A Square begins by explicitly laying down a fundamental social rule, which has been only assumed thus far. He states that “every human being in Flatland is a Regular Figure” and that the equality of sides is a fact of Nature.
Notice how Flatlanders are referred to analogously as “human beings.” Furthermore, the idea of “regularity” in math may allow the circles to promote it as an essential quality. However, in real life, there is no such quality, which makes it even more absurd that British society is dictated by similarly arbitrary social criteria.
A Square posits that if Flatlanders were irregular, then civilization would “relapse into barbarism” because most, if not all, of the time would devoted to feeling all the angles of another person. Thus, “irregularity” in Flatland is considered equivalent to moral depravity and criminality.
The absurd way in which irregularity is equated with moral defunctness illustrates how those in power establish arbitrary definitions that are advantageous to themselves.
A Square defends the way in which the ancestors of Flatland have secured the safety of the state by purging Irregulars. Although A Square finds the strict program of executing infants whose angles deviate even by half a degree extreme, he still advocates for the execution of Irregular Offspring who cannot even be medically repaired.
As much as A Square is a revolutionist for writing Flatland, he still cannot escape from thinking in the way that the circles have taught him, that is, to consider irregulars undesirable in society (and even deserving of death). Thus, knowledge and control of a society’s worldview is an essential aspect to maintaining power.