Content Warning: The analysis of this portion of the novel contains references to sexual assault.

In this section, the Square elaborates on the social position of Irregular shapes in Flatland. He gives as an example of an Irregular shape, a tradesman who “drags behind his regular and respectable vertex, a parallelogram of twelve or thirteen inches in diagonal” (12). In Flatland, these kinds of deformities are equated with immorality and criminal behavior, and the Square declares that tolerating Irregular figures actually puts the entire country in danger. Irregular figures are, throughout their lives, mocked, neglected, and excluded from respectable social positions and activities. The Square adds that it is necessary for the government to measure and document the shapes of all Flatland’s inhabitants to ensure that civilization does not descend into chaos and violence. He emphasizes that Irregular figures violate Nature’s laws as well as those of the state.

However, he speaks out against the choice by certain Flatland districts to kill any infant born with as much as half a degree of deviation. Some of Flatland’s “ablest and best men, men of real genius” suffer from irregularities, and society would have suffered without their contributions (25). He adds that certain therapies have been developed that can partly or wholly cure these deformities; however, he undermines his seemingly progressive position by arguing that once a shape is developed to the point at which no cures will be effective, the Irregular infant should be mercifully killed.