A Romance of Many Dimensions, by Edwin A. Abbot
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those who wish to do so. To be sure you have an >> A Romance of Many Dimensions, by Edwin A. Abbot
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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 a most 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 the comparatively harmless
angle of the Equilateral Triangle. Thus, in the most brutal
and formidable of 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 this 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 in Flatland!
By a judicious use of this Law of Nature, the Polygons and Circles
are almost always able to stifle sedition in its very cradle,
taking advantage of the irrepressible and boundless hopefulness
of the human mind. Art also comes to the aid of Law and Order.
It is generally found possible -- by a little artificial
compression or expansion on the part of the State physicians --
to make some of the more intelligent leaders of a rebellion
perfectly Regular, and 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 more obstinate, foolish, and hopelessly irregular are led
to execution.
Then the wretched rabble of the Isosceles, planless and leaderless,
are either 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 suspicions skilfully 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.
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 a 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 in 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 in the Eastern side,
for the use of Females only; by which all females shall enter
"in a becoming and respectful manner" and not by the Men's
or Western door. [Note: When I was in Spaceland I understood that
some of your Priestly circles have in the same way a separate entrance
for Villagers, Farmers and Teachers of Board Schools (`Spectator',
Sept. 1884, p. 1255) that they may "approach in a becoming
and respectful manner."]
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;
others oblige a Woman, when travelling, to be followed by one
of her sons, or servants, or by her husband; others confine Women
altogether to their houses except during the religious festivals.
But it has been 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 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 victim, 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 admired and copied
by the wife of the progressive and aspiring Isosceles,
in the females of whose family 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 brain-power,
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 her 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 get 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 simulation, 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 Circles 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 its 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
towards 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 seem
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 hopes 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 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 or 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 our personal friends, but even to discriminate
between different classes, at least so far as concerns
the three lowest orders, the Equilateral, the Square, and the Pentagon
-- for of the Isosceles I take no account. But as we ascend
in 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 shall speak 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 schools 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 unhesitatingly 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 Feeler 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 votes 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 unfortunate 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 calamities from one
little accident in the process of Feeling.
At 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 can 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 one straight line
at a time, or at all events only a number of bits of straight lines
all in one straight line -- how can you ever discern any 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,
Specimens 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 civic 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 class rooms of our Infant Schools,
and there they are utilized by the Board of Education for the purpose
of imparting to the offspring of the Middle Classes that tact
and intelligence of which these wretched creatures themselves
are utterly devoid.
In some States the Specimens are occasionally fed and suffered
to exist for several years; but in 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 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.
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