Unlike those who are fortunate enough to perceive light and shade in Spaceland, Flatlanders must take other measures to recognize each other’s configurations. A Square lists three methods of recognition. First, hearing is a basic way of distinguishing each other by voice. But this is not particularly useful because of the potential for trickery and voice assimilation.
That there are three different ways of ascertaining the social status of other beings in Flatland exemplifies how much social hierarchism dominates the citizens’ lives. Flatlanders accept everything they know to be the entirety of knowledge, and distinguish each other by convoluted ways.
Feeling is a second method that is more commonly used, mostly by Women and the lower classes. Introductions occur by touching the angles of the other party and ascertaining his or her configuration. The practice of feeling is taught extensively in school. However, the reliability of this method breaks down with members of the higher classes, since it becomes difficult to distinguish between twenty- and twenty-four-sided figures.
Even the methods of recognition are hierarchized and practiced by specific classes. Flatland institutionalizes the education of recognition and, thus, the knowledge that each class is allowed to learn and retain.
A Square states that introduction by contact can also be potentially dangerous, as any sudden, unexpected movement can cause injury. As an example, he tells the story that his grandfather had told him of his own great-great-great grandfather, a working man with a brain of 59.5 degrees (intelligence is measured by their angles) who had accidentally killed a polygon while being felt. He was sent to prison and his family was thrown back 1.5 degrees, to 58 degrees.
The precise numerical measurement of intelligence through angles (perhaps a reference to eugenics, a racist pseudoscience that linked intelligence to skull size and shape) and the harsh punishment of A Square’s ancestor for an accident simply add to the long list of ways that the circles maintain the social status quo.
At this point, A Square addresses a question he believes his readers may have about discerning an angle and its precise measurement. He answers that though Flatlanders cannot see angles, they can infer through touch.
A Square immediately introduces a weak point in the Flatland system of distinguishing: they do not see, but infer. Through analogy, a reader may recognize that each social system has weak spots that can easily be argued against.
A Square describes another law of Nature in Flatland that dictates that the brain of the Isosceles class begins at 30 minutes, or half a degree, and increases by half a degree generationally until it reaches 60 degrees and may enter the class of Regulars.
One should recognize how absurd this “law” is. In fact, it is entirely arbitrary. Although it’s considered natural, whether the isosceles “brain” begins at 30 minutes or 29 makes no difference—instead, this “law” is about creating clear boundaries between the lower and upper classes.
A Square then digresses into a topic of school board politics. Due to the abundance of individuals with angles ranging between 0.5 and 10 degrees (called Specimens), Flatland accords them no civic rights and, instead, utilizes them to educate the children of the middle class.