As he tries to explain how shapes perceive each other to the reader, A Square highlights a recurring motif and a central point of Flatland’s satire. Shapes that exist in two dimensions, as they do in Flatland, actually struggle to visually distinguish one polygon from another:
[H]ow shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one another’s configuration? Recall what I told you above. All beings in Flatland, animate or inanimate, no matter what their form, present to our view the same, or nearly the same, appearance, viz. that of a straight Line. How then can one be distinguished from another, where all appear the same?
In Flatland, just as in the real world of Abbot's England, it’s far easier to tell someone’s social standing from their behavior or the company they keep than by looking at their body. As A Square explains, a shape looking at another shape on a two-dimensional plane can only see a “straight Line.” Flatland is a world obsessed with social position, but the shapes who live there are only actually able to make educated guesses about the number of sides those around them have. It is impossible ever to know another polygon's shape as an empirical truth without using context clues.
This is part of the reason for the ban on color in Flatland, which helped certain shapes pose as others. It means that the Shapes have to devise all sorts of methods to “see” each other. They are forced to rely on the help of environmental factors like the way other shapes recede into the "fog," their powers of deduction and the “art of Feeling.” Of course, these are all processes that also come with internal hierarchies and have their own social implications. This motif of imperfect perception recurs over and over, satirizing the arbitrary nature of social distinctions and making Flatland’s rigid laws seem even more absurd to the reader.
