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Literature Study GuidesFlatlandPart 2 Chapters 13 14 Summary

Flatland | Study Guide

Edwin Abbott Abbott

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Flatland | Part 2, Chapters 13–14 : Other Worlds | Summary



Chapter 13: How I Had a Vision of Lineland

On the penultimate day of the year 1999, A Square has a dream in which he travels to Lineland, a world with only one dimension. He perceives Lineland as hundreds of a small straight Lines, which he assumes to be women, interspersed with single Points, all moving back and forth on the same trajectory at about the same speed. All of the Lines and Points chirp in chorus, and sometimes they stop moving and quiet. Square approaches what he assumes to be the largest of the women and asks what's going on.

The Line replies that he is not a woman—he is the king of the entire world, Lineland. Square apologizes and tries to ask questions, but the two have trouble communicating. The King assumes that Square has the same frame of reference he does and gets irritated by any question to which he considers the answer obvious. Likewise, he discounts anything Square says that does not make sense within his own understanding of the world.

The King believes that the straight line in which he lives is the whole world and that nothing exists outside of it. When he hears Square's voice from outside the line, it seems to him to come from inside himself. He cannot even see Square until Square intrudes across the line.

The King can only see others as single points, much as Square can only see other Flatlanders as lines. The men of Lineland are single lines, the women are single points, and age and sex can only be determined by voice. Furthermore, because there is only one dimension in which to move, the people of Lineland cannot pass each other or change their order or configuration. Square imagines that this must be very boring and doesn't see how people can "enjoy the pleasures of a conjugal union." The King thinks that this is an absurd question and replies that his wives and children are very happy.

Square is baffled and asks if proximity is somehow not necessary to produce children. The affronted King replies that it would be absurd for so important a thing to rely on proximity. Linelanders use sound and hearing for marriage and reproduction. Each man has two voices, a bass and a tenor, and harmonizes with two women, one a contralto and the other a soprano. (The King is convinced that Square is a woman, because he has only one voice, even though it is deep.) Once a week, the people of Lineland move back and forth more violently than usual and sing their sweetest songs. Across the entire distance of Lineland, people can recognize the voices of their beloveds. When all four voices harmonize, three children are conceived, one male and two female. The King uses the phrase "the Alphabet of Nature" to describe the ratio of the sexes. This is the same phrase that Square uses to describe Flatlanders' intrinsic understanding of angles.

Chapter 14: How I Vainly Tried to Explain the Nature of Flatland

Square decides that the King is talking nonsense and that it is time to educate him on the truth about Flatland. He tries to explain that he has seen Lineland from outside the line, but the King replies that this is impossible. One cannot see a line, he argues; one can only hear the difference between the voice at one end and the other. He demonstrates how he helps his wives discern his length by chirping with both of his mouths. Square asks how they can know if a man isn't imitating someone else's voice. Do they feel each other to verify identity? The King is horrified, as touching another person is punishable by death, since a man touching a woman would crush her and men cannot be distinguished from women by sight. The King wonders what the point of touching could possibly even be, when hearing is so much superior. The King declares that he will take an immediate census of his whole kingdom to demonstrate, and the line makes a sound that Square thinks sounds like grasshoppers.

Square tries to demonstrate to the King that he can see the people around him in the line from the side but succeeds only in reciting information the King knows by sound. The King does not accept this as proof. Square asks the King to step out of his line so he can show him perpendicular movement, but the King doesn't understand what he means and Square cannot explain it in a way the King can understand. Square tries to demonstrate by moving himself in and out of Lineland. He places his face flat against the line and moves through, and though the King can see him, he declares that Square is not moving. Square is only visible as a point, and because he only has one voice, the King has no way of perceiving his other end. When he leaves Lineland, the King believes he has died.

Square speaks to the King from two-dimensional space, assuming that this will convince him, but the King is frustrated and angry that Square will not say what he means in words the King can understand. He demands that Square admit he's wrong or leave Lineland. Annoyed at being misunderstood and misgendered, Square declares that the King is an idiot and infinitely inferior to Square, who is not even that important a person in Flatland. The King and his subjects attempt to attack Square, but he wakes up from his dream.


In dealing with Lineland, Square is in the same position as readers who are first encountering the confusing existence of people in Flatland. The King, meanwhile, occupies the same narrative position Square will occupy later, when he is visited by the Sphere. This functions to foreshadow the visit of the Sphere. Square cannot convince the King of the existence of a perpendicular direction or any dimension outside his line. When he crosses the line, he appears to the King only as a point. When the Sphere tries similar tactics later, readers can more easily understand what is going on because they have already seen them from Square's perspective. As an educator, Abbott was well aware that it is often useful to demonstrate a premise simply first and then expand it to be more complex.

There is no proof Square can offer the King that will suffice, because any proof would require the King to be both willing and able to conceive of a second dimension. Every proof that Square can offer must, by necessity, be something the King can verify with the senses he possesses. However, if it is information that can be obtained by other means, then it is not definitive proof of something outside of the line. In order to believe in other dimensions, the King must make an extreme leap of faith.

Many of the King's concepts about the world are designed by Abbott to baffle and morally anger Square, including polygamy. Perhaps the most pointed of these is that the King continues to believe that Square is a woman, though Square initially believes the same of the King. Both of them offend the other by presuming their own superiority, and their unwillingness and inability to consider the world from each other's perspectives leads to hostility and a total breakdown in communications.

The Victorian era saw the early endeavors of the discipline of anthropology and the publication of various ethnographies, or studies of other cultures. These early works had as a distinct function demonstrating the superiority of European culture over other "primitive" and "exotic" cultures. Square's description of Lineland resembles these works in several ways, including the documentation of marriage customs and daily routines that he observes and comments on as a "superior" outsider. Because readers exist in three dimensions and have no emotional attachment to either Flatland or Lineland, they are able to see that both the King and Square are operating on limited perspectives, where each thinks himself superior to the other. Both are convinced of their own superiority and unable to "cultivate modesty" and learn from each other. The view that Victorian culture was the best and most advanced contributed to colonialism and the poor treatment of British subjects in its many conquered territories.

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