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Literature Study GuidesFlatlandPart 2 Chapters 17 18 Summary

Flatland | Study Guide

Edwin Abbott Abbott

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Flatland | Part 2, Chapters 17–18 : Other Worlds | Summary



Chapter 17: How the Sphere, Having in Vain Tried Words, Resorted to Deeds

A Square tries to attack Sphere but cannot hurt him, as he slips out of Flatland altogether. Sphere had hoped that Square, a mathematician, would be able to understand the Gospel of the Third Dimension. As proof that a third dimension exists, Sphere describes the contents of closed cabinets and boxes that are visible to him from above and moves one of these to Square by lifting it out of Flatland without opening the door.

When this does not convince Square, Sphere tells him that he is going to gently press on Square's middle from above. It will hurt, but it is necessary to educate him. Square's guts hurt, and he hears Sphere, who returns a moment later to make sure he hasn't hurt Square badly. Still upset and frightened, Square continues to lash out, trying to rouse the house to help him fight off the intruder. Sphere hides and says that no one else must see him. He has been waiting 1,000 years to bring the Gospel of Three Dimensions to Flatland. Sphere then lifts Square out of Flatland.

Chapter 18: How I Came to Spaceland, and What I Saw There

Square is terrified and cannot initially make sense of the sensation of three dimensions. Sphere tells him to be calm and look again. His first glimpse of the true form of Sphere fills him with awe. This is the first time he has ever seen the side of a person before, and he asks why he cannot see inside Sphere, who looks to him like what he understands to be the outline of a circle. Sphere replies that he is a different order of being than the people of Flatland and that it is impossible to see inside him from any angle. He is solid.

Square still doesn't understand, but now he worships Sphere as a teacher. Sphere tells him not to worry if he doesn't immediately understand; it will become clearer to him as he thinks about it. Sphere shows Square his house and all its inhabitants from above. Everything that Square had inferred about Flatland is now plainly visible from this new angle. Sphere tells him not to worry about his wife, who is wondering where he has gone, and that the two of them will survey Flatland.

Square says that he is experiencing "omnividence"—the ability to perceive everything—which the priests say is an attribute reserved for God alone. Sphere says that even the lowest pickpocket of his world has this attribute and that in his world the virtues to be praised as divine are mercy, selflessness, and love. Square protests that these are the attributes of women and that everyone knows that Circles are the most virtuous with their knowledge and wisdom. Sphere says that in Spaceland, Straight Lines are often more highly regarded than Circles.

Sphere takes Square to the General Assembly Hall, where Square's brother is the Chief Clerk of the High Council. The council reveals that every millennium, new "ill-intentioned persons" pretend to have received visions from another world about the third dimension. There are special instructions that these persons should be arrested and destroyed if they are Isosceles, imprisoned if Equilaterals, sent to the asylum if a Square or Pentagon, and sent to the capital if they are of any higher rank. Sphere tells Square that this is the fate that awaits him, but Square is convinced he could make the council members understand if he could only speak to them. Sphere says that it is not time and manifests himself in the council chambers, saying, "I come to proclaim that there is a land of Three Dimensions." The guards try to arrest Sphere, but he passes through. The president says that there is no need to be alarmed, as this manifestation happens every millennium, according to his papers. He proclaims that this must be kept absolutely secret and arrests Square's brother to keep him from talking.


When Square looks down onto Flatland, he sees things that he has always known to be true but has never been able to visualize. A huge portion of his life has been concerned with using inference to determine shapes and angles, but from a higher dimension, he can see not only shapes, but also their hidden interiors. Things that required intense conscious thought to understand become easily perceptible. Nothing has changed other than the angle from which he is viewing Flatland, but that angle changes how he sees it dramatically.

The capacity to view one's world from a different perspective is one Abbott may have been familiar with because of accounts of living humans who claimed they had been carried into other realms such as heaven or hell from which their own world could be viewed. One example of such a literary traveler might have come from Italian poet Dante Alighieri's (1265–1321) three-part epic The Divine Comedy (c. 1308–21).

The book provides a useful contrast between the religious orthodoxy of the Circles and the revelations of Sphere's Gospel of Three Dimensions. This is highlighted by the fact that the Circles actively suppress talk about the possibility of a third dimension and have done so for at least 3,000 years. One example of this is the concept of "omnividence," or the ability to see everything in Flatland. The Circles have said that this power is reserved for only the divine, while Sphere says that it belongs to everyone. This is in direct contrast to one of the most fundamental tenets of Flatland and invites Square to see himself in a completely different light—as powerful and divine. Sphere even asserts that Square could have left Flatland by himself if he could have understood how to do so. Sphere also considers compassion a virtue and Straight Lines in many respects superior to Circles. He proposes an understanding of the world that expands the definition of who and what is important rather than restricts it.

It is likely the Circles do not understand the concept of a third dimension any better than Square did before he was pulled into it. They do, however, clearly perceive it as a threat to their power structure, possibly because they do not understand it. The reader has already seen the Circles put down the color revolution, and the arrest of Square's brother removes any question about the seriousness of the fate that awaits Square. However, both Square and Sphere view the truth of the third dimension as more beautiful and more important than the danger.

In Victorian England, there were many who faced the dangers of challenging the orthodoxy of the ruling class. Proponents of Chartism (1838–48), for example, proposed radically reforming Britain's electoral system to allow universal male suffrage and more equal parliamentary representation. Labor advocates fought against child labor, dangerous and exploitative conditions, and the 12-hour workday. Victorian workhouses, with their harsh conditions and focus on poverty as a moral failing, drew outrage from working people and humanitarians. Anti-imperial protesters boycotted goods from colonies and advocated disentangling Britain from foreign military commitments, particularly in India. Women's restricted roles were challenged by early feminists in essays and literature. In many cases, those advocating reform faced significant pushback from the political system, including arrests for writers and protesters. Square's imprisonment follows this pattern.

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