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Literature Study GuidesFlatlandPart 2 Chapters 21 22 Summary

Flatland | Study Guide

Edwin Abbott Abbott

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Flatland | Part 2, Chapters 21–22 : Other Worlds | Summary



Chapter 21: How I Tried to Teach the Theory of Three Dimensions to My Grandson, and With What Success

A Square wakes up with a fresh enthusiasm to preach the Gospel of the Third Dimension. However, town criers repeat the council's resolution that anyone professing revelations from another world should be arrested and possibly executed. He decides to try to focus on the math rather than the revelations. He repeats the phrase "Upward, not Northward" to remind himself how three-dimensional space works. Square begins by trying to talk to his hexagonal Grandson about the math problem from the previous night. However, the heralds cry out the news again, and his Grandson frantically disavows that he believes in a third dimension or that he could even conceive of such a thing.

Square tells him that it isn't silly and tries to explain, but his Grandson insists that it is a joke and runs away.

Chapter 22: How I Then Tried to Diffuse the Theory of Three Dimensions by Other Means, and of the Result

Square is now convinced that he will not be able to simply explain the third dimension and that telling his story would be dangerous. He spends several months writing a version of his experiences, edited somewhat to try to circumvent the law. Instead of three dimensions, he talks about a realm of pure thought where a figure could hypothetically look down on Flatland and perceive things from the side.

Meanwhile, Square is increasingly agitated with not being able to talk about three dimensions and occasionally lets things slip. He is also worried that he's beginning to forget how three dimensions work. One day, at a function in the home of an important official, someone is talking about how it has been proven that there can be no more than two dimensions. Square tells his whole story in a fit of frustration. He is arrested and brought before the council, who replace his guards with more acute Triangles, signaling that they mean to kill the Triangles to keep information from leaving the room. Square tells the council his story, and the president asks him two questions: (1) Can he indicate the direction he means when he says "up"? and (2) Can he draw or describe a cube without resorting to math about angles?

Square cannot do either of these things but declares that the truth will prevail in the end. The president agrees and says that they'll let him out of prison if the truth proves him right. Square will be made relatively comfortable in prison and allowed to see his brother. Square spends seven years in prison writing the memoir the reader now holds, unable to convince even his brother, who also saw Sphere. He hopes that this book will inspire people to think beyond their own dimensions, or, as he puts it, "may stir up a race of rebels who shall refuse to be confined to limited Dimensionality." However, more and more he feels his own grasp of the book's concepts slipping away. Some days, he wonders if it wasn't all just a dream.


Square refers to himself more than once as Prometheus, the Titan of ancient Greek mythology who stole fire from the Gods to bring it to humanity and who was punished for the theft. This gift of fire allowed humans to progress from living in fear of their environment to being masters of it. It also represents the knowledge of the gods, blurring the line between humanity and divinity. Square talks about his new ideas as "a rebellion against the conceit" that dimensions might be limited. Both of these ideas posit him in direct opposition to the authority of the Circles, who stifle ideas that might upset a hierarchy that puts them at the apex. His goal, to spread the knowledge he has gained, requires not just intellectual understanding, but moral fortitude. Square's Grandson has the former but not the latter, and he quickly disavows his former questions.

The Victorian era saw a huge leap forward in scientific understanding, including advances in biology, chemistry, electromagnetism, and engineering. There was a great deal of worry about what new knowledge and technology meant for the established hierarchy. For example, Charles Darwin (1809–83) faced criticism for his theory of evolution, which undermined the Christian belief that God created the world in seven days. Abbott himself advocated strongly for scientific education for all students as part of any real understanding of the world around them.

The book ends on a mixed note of hope and despair. Square never manages to convince a single Flatlander, not even his brother. Still, he is hopeful, despite the odds. By ending the book with Square incarcerated and forgetting how to understand the third dimension, Abbott concedes that expanding human consciousness and understanding is not easy. He also implicitly agrees with Plato and Socrates's conclusion to the allegory of the cave, that those still living with illusion rather than reality will be unable to understand the truth. More than that, they will be hostile to it, as it seems to have damaged the person who brings truth back to them. To bear a truth may be very dangerous, especially when one's conclusions threaten the orthodoxy. However, the book resoundingly endorses this as the best aspiration of any human mind.

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