A Romance of Many Dimensions, by Edwin A. Abbot

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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 middle 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 had
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 his 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 like 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 the 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 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.

<>

<>
<>

M
_____
/ \ - C_
/ \|| - _
| || - _
A|- - - - - - -||B- - - - - -_-+(> (Eye)
| || _ -
\ /||_ -
\ _____ / - D

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 of 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 Women
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 commands in the name of a priestly Circle;
out of doors the striking combination of red and green,
without addition of any other colours, would be sure to lead
the common people into endless mistakes, and the Women 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 Universal 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
its 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.
Worse 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 Bill; 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 appeal
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 opportunity, 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 introducing 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 now 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 Military, 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, invisibly 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 visitations 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 the 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 now 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 structures 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 from 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 those
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 have 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 a Circle
would be a mere question of pedigree and arithmetic,
and the four hundred 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 antagonistic decrees affecting Circular propagation;
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 the 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 doubles
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 a 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 determines 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 occasions
a glad procession bears 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 similar domestic sacrifices,
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; similarly, 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 either 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 there's an end of the matter.
But in little domestic difficulties, where 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 the 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.

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