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Literature Study GuidesFlatlandPart 1 Chapters 1 2 Summary

Flatland | Study Guide

Edwin Abbott Abbott

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Flatland | Part 1, Chapters 1–2 : This World | Summary



Chapter 1: Of the Nature of Flatland

"Flatland" is not actually what the people of A Square's world call their realm. It is merely the name he uses to help people who exist in three dimensions understand the nature of his world. "A few years ago," he foreshadows, "I should have said 'my universe': but now my mind has been opened to higher views of things."

Flatland is a flat surface on which geometric figures such as Triangles, Squares, and Hexagons move about freely in two dimensions but cannot move up or down. They also cannot perceive each other from any angle but straight on along the plane of the flat surface and thus see each other only as straight lines. To help readers understand, Square asks them to look at a penny on a table from above, where it looks like a circle. Then he asks them to gradually bring their eye level down to the plane of the table, where the penny viewed from its edge appears as a straight line.

Residents of Flatland perceive the lines of others as growing bigger or smaller as they travel closer or farther away, but they always see only a straight line. Square promises to deal with how they tell each other apart later, after talking a bit about his world.

Chapter 2: Of the Climate and Houses in Flatland

Flatland has no sun or other celestial bodies but does have the four cardinal directions: north, south, east, and west. Flatland exerts a sort of southward gravity, and figures not resting against a barrier or exerting pressure will drift south. People in Flatland use this gravity and the rain that falls from the north at regular intervals to orient themselves. Adding that houses and trees point northward, Square assures readers that residents are usually able to tell where they are. Because the southward gravity exerts a greater strain on "the weak and aged, and especially on delicate Females," courtesy demands any polite man let a woman pass him on the north side of the street. This is difficult on short notice if the man is not properly oriented.

There is light everywhere in Flatland but without an apparent source. Some philosophers have asked where the light comes from but without solution. The Circles have declared the question a nuisance and assigned it a punitive tax; currently, investigation is completely prohibited. Square knows that the light comes from a third dimension but is derided as "the maddest of the mad," which he promises to talk more about later.

Houses in Flatland are constructed as pentagons by convention, as other figures have angles sharp enough to be dangerous to passersby. The only buildings allowed to be triangles are military fortifications. Men and women have separate doors: a large one on the western side for men and a small one on the eastern side for women. While square houses are technically permitted in towns with a population under 10,000, they are discouraged by taxes and are very rare.


One of the most important and subtle points in Flatland is the inability of characters to fully perceive even their own reality and especially the other people in it. People moving about in Flatland are two-dimensional figures but perceive each other as one-dimensional lines. In Lineland, figures are one-dimensional lines but perceive each other only as single points. For readers in the real world, there is little perceptible difference between a three-dimensional object and a convincingly rendered two-dimensional representation of that three-dimensional object. In each of these realms, people fill in the gaps in their perception with other senses, reason, and intuition. In drawing attention to this, Abbott is making an important point about the ability to comprehend reality. This incomplete perception, limited understanding, and striving to build a picture of the world from insufficient information is at the heart of Flatland as a work.

In dealing with the light, these first chapters weave in another major theme of the book: how the Circles, as the ruling class, exercise their power to suppress any knowledge or innovation that might threaten their position. Coming from outside perceptible space and touching everything, the light represents a true conception of the divine, accessible to all if it is pursued. However, it is in the Circles' interest to curtail questions about truth. Compared to suppressive measures introduced in later chapters, this prohibition is relatively innocuous. However, it is an important way Abbott shows that the Circles are not interested in advancing science, philosophy, or genuine interaction with the divine.

The light specifically and the book Flatland more generally also share several parallels with the Greek philosopher Plato's (428–348 BCE) famous allegory of the cave. Plato describes a story told by Greek philosopher Socrates (c. 470–399 BCE) in which prisoners had lived their entire lives inside a cave, facing a blank wall where they saw shadows whose source they could not turn to view. These shadows were cast by objects being carried by people moving in front of a torch on the other side of a low wall, but because the prisoners knew nothing else, they would infer this was all of reality. Living in such conditions, to turn and see even the torchlight would blind and confuse them. In contrast, a man brought into the sunlight would take time to understand the real forms of the world, which had only cast shadows onto the wall before. Moreover, once his eyes had adjusted to the light, were he to descend again to try to explain the truth to his fellow prisoners, he would seem blind and mad to them. His perceived infirmity would make them unwilling to try to see the light themselves, and they would punish him for his efforts. The narrative of Flatland mirrors this parable on philosophical searching, with Square's journey, his enlightenment, and his imprisonment. The light that comes into Flatland is, at this point in the story, much like the light casting shadows on the cave wall, and the population is discouraged from investigating. Not immune to easy humor, Abbott sneaks in a bit of a pun in his geometric diagram, labeling the northernmost lines RO and OF to indicate the roof.

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