Mr. A Square is describing the 2-dimensional world of Flatland. He can do so, due to having knowledge of Spaceland (our world) and other dimensions.
Flatland is comprised of people of varying shapes. The lowest class is that of women, which are straight line segments. Women have no sides and no angles and thus, no brain. They are considered mindless and lacking all reasoning power. They are, in consequence, considered emotional and prone to rage.
The ability of women to arrange themselves forward and become but invisible, makes them extremely dangerous to others. This, coupled with their lack of sense, necessitates stringent laws for their public appearance. There are only to enter a building through a designated door in the East, they are to sway continuously to be clearly seen and they are to cry out at all times to make their presence clear. Their only redeeming feature is their ability to reproduce and to remember nothing.
This is followed by soldiers and other low classes, which are irregular triangles. Irregular in this case means two sides are the same, while one is of a different configuration. The most common size of an adult soldier of the very lowest class is 11 inches for the same sides and ½ inch for the adjacent side.
The soldier and worker class, known as Isosceles, is made up of varying degrees of angulation and those just outside of regularity may be able to hope for the elevation (and thus, freedom) of their child to the Regular class through evolution.
The first class of the Regulars are equilateral triangles. They are considered respectable and make up the professionals of this society. Above them are squares, such as our commentators and pentagons.
Exceeding five sides, is the polygonal class. The lowest of those can be considered gentlemen and the highest nobility. This class seeks is well educated.
Lastly, there is the circular class, comprising the priests. A priest might have 300 sides of more and the very rare case of a person having somewhere around 1000 sides, will see this man be elevated to Chief Circle.
The circular class has absolute rulership. All important matters are delegated by the priestly people.
The lower classes of almost-circular polygons will send their sons to Circular Neo-Therapeutic Gymnasiums to achieve malleability of their sides, to increase into more circularity. Only one of every 10 children will survive such measures.
Irregularity in other ways but that of the Isosceles, is considered degeneration unless it can be medically corrected. It is seen as moral irregularity and criminal and offenders get destroyed.
Flatlanders recognize each other either by hearing - the cadence of one’s voice, by feeling or by sight.
Feeling is the most common form of recognition and used by all but the highest classes.
The highest classes use sight recognition, which is a difficult art of recognizing someone in a world that appears full of flat lines. The process involves fog, which highlights prominent points (e.g. the tip of a triangle) and dims less prominent ones (e.g. the triangle’s sides). It is taught in university and only to those of polygonal birth.
At one time, an enterprising gentlemen had introduces colour to Flatland. Colour would make the world interesting and almost all classes more special. The only classes exempt were women and priests, because they are only one line, not worth painting.
While initially popular, the introduction of colour would soon prove to be detrimental to the higher classes, for it lowered their status.
The ease in which a person could be recognized by their colourful sides, deteriorated sight recognition and thus intelligence, and it soon occured to the brighter of the Isosceles that their status had been equalized and they were now in a position to demand change.
The tipping point occured when Chromatistes, champions of the colour revolution, demanded that women and priests be painted too. Women should be painted red on the side in which their mouth and eye was placed and green on their behind. The same was to be done to the priests.
The resultant change would mean that circles could be easily confused with straight lines and thus women would get respect and the undermining of the highest class would be complete.
In a daring move, the upper classes assembles the Chromatistes and the public and agreed to the proposed Universal Colour Bill - but not before laying out the disadvantages for the lower classes. Do the Isosceles really want to give up their potential for elevation through hereditary gain of regularity?
The people were eventually swayed when women took up the cry against the Bill, after a respectable woman was heinously tricked by a lowly Isosceles who had painted himself in the style of a polygon, after which she felt the need to kill herself.
Colour was hereafter forbidden.
A very brief analysis of some aspects of Flatland society in light of potential confusion:
Flatland is satire. It was first published in 1884, at the height of Victorian society. Abbott, as he himself said in the revised version of the book, is trying to portray the questionable side of Victorian society.
The book focuses heavily on women and the attitude towards them; a clear sign of its satirical nature. How often do women come up in historical literature outside of their role as mother, wife and daughter? How often do women get portrayed as anything more than a men’s help meet?
Abbott is showcasing just this disparity by pointing out the hypocrisy of Victorian society, a society equally belittling, patronizing and fearing women.
The women in Flatland are straight lines with no sides and no angles. They are not like men, they are closest to priests - odd and curious.
Women are to be feared, because of their lack of sense, Flatland society (and Victorian society) says, because they can, due to their pointy end and their invisibility, easily kill. Why don’t they? Because they are emotional and prone to hysterics.
Yet, A Square worries that the refusal to educate women may lead to a disadvantage for MEN, because a boy child will have to learn two languages: the one to talk to and betray women (chivalry) and the one to talk to men (logic). Curiously, he also worries what might happen if a woman does get educated - would she not rebel and incite rebellion in other women?
Abbott seems to imply that part of the hypocrisy lies in the knowledge that men are aware, deep down, that women are not actually incapable but made so, by nurture.
The lower classes in Flatland, the Isosceles, are not free citizens. Only those who have reached 60° are elevated to the Regular, free class. Regularity can only be reached by hoping one’s son has gain a degree close enough to the norm. Abbott appears to reference the living situation of slaves and the one-drop-rule here.
Just like elevation to the Regular class happens only through generational growth, so power is only attained and kept through purity of breeding. High class in Flatland, means high (degree) birth. No other merit matters.
Interestingly, Mr. Square does bemoan the common practice of the highest classes of taking unsuitable wives, purely because they are lustier than the suitable ones. It seems that the highest classes are unconcerned about their status, perhaps because they cannot imagine a different life. A Square, as a respectable professional, worries a great deal however.
Clearly, Abbott wants us to take a look at hereditary monarchies.
The priestly class, is the ruling class in all matters, with no exception. This appears as a look back to the early middle ages, when Christianity had exclusive rule in much of Europe.
Flatland is a utilitarian state and only concerned with the purity and betterment of its free citizens. The very lowest Flatlanders, namely Irregulars, are destroyed. Rebels and rioters are likewise destroyed. Anyone, especially women, who violate the laws regarding them, is destroyed. No one seems to worry about executions being carried out freely and often on infants.
Perhaps a nod to Sparta?
Irregulars are solely judge on their one, inborn feature. There is no betterment for them. They are assumed to be morally unsound and dangerous. Irregulars are feared by men and women alike, for they may “trick” men into thinking they are of a respectable class and women into fornication, which can only lead to their demotion. Black people - that’s what Abbott is referring to.