memory of
Figures can reach. It is considered a disgrace to any state that
legislation should have to enforce what ought to be, and is in every
respectable female, a natural instinct. The rhythmical and, if I may
so say, well-modulated undulation of the back in our ladies of
Circular rank is envied and imitated by the wife of a common
Equilateral, who can achieve nothing beyond a mere monotonous swing,
like the ticking of a pendulum; and the regular tick of the
Equilateral is no less advmired and copied by the wife of the
progressive and aspiring Isosceles, in the females of whose famil no
"back-motion" of any kind has become as yet a necessity of life.
Hence, in every family of position and consideration, "back motion" is
as prevalent as time itself; and the husbands and sons in these
households enjoy immunity at least from invisible attacks.
Not that it must be for a moment supposed that our Women are
destitute of affection. But unfortunately the passion of the moment
predominates, in the Frail Sex, over every other consideration. This
is, of course, a necessity arising from their unfortunate
conformation. For as they have no pretensions to an angle, being
inferior in this respect to the very lowest of the Isosceles, they are
consequently wholly devoid of brainpower, and have neither reflection,
judgment nor forethought, and hardly any memory. Hence, in their fits
of fury, they remember no claims and recognize no distinctions. I
have actually known a case where a Woman has exterminated her whole
household, and half an hour afterwards, when her rage was over and the
fragments swept away, has asked what has become of her husband and
children.
Obviously then a Woman is not to be irritated as long as she is in
a position where she can turn round. When you have them in their
apartments -- which are constructed with a view to denying them that
power -- you can say and do what you like; for they are then wholly
impotent for mischief, and will not remember a few minutes hence the
incident for which they may be at this moment threatening you with
death, nor the promises which you may have found it necessary to make
in order to pacify their fury.
On the whole we got on pretty smoothly in our domestic relations,
except in the lower strata of the Military Classes. There the want of
tact and discretion on the part of the husbands produces at times
indescribable disasters. Relying too much on the offensive weapons of
their acute angles instead of the defensive organs of good sense and
seasonable simulations, these reckless creatures too often neglect the
prescribed construction of the women's apartments, or irritate their
wives by ill-advised expressions out of doors, which they refuse
immediately to retract. Moreover a blunt and stolid regard for
literal truth indisposes them to make those lavish promises by which
the more judicious Circle can in a moment pacify his consort. The
result is massacre; not, however, without its advantages, as it
eliminates the more brutal and troublesome of the Isosceles; and by
many of our Circles the destructiveness of the Thinner Sex is regarded
as one among many providential arrangements for suppressing redundant
population, and nipping Revolution in the bud.
Yet even in our best regulated and most approximately Circular
families I cannot say that the ideal of family life is so high as with
you in Spaceland. There is peace, in so far as the absence of
slaughter may be called by that name, but there is necessarily little
harmony of tastes or pursuits; and the cautious wisdom of the FCircles
has ensured safety at the cost of domestic comfort. In every Circular
or Polygonal household it has been a habit from time immemorial -- and
now has become a kind of instinct among the women of our higher
classes -- that the mothers and daughters should constantly keep their
eyes and mouths towards their husband and his male friends; and for a
lady in a family of distinction to turn her back upon her husband
would be regarded as a kind of portent, involving loss of _status._
But, as I shall soon shew, this custom, though it has the advantage of
safety, is not without disadvantages.
In the house of the Working Man or respectable Tradesman -- where
the wife is allowed to turn her back upon her husband, while pursuing
her household avocations -- there are at least intervals of quiet,
when the wife is neither seen nor heard, except for the humming sound
of the continuous Peace-cry; but in the homes of the upper classes
there is too often no peace. There the voluble mouth and bright
penetrating eye are ever directed toward the Master of the household;
and light itself is not more persistent than the stream of Feminine
discourse. The tact and skill which suffice to avert a Woman's sting
are unequal to the task of stopping a Woman's mouth; and as the wife
has absolutely nothing to say, and absolutely no constraint of wit,
sense, or conscience to prevent her from saying it, not a few cynics
have been found to aver that they prefer the danger of the death-
dealing but inaudible sting to the safe sonorousness of a Woman's
other end.
To my readers in Spaceland the condition of our Women may seen
truly deplorable, and so indeed it is. A Male of the lowest type of
the Isosceles may look forward to some improvement of his angle, and
to the ultimate elevation of the whole of his degraded caste; but no
Woman can entertain such opes for her sex. "Once a Woman, always a
Woman" is a Decree of Nature; and the very Laws of Evolution seem
suspended in her disfavour. Yet at least we can admire the wise
Prearrangement which has ordained that, as they have no hopes, so they
shall have no memory to recall, and no forethought to anticipate, the
miseries and humiliations which are at once a necessity of their
existence and the basis of the constitution of Flatland.
* * *
SECTION 5. -- Of our Methods of Recognizing one another
You, who are blessed with shade as well as light, you, who are
gifted with two eyes, endowed with a knowledge of perspective, and
charmed with the enjoyment of various colours, you, who can actually
_see_ an angle, and contemplate the complete circumference of a Circle
in the happy region of the Three Dimensions -- how shall I make it
clear to you the extreme difficulty which we in Flatland experience in
recognizing one another's configuration?
Recall what I told you above. All beings in Flatland, animate and
inanimate, no matter what their form, present _to our view_ the same,
or nearly the same, appearance, viz. that of a straight Line. How
then can one be distinguished from another, where all appear the same?
The answer is threefold. The first means of recognition is the
sense of hearing; which with us is far more highly developed than with
you, and which enables us not only to distinguish by the voice of our
personal friends, but even to discriminate between different clases,
at least so far as concerns the three lowest orders, the Equilateral,
the Square, and the Pentagon -- for the Isosceles I take no account.
But as we ascend the social scale, the process of discriminating and
being discriminated by hearing increases in difficulty, partly because
voices are assimilated, partly because the faculty of voice-
discrimination is a plebeian virtue not much developed among the
Aristocracy. And wherever there is any danger of imposture we cannot
trust to this method. Amongst our lowest orders, the vocal organs are
developed to a degree more than correspondent with those of hearing,
so that an Isosceles can easily feign the voice of a Polygon, and,
with some training, that of a Circle himself. A second method is
therefore more commonly resorted to.
_Feeling_ is, among our Women and lower classes -- about our upper
classes I shalls peak presently -- the principal test of recognition,
at all events between strangers, and when the question is, not as to
the individual, but as to the class. What therefore "introduction" is
among the higher classes in Spaceland, that the process of "feeling"
is with us. "Permit me to ask you to feel and be felt by my friend
Mr. So-and-so" -- is still, among the more old-fashioned of our
country gentlemen in districts remote from towns, the customary
formula for a Flatland introduction. But in the towns, and among men
of business, the words "be felt by" are omitted and the sentence is
abbreviated to, "Let me ask you to feel Mr. So-and-so"; although it is
assumed, of course, that the "feeling" is to be reciprocal. Among our
still more modern and dashing young gentlemen -- who are extremely
averse to superfluous effort and supremely indifferent to the purity
of their native language -- the formula is still further curtailed by
the use of "to feel" in a technical sense, meaning, "to recommend-for-
the-purposes-of-feeling-and-being-felt"; and at this moment the
"slang" of polite or fast society in the upper classes sanctions such
a barbarism as "Mr. Smith, permit me to feel Mr. Jones."
Let not my Reader however suppose that "feeling" is with us the
tedious process that it would be with you, or that we find it
necessary to feel right round all the sides of every individual before
we determine the class to which he belongs. Long practice and
training, begun in the schooles and continued in the experience of
daily life, enable us to discriminate at once by the sense of touch,
between the angles of an equal-sided Triangle, Square, and Pentagon;
and I need not say that the brainless vertex of an acute-angled
Isosceles is obvious to the dullest touch. It is therefore not
necessary, as a rule, to do more than feel a single angle of an
individual; and this, once ascertained, tells us the class of the
person whom we are addressing, unless indeed he belongs to the higher
sections of the nobility. There the difficulty is much greater. Even
a Master of Arts in our University of Wentbridge has been known to
confuse a ten-sided with a twelve-sided Polygon; and there is hardly a
Doctor of Science in or out of that famous University who could
pretend to decide promptly and unhestitatingly between a twenty-sided
and a twenty-four sided member of the Aristocracy.
Those of my readers who recall the extracts I gave above from the
Legislative code concerning Women, will readily perceive that the
process of introduction by contact requires some care and discretion.
Otherwise the angles might inflict on the unwary Feeling irreparable
injury. It is essential for the safety of the Feeler that the Felt
should stand perfectly still. A start, a fidgety shifting of the
position, yes, even a violent sneeze, has been known before now to
prove fatal to the incautious, and to nip in the bud many a promising
friendship. Especially is this true among the lower classes of the
Triangles. With them, the eye is situated so far from their vertex
that they can scarcely take cognizance of what goes on at that
extremity of their frame. They are, moreover, of a rough coarse
nature, not sensitive to the delicate touch of the highly organized
Polygon. What wonder then if an involuntary toss of the head has ere
now deprived the State of a valuable life!
I have heard that my excellent Grandfather -- one of the least
irregular of his unhappy Isosceles class, who indeed obtained, shortly
before his decease, four out of seven botes from the Sanitary and
Social Board for passing him into the class of the Equal-sided --
often deplored, with a tear in his venerable eye, a miscarriage of
this kind, which had occured to his great-great-great-Grandfather, a
respectable Working Man with an angle or brain of 59 degrees 30
minutes. According to his account, my unfortunately Ancestor, being
afflicted with rheumatism, and in the act of being felt by a Polygon,
by one sudden start accidentally transfixed the Great Man through the
diagonal and thereby, partly in consequence of his long imprisonment
and degradation, and partly because of the moral shock which pervaded
the whole of my Ancestor's relations, threw back our family a degree
and a half in their ascent towards better things. The result was that
in the next generation the family brain was registered at only 58
degrees, and not till the lapse of five generations was the lost
ground recovered, the full 60 degrees attained, and the Ascent from
the Isosceles finally achieved. And all this series of calamaties
from one little accident in the process of Feeling.
As this point I think I hear some of my better educated readers
exclaim, "How could you in Flatland know anything about angles and
degrees, or minutes? We _see_ an angle, because we, in the region of
Space, can see two straight lines inclined to one another; but you,
who can see nothing but on straight line at a time, or at all events
onlly a number of bits of straight lines all in one straight line, --
how can you ever discern an angle, and much less register angles of
different sizes?"
I answer that though we cannot _see- angles, we can _infer_ them,
and this with great precision. Our sense of touch, stimulated by
necessity, and developed by long training, enables us to distinguish
angles far more accurately than your sense of sight, when unaided by a
rule or measure of angles. nor must I omit to explain that we have
great natural helps. It is with us a Law of Nature that the brain of
the Isosceles class shall begin at half a degree, or thirty minutes,
and shall increase (if it increases at all) by half a degree in every
generation until the goal of 60 degrees is reached, when the condition
of serfdom is quitted, and the freeman enters the class of Regulars.
Consequently, Nature herself supplies us with an ascending scale
or Alphabet of angles for half a degree up to 60 degrees, Specimen of
which are placed in every Elementary School throughout the land.
Owing to occasional retrogressions, to still more frequent moral and
intellectual stagnation, and to the extraordinary fecundity of the
Criminal and Vagabond classes, there is always a vast superfluity of
individuals of the half degree and single degree class, and a fair
abundance of Specimens up to 10 degrees. These are absolutely
destitute of civil rights; and a great number of them, not having even
intelligence enough for the purposes of warfare, are devoted by the
States to the service of education. Fettered immovably so as to
remove all possibility of danger, they are placed in the classrooms of
our Infant Schools, and there they are utilized by the Board of
Education for the pupose of imparting to the offspring of the Middle
Classes the tact and intelligence which these wretched creatures
themselves are utterly devoid.
In some States the Specimens are occasionally fed and suffered to
exist for several years; butin the more temperate and better regulated
regions, it is found in the long run more advantageous for the
educational interests of the young, to dispense with food, and to
renew the Specimens every month -- which is about the average duration
of the foodless existence of the Criminal class. In the cheaper
schools, what is gained by the longer existence of the Specimen is
lost, partly in the expenditure for food, and partly in the diminished
accuracy of the angles, which are impaired after a few weeks of
constant "feeling." Nor must we forget to add, in enumerating the
advantages of the more expensive system, that it tends, though
slightly yet perceptibly, to the diminution of the redundant Isosceles
population -- an object which every statesman in Flatland constantly
keeps in view. On the whole therefore -- although I am not ignorant
that, in many popularly elected School Boards, there is a reaction in
favour of "the cheap system" as it is called -- I am myself disposed
to think that this is one of the many cases in which expense is the
truest economy.
But I must not allow questions of School Board politics to divert
me from my subject. Enough has been said, I trust, to shew that
Recognition by FEeling is not so tedious or indecisive a process as
might have been supposed; and it is obviously more trustworthy than
Recognition by hearing. Still there remains, as has been pointed out
above, the objection that this method is not without danger. For this
reason many in the Middle and Lower classes, and all without exception
in the Polygonal and Circular orders, prefer a third method, the
description of which shall be reserved for the next section.
* * *
SECTION 6. -- Of Recognition by Sight
I am about to appear very inconsistent. In the previous sections
I have said that all figures in Flatland present the appearance of a
straight line; and it was added or implied, that it is consequently
impossible to distinguish by the visual organ between individuals of
different classes: yet now I am about to explain to my Spaceland
critics how we are able to recognize one another by the sense of
sight.
If however the Reader will take the trouble to refer to the
passage in which Recognition by Feeling is stated to be universal, he
will find this qualification -- "among the lower classes." It is only
among the higher classes and in our more temperate climates that Sight
Recognition is practised.
That this power exists in any regions and for any classes is the
result of Fog; which prevails during the greater part of the year in
all parts save the torrid zones. That which is with you in Spaceland
an unmixed evil, blotting out the landscape, depressing the spirits,
and enfeebling the health, is by us recognized as a blessing scarcely
inferior to air itself, and as the Nurse of arts and Parent os
sciences. But let me explain my meaning, without further eulogies on
this beneficent Element.
If Fog were non-existent, all lines would appear equally and
indistinguishably clear; and this is actually the case in those
unhappy countries in which the atmosphere is perfectly dry and
transparent. But wherever there is a rich supply of Fog, objects that
are at a distance, say of three feet, are appreciably dimmer than
those at the distance of two feet eleven inches; and the result is
that by careful and constant experimental observation of comparative
dimness and constant experimental observation of comparative dimness
and clearness, we are enabled to infer with great exactness the
configuration of the object observed.
An instace will do more than a volume of generalities to make my
meaning clear.
Suppose I see two individuals approaching whose rank I wish to
ascertain. They are, we will suppose, a Merchant and a Physician, or
in other words, an Equilaterial Triangle and a Pentagon; how am I to
distinuish them?
It will be obvious, to every child in Spaceland who has touched
the threshold of Geometrical Studies, that, if I can bring my eye so
that its glance may bisect an angle (A) of the approaching stranger,
my view will lie as it were evenly between the two sides that are next
to me (viz. CA and AB), so that I shall contemplate the two
impartially, and both will appear of the same size.
Now inthe case of (1) the Merchant, what shall I see? I shall see
a straight line DAE, in which the middle point (A) will be very bright
because it is nearest to me; but on either side the line will shade
away _rapidly to dimness,_ because the sides AC and AB _recede rapidly
into the fog_ and what appear to me as the Merchant's extremities,
viz. D and E, will be _very dim indeed._
On the other hand in the case of (2) the Physician, though I shall
here also see a line (D'A'E') with a bright centre (A'), yet it will
shade away _less rapidly_ to dimness, because the sides (A'C', A'B')
_recede less rapidly into the fog:_ and what appear to me the
Physician's extremities, viz. D' and E', will not be _not so dim_ as
the extremities of the Merchant.
The Reader will probably understand from these two instances how -
- after a very long training supplemented by constant experience -- it
is possible for the well-educated classes among us to discriminate
with fair accuracy between the middle and lowest orders, by the sense
of sight. If my Spaceland Patrons have grasped this general
conception, so far as to conceive the possibility of it and not to
reject my account as altogether incredible -- I shall have attained
all I can reasonably expect. Were I to attempt further details I
should only perplex. Yet for the sake of the young and inexperienced,
who may perchance infer -- from the two simple instances I have given
above, of the manner in which I should recognize my Father and my Sons
-- that Recognition by sight is an easy affair, it may be needful to
point out that in actual life most of the problems of Sight
Recognition are far more subtle and complex.
If for example, when my Father, the Triangle, approaches me, he
happens to present his side to me instead of his angle, then, until I
have asked him to rotate, or until I have edged my eye around him, I
am for the moment doubtful whether he may not be a Straight Line, or,
in other words, a Woman. Again, when I am in the company of one of my
two hexagonal Grandsons, contemplating one of his sides (AB) full
front, it will be evident from the accompanying diagram that I shall
see one whole line (AB) in comparative brightness (shading off hardly
at all at the ends) and two smaller lines (CA and BD) dim throughout
and shading away into greater dimness towards the extremities C and D.
But I must not give way to the temptating of enlarging on these
topics. The meanest mathematician in Spaceland will readily believe
me when I assert that the problems of life, which present themselves
to the well-educated -- when they are themselves in motion, rotating,
advancing or retreating, and at the same time attempting to
discriminate by the sense of sight between a number of Polygons of
high rank moving in different directions, as for example in a ball-
room or conversazione -- must be of a nature to task the angularity of
the most intellectual, and amply justify the rich endowments of the
Learned Professors of Geometry, both Static and Kinetic, in the
illustrious University of Wentbridge, where the Science and Art of
Sight Recognition are regularly taught to large classes of the _elite_
of the States.
It is only a few of the scions of our noblest and wealthies
houses, who are able to give the time and money necessary for the
thorough prosecution of this noble and valuable Art. Even to me, a
Mathematician of no mean standing, and the Granddfather of two most
hopeful and perfectly regular Hexagons, to find myself in the midst of
a crowd of rotating Polygons of the higher classes, is occasionally
very perplexing. And of course to a common Tradesman, or Serf, such a
sight is almost as unintelligible as it would be to you, my Reader,
were you suddenly transported to my country.
In such a crowd you could see on all sides of you nothing but a
Line, apparently straight, but of which the parts would vary
irregularly and perpetually in brightness or dimness. Even if you had
completed your third year in the Pentagonal and Hexagonal classes in
the University, and were perfect in the theory of the subject, you
would still find there was need of many years of experience, before
you could move in a fashionable crowd without jostling against your
betters, whom it is against etiquette to ask to "feel," and who, by
their superior culture and breeding, know all about your movements,
while you know very little or nothing about theirs. in a word, to
comport oneself with perfect propriety in Polygonal society, one ought
to be a Polygon oneself. Such at least is the painful teaching of my
experience.
It is astonishing how much the Art -- or I may almost call it
instinct -- of Sight Recognition is developed by the habitual practice
of it and by the avoidance of the custom of "Feeling." Just as, with
you, the deaf and dumb, if once allowed to gesticulate and to use the
hand-alphabet, will never acquire the more difficult but far more
valuable art of lip-speech and lip-reading, so it is with us as
regards "Seeing" and "Feeling." None who in early life resort to
"Feeling" will ever learn "Seeing" in perfection.
For this reason, among our Higher Classes, "Feeling" is
discouraged or absolutely forbidden. From the cradle their children,
instead of going to the Public Elementary schools (where the art of
Feeling is taught,) are sent to higher Seminaries of an exclusive
character; and at our illustrius University, to "feel" is regarded as
a most serious fault, involving Rustication for the first offence, and
Expulsion for the second.
But among the lower classes the art of Sight Recognition is
regarded as an unattainable luxury. A common Tradesman cannot afford
to let his sun spend a third of his life in abstract studies. The
children of the poor are therefore allowed to "feel" from their
earliest years, and they gain thereby a precocity and an early
vivacity which contrast at first most favourably with the inert,
undeveloped, and listless behaviour of the half-instructed youths of
the Polygonal class; but when the latter have at last completed their
University course, and are prepared to put their theory into practice,
the change that comes over them may almost be described as a new
birth, and in every art, science, and social pursuit they rapidly
overtake and distance their Triangular competitors.
Only a few of the Polygonal Class fail to pass the Final Test or
Leaving Examination at the University. The condition of the
unsuccessful minority is truly pitiable. Rejected from the higher
class,, they are also despised by the lower. They have neither the
matured and systematically trained powers of the Polygonal Bachelors
and Masters of Arts, nor yet the native precocity and mercurial
versatility of the youthful Tradesman. The professions, the public
services, are closed against them, and though in most States they are
not actually debarred from marriage, yet they have the greatest
difficulty in forming suitable alliances, as experience shews that the
offspring of such unfortunate and ill-endowed parents is generally
itself unfortunate, if not positively Irregular.
It is from these specimens of the refuse of our Nobility that the
great Tumults and Seditions of past ages have generally derived their
leaders; and so great is the mischief thence arising that an
increasing minotiry of our more progressive Statesmen are of opinion
that true mercy would dictate their entire suppression, by enacting
that all who fail to pass the Final Examination of the University
should be either imprisoned for life, or extinguished by a painless
death.
But I find myself digressing into the subect of Irregularities, a
matter of such vital interest that it demans a separate section.
* * *
SECTION 7. -- Concerning Irregular Figures
Throughout the previous pages I have been assuming -- what perhaps
should have been laid down at the beginning as a distinct and
fundamental proposition -- that every human being in Flatland is a
Regular Figure, that is to say of regular construction. By this I
mean that a Woman must not only be a line, but a straight line; that
an Artisan or Soldier must have two of his sides equal; that Tradesmen
must have three sides equal; Lawyers (of which class I am a humble
member), four sides equal, and, generally, that in every Polygon, all
the sides must be equal.
The sizes of the sides would of course depend upon the age of the
individual. A Female at birth would be about an inch long, while a
tall adult Woman might extend to a foot. As to the Males of every
class, it may be roughly said that the length of an adult's size, when
added together, is two feet or a little more. But the size of our
sides is not under consideration. I am speaking of the _equality_ of
sides, and it does not need much reflection to see that the whole of
the social life in Flatland rests upon the fundamental fact that
Nature wills all Figures to have their sides equal.
If our sides were unequal our angles might be unequal. Instead of
its being sufficient to feel, or estimate by sight, a single angle in
order to determine the form of an individual, it would be necessary to
ascertain each angle by the experiment of Feeling. But life would be
too short for such a tedious groping. The whole science and art of
Sight Recognition would at once perish; Feeling, so far as it is an
art, would not long survive; intercourse would become perilous or
impossible; there would be an end to all confidence, all forethought;
no one would be safe in making the most simple social arrangements; in
a word, civilization might relapse into barbarism.
Am I going too fast to carry my Readers with me to these obvious
conclusions? Surely a moment's reflection, and a single instance from
common life, must convince every one that our social system is based
upon Regularity, or Equality of Angles. You meet, for example, two or
three Tradesmen in the street, whom your recognize at once to be
Tradesman by a glance at their angles and rapidly bedimmed sides, and
you ask them to step into your house to lunch. This you do at present
with perfect confidence, because everyone knows to an inch or two the
area occupied by an adult Triangle: but imagine that your Tradesman
drags behind his regular and respectable vertex, a parallelogram of
twelve or thirteen inches in diagonal: -- what are you to do with such
a monster sticking fast in your house door?
But I am insulting the intelligence of my Readers by accumulating
details which must be patent to everyone who enjoys the advantages of
a Residence in Spaceland. Obviously the measurements of a single
angle would no longer be sufficient under such portentous
circumstances; one's whole life would be taken up in feeling or
surveying the perimeter of one's acquaintances. Already the
difficulties of avoiding a collision in a crowd are enough to tax the
sagacity of even a well-educated Square; but if no one could calculate
the Regularity of a signle figure in the company, all would be chaos
and confusion, and the slightest panic would cause serious injuries,
or -- if there happened to be any Women or Soldiers present -- perhaps
considerable loss of life.
Expediency therefore concurs with Nature in stamping the seal of
its approval upon Regularity of conformation: nor has the Law been
backward in seconding their efforts. "Irregularity of Figure" means
with us the same as, or more than, a combination of moral obliquity
and criminality with you, and is treated accordingly. There are not
wanting, it is true, some promulgators of paradoxes who maintain that
there is no necessary connection between geometrical and moral
Irregularity. "The Irregular," they say, "is from his birth scouted
by his own parents, derided by his brothers and sisters, neglected by
the domestics, scorned and suspected by society, and excluded from all
posts of responsibility, trust, and useful activity. His every
movement is jealously watched by the police till he comes of age and
presents himself for inspection; then he is either destroyed, if he is
found to exceed the fixed margin of deviation, at an uninteresting
occupation for a miserable stipend; obliged to live and board at the
office, and to take even his vacation under close supervision; what
wonder that human nature, even in the best and purest, is embittered
and perverted by such surroundings!"
All this very plausible reasoning does not convince me, as it has
not convinced the wisest of our Statesmen, that our ancestors erred in
laying it down as an axiom of policy that the toleration of
Irregularity is incompatible with the safety of the State. Doubtless,
the life of an Irregular is hard; but the interests of the Greater
Number require that it shall be hard. If a man with a triangular frnt
and a polygonal back were allowed to exist and to propagate a still
more Irregular posterity, what would become of the arts of life? Are
the houses and doors and churches in Flatland to be altered in order
to accommodate such monsters? Are our ticket-collectors to be
required to measure every man's perimeter before they allow him to
enter a theatre, or to take his place in a lecture room? Is an
Irregular to be exempted from the militia? And if not, how is he to
be prevented from carrying desolation into the ranks of his comrades?
Again, what irresistible temptations to fraudulent impostures must
needs beset such a creature! How easy for him to enter a shop with
his polygonal front foremost, and to order goods to any extent from a
confiding tradesman! Let the advocates of a falsely called
Philanthropy plead as they may for the abrogation of the Irregular
Penal Laws, I for my part have never known an Irregular who was not
also what Nature evidently intended him to be -- a hypocrite, a
misanthropist, and, up to the limits of his power, a perpetrator of
all manner of mischief.
Not that I should be disposed to recommend (at present) the
extreme measures adopted by some States, where an infant whose angle
deviates by half a degree from the correct angularity is summarily
destroyed at birth. Some of our highest and ablest men, men of real
genius, have during their earliest days laboured under deviations as
great as, or even greater than forty-five minutes: and the loss of
their precious lives would have been an irreparable injury to the
State. The art of healing also has achieved some of its most glorious
triumphs in the compressions, extensions, trepannings, colligations,
and other surgical or diaetetic operations by which Irregularity has
been partly or wholly cured. Advocating therefore a _Via Media,_ I
would lay down no fixed or absolute line of demarcation; but at the
period when the frame is just beginning to set, and when the Medical
Board has reported that recovery is improbably, I would suggest that
the Irregular offspring be painlessly and mercifully consumed.
* * *
SECTION 8. -- Of the Ancient Practice of Painting
If my Readers have followed me with any attention up to this
point, they will not be surprised to hear that life is somewhat dull
in Flatland. I do not, of course, mean that there are not battles,
conspiracies, tumults, factions, and all those other phenomena which
are supposed to make History interesting; nor would I deny that the
strange mixture of the problems of life and the problems of
Mathematics, continually inducing conjecture and giving an opportunity
of immediate verification, imparts to our existence a zest which you
in Spaceland can hardly comprehend. I speak now from the aesthetic
and artistic point of view when I say that life with us is dull;
aesthetically and artistically, very dull indeed.
How can it be otherwise, when all one's prospect, all one's
landscapes, historical pieces, portraits, flowers, still life, are
nothing but a single line, with no varieties except degrees of
brightness and obscurity?
It was not always thus. Colour, if Tradition speaks the truth,
once for the space of half a dozen centuries or more, threw a
transient splendour over the lives of our ancestors in the remotest
ages. Some private individual -- a Pentagon whose name is variously
reported -- having casually discovered the constituents of the simpler
colours and a rudimentary method of painting, is said to have begun by
decorating first his house, then his slaves, then his Father, his
Sons, and Grandsons, lastly himself. The convenience as well as the
beauty of the results commended themselves to all. Wherever
Chromatistes, -- for by that name the most trustworthy authorities
concur in calling him, -- turned his variegated frame, there he at
once excited attention, and attracted respect. No one now needed to
"feel" him; no one mistook his front for his back; all his movements
were readily ascertained by his neighbours without the slightest
strain on their powers of calculation; no one jostled him, or failed
to make way for him; his voice was saved the labour of that exhausting
utterance by which we colourless Squares and Pentagons are often
forced to proclaim our individuality when we move amid a crowd of
ignorant Isosceles.
The fashion spread like wildfire. Before a week was over, every
Square and Triangle in the district had copied the example of
Chromatistes, and only a few of the more conservative Pentagons still
held out. A month or two found even the Dodecagons infected with the
innovation. A year had not elapsed before the habit had spread to all
but the very highest of the Nobility. Needless to say, the custom
soon made its way from the district of Chromatistes to surrounding
regions; and within two generations no one in all Flatland was
colourless except the Women and the Priests.
Here Nature herself appeared to erect a barrier, and to plead
against extending the innovations to these two classes. Many-
sidedness was almost essential as a pretext for the Innovators.
"Distinction of sides is intended by Nature to imply distinction of
colours" -- such was the sophism which in those days flew from mouth
to mouth, converting whole towns at a time to a new culture. But
manifestly to our Priests and Women this adage did not apply. The
latter had only one side, and therefore -- plurally and pedanticallly
speaking -- _no sides._ The former -- if at least they would assert
their claim to be readily and truly Circles, and not mere high-class
Polygons, with an infinitely large number of infinitesimally small
sides -- were in the habit of boasting (what Women confessed and
deplored) that they also had no sides, being blessed with a perimeter
of only one line, or, in other words, a Circumference. Hence it came
to pass that these two Classes could see no force in the so-called
axiom about "Distinction of Sides implying Distinction of Colour;" and
when all others had succumbed to the fascinations of corporal
decoration, the Priests and the Women alone still remained pure from
the pollution of paint.
Immoral, licentious, anarchical, unscientific -- call them by what
named you will -- yet, from an aesthetic point of view, those ancient
days of the Colour Revolt were the glorious childhood of Art in
Flatland -- a childhood, alas, that never ripened into manhood, nor
even reached the blossom of youth. To live then in itself a delight,
because living implied seeing. Even at a small party, the company was
a pleasure to behold; the richly varied hues of the assembly in a
church or theatre are said to have more than once proved too
distracting from our greatest teachers and actors; but most ravishing
of all is said to have been the unspeakable magnificence of a military
review.
The sight of a line of battle of twenty thousand Isosceles
suddenly facing about, and exchanging the sombre black of their bases
for the orange of the two sides including their acute angle; the
militia of the Equilateral Triangles tricoloured in red, white, and
blue; the mauve, ultra-marine, gamboge, and burnt umber of the Square
artillerymen rapidly rotating near their vermillion guns; the dashing
and flashing of the five-coloured and six-coloured Pentagons and
Hexagons careering across the field in their offices of surgeons,
geometricians and aides-de-camp -- all these may well have been
sufficient to render credible the famous story how an illustrious
Circle, overcome by the artistic beauty of the forces under his
command, threw aside his marshal's baton and his royal crown,
exclaiming that he henceforth exchanged them for the artist's pencil.
How great and glorious the sensuous development of these days must
have been is in part indicated by the very language and vocabulary of
the period. The commonest utterances of the commonest citizens in the
time of the Colour Revolt seem to have been suffused with a richer
tinge of word or thought; and to that era we are even now indebted for
our finest poetry and for whatever rhythm still remains in the more
scientific utterance of those modern days.
* * *
SECTION 9. -- Of the Universal Colour Bill
But meanwhile the intellectual Arts were fast decaying.
The Art of Sight Recognition, being no longer needed, was no
longer practised; and the studies of Geometry, Statics, Kinetics, and
other kindred subjects, came soon to be considered superfluous, and
feel into disrespect and neglect even at our University. The inferior
Art of Feeling speedly experienced the same fate at our Elementary
Schools. Then the Isosceles classes, asserting that the Specimens
were no longer used nor needed, and refusing to pay the customary
tribute from the Criminal classes to the service of Education, waxed
daily more numerous and more insolent on the strength of their
immunity from the old burden which had formerly exercised the twofold
wholesome effect of at once taming their brutal nature and thinning
their excessive numbers.
Year by year the Soldiers and Artisans began more vehemently to
assert -- and with increasing truth -- that there was no great
difference between them and the very highest class of Polygons, now
that they were raised to an equality with the latter, and enabled to
grapple with all the difficulties and solve all the problems of life,
whether Statical or Kinetical, by the simple process of Colour
Recognition. Not content with the natural neglect into which Sight
Recognition was falling, they began boldly to demand the legal
prohibition of all "monopolizing and aristocratic Arts" and the
consequent abolition of all endowments for the studies of Sight
Recognition, Mathematics, and Feeling. Soon, they began to insist
that inasmuch as Colour, which was a second Nature, had destroyed the
need of aristocratic distinctions, the Law should follow in the same
path, and that henceforth all individuals and all classes should be
recognized as absolutely equal and entitled to equal rights.
Finding the higher Orders wavering and undecided, the leaders of
the Revolution advanced still further in their requirements, and at
last demanded that all classes alike, the Priests and the Women not
excepted, should do homage to Colour by submitting to be painted.
When it was objected that Priests and Women had no sides, they
retorted that Nature and Expediency concurred in dictating that the
front half of every human being (that is to say, the half containing
his eye and mouth) should be distinguishable from his hinder half.
They therefore brought before a general and extraordinary Assembly of
all the States of Flatland a Bill proposing that in every Woman the
half containing the eye and mouth should be coloured red, and the
other half green. The Priests were to be painted in the same way, red
being applied to that semicircle in which the eye and mouth formed the
mmiddle point; while the other or hinder semicircle was to be coloured
green.
There was no little cunning in this proposal, which indeed
emanated not from any Isosceles -- for no being so degraded would have
angularity enough to appreciate, much less to devise, such a model of
state-craft -- but from an Irregular Circle who, instead of being
destroyed in his childhood, was reserved by a foolish indulgence to
bring desolation on his country and destruction on myriads of
followers.
On the one hand the proposition was calculated to bring the Women
in all classes over to the side of the Chromatic Innovation. For by
assigning to the Women the same two colours as were assigned to the
Priests, the Revolutionists thereby ensured that, in certain
positions, every Woman would appear as a Priest, and be treated with
corresponding respect and deference -- a prospect that could not fail
to attract the Female Sex in a mass.
But by some of my Readers the possibility of the identical
appearance of Priests and Women, under a new Legislation, may not be
recognized; if so, a word or two will make it obvious.
Imagine a woman duly decorated, according to the new Code; with
the front half (i.e., the half containing the eye and mouth) red, and
with the hinder half green. Look at her from one side. Obviously you
will see a straight line, _half red, half green._
Now imagine a Priest, whose mouth is at M, and whose front
semicircle (AMB) is consequently coloured red, while his hinder
semicircle is green; so that the diameter AB divides the green from
the red. If you contemplate the Great Man so as to have your eye in
the same straight line as his dividing diameter (AB), what you will
see will be a straight line (CBD), of which _one half_ (CB) _will be
red, and the other_ (BD) _green._ The whole line (CD) will be rather
shorter perhaps than that of a full-sized Woman, and will shade off
more rapidly towards its extremities; but the identity of the colours
would give you an immediate impression of identity in Class, making
you neglectful of other details. Bear in mind the decay of Sight
Recognition which threatened society at the time of the Colour revolt;
add too the certainty that Woman would speedily learn to shade off
their extremities so as to imitate the Circles; it must then be surely
obvious to you, my dear Reader, that the Colour Bill placed us under a
great danger of confounding a Priest with a young Woman.
How attractive this prospect must have been to the Frail Sex may
readily be imagined. They anticipated with delight the confusion that
would ensue. At home they might hear political and ecclesiastical
secrets intended not for them but for their husbands and brothers, and
might even issue some commands in the name of a priestly Circle; out
of doors the striking combination of red and green without adddition
of any other colours, would be sure to lead the common people into
endless mistakes, and the Woman would gain whatever the Circles lost,
in the deference of the passers by. As for the scandal that would
befall the Circular Class if the frivolous and unseemly conduct of the
Women were imputed to them, and as to the consequent subversion of the
Constitution, the Female Sex could not be expected to give a thought
to these considerations. Even in the households of the Circles, the
Women were all in favour of the Univsersal Colour Bill.
The second object aimed at by the Bill was the gradual
demoralization of the Circles themselves. In the general intellectual
decay they still preserved their pristine clearness and strength of
understanding. From their earliest childhood, familiarized in their
Circular households with the total absence of Colour, the Nobles alone
preserved the Sacred Art of Sight Recognition, with all the advantages
that result from that admirable training of the intellect. Hence, up
to the date of the introduction of the Universal Colour Bill, the
Circles had not only held their own, but even increased their lead of
the other classes by abstinence from the popular fashion.
Now therefore the artful Irregular whom I described above as the
real author of this diabolical Bill, determined at one blow to lower
the status of the Hierarchy by forcing them to submit to the pollution
of Colour, and at the same time to destroy their domestic
opportunities of training in the Art of Sight Recognition, so as to
enfeeble their intellects by depriving them of their pure and
colourless homes. Once subjected to the chromatic taint, every
parental and every childish Circle would demoralize each other. Only
in discerning between the Father and the Mother would the Circular
infant find problems for the exercise of his understanding -- problems
too often likely to be corrupted by maternal impostures with the
result of shaking the child's faith in all logical conclusions. Thus
by degrees the intellectual lustre of the Priestly Order would wane,
and the road would then lie open for a total destruction of all
Aristocratic Legislature and for the subversion of our Privileged
Classes.
* * *
SECTION 10. -- Of the Suppression of the Chromatic Sedition
The agitation for the Universal Colour Bill continued for three
years; and up to the last moment of that period it seemed as though
Anarchy were destined to triumph.
A whole army of Polygons, who turned out to fight as private
soldiers, was utterly annihilated by a superior force of Isosceles
Triangles -- the Squares and Pentagons meanwhile remaining neutral.
Worsez than all, some of the ablest Circles fell a prey to conjugal
fury. Infuriated by political animosity, the wives in many a noble
household wearied their lords with prayers to give up their opposition
to the Colour Billl; and some, finding their entreaties fruitless,
fell on and slaughtered their innocent children and husband, perishing
themselves in the act of carnage. It is recorded that during that
triennial agitation no less than twenty-three Circles perished in
domestic discord.
Great indeed was the peril. It seemed as though the Priests had
no choice between submission and extermination; when suddenly the
course of events was completely changed by one of those picturesque
incidents which Statesmen ought never to neglect, often to anticipate,
and sometimes perhaps to originate, because of the absurdly
disproportionate power with which they appearl to the sympathies of
the populace.
It happened that an Isosceles of a low type, with a brain little
if at all above four degrees -- accidentally dabbling in the colours
of some Tradesman whose shop he had plundered -- painted himself, or
caused himself to be painted (for the story varies) with the twelve
colours of a Dodecagon. Going into the Market Place he accosted in a
feigned voice a maiden, the orphan daughter of a noble Polygon, whose
affection in former days he had sought in vain; and by a series of
deceptions -- aided, on the one side, by a string of lucky accidents
too long to relate, and, on the other, by an almost inconceivable
fatuity and neglect of ordinary precautions on the part of the
relations of the bride -- he succeeded in consummating the marriage.
The unhappy girl committed suicide on discovering the fraud to which
she had been subjected.
When the news of this catastrophe spread from State to State the
minds of the Women were violently agitated. Sympathy with the
miserable victim and anticipations of similar deceptions for
themselves, their sisters, and their daughters, made them now regard
the Colour Bill in an entirely new aspect. Not a few openly avowed
themselves converted to antagonism; the rest needed only a slight
stimulus to make a similar avowal. Seizing this favourable
apportunity, the Circles hastily convened an extraordinary Assembly of
the States; and besides the usual guard of Convicts, they secured the
attendance of a large number of reactionary Women.
Amidst an unprecedented concourse, the Chief Circle of those days
-- by name Pantocyclus -- arose to find himself hissed and hooted by a
hundred and twenty thousand Isosceles. But he secured silence by
declaring that henceforth the Circles would enter on a policy of
Concession; yielding to the wishes of the majority, they would accept
the Colour Bill. The uproar being at once converted to applause, he
invited Chromatistes, the leader of the Sedition, into the centre of
the hall, to receive in the name of his followers the submission of
the Hierarchy. Then followed a speech, a masterpiece of rhetoric,
which occupied nearly a day in the delivery, and to which no summary
can do justice.
With a grave appearance of impartiality he declared that as they
were now finally committing themselves to Reform or Innovation, it was
desirable that they should take one last view of the perimeter of the
whole subject, its defects as well as its advantages. Gradually
introduction the mention of the dangers to the Tradesmen, the
Professional Classes and the Gentlemen, he silenced the rising murmurs
of the Isosceles by reminding them that, in spite of all these
defects, he was willing to accept the Bill if it was approved by the
majority. But it was manifest that all, except the Isosceles, were
moved by his words and were either neutral or averse to the Bill.
Turning now to the Workmen he asserted that their interests must
not be neglected, and that, if they intended to accept the Colour
Bill, they ought at least to do so with full view of the consequences.
Many of them, he said, were on the point of being admitted to the
class of the Regular Triangles; others anticipated for their children
a distinction they could not hope for themselves. That honourable
ambition would not have to be sacrificed. With the universal adoption
of Colour, all distinctions would cease; Regularity would be confused
with Irregularity; development would give place to retrogression; the
Workman would in a few generations be degraded to the level of the
Militar, or even the Convict Class; political power would be in the
hands of the greatest number, that is to say the Criminal Classes, who
were already more numerous than the Workmen, and would soon out-number
all the other Classes put together when the usual Compensative Laws of
Nature were violated.
A subdued murmur of assent ran through the ranks of the Artisans,
and Chromatistes, in alarm, attempted to step forward and address
them. But he found himself encompassed with guards and forced to
remain silent while the Chief Circle in a few impassioned words made a
final appeal to the Women, exclaiming that, if the Colour Bill passed,
no marriage would henceforth be safe, no woman's honour secure; fraud,
deception, hypocrisy would pervade every household; domestic bliss
would share the fate of the Constitution and pass to speedy perdition.
"Sooner than this," he cried, "Come death."
At these words, which were the preconcerted signal for action, the
Isosceles Convicts fell on and transfixed the wretched Chromatistes;
the Regular Classes, opening their ranks, made way for a band of Women
who, under direction of the Circles, moved back foremost, inivisibly
and unerringly upon the unconscious soldiers; the Artisans, imitating
the example of their betters, also opened their ranks. Meantime bands
of Convicts occupied every entrance with an impenetrable phalanx.
The battle, or rather carnage, was of short duration. Under the
skillful generalship of the Circles almost every Woman's charge was
fatal and very many extracted their sting uninjured, ready for a
second slaughter. But no second blow was needed; the rabble of the
Isosceles did the rest of the business for themselves. Surprised,
leader-less, attacked in front by invisible foes, and finding egress
cut off by the Convicts behind them, they at once -- after their
manner -- lost all presence of mind, and raised the cry of
"treachery." This sealed their fate. Every Isosceles now saw and
felt a foe in every other. In half an hour not one of that vast
multitude was living; and the fragments of seven score thousand of the
Criminal Class slain by one another's angles attested the triumph of
Order.
The Circles delayed not to push their victory to the uttermost.
The Working Men they spared but decimated. The Militia of the
Equilaterals was at once called out, and every Triangle suspected of
Irregularity on reasonable grounds, was destroyed by Court Martial,
without the formality of exact measurement by the Social Board. The
homes of the Military and Artisan classes were inspected in a course
of visitation extending through upwards of a year; and during that
period every town, village, and hamlet was systematically purged of
that excess of the lower orders which had been brought about by the
neglect to pay the tribute of Criminals to the Schools and University,
and by the violation of other natural Laws of the Constitution of
Flatland. Thus the balance of classes was again restored.
Needless to say that henceforth the use of Colour was abolished,
and its possession prohibited. Even the utterance of any word
denoting Colour, except by the Circles or by qualified scientific
teachers, was punished by a severe penalty. Only at our University in
some of the very highest and most esoteric classes -- which I myself
have never been privileged to attend -- it is understood that the
sparing use of Colour is still sanctioned for the purpose of
illustrating some of the deeper problems of mathematics. But of this
I can only speak from hearsay.
Elsewhere in Flatland, Colour is no non-existent. The art of
making it is known to only one living person, the Chief Circle for the
time being; and by him it is handed down on his death-bed to none but
his Successor. One manufactory alone produces it; and, lest the
secret should be betrayed, the Workmen are annually consumed, and
fresh ones introduced. So great is the terror with which even now our
Aristocracy looks back to the far-distant days of the agitation for
the Universal Colour Bill.
* * *
SECTION 11. -- Concerning our Priests
It is high time that I should pass from these brief and discursive
notes about things in Flatland to the central event of this book, my
initiation into the mysteries of Space. _That_ is my subject; all
that has gone before is merely preface.
For this reason I must omit many matters of which the explanation
would not, I flatter myself, be without interest for my Readers: as
for example, our method of propelling and stopping ourselves, although
destitute of feet; the means by which we give fixity to structuers of
wood, stone, or brick, although of course we have no hands, nor can we
lay foundations as you can, nor avail ourselves of the lateral
pressure of the earth; the manner in which the rain originates in the
intervals between our various zones, so that the northern regions do
not intercept the moisture falling on the southern; the nature of our
hills and mines, our trees and vegetables, our seasons and harvests;
our Alphabet and method of writing, adapted to our linear tablets;
these and a hundred other details of our physical existence I must
pass over, nor do I mention them now except to indicate to my readers
that their omission proceeds not from forgetfulness on the part of the
author, but from his regard for the time of the Reader.
Yet before I proceed to my legitimate subject some few final
remarks will no doubt be expected by my Readers upon these pillars and
mainstays of the Constitution of Flatland, the controllers of our
conduct and shapers of our destiny, the objects of universal homage
and almost of adoration: need I say that I mean our Circles or
Priests?
When I call them Priests, let me not be understood as meaning no
more than the term denotes with you. With us, our Priests are
Administrators of all Business, Art, and Science; Directors of Trade,
Commerce, Generalship, Architecture, Engineering, Education,
Statesmanship, Legislature, Morality, Theology; doing nothing
themselves, they are the Causes of everything worth doing, that is
done by others.
Although popularly everyone called a Circle is deemed a Circle,
yet among the better educated Classes it is known that no Circle is
really a Circle, but only a Polygon with a very large number of very
small sides. As the number of the sides increases, a Polygon
approximates to a Circle; and, when the number is very great indeed,
say for example three or four hundred, it is extremely difficult for
the most delicate touch to feel any polygonal angles. Let me say
rather it _would_ be difficult: for, as I hav shown above,
Recognition by Feeling is unknown among the highest society, and to
_feel_ a Circle would be considered a most audacious insult. This
habit of abstention from Feeling in the best society enables a Circle
the more easily to sustain the veil of mystery in which, from his
earliest years, he is wont to enwrap the exact nature of his Perimeter
or Circumference. Three feet being the average Perimeter it follows
that, in a Polygon of three hundred sides each side will be no more
than the hundredth part of a foot in length, or little more than the
tenth part of an inch; and in a Polygon of six or seven hundred sides
the sides are little larger than the diameter of a Spaceland pin-head.
It is always assumed, by courtesy, that the Chief Circle for the time
being has ten thousand sides.
The ascent of the posterity of the Circles in the social scale is
not restricted, as it is among the lower Regular classes, by the Law
of Nature which limits the increase of sides to one in each
generation. If it were so, the number of sides in the Circle would be
a mere question of pedigree and arithmetic, and the four hundrd and
ninety-seventh descendant of an Equilateral Triangle would necessarily
be a polygon With five hundred sides. But this is not the case.
Nature's Law prescribes two antagonstic decrees affecting Circular
propogation; first, that as the race climbs higher in the scale of
development, so development shall proceed at an accelerated pace;
second, that in the same proportion, the race shall become less
fertile. Consequently in the home of a Polygon of four or five
hundred sides it is rare to find a son; more than one is never seen.
On the other hand the son of a five-hundred-sided Polygon has been
known to possess five hundred and fifty, or even six hundred sides.
Art also steps in to help the process of higher Evolution. Our
physicians have discovered that the small and tender sides of an
infant Polygon of the higher class can be fractured, and his whole
frame re-set, with such exactness that a Polygon of two or three
hundred sides sometimes -- by no means always, for the process is
attended with serious risk -- but sometimes overleaps two or three
hundred generations, and as it were double at a stroke, the number of
his progenitors and the nobility of his descent.
Many a promising child is sacrificed in this way. Scarcely one
out of ten survives. Yet so strong is the parental ambition among
those Polygons who are, as it were, on the fringe of the Circular
class, that it is very rare to find the Nobleman of that position in
society, who has neglected to place his first-born in the Circular
Neo-Therapeutic Gymnasium before he has attained the age of a month.
One year determins success or failure. At the end of that time
the child has, in all probability, added one more to the tombstones
that crowd the Neo-Therapeutic Cemetery; but on rare occasional a glad
procession bares back the little one to his exultant parents, no
longer a Polygon, but a Circle, at least by courtesy: and a single
instance of so blessed a result induces multitudes of Polygonal
parents to submit to simialr domestic sacrifice, which have a
dissimilar issue.
* * *
SECTION 12. -- Of the Doctrine of our Priests
As to the doctrine of the Circles it may briefly be summed up in a
single maxim, "Attend to your Configuration." Whether political,
ecclesiastical, or moral, all their teaching has for its object the
improvement of individual and collective Configuration -- with special
reference of course to the Configuration of the Circles, to which all
other objects are subordinated.
It is the merit of the Circles that they have effectually
suppressed those ancient heresies which led men to waste energy and
sympathy in the vain belief that conduct depends upon will, effort,
training, encouragement, praise, or anything else but Configuration.
It was Pantocyclus -- the illustrious Circle mentioned above, as the
queller of the Colour Revolt -- who first convinced mankind that
Configuration makes the man; that if, for example, you are born an
Isosceles with two uneven sides, you will assuredly go wrong unless
you have them made even -- for which purpose you must go to the
Isosceles Hospital; similiarly, if you are a Triangle, or Square, or
even a Polygon, born with any Irregularity, you must be taken to one
of the Regular Hospitals to have your disease cured; otherwise you
will end your days in the State Prison or by the angle of the State
Executioner.
All faults or defects, from the slightest misconduct to the most
flagitious crime, Pantocyclus attributed to some deviation from
perfect Regularity in the bodily figure, caused perhaps (if not
congenital) by some collision in a crowd; by neglect to take exercise,
or by taking too much of it; or even by a sudden change of
temperature, resulting in a shrinkage or expansion in some too
susceptible part of the frame. Therefore, concluded that illustrious
Philosopher, neither good conduct nor bad conduct is a fit subject, in
any sober estimation, for eithe praise or blame. For why should you
praise, for example, the integrity of a Square who faithfully defends
the interests of his client, when you ought in reality rather to
admire the exact precision of his right angles? Or again, why blame a
lying, thievish Isosceles, when you ought rather to deplore the
incurable inequality of his sides?
Theoretically, this doctrine is unquestionable; but it has
practical drawbacks. In dealing with an Isosceles, if a rascal pleads
that he cannot help stealing because of his unevenness, you reply that
for that very reason, because he cannot help being a nuisance to his
neighbours, you, the Magistrate, cannot help sentencing him to be
consumed -- and tehre's an end of the matter. But in little domestic
difficulties, when the penalty of consumption, or death, is out of the
question, this theory of Configuration sometimes comes in awkwardly;
and I must confess that occasionally when one of my own Hexagonal
Grandsons pleads as an excuse for his disobedience that a sudden
change of temperature has been too much for his Perimeter, and that I
ought to lay the blame not on him but on his Configuration, which can
only be strengthened by abundance of the choicest sweetmeats, I
neither see my way logically to reject, nor practically to accept, his
conclusions.
For my own part, I find it best to assume that a good sound
scolding or castigation has some latent and strengthening influence on
my Grandson's Configuration; though I own that I have no grounds for
thinking so. At all events I am not alone in my way of extricating
myself from this dilemma; for I find that many of the highest Circles,
sitting as Judges in law courts, use praise and blame towards Regular
and Irregular Figures; and in their homes I know by experience that,
when scolding their children, they speak about "right" and "wrong" as
vehemently and passionately as if they believe that these names
represented real existence, and that a human Figure is really capable
of choosing between them.
Constantly carrying out their policy of making Configuration the
leading idea in every mind, the Circles reverse the nature of that
Commandment which in Spaceland regulates the relations between parents
and children. With you, children are taught to honour their parents;
with us -- next to the Circles, who are the chief object of universal
homage -- a man is taught to honour his Grandson, if he has one; or,
if not, his Son. By "honour," however, is by no means mean
"indulgence," but a reverent regard for their highest interests: and
the Circles teach that the duty of fathers is to subordinate their own
interests to those of posterity, thereby advancing the welfare of the
whole State as well as that of their own immediate descendants.
The weak point in the system of the Circles -- if a humble Square
may venture to speak of anything Circular as containing any element of
weakness -- appears to me to be found in their relations with Women.
As it is of the utmost importance for Society that Irregular
births should be discouraged, it follows that no Woman who has any
Irregularities in her ancestry is a fit partner for one who desires
that his posterity should rise by regular degrees in the social scale.
Now the Irregularity of a Male is a matter of measurement; but as
all Women are straight, and therefore visibly Regular so to speak, one
has to device some other means of ascertaining what I may call their
invisible Irregularity, that is to say their potential Irregularities
as regards possible offspring. This is effected by carefully-kept
pedigrees, which arepreserved and supervised by the State; and without
a certified pedigree no Woman is allowed to marry.
Now it might have been supposed the a Circle -- proud of his
ancestry and regardful for a posterity which might possibly issue
hereafter in a Chief Circle -- would be more careful than any other to
choose a wife who had no blot on her escutcheon. But it is not so.
The care in choosing a Regular wife appears to diminish as one rises
in the social scale. Nothing would induce an aspiring Isosceles, who
has hopes of generating an Equilateral Son, to take a wife who
reckoned a single Irregularity among her Ancestors; a Square or
Pentagon, who is confident that his family is steadily on the rise,
does not inqure above the five-hundredth generation; a Hexagon or
Dodecagon is even more careless of the wife's pedigree; but a Circle
has been known deliberately to take a wife who has had an Irregular
Great-Grandfather, and all because of some slight superiority of
lustre, or because of the charms of a low voice -- which, with us,
even more than with you, is thought "an excellent thing in a Woman."
Such ill-judged marriages are, as might be expected, barren, if
they do not result in positive Irregularity or in diminution of sides;
but none of these evils have hitherto provied sufficiently deterrent.
The loss of a few sides in a highly-developed Polygon ios not easily
noticed, and is sometimes compensated by a successful operation in the
Neo-Therapeutic Gymnasium, as I have described above; and the Circles
are too much disposed to acquiesce in infecundity as a law of the
superior development. Yet, if this evil be not arrested, the gradual
diminution of the Circular class may soon become more rapid, and the
time may not be far distant when, the race being no longer able to
produce a Chief Circle, the Constitution of Flatland must fall.
One other word of warning suggest itself to me, though I cannot so
easily mention a remedy; and this also refers to our relations with
Women. About three hundred years ago, it was decreed by the Chief
Circle that, since women are deficient in Reason but abundant in
Emotion, they ought no longer to be treated as rational, nor receive
any mental education. The consequence was that they were no longer
taught to read, nor even to master Arithmetic enough to enable them to
count the angles of their husband or children; and hence they sensibly
declined during each generation in intellectual power. And this
system of female non-education or quietism still prevails.
My fear is that, with the best intentions, this policy has been
carried so far as to react injuriously on the Male Sex.
For the consequence is that, as things now are, we Males have to
lead a kind of bi-lingual, and I may almost say bimental, existence.
With Women, we speak of "love," "duty," "right," "wrong," "pity,"
"hope," and other irrational and emotional conceptions, which have no
existence, and the fiction of which has no object except to control
feminine exuberances; but among ourselves, and in our books, we have
an entirely different vocabulary and I may also say, idion. "Love"
them becomes "the anticipation of benefits"; "duty" becomes
"necessity" or "fitness"; and other words are correspondingly
transmuted. Moreover, among Women, we use language implying the
utmost deference for their Sex; and they fully believe that the Chief
Circle Himself is not more devoutly adored by us than they are: but
behind their backs they are both regarded and spoken of -- by all but
the very young -- as being little better than "mindless organisms."
Our Theology also in the Women's chambers is entirely different
from our Theology elsewhere.
Now my humble fear is that this double training, in language as
well as in thought, imposes somewhat too heavy a burden upon the
young, especially when, at the age of three years old, they are taken
from the maternal care and taught to unlearn the old language --
except for the purpose of repeating it in the presence of the Mothers
and Nurses -- and to learn the vocabulary and idiom of science.
Already methinks I discern a weakness in the grasp of mathematical
truth at the present time as compred with the more robust intellect of
our ancestors three hundred years ago. I say nothing of the possible
danger if a Woman should ever surrpetitously learn to read and convey
to her Sex the result of her perusal of a single popular volumne; nor
of the possibility that the indiscretion or disobedience of some
infant Male might reveal to a Mother the secrets of the logical
dialect. On the simple ground of the enfeebling of the male
intellect, I rest this humble appeal to the highest Authorities to
reconsides the regulations of Female education.
* * *
PART II
OTHER WORLDS
"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 Gemoetry, 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 third appeal on my
part were equally ineffectual. Losing patience at what appeared to me
intolerable rudeness, I brought my mouth to 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 preserving 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 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 any one
ever see anything but a Point. Man, woman, child, thing -- each as 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 m ove to the right or left to make way
for passers by, it followed that no Linlander 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 that 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
hestitated 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
Manarch (as I had noted in my dream befor 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 se or approach
their Majesties, when there 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 by 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 uus 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 and 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 instance 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-voice 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 congtrary, the process is by most of us many times repeated.
Few are the hearts whose happy lot is at once to recognize in each
other's voice 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, befor 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."
* * *
SECTION 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 snese 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 voice, 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 course 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, 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 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 cocnerned, though I know now 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 setp 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 clearer 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 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 enightening 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 movement
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.
* * *
SECTION 15. -- Concerning a Stranger from Spaceland
From dreams I proceed to facts.
It was the last day of our 1999th year of our era. The patterning
of the rain had long ago announced nightfall; and I was sitting
(footnote 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
comming 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
three-to-the-second, or nine, represents the number of square inches
in a Square whose side is three inches long."
The little Hexagon meditated on this a while and then said to me;
"But you have been teaching me to raise numbers to the third power: I
suppose three-to-the-third 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 shew the boy
how a Point by moving through a length of three inches makes a Line of
three inches, which may be represented by three; 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 three-to-the-second.
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
three; and if a straight Line of three inches, moving parallel to
itself, makes a Square of three inches every way, represented by
three-to-the-second; it must be that a Square of three inches every
way, moving somehow parallel to itself (but I don't see how) must make
Something else (but I don't see what) of three inches every way -- and
this must be represented by three-to-the-third."
"Go to bed," said I, a little ruffled by this 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 of 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 around 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; three-
to-the-third can have no meaning in Geometry." At once there came a
distinctly audible reply, "The boy is not a fool; and three-to-the-
third 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 apeture. "How comes this
person here?" she exclaimed, "you promised me, my dear, that there
should be no ventilators in our new house." "Nor are they any," said
I; "but what makes you think that the stranger is a Woman? I see by
my power of Sight Recoginition --" "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 propsal that our
august Visitor should so incommode himself, and assuring the Circle
that the hour of 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
third Millennium had begun.
----------
Footnote 3. When I say "sitting," of course I do not mean any change
of attitude such as you in Spaceland signify by that word; for as we
have no feet, we can no more "sit" nor "stand" (in your sense of the
word) than one of your soles or flounders.
Nevertheless, we perfectly well recognize the different mental
states of volition implied by "lying," "sitting," and "standing,"
which are to some extent indicated to a beholder by a slight increase
of lustre corresponding to the increase of volition.
But on this, and a thousand other kindred subjects, time forbids
me to dwell.
* * *
SECTION 16. -- How the Stranger vainly endeavoured to reveal to me
in words the mysteries of Spaceland
As soon as the sound of the Peace-cry of my departing Wife had
died away, I began to approach the Stranger with the intention of
taking a nearer view and of bidding him be seated: but his appearance
struck me dumb and motionless with astonishment. Without the
slightest symptoms of angularity hee nevertheless varied every instant
with graduations of size and brightness scarcely possible for any
Figure within the scope of my experience. The thought flashed across
me that I might have before me a burglar or cut-throat, some monstrous
Irregular Isosceles, who, by feigning the voice of a Circle, had
obtained admission somehow into the house, and was now preparing to
stab me with his acute angle.
In a sitting-room, the absence of Fog (and the season happened to
be remarkably dry), made it difficult for me to trust to Sight
Recognition, especially at the short distance at which I was standing.
Desperate with fear, I rushed forward with an unceremonious, "You must
permit me, Sir --" and felt him. My Wife was right. There was not
the trace of an angle, not the slightest roughness or inequality:
never in my life had I met with a more perfect Circle. He remained
motionless while I walked around him, beginning from his eye and
returning to it again. Circular he was throughout, a perfectly
satisfactory Circle; there could not be a doube of it. Then followed
a dialogue, which I will endeavour to set down as near as I can
recollect it, omitting only some of my profuse apologies -- for I was
covered with shame and humiliation that I, a Square, should have been
guilty of the impertinence of feeling a Circle. It was commenced by
the Stranger with some impatience at the lengthiness of my
introductory process.
Stranger. Have you felt me enough by this time? Are you not
introduced to me yet?
I. Most illustrious Sir, excuse my awkwardness, which arises not
from ignorance of the usages of polite society, but from a little
surprise and nervousness, consequent on this somewhat unexpected
visit. And I beseech you to reveal my indiscretion to no one, and
especially not to my Wife. But before your Lordship enters into
further communications, would he deign to satisfy the curiosity of one
who would gladly know whence his visitor came?
Stranger. From Space, from Space, Sir: whence else?
I. Pardon me, my Lord, but is not your Lordship already in Space,
your Lordship and his humble servant, even at this moment?
Stranger. Pooh! what do you know of Space? Define Space.
I. Space, my Lord, is height and breadth indefinitely prolonged.
Stranger. Exactly: you see you do not even know what Space is.
You think it is of Two Dimensions only; but I have come to announce to
you a Third -- height, breadth, and length.
I. Your Lordship is pleased to be merry. We also speak of length
and height, or breadth and thickness, thus denoting Two Dimensions by
four names.
Stranger. But I mean not only three names, but Three Dimensions.
I. Would your Lordship indicate or explain to me in what
direction is the Third Dimension, unknown to me?
Stranger. I came from it. It is up above and down below.
I. My Lord means seemingly that it is Northward and Southward.
Stranger. I mean nothing of the kind. I mean a direction in
which you cannot look, because you have no eye in your side.
I. Pardon me, my Lord, a moment's inspection will convince your
Lordship that I have a perfectly luminary at the juncture of my two
sides.
Stranger: Yes: but in order to see into Space you ought to have
an eye, not on your Perimeter, but on your side, that is, on what you
would probably call your inside; but we in Spaceland should call it
your side.
I. An eye in my inside! An eye in my stomach! Your Lordship
jests.
Stranger. I am in no jesting humour. I tell you that I come from
Space, or, since you will not understand what Space means, from the
Land of Three Dimensions whence I but lately looked down upon your
Plane which you call Space forsooth. From that position of advantage
I discerned all that you speak of as _solid_ (by which you mean
"enclosed on four sides"), your houses, your churches, your very
chests and safes, yes even your insides and stomachs, all lying open
and exposed to my view.
I. Such assertions are easily made, my Lord.
Stranger. But not easily proved, you mean. But I mean to prove
mine.
When I descended here, I saw your four Sons, the Pentagons, each
in his apartment, and your two Grandsons the Hexagons; I saw your
youngest Hexagon remain a while with you and then retire to his room,
leaving you and your Wife alone. I saw your Isosceles servants, three
in number, in the kitchen at supper, and the little Page in the
scullery. Then I came here, and how do you think I came?
I. Through the roof, I suppose.
Strange. Not so. Your roof, as you know very well, has been
recently repaired, and has no aperture by which even a Woman could
penetrate. I tell you I come from Space. Are you not convinced by
what I have told you of your children and household?
I. Your Lordship must be aware that such facts touching the
belongings of his humble servant might be easily ascertained by any
one of the neighbourhood possessing your Lordship's ample means of
information.
Stranger. (_To himself._) What must I do? Stay; one more
argument suggests itself to me. When you see a Straight Line -- your
wife, for example -- how many Dimensions do you attribute to her?
I. Your Lordship would treat me as if I were one of the vulgar
who, being ignorant of Mathematics, suppose that a Woman is really a
Straight Line, and only of One Dimension. No, no, my Lord; we Squares
are better advised, and are as well aware of your Lordship that a
Woman, though popularly called a Straight Line, is, really and
scientifically, a very thin Parallelogram, possessing Two Dimensions,
like the rest of us, viz., length and breadth (or thickness).
Stranger. But the very fact that a Line is visible implies that
it possesses yet another Dimension.
I. My Lord, I have just acknowledge that a Woman is broad as well
as long. We see her length, we infer her breadth; which, though very
slight, is capable of measurement.
Stranger. You do not understand me. I mean that when you see a
Woman, you ought -- besides inferring her breadth -- to see her
length, and to _see_ what we call her _height_; although the last
Dimension is infinitesimal in your country. If a Line were mere
length without "height," it would cease to occupy Space and would
become invisible. Surely you must recognize this?
I. I must indeed confess that I do not in the least understand
your Lordship. When we in Flatland see a Line, we see length and
_brightness._ If the brightness disappears, the Line is extinguished,
and, as you say, ceases to occupy Space. But am I to suppose that
your Lordship gives the brightness the title of a Dimension, and that
what we call "bright" you call "high"?
Stranger. No, indeed. By "height" I mean a Dimension like your
length: only, with you, "height" is not so easily perceptible, being
extremely small.
I. My Lord, your assertion is easily put to the test. You say I
have a Third Dimension, which you call "height." Now, Dimension
implies direction and measurement. Do but measure my "height," or
merely indivate to me the direction in which my "height" extends, and
I will become your convert. Otherwise, your Lordship's own understand
must hold me excused.
Stranger. (_To himself._) I can do neither. How shall I
convince him? Surely a plain statement of facts followed by ocular
demonstration ought to suffice. -- Now, Sir; listen to me.
You are living on a Plane. What you style Flatland is the vast
level surface of what I may call a fluid, or in, the top of which you
and your countrymen move about, without rising above or falling below
it.
I am not a plane Figure, but a Solid. You call me a Circle; but in
reality I am not a Circle, but an infinite number of Circles, of size
varying from a Point to a Circle of thirteen inches in diameter, one
placed on the top of the other. When I cut through your plane as I am
now doing, I make in your plane a section which you, very rightly,
call a Circle. For even a Sphere -- which is my proper name in my own
country -- if he manifest himself at all to an inhabitant of Flatland
-- must needs manfest himself as a Circle.
Do you not remember -- for I, who see all things, discerned last
night the phantasmal vision of Lineland written upon your brain -- do
you not remember, I say, how when you entered the realm of Lineland,
you were compelled to manifest yourself to the King, not as a Square,
but as a Line, because that Linear Realm had not Dimensions enough to
represent the whole of you, but only a slice or section of you? In
precisely the same way, your country of Two Dimensions is not spacious
enough to represent me, a being of Three, but can only exhibit a slice
or section of me, which is what you call a Circle.
The diminished brightness of your eye indicates incredulity. But
now prepare to receive proof positive of the truth of my assertions.
You cannot indeed see more than one of my sections, or Circles, at a
time; for you have no power to raise your eye out of the plane of
Flatland; but you can at least see that, as I rise in Space, so my
sections become smaller. See now, I will rise; and the effect upon
your eye will be that my Circle will become smaller and smaller till
it dwindles to a point and finally vanishes.
There was no "rising" that I could see; but he diminished and
finally vanished. I winked once or twice to make sure that I was not
dreaming. But it was no dream. For from the depths of nowhere came
forth a hollow voice -- close to my heart it seemed -- "Am I quite
gone? Are you convinced now? Well, now I will gradually return to
Flatland and you shall see my section become larger and larger."
Every reader in Spaceland will easily understand that my
mysterious Guest was speaking the language of truth and even of
simplicity. But to me, proficient though I was in Flatland
Mathematics, it was by no means a simple matter. The rough diagram
given above will make it clear to any Spaceland child that the Sphere,
ascending in the three positions indicated there, must needs have
manifested himself to me, or to any Flatlander, as a Circle, at first
of full size, then small, and at last very small indeed, approaching
to a Point. But to me, although I saw the facts before me, the causes
were as dark as ever. All that I could comprehend was, that the
Circle had made himself smaller and vanished, and that he had now re-
appeared and was rapidly making himself larger.
When he regained his original size, he heaved a deep sigh; for he
perceived by my silence that I had altogether failed to comprehend
him. And indeed I was now inclining to the belief that he must be no
Circle at all, but some extremely clever juggler; or else that the old
wives' tales were true, and that after all there were such people as
Enchanters and Magicians.
After a long pause he muttered to himself, "One resource alone
remains, if I am not to resort to action. I must try the method of
Analogy." Then follwed a still longer silence, after which he
continued our dialogue.
Sphere. Tell me, Mr. Mathematician; if a Point moves Northward,
and leaves a luminous wake, what name would you give to the wake?
I. A straight Line.
Sphere. And a straight Line has how many extremities?
I. Two.
Sphere. Now conceive the Northward straight Line momving parallel
to itself, East and West, so that every point in it leaves behind it
the wake of a straight Line. What name will you give to the Figure
thereby formed? We will suppose that it moves through a distance
equal to the original straight line. --- What name, I say?
I. A square.
Sphere. And how many sides has a Square? How many angles?
I. Four sides and four angles.
Sphere. Now stretch your imagination a little, and conceive a
Square in Flatland, moving parallel to itself upward.
I. What? Northward?
Sphere. No, not Northward; upward; out of Flatland altogether.
If it moved Northward, the Southern points in the Square would
have to move through the positions previously occupied by the Northern
points. But that is not my meaning.
I mean that every Point in you -- for you are a Square and will
serve the purpose of my illustration -- every Point in you, that is to
say in what you call your inside, is to pass upwards through Space in
such a way that no Point shall pass through the position previously
occupied by any other Point; but each Point shall describe a straight
Line of its own. This is all in accordance with Analogy; surely it
must be clear to you.
Restraining my impatience -- for I was now under a strong
temptation to rush blindly at my Visitor and to precipitate him into
Space, or out of Flatland, anywhere, so that I could get rid of him --
I replied: --
"And what may be the nature of the Figure which I am to shape out
by this motion which you are pleased to denote by the word 'upward'?
I presume it is describable in the language of Flatland."
Sphere. Oh, certainly. It is all plain and simple, and in strict
accordance with Analogy -- only, by the way, you must not speak of the
result as being a Figure, but as a Solid. But I will describe it to
you. Or rather not I, but Analogy.
We began with a single Point, which of course -- being itself a
Poine -- has only _one_ terminal Point.
One Point produces a Line with _two_ terminal Points.
One Line produces a Square with _four_ terminal Points.
Now you can give yourself the answer to your own question: 1, 2,
4, are evidently in Geometrical Progression. What is the next number?
I. Eight.
Sphere. Exactly. The one Square produces a _Something-which-you-
do-not-as-yet-know-a-name-for-but-which-we-call-a-Cube_ with _eight_
terminal Points. Now are you convinced?
I. And has this Creature sides, as well as Angles or what you
call "terminal Points"?
Sphere. Of course; and all according to Analogy. But, by the
way, not what _you_ call sides, but what _we_ call sides. You would
call them _solids._
I. And how many solids or sides will appertain to this Being whom
I am to generate by the motion of my inside in an "upward" direction,
and whom you call a Cube?
Sphere. How can you ask? And you a mathematician! The side of
anything is always, if I may so say, one Dimension behind the thing.
Consequently, as there is no Dimension behind a Point, a Point has 0
sides; a Line, if I may so say, has 2 sides (for the points of a Line
may be called by courtesy, its sides); a Square has 4 sides; 0, 2, 4;
what Progression do you call that?
I. Arithmetical.
Sphere. And what is the next number?
I. Six.
Sphere. Exactly. Then you see you have answered your own
question. The Cube which you will generate will be bounded by six
sides, that is to say, six of your insides. You see it all now, eh?
"Monster," I shrieked, "be thou juggler, enchanter, dream, or
devil, no more will I endure thy mockeries. Either thou or I must
perish." And saying these words I precipitated myself upon him.
* * *
SECTION 17. -- How the Sphere, having in vain tried words,
resorted to deeds
It was in vain. I brought my hardest right angle into violent
collision with the Stranger, pressing on him with a force sufficient
to have destroyed anyt ordinary Circle: but I could feel him slowly
and unarrestably slipping from my contact; not edging to the right nor
to the left, but moving somehow out of the world, and vanishing into
nothing. Soon there was a blank. But still I heard the Intruder's
voice.
Sphere. Why will you refuse to listen to reason? I had hoped to
find in you -- as being a man of sense and an accomplished
mathematician -- a fit apostle for the Gospel of the Three Dimensions,
which I am allowed to preach once only in a thousand years: but now I
know not how to convince you. Stay, I have it. Deeds, and not words,
shall proclaim the truth. Listen, my friend.
I have told you I can see from my position in Space the inside of
all things that you consider closed. For example, I see in yonder
cupboard near which you are standing, several of what you call boxes
(but like everything else in Flatland, they have no tops or bottom)
full of money; I see also two tablets of accounts. I am about to
descend into that cupboard and to bring you one of those tablets. I
saw you lock the cupboard half an hour ago, and I know you have the
key in your possession. But I descend from Space; the doors, you see,
remain unmoved. Now I am in the cupboard and am taking the tablet.
Now I have it. Now I ascent with it.
I rushed to the closet and dashed the door open. One of the
tablets was gone. With a mocking laugh, the Stranger appeared in the
other corner of the room, and at the same time the tablet appeared
upon the floor. I took it up. There could be no doubt -- it was the
missing tablet.
I groaned with horror, doubting whether I was not out of my sense;
but the Stranger continued: "Surely you must now see that my
explanation, and no other, suits the phenomena. What you call Solid
things are really superficial; what you call Space is really nothing
but a great Plane. I am in Space, and look down upon the insides of
the things of which you only see the outsides. You could leave the
Plane yourself, if you could but summon up the necessary volition. A
slight upward or downward motion would enable you to see all that I
can see.
"The higher I mount, and the further I go from your Plane, the
more I can see, though of course I see it on a smaller scale. For
example, I am ascending; now I can see your neighbour the Hexagon and
his family in their several apartments; now I see the inside of the
Theatre, ten doors off, from which the audience is only just
departing; and on the other side a Circle in his study, sitting at his
books. Now I shall come back to you. And, as a crowning proof, what
do you say to my giving you a touch, just the least touch, in your
stomach? It will not seriously injure you, and the slight pain you
may suffer cannot be compared with the mental benefit you will
receive."
Before I could utter a word of remonstrance, I felt a shooting
pain in my inside, and a demoniacal laugh seemed to issue from within
me. A moment afterwards the sharp agony had ceased, leaving nothing
but a dull ache behind, and the Stranger began to reappear, saying, as
he gradually increased in size, "There, I have not hurt you much, have
I? If you are not convinced now, I don't know what will convince you.
What say you?"
My resolution was taken. It seemed intolerable that I should
endure existence subject to the arbitrary visitations of a Magician
who could thus play tricks with one's very stomach. If only I could
in any way manage to pin him against the wall till help came!
Once more I dashed my hardest angle against him, at the same time
alarming the whole household by my cries for aid. I believe, at the
moment of my onset, the Stranger had sunk below our Plane, and really
found difficulty in rising. In any case he remained motionless, while
I, hearing, as I thought, the sound of some help approaching, pressed
against him with redoubled vigor, and continued to shout for
assistance.
A convulsive shudder ran through the Sphere. "This must not be,"
I thought I heard him say: "either he must listen to reason, or I
must have recourse to the last resource of civilization." Then,
addressing me in a louder tone, he hurriedly exclaimed, "Listen: no
stranger must witness what you have witnessed. Send your Wife back at
once, before she enters the apartment. The Gospel of Three Dimensions
must not be thus frustrated. Not thus must the fruits of one thousand
years of waiting be thrown away. I hear her coming. Back! back!
Away from me, or you must go with me -- wither you know not -- into
the Land of Three Dimensions!"
"Fool! Madman! Irregular!" I exclaimed; "never will I release
thee; thou shalt pay the penalty of thine impostures."
"Ha! Is it come to this?" thundered the Stranger: "then meet
your fate: out of your Plane you go. Once, twice, thrice! 'Tis
done!"
* * *
SECTION 18. -- How I came to Spaceland, and what I saw there
An unspeakable horror seized me. There was a darkness; then a
dizzy, sickening sensation of sight that was not like seeing; I saw a
Line that was no Line; Space that was not Space: I was myself, and
not myself. When I could find voice, I shrieked loud in agony,
"Either this is madness or it is Hell." "It is neither, calmly
replied the voice of the Sphere, "it is Knowledge; it is Three
Dimensions: open your eye once again and try to look steadily."
I looked, and, behold, a new world! There stood before me,
visibly incorporate, all that I had before inferred, conjectured,
dreamed, of perfect Circular beauty. What seemed the centre of the
Stranger's form lay open to my view: yet I could see no heart, lungs,
nor arteries, only a beautiful harmonious Something -- for which I had
no words; but you, my Readers in Spaceland, would call it the surface
of the Sphere.
Prostrating myself mentally before my Guide, I cried, "How it is,,
O divine ideal of consummate loveliness and wisdom that I see thy
inside, and yet cannot discern thy heart, thy lungs, thy arteries, thy
liver?" "What you think you see, you see not," he replied; "it is not
giving to you, nor to any other Being, to behold my internal parts. I
am of a different order of Beings from those in Flatland. Where I a
Circle, you could discern my intestines, but I am a Being, composed as
I told you before, of many Circles, the Many in the One, called in
this country a Sphere. And, just as the outside of a Cube is a
Square, so the outside of a Sphere represents the appearance of a
Circle."
Bewildered though I was by my Teacher's enigmatic utterance, I no
longer chafed against it, but worshipped him in silent adoration. He
continued, with more mildness in his voice. "Distress not yourself if
you cannot at first understand the deeper mysteries of Spaceland. By
degrees they will dawn upon you. Let us begin by casting back a
glance at the region whence you came. Return with me a while to the
plains of Flatland and I will shew you that which you have often
reasoned and thought about, but never seen with the sense of sight --
a visible angle." "Impossible!" I cried; but, the Sphere leading the
way, I followed as if in a dream, till once more his voice arrested
me: "Look yonder, and behold your own Pentagonal house, and all its
inmates."
I looked below, and saw with my physical eye all that domestic
individuality which I had hitherto merely inferred with the
understanding. And how poor and shadowy was the inferred conjecture
in comparison with the reality which I now behold! My four Sons
calmly asleep in the North-Western rooms, my two orphan Grandsons to
the South; the Servants, the Butler, my Daughter,, all in their
several apartments. Only my affection Wife, alarmed by my continued
absence, had quitter her room and was roving up and down in the Hall,
anxiously awaiting my return. Also the Page, aroused by my cries, had
left his room, and under pretext of ascertaining whether I had fallen
somewhere in a faint, was prying into the cabinet in my study. All
this I could now _see,_ not merely infer; and as we came nearer and
nearer, I could discern even the contents of my cabinet, and the two
chests of gold, and the tablets of which the Sphere had made mention.
Touched by my Wife's distress, I would have sprung downward to
reassure her, but I found myself incapable of motion. "Trouble not
yourself about your Wife," said my Guide: "she will not be long left
in anxiety; meantime, let us take a survey of Flatland."
Once more I felt myself rising through space. It was even as the
Sphere had said. The further we receded from the object we beheld,
the larger became the field of vision. My native city, with the
interior of every house and every creature therein, lay open to my
view in miniature. We mounted higher, and lo, the secrets of the
earth, the depths of the mines and inmost caverns of the hills, were
bared before me.
Awestruck at the sight of the mysteries of the earth, thus
unveiled before my unworthy eye, I said to my Companion, "Behold, I am
become as a God. For the wise men in our country say that to see all
things, or as they express it, _omnividence,_ is the attribute of God
alone." There was something of scorn in the voice of my Teacher as he
made answer: "it is so indeed? Then the very pick-pockets and cut-
throats of my country are to be worshipped by your wise men as being
Gods: for there is not one of them that does not see as much as you
see now. But trust me, your wise men are wrong."
I. Then is omnividence the attribute of others besides Gods?
Sphere. I do not know. But, if a pick-pocket or a cut-throat of
our country can see everything that is in your country, surely that is
no reason why the pick-pocket or cut-throat should be accepted by you
as a God. This omnividence, as you call it -- it is not a common word
in Spaceland -- does it make you more just, more merciful, less
selfish, more loving? Not in the least. Then how does it make you
more divine?
I. "More merciful, more loving!" But these are the qualities of
women! And we know that a Circle is a higher Being than a Straight
Line, in so far as knowledge and wisdom are more to be esteemed than
mere affection.
Sphere. It is not for me to classify human faculties according to
merit. Yet many of the best and wisest in Spaceland think more of the
affections than of the understand, more of your despised Straight
Lines than of your belauded Circles. But enough of this. Look
yonder. Do you know that building?
I looked, and afar off I saw an immense Polygonal structure, in
which I recognized the General Assembly Hall of the States of
Flatland, surrounded by dense lines of Pentagonal buildings at right
angles to each other, which I knew to be streets; and I perceived that
I was approaching the great Metropolis.
"Here we descend," said my Guide. It was now morning, the first
hour of the first day of the two thousandth year of our era. Acting,
as was their wont, in strict accordance with precedent, the highest
Circles of the realm were meeting in solemn conclave, as they had met
on the first hour of the first day of the year 1000, and also on the
first hour of the first day of the year 0.
The minutes of the previous meetings were now read by one whom I
at once recognized as my brother, a perfectly Symmetrical Square, and
the Chief Clerk of the High Council. It was found recorded on each
occasion that: "Whereas the States had been troubled by divers ill-
intentioned persons pretending to have received revelations from
another World, and professing to produce demonstrations whereby they
had instigated to frenzy both themselves and others, it had been for
this cause unanimously resolved by the Grand Council that on the first
day of each millenary, special injunctions be sent to the Prefects in
the several districts of Flatland, to make strict search for such
misguided persons, and without formality of mathematical exanimation,
to destroy all such as were Isosceles of anyt degree, to scourge and
imprison any regular Triangle, to cause any Square or Pentagon to be
sent to the district Asylum, and to arrest any one of higher rank,
sending him straightway to the Capital to be examined and judged by
the Council."
"You hear your fate," said the Sphere to me, while the Council was
passing for the third time the formal resolution. "Death or
imprisonment awaits the Apostle of the Gospel of Three Dimensions."
"Not so," replied I, "the matter is now so clear to me, the nature of
real space so palpable, that methinks I could make a child understand
it. Permit me but to descend at this moment and enlighten them."
"Not yet," said my Guide, "the time will come for that. Meantime I
must perform my mission. Stay thou there in thy place." Saying these
words, he leaped with great dexterity into the sea (if I may so call
it) of Flatland, right in the midst of the ring of Counsellors. "I
come," said he, "to proclaim that there is a land of Three
Dimensions."
I could see many of the younger Counsellors start back in manifest
horror, as the Sphere's circular section widened before them. But on
a sign from the presiding Circle -- who shewed not the slightest alarm
or surprise -- six Isosceles of a low type from six different quarters
rushed upon the Sphere. "We have him," they cried; "No; yes; we have
him still! he's going! he's gone!"
"My Lords," said the President to the Junior Circles of the
Council, "there is not the slightest need for surprise; the secret
archives, to which I alone have access, tell me that a similar
occurrence happened on the last two millennial commencements. You
will, of course, say nothing of these trifles outside the Cabinet."
Raising his voice, he now summoned the guards. "Arrest the
policemen; gag them. You know your duty." After he had consigned to
their fate the wretched policemen -- ill-fated and unwilling witnesses
of a State-secret which they were not to be permitted to reveal -- he
again addressed the Counsellors. "My Lords, the business of the
Council being concluded, I have only to wish you a happy New Year."
Before departing, he expressed, at some length, to the Clerk, my
excellent but most unfortunate brother, his sincere regret that, in
accordance with recedent and for the sake of secrecy, he must condemn
him to perpetual imprisonment, but added his satisfaction that, unless
some mention were made by him of that day's incident, his life would
be spared.
* * *
SECTION 19. -- How, though the Sphere shewed me other mysteries of
Spaceland, I still desire more; and what came of it
When I saw my poor brother led away to imprisonment, I attempted
to leap down into the Council Chamber, desiring to intercede on his
behalf, or at least bid him farewell. But I found that I had no
motion of my own. I absolutely depended on the volition of my Guide,
who said in gloomy tones, "Heed not thy brother; haply thou shalt have
ample time hereafter to condole with him. Follow me."
Once more we ascended into space. "Hitherto," said the Sphere, "I
have shewn you naught save Plane Figures and their interiors. Now I
must introduce you to Solids, and reveal to you the plan upon which
they are constructed. Behlod this multitude of moveable square cards.
See, I put on on another, not, as you supposed, Northward of the
other, but _on_ the other. Now a second, now a third. See, I am
building up a Solid by a multitude of Squares parallel to one another.
Now the Solid is complete, being as high as it is long and broad, and
we call it a Cube."
"Pardon me, my Lord," replied I; "but to my eye the appearance is
as of an Irregular Figure whose inside is laid open to view; in other
words, methinks I see no Solid, but a Plane such as we infer in
Flatland; only of an Irregularity which betokens some monstrous
criminal, so that the very sight of it is painful to my eyes."
"True," said the Sphere; "it appears to you a Plane, because you
are not accustomed to light and shade and perspective; just as in
Flatland a Hexagon would appear a Straight Line to one who has not the
Art of Sight Recognition. But in reality it is a Solid, as you shall
learn by the sense of Feeling."
He then introduced me to the Cube, and I found that this
marvellous Being was indeed no Plane, but a Solid; and that he was
endowed with six plane sides and eight terminal points called solid
angles; and I remembered the saying of the Sphere that just such a
Creature as this would be formed by the Square moving, in Space,
parallel to himself: and I rejoiced to think that so insignificant a
Creature as I could in some sense be called the Progenitor of so
illustrious an offspring.
But still I could not fully understand the meaning of what my
Teacher had told me concerning "light" and "shade" and "perspective";
and I did not hesitate to put my difficulties before him.
Were I to give the Sphere's explanation of these matters, succinct
and clear though it was, it would be tedious to an inhabitant of
Space, who knows these things already. Suffice it, that by his lucid
statements, and by changing the position of objects and lights, and by
allowing me to feel the several objects and even his own sacred
Person, he atlast made all things clear to me, so that I could now
readily distinguish between a Circle and a Sphere, a Plane Figure and
a Solid.
This was the Climax, the Paradise, of my strange eventful History.
Henceforth I have to relate the story of my miserable Fall: -- most
miserable, yet surely most undeserved! For why should the thirst for
knowledge be aroused, only to be disappointed and punished? My
volition shrinks from the painful task of recalling my humiliation;
yet, like a second Prometheus, I will endure this and worse, if by any
means I may arouse in the interiors of Plane and Solid Humanity a
spirit of rebellion against the Conceit which would limit our
Dimensions to Two or Three or any number short of Infinity. Away then
with all personal considerations! Let me continue to the end, as I
began, without further digressions or anticipations, pursuing the
plain path of dispassionate History. The exact facts, the exact
words, -- and they are burnt in upon my brain, -- shall be set down
without alteration of an iota; and let my Readers judge between me and
Destiny.
The Sphere would willingly have continued his lessons by
indoctrinating me in the conformation of all regular Solids,
Cylinders, Cones, Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons,
and Spheres: but I ventured to interrupt him. Not that I was wearied
of knowledge. On the contrary, I thirsted for yet deeper and fuller
draughts than he was offering to me.
"Pardon me," said I, "O Thou Whom I must no longer address as the
Perfection of all Beauty; but let me beg thee to vouchsafe thy servant
a slight of thine interior."
Sphere. My what?
I. Thine interior: thy stomach, thy intestines.
Sphere. Whence this ill-timed impertinent request? And what mean
you by saying that I am no longer the Perfection of all Beauty?
I. My Lord, your own wisdom has taught me to aspire to One even
more great, more beautiful, and more closely approximate to Perfection
than yourself. As you yourself, superior to all Flatland forms,
combine many Circles in One, so doubtless there is One above you who
combines many Spheres in One Supreme Existence, surpassing even the
Solids of Spaceland. And even as we, who are now in Space, look down
on Flatland and see the insides of all things, so of a certainty there
is yet above us some higher, purer region, whither thou dost surely
purpose to lead me -- O Thou Whom I shall always call, everywhere and
in all Dimensions, my Priest, Philosopher, and Friend -- some yet more
spacious Space, some more dimensionable Dimensionality, from the
vantage-ground of which we shall look down together upon the revealed
insides of Solid things, and where thine own intestines, and those of
thy kindred Spheres, will lie exposed to the view of the poor
wandering exile from Flatland, to whom so much has already been
vouchsafed.
Sphere. Pooh! Stuff! Enough of this trifling! The time is
short, and much remains to be done before you are fit to proclaim the
Gospel of Three Dimensions to your blind benighted countrymen in
Flatland.
I. Nay, gracious Teacher, deny me not what I know it is in thy
power to reform. Grant me but one glimpse of thine interior, and I am
satisfied for ever, remaining henceforth thy docile pupil, thy
unemacipable slave, ready to receive all thy teachings and to feed
upon the words that fall from thy lips.
Sphere. Well, then, to content and silence you, let me say at
once, I would shew you what you wish if I could; but I cannot. Would
you have me turn my stomach inside out to oblige you?
I. But my Lord has shewn me the intestines of all my countrymen
in the Land of Two Dimensions by taking me with him into the Land of
Three. What therefore more easy than now to take his servant on a
second journey into the blessed region of the Fourth Dimension, where
I shall look down with him once more upon this land of Three
Dimensions, and see the inside of every three-dimensioned house, the
secrets of the solid earth, the treasures of the mines of Spaceland,
and the intestines of every solid living creature, even the noble and
adorable Spheres.
Sphere. But where is this land of Four Dimensions?
I. I know not: but doubtless my Teacher knows.
Sphere. Not I. There is no such land. The very idea of it is
utterly inconceivable.
I. Not inconceivable, my Lord, to me, and therefore still less
inconceivable to my Master. Nay, I despair not that, even here, in
this region of Three Dimensions, your Lordship's art may make the
Fourth Dimension visible to me; just as in the Land of Two Dimensions
my Teacher's skill would fain have opened the eyes of his blind
servant to the invisible presence of a Third Dimension, though I saw
it not.
Let me recall the past. Was I not taught below that when I saw a
Line and inferred a Plane, I in reality saw a Third unrecognized
Dimension, not the same as brightness, called "height"? And does it
not now follow that, in this region, when I see a Plane and infer a
Solid, I really see a Fourth unrecognized Dimension, not the same as
colour, but existent, though infinitesimal and incapable of
measurement?
And besides this, there is the Argument from Analogy of Figures.
Sphere. Analogy! Nonsense: what analogy?
I. Your Lordship tempts his servant to see whether he remembers
the revelations imparted to him. Trifle not with me, my Lord; I
crave, I thirst, for more knowledge. Doubtless we cannot _see_ that
other higher Spaceland now, becauswe we have no eye in our stomachs.
But, just as there _was_ the realm of Flatland, though that poor puny
Lineland Monarch could neither turn to left nor right to discern it,
and just as there _was_ close at hand, and touching my frame, the land
of Three Dimensions, though I, blind senseless wretch, had no power to
touch it, no eye in my interior to discern it, so of a surety there is
a Fourth Dimension, which my Lord perceivesa with the inner eye of
thought. And that it must exist my Lord himself has taught me. Or
can he have forgotten what he himself imparted to his servant?
In One Dimension, did not a moving Point produce a Line with _two_
terinal points?
In Two Dimensions, did not a moving Line produce a Square with
_four_ terminal points?
In Three Dimensions, did not a moving Square produce -- did not
this eye of mine behold it -- that blessed Being, a Cube, with _eight_
terminal points?
And in Four Dimensions shall not a moving Cube -- alas, for
Analogy, and alas for the Progress of Truth, if it be not so -- shall
not, I say, the motion of a divine Cube result in a still more divine
Organization with _sixteen_ terminal points?
Behold the infallible confirmation of the Series, 2, 4, 8, 16: is
not this a Geometrical Progression? Is not this -- if I might quote
my Lord's own words -- "strictly according to Analogy"?
Again, was I not taught by my Lord that as in a Line there are
_two_ bounding Points, and in a Square there are _four_ bounding
LInes, so in a Cube there must be _six_ bounding Squares? Behold once
more the confirming Series, 2, 4, 6: is not this an Arithemtical
Progression? And consequently does it not of necessity follow that
the more divine offspring of the divine Cube in the Land of Four
Dimensions, must have 8 bounding Cubes: and is not this also, as my
Lord has taught me to believe, "strictly according to Analogy"?
O, my Lord, my Lord, behold, I cast myself in faith upon
conjecture, not knowing the facts; and I appeal to your Lordship to
confirm or deny my logical anticipations. If I am wrong, I yield, and
will no longer demand a Fourth Dimension; but, if I am right, my Lord
will listen to reason.
I ask therefore, is it, or is it not, the fact, that ere now your
countrymen also have witnessed the descent of Beings of a higher order
than their own, entering closed rooms, even as your Lordship entered
mine, without the opening of doors or windows, and appearing and
vanishing at will? On the reply to this question I am reaedy to stake
everything. Deny it, and I am henceforth silent. Only vouchsafe an
answer.
Sphere (_after a pause_). It is reported so. But men are divided
in opinion as to the facts. And even granting the facts, they explain
them in different ways. And in any case, however great may be the
number of different explanations, no one has adopted or suggested the
theory of a Fourth Dimension. Therefore, pray have done with this
trifling, and let us return to business.
I. I was certain of it. I was certain that my anticipations
would be fulfilled. And now have patience with me and answer me yet
one more question, best of Teachers! Those who have thus appeared --
no one knows whence -- and have returned -- no one knows whither --
have they also contracted their sections and vanished somehow into
that more Spacious Space, whither I now entreat you to conduct me?
Sphere (_moodily_). They have vanished, certainly -- if they ever
appeared. But most people say that these visions arose from the
thought -- you will not understand me -- from the brain; from the
perturbed angularity of the Seer.
I. Say they so? Oh, believe them not. Or if it indeed be so,
that this other SPace is really Thoughtland, then take me to that
blessed Region where I in Thought shall see the insides of all solid
things. There, before my ravished eye, a Cube moving in some
altogether new direction, but strictly according to Analogy, so as to
make every particle of his interior pass through a new kind of Space,
with a wake of its own -- shall create a still more perfect perfection
than himself, with sixteen terminal Extra-solid angles, and Eight
solid Cubes for his Perimeter. And once there, shall we stay our
upward course? In that blessed region of Four Dimensions, shall we
linger at the threshold of the Fifth, and not enter therein? Ah, no!
Let us rather resolve that our ambition shall soar with our corporal
ascent. Then, yielding to our intellectual onset, the gates of the
Six Dimension shall fly open; after that a Seventh, and then an Eighth
--
How long I should have continued I know not. In vain did the
Sphere, in his voice of thunder, reiterate his command of silence, and
threaten me with the direst penalties if I persisted. Nothing could
stem the flood of my ecstatic aspirations. Perhaps I was to blame;
but indeed I was intoxicated with the recent draughts of Truth to
which he himself had introduced me. However, the end was not long in
coming. My words were cut short by a crash outside, and a
simultaneous crash inside me, which impelled me through space with a
velocity that precluded speech. Down! down! down! I was rapidly
descending; and I knew that return to Flatland was my doom. One
glimpse, one last and never-to-be-forgotten glimpse I had of that dull
level wilderness -- which was now to become my Universe again --
spread out before my eye. Then a darkness. Then a final, all-
consummating thunder-peal; and, when I came to myself, I was once more
a common creeping Square, in my Study at home, listening to the Peace-
Cry of my approaching Wife.
* * *
SECTION 20. -- How the Sphere encouraged me in a Vision.
Although I had less than a minute for reflection, I felt, by a
kind of instinct, that I must conceal my experiences from my Wife.
Not that I apprehended, at the moment, any danger from her divulging
my secret, but I knew that to any Woman in Flatland the narrative of
my adventures must needs be unintelligible. So I endeavoured to
reassure her by some story, invented for the occasion, gthat I had
accidentally fallen through the trap-door of the cellar, and had there
lain stunned.
The Southward attraction in our country is so slight that even to
a Woman my tale necessarily appeared extraordinary and well-nigh
incredible; but my Wife, whose good sense far exceeds that of the
average of her Sex, and who perceived that I was unusually excited,
did not argue with me on the subject, but insisted that I was will and
required repose. I was glad of an excuse for retiring to my chamber
to think quietly over what had happened. When I was at last by
myself, a drowsy sensation fell on me; but before my eyes closed I
endeavoured to reproduce the Third Dimension, and especially the
process by which a Cube is constructed through the motion of a Square.
It was not so clear as I could have wished; but I remembered that it
must be "Upward, and yet not Northward," and I determined steadfastly
to retain these words as the clue which, if firmly grasped, could not
fail to guide me to the solution. So mechanically repeating, like a
charm, the words, "Upwaqrd, yet not Northward," I fell into a sound
refreshing sleep.
During my slumber I had a dream. I thought I was once more by the
side of the Sphere, whose lustrous hue betokened that he had exchanged
his wrath against me for perfectly placability. We were moving
together towards a bright but infinitesimally small Ppoint, to which
my Master directed my attention. As we approached, methought there
issued from it a slight humming noise as from one of your Spaceland
bluebottles, only less resonant by far, so slight indeed that even in
the perfect stillness of the Vacuum through which we soard, the sound
reached not our ears till we checked our flight at a distant from it
of something under twenty human diagonals.
"Look yonder," said my Guide, "in Flatland thou hast lived; of
Lineland thou hast received a vision; thou hast soarred with me to the
heights of Spaceland; now,, in order to complete the range of thy
experience, I conduct thee downward to the lowest depth of existence,
even to the realm of Pointland, the Abyss of No dimensions.
"Behold yon miserable creature. That Point is a Being like
ourselves, but confined to the non-dimensional Gulf. He is himself
his own World, his own Universe; of any other than himself he can form
no conception; he knows not Length, nor Breadth, nor Height, for he
has had no experience of them; he has no cognizance even of the number
Two; nor has he a thought of Plurality; for he is himself his One and
All, being really Nothing. Yet mark his perfect self-contentment, and
hence learn his lesson, that to be self-contented is to be vile and
ignorant, and that to aspire is better than to be blindly and
impotently happy. Now listen."
He ceased; and there arose from the little buzzing creature a
tiny, low, monotonous, but distinct tinkling, as from one of your
Spaceland phonographs, from which I caught these words, "Infinite
beatitude of existence! It is; and there is nothing else beside It."
"What," said I, "does the puny creature mean by 'it'?" "He means
himself," said the Sphere: "have you not noticed before now, that
babies and babyish peoplle who cannot distinguish themselves from the
world, speak of themselves in the Third Person? But hush!"
"It fills all Space," continued the little soliloquizing Creature,
"and what It fills, It is. What It thinks, that It utters; and what
It utters, that It hears; and It itself is Thinker, Utterer, Hearer,
THought, Word, Audition; it is the One, and yet the All in All. Ah,
the happiness, ah, the happiness of Being!"
"Can you not startle the little thing out of its complacency?"
said I. "Tell it what it really is, as you told me; reveal to it the
narrow limitations of Pointland, and lead it up to something higher."
"That is no easy task," said my Master; "try you."
Hereon, raising by voice to the uttermost, I addressed the Point
as follows:
"Silence, silence, contemptible Creature. You call yourself the
All in All, but you are the Nothing: your so-called Universe is a
mere speck in a Line, and a Line is a mere shadow as compared with --"
"Hush, hush, you have said enough," interrupted the Sphere, "now
listen, and mark the effect of your harangue on the King of
Pointland."
The lustre of the Monarch, who beamed more brightly than ever upon
hearing my words, shewed clearly that he retained his complacency; and
I had hardly ceased when he took up his strain again. "Ah, the joy,
ah, the joy of Thought1 What can It not achieve by thinking! Its own
Thought coming to Itself, suggestive of ts disparagement, thereby to
enhance Its happiness! Sweet rebellion stirred up to result in
triumph! Ah, the divine creative power of the All in One! Ah, the
joy, the joy of Being!"
"You see," said my Teacher, "how little your words have done. So
far as the Monarch understand them at all, he accepts them as his own
-- for he cannot conceive of any other except himself -- and plumes
himself upon the variety of 'Its Thought' as an instance of creative
Power. Let us leave this God of Pointland to the ignorant fruition of
his omnipresence and omniscience: nothing that you or I can do can
rescue him from his self-satisfaction."
After this, as we floated gently back to Flatland, I could hear
the mild voice of my Companion pointing the moral of my vision, and
stimulating me to aspire, and to teach others to aspire. He had been
angered at first -- he confessed -- by my ambition to soar to
Dimensions above the Third; but, since then, he had received fresh
insight, and he was not too proud to acknowledge his error to a Pupil.
Then he proceeded to initiate me into mysteries yethigher than those I
had witnessed, shewing me how to construct Extra-Solids by the motion
of Solids, and Double Extra-Solids by the motion of Extra-Solids, and
all "strictly according to Analogy," all by methods so simple, so
easy, as to be patent even to the Female Sex.
* * *
SECTION 21. -- How I tried to teach the Theory of Three Dimensions
to my Grandson, and with what success
I awoke rejoicing, and began to reflect on the glorious career
before me. I would go forth, methought, at once, and evangelize the
whole of Flatland. Even to Women and Soldiers should the Gospel of
Three Dimensions be proclaimed. I would begin with my Wife.
Just as I had decided on the plan of my operations, I heard the
sound of many voices in the street commanding silence. Then followed
a louder voice. It was a herald's proclamation. Listening
attentively, I recognized the words of the Resolution of the Council,
enjoining the arrest, imprisonment, or execution of any one who should
pervert the minds of people by delusions, and by professing to have
received revelations from another World.
I reflected. This danger was not to be trifled with. It would be
better to avoid it by omitting all mention of my Revelation, and by
proceeding on the path of Demonstration -- which after all, seemed so
simple and so conclusive that nothing would be lost by discarding the
former means. "Upward, not Northward" -- was the clue to the whole
proof. It had seemed to me fairly clear before I fell asleep; and
when I first awoke, fresh from my dream, it had appeared as patent as
Arithmetic; but somehow it did not seem to me quite so obvious now.
Though my Wife entered the room opportunely at just that moment, I
decided, after we had exchanged a few words of commonplace
conversation, not to begin with her.
My Pentagonal Sons were men of character and standing, and
physicians of no mean reputation, but not great in mathematics, and,
in that respect, unfit for my purpose. But it occurred to me that a
young and docile Hexagon, with a mathematical turn, would be a most
suitable pupil. Why therefore not make my first experiment with my
little precocious Grandson, whose casual remarks on the meaning of
three-to-the-third had met with the approval of the Sphere?
Discussing the matter with him, a mere boy, I should be in perfect
safety; for he would know nothing of the Proclamation of the Council;
whereas I could not feel sure that my Sons -- so greatly did their
patriotism and reverence for the Circles predominate over mere blind
affection -- might not feel compelled to hand me over to the Prefect,
if they found me seriously maintaining the seditious heresy of the
Third Dimension.
But the first thing to be done was to satisfy in some way the
curiosity of my Wife, who naturally wished to know something of the
reasons for which the Circle had desired that mysterious interview,
and of the means by which he had entered the house. Without entering
into the details of the elaborate account I gave her, -- an account, I
fear, not quite so consistent with truth as my Readers in Spaceland
might desire, -- I must be content with saying that I succeeded at
last in persuading her to return quitely to her household duties
without eliciting from me any reference to the World of Three
Dimensions. This done, I immediately sent for my Grandson; for, to
confess the truth, I felt that all that I had seen and heard was in
some strange way slipping away from me, like the image of a half-
grasped, tantalizing dream, and I longed to essay my skill in making a
first disciple.
When my Grandson entered the room I carefully secured the door.
Then, sitting down by his side and taking our mathematical tablets, --
or, as you would call them, Lines -- I told him we would resume the
lesson of yesterday. I taught him once more how a Point by motion in
One Dimension produces a Line, and how a straight Line in Two
Dimensions produces a Square. After this, forcing a laugh, I said,
"And now, you scamp, you wanted to make believe that a Square may in
the same way by motion 'Upward, not Northward' produce another figure,
a sort of extra square in Three Dimensions. Say that againn, you
young rascal."
At this moment we heard once more the herald's "O yes! O yes!"
outside in the street proclaiming the REsolution of the Council.
Young though he was, my Grandson -- who was unusually intelligent for
his age, and bred up in perfect reverence for the authority of the
Circles -- took in the situation with an acuteness for which I was
quite unprepared. He remained silent till the last words of the
Proclamation had died away, and then, bursting into tears, "Dear
Grandpapa," he said, "that was only my fun, and of course I meant
nothing at all by it; and we did not know anything then about the new
Law; and I don't think I said anything about the Third Dimension; and
I am sure I did not say one word about 'Upward, not Northward,' for
that would be such nonsense, you know. How could a thing move Upward,
and not Northward? Upward and not Northward! Even if I were a baby,
I could not be so absurd as that. How silly it is! Ha! ha! ha!"
"Not at all silly," said I, losing my temper; "here for example, I
take this Square," and, at the word, I grasped a moveable Square,
which was lying at hand -- "and I move it, you see, not Northward but
-- yes, I move it Upward -- that is to say, Northward but I move it
somewhere -- not exactly like this, but somehow --" Here I brought my
sentence to an inane conclusion, shaking the Square about in a
purposeless manner, much to the amusement of my Grandson, who burst
out laughing louder than ever, and declared that I was not teaching
him, but joking with him; and so saying he unlocked the door and ran
out of the room. Thus ended my first attempt to convert a pupil to
the Gospel of Three Dimensions.
* * *
SECTION 22. -- How I then tried to diffuse the Theory of Three
Dimensions by other means, and of the result
My failure with my Grandson did not encourage me to communicate my
secret to others of my household; yet neither was I led by it to
despair of success. Only I saw that I must not wholly rely on the
catch-phrase, "Upward, not Northward," but must rather endeavour to
seek a demonstration by setting before the public a clear view of the
whole subject; and for this purpose it seemed necessary to resort to
writing.
So I devoted several months in privacy to the composition of a
treatise on the mysteries of Three Dimensions. Only, with the view of
evading the Law, if possible, I spoke not of a physical Dimension, but
of a Thoughtland whence, in theory, a Figure could look down upon
Flatland and see simultaneously the insides of all things, and where
it was possible that there might be supposed to exist a Figure
environed, as it were, with six Squares, and containing eight terminal
Points. But in writing this book I found myself sadly hampered by the
impossibility of drawing such diagrams as were necessary for my
purpose: for of course, in our country of Flatland, there are no
tablets but Lines, and no diagrams but Lines, all in one straight Line
and only distinguishable by difference of size and brightness; so
that, when I had finished my treatise (which I entitled, "Through
Flatland to Thoughtland") I could not feel certain that many would
understand my meaning.
Meanwhile my wife was under a cloud. All pleasures palled upon
me; all sights tantalized and tempted me to outspoke treason, because
I could not compare what I saw in Two Dimensions with what it really
was if seen in Three, and could hardly refrain from making my
comparisons aloud. I neglected my clients and my own business to give
myself to the contemplation of the mysteries which I had once beheld,
yet which I could impart to no one, and found daily more difficult to
reproduce even before my own mental vision.
One day, about eleven months after my return from Spaceland, I
tried to see a Cube with my eye closed, but failed; and though I
succeeded afterwards, I was not then quite certain (nor have I been
ever aftewards) that I had exactly realized the original. This made
me more melancholy than before, and determined me to take some step;
yet what, I knew not. I felt that I would have been willing to
sacrifice my life for the Cause, if thereby I could have produced
conviction. But if I could not convince my Grandson, how could I
convince the highest and most developed Circles in the land?
And yet at times my spirit was too strong for me, and I gave vent
to dangerous utterances. Already I was considered heterodox if not
treasonable, and I was keenly alive to the danger of my position;
nevertheless I could not at times refrain from bursting out into
suspicious or half-seditious utterances, even among the highest
Polygonal or Circular society. When, for example, the question arose
about the treatment of those lunatics who said that they had received
the power of seeing the insides of things, I would quote the saying of
an ancient Circle, who declared that prophets and inspired people are
always considered by the majority to be mad; and I could not help
occasionally dropping such expressions as "the eye that discerns the
interiors of things," and "the all-seeing land"; once or twice I even
let fall the forbidden terms "the Third and Fourth Dimensions." At
last, to complete a series of minor indiscretions, at a meeting of our
Local Speculative Society held at the palace of the Prefect himself, -
- some extremely silly person having read an elaborate paper
exhibiting the precise reasons why Providence has limited the number
of Dimensions to Two, and why the attribute of omnividence is assigned
to the Supreme alone -- I so far forgot myself as to give an exact
account of the whole of my voyage with the Sphere into Space, and to
the Assembly Hall in our Metropolis, and then to Space again, and of
my return home, and of everything that I had seen and heard in fact or
vision. At first, indeed, I pretended that I was describing the
imaginary experiences of a ficitious person; but my enthusiasm soon
forced me to throw off all disguise, and finally, in a fervent
peroration, I exhorted all my hearers to divest themselves of
prejudice and to become believers in the Third Dimesnsion.
Need I say that I was at onc arrested and taken before the
Council?
Next morning, standing in the very place where but a very few
months ago the Sphere had stood in my company, I was allowed to begin
and to continue my narration unquestioned and uninterrupted. But from
the first I foresaw my fate; for the President, noting that a guard of
the better sort of Policemen was in attendance, of angularity little,
if at all, under 55 degrees, ordered them to be relieved before I
began my defence, by an inferior class of 2 or 3 degrees. I knew only
too well what that meant. I was to be executed or imprisoned, and my
story was to be kept secret from the world by the simultaneous
destruction of the officials who had heard it; and, this beig the
case, the Presdient desired to substitute the cheaper for the more
expensive victims.
After I had concluded my defence, the President, perhaps
perceiving that some of the junior Circles had been moved by evident
earnestness, asked me two questions: --
1. Whether I could indicate the direction which I meant when I
used the words "Upward, not Northward"?
2. Whether I could by any diagrams or descriptions (other than
the enumeration of imaginary sides and angles) indicate the Figure I
was pleased to call a Cube?
I declared that I could say nothing more, and that I must commit
myself to the Truth, whose cause would surely prevail in the end.
The President replied that he quite concurred in my sentiment, and
that I could not do better. I must be sentenced to perpetual
imprisonment; but if the Truth intended that I should emerge from
prison and evangelize the world, the Truth might be trusted to bring
that result to pass. Meanwhile I should be subjected to no discomfort
that was not necessary to preclude escape, and, unless I forfeited the
privilege by misconduct, I should be occasionally permitted to see my
brother who had preceded me to my prison.
Seven years have elapsed and I am still a prisoner, and -- if I
except the occasional visits of my brother -- debarred from all
companionship save that of my jailers. My brother is one of the best
of Squares, just sensible, cheerful, and not without fraternal
affection; yet I confess that my weekly interviews, at least in one
respect, cause me the bitterest pain. He was present when the Sphere
manifested himself in the Council Chamber; he saw the Sphere's
changing sections; he heard the explanation of the phenomena then give
to the Circles. Since that time, scarcely a week has passed during
seven whole years, without his hearing from me a repitition of the
part I played in that manifestation, together with ample descriptions
of all the phenomena in Spaceland, and the arguments for the existence
of Solid things derivable from Analogy. Yet -- I take shame to be
forced to confess it -- my brother has not yet grasped the nature of
Three Dimensions, and frankly avows his disbelief in the existence of
a Sphere.
Hence I am absolutely destitute of converts, and, for aught that I
can see, the millennial Revelation has been made to me for nothing.
Prometheus up in Spaceland was bound for bringing down fire for
mortals, but I -- poor Flatland Prometheus -- lie here in prison for
bringing down nothing to my countrymen. Yet I existin the hope that
these memoirs, in some manner, I know not how, may find their way to
the minds of humanity in Some Dimension, and may stir up a race of
rebels who shall refuse to be confined to limited Dimensionality.
That is the hope of my brighter moments. Alas, it is not always
so. Heavily weights on me at times the burdensome reflection that I
cannot honestly say I am confident as to the exact shape of the once-
seen, oft-regretted Cube; and in my nightly visions the mysterious
precept, "Upward, not Northward," haunts me like a soul-devouring
Sphinx. It is part of the martyrdom which I endure for the cause of
Truth that there are seasons of mental weakness, when Cubes and
Spheres flit away into the background of scarce-possible existences;
when the Land of Three Dimensions seems almost as visionary as the
Land of One or None; nay, when even this hard wall that bars me from
my freedom, these very tablets on which I am writing, and all the
substantial realities of Flatland itself, appear no better than the
offspring of a diseased imagination, or the baseless fabric of a
dream.
THE END
of
FLATLAND
* * *
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