In the two-dimensional world of Flatland, beings appear to each other only as straight lines, making mutual recognition extremely difficult. To solve this problem, inhabitants rely primarily on the sense of hearing to distinguish personal friends and lower social classes. However, voices can be easily imitated by lower-order individuals, and upper-class aristocrats place little trust in auditory recognition. Because of these limitations and risks of imposture, residents frequently turn to alternative methods for identifying one another across the society.
The most common method for women and lower classes is the sense of touch. Through long practice and training, individuals can immediately identify the angles of triangles, squares, or pentagons upon contact. Among gentlemen in the countryside and businessmen in cities, this tactile interaction serves as the formal equivalent of a social introduction. However, touching carries significant physical dangers, as an accidental movement or sneeze by one party can cause sharp angles to inflict fatal injuries. The narrator shares a family anecdote about an ancestor whose sudden twitch during a rheumatic episode accidentally pierced a high-ranking polygon, resulting in a multi-generational downward slide in social standing for the family.
To train the population in tactile discernment, schools utilize a natural gradient of angles. The state employs impoverished and criminal lower-class specimens with acute angles as teaching tools in elementary schools. Although some educational districts prefer a cheaper system that keeps specimens alive longer, more regulated regions replace them monthly to maintain precise, unblunted angles while helping control the overabundant lower-class population. Despite the risks and careful precautions required, tactile recognition remains far more reliable than the auditory method for the middle and lower classes.