Chapter 13 marks the beginning of Part II, which describes other worlds visited by A Square. On the last day of the 1999th year, he dreams of visiting Lineland, a one-dimensional, linear world populated by small straight lines and points. An illustration of A Square’s view of Lineland is included. In the dream, A Square assumes that the strange chirping creatures he sees must be women. He approaches one of the largest, which happens to be the Monarch of Lineland, and places his mouth right in front of the creature.
Part II marks the section where Abbott more directly deals with knowledge and ignorance. Lineland represents a world that is devoid of higher truths, such as the second dimension that Flatlanders enjoy. It then demonstrates the consequences of remaining ignorant, as made evident in the way the Monarch of Lineland is portrayed.
A Square apologizes for possibly startling the Monarch of Lineland, and proceeds to ask him questions about Lineland, despite the king’s arrogance in responding. A Square finds out that the ignorant king believes the Straight Line (on which they live) is the entirety of his kingdom, world, and universe. The Monarch is incapable of conceiving of anything outside the line that he inhabits. Therefore, he did not acknowledge A Square at all until he positioned his mouth along the line, in the king’s world.
The Monarch is a good example of what a person can become if they refuse to think beyond what they already know. He is arrogant and does not offer a listening ear to A Square at all. In some way, the Monarch is an analogical representation of the Circles in Flatland, content with the power they hold and refusing to accept any new knowledge that threatens the status quo.
The inhabitants of Lineland are male lines and female points who are stuck in motion and in vision to the straight line that consists of their whole world. All Linelanders can see are points, and they distinguish another’s sex and age through voice. Since no one can move left or right, no Linelander can pass each other, and thus they have the same neighbors for life. A Square notes that the limited lives of the Linelanders seem dismal, and he is surprised that the Monarch of Lineland is so cheerful and lively.
Lineland offers a bleak view of what it is like to be willfully ignorant. Physically stuck on a line, the people of Lineland are doomed for life, in both literal and religious senses. Thus, Abbott suggests how important it is to seek knowledge and religious truths. At the time Abbott firmly opposed the Tractarians, whose influence was growing in England, and who strongly emphasized the authority of the Church and scripture, much in the same way that the Linelanders take for granted their world as the entirety of existence.
A Square then asks the Monarch of Lineland how his people marry and produce offspring when they are confined to a line. The Monarch answers impatiently that proximity is not necessary for the generation of children, and that it instead occurs through sound and the sense of hearing.
Since the Linelanders are limited to one dimension, they depend solely on their sense of hearing. However, take note of the fact that they still have the means to perceive new ideas if ever presented them. Thus, Abbott argues that wisdom depends on the will to receive new knowledge and the humility to accept one’s ignorance.
The Monarch of Lineland continues by explaining that every man has two mouths and two voices, a bass and a tenor one. He admits that he assumed A Square to be a feminine monster with a bass voice. The king then states that Nature has dictated that every man should wed two wives to harmoniously meld the bass and tenor of the man to the soprano and contralto voices of two women. Once a week, every man sends out their most beautiful sound, marriages are consummated, and two girls and one boy are born from each union.