A Square describes the inhabitants of Flatland and how they are organized into social classes based on their shape. Women are straight lines, and isosceles triangles compose the lowest class of workmen and soldiers. The middle class consists of equilateral triangles, and the professional and gentlemen class are squares and pentagons. The nobility begins with hexagons and other polygons. When the number of sides become too numerous that they cannot be distinguished from a circle, that figure is accepted into the highest class, the Circular or Priestly order.
The intricate way in which Abbott (or A Square) describes the organization of Flatland society eerily coincides with the way Victorian Britain was arranged in social classes. It is difficult to overlook these similarities, especially since Abbott uses familiar terms, such as workmen, soldiers, and gentlemen, to illustrate Flatland. Thus, this extended analogy of Flatland as Britain is fundamental to his satirical objective.
Another “Law of Nature” dictates that a male child is born with one more side than his father. However, A Square says, this rule does not consistently apply to the lower social classes of the triangles. Only through difficult demonstrations of greatness or intermarriages between more intellectual members are the isosceles able to give birth to an equal-sided triangle.
Once again, “nature” is used to manipulate the way in which power resides with the upper class. The social hierarchy remains rigid because fewer opportunities are given to those with lower status, while the upper classes find it easier to climb even higher up the social ladder.
The birth of a true equilateral triangle from isosceles parents is strictly regulated by the state. The child must be examined by the Sanitary and Social Board. If he is certified as “Regular,” he is ceremonially admitted into the class of Equilaterals. He is also adopted by new Equilateral parents to prevent the child from reverting to his hereditary disposition.
Even though Flatland is a made-up world of shapes, it also looks like an actual society, with an official state department, such that the reader cannot help but compare Flatland to their own world and the bureaucracies therein. That births are so highly regulated illustrates how social hierarchy is strictly maintained, even through cruel and inhumane practices like taking a child from its parents.
This tedious method of social mobility offers a glimmer of hope to those of the lower classes and prevents them from staging revolution against the upper echelons of society.
The way the statesmen of Flatland regulate the lower classes is terrifyingly sophisticated. Instead of exerting brute force, they provide small ways of gaining power that keep rebellions at bay.
A Square adds that the natural “Law of Compensation” also stifles sedition, because as the working class gain intelligence generationally, they wane in the power of penetration (meaning the acuteness of their angles) that could be used to their own advantage. The Circular Party also incites jealousy and suspicion within the working class and pits them against each other through mutual warfare.
The circles hoard power for themselves by specifically regulating knowledge and defining what “nature” is. The fact that the circles are “priests” is notable as well, since they can define their “laws of nature” as divine laws that also happen to keep the circles themselves in power. Here Abbott also slyly mentions the common truth that the oppressed masses usually have the potential to overthrow their oppressors—they just rarely take advantage of this potential because they are distracted by things like “mutual warfare.”