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Flatland | Study Guide

Edwin Abbott Abbott

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Flatland | Quotes


May aspire yet higher and higher / To the Secrets of FOUR FIVE or EVEN SIX Dimensions / Thereby contributing / To the Enlargement of THE IMAGINATION.

A Square, Preface

The dedication lays out the purpose of the book: to inspire its readers to ever more ambitious scientific and philosophical inquiry. Edwin A. Abbott, writing as A Square, also encourages readers to cultivate a scientific modesty that is the antithesis of self-contented ignorance. This, he says, is a rare virtue.


Alas, a few years ago, I should have said 'my universe': but now my mind has been opened to higher views of things.

A Square, Part 1, Chapter 1

One of the book's themes is the limitations of characters' perspective. The plot of the novel deals with Square coming to understand that the universe has more than the two dimensions in which he grew up.


No one would be safe in making the most simple social arrangements; in a word, civilization would relapse into barbarism.

A Square, Part 1, Chapter 7

In this passage, Square is explaining why Flatland society cannot tolerate irregular figures. Flatland has rigid hierarchies of class and gender, as well as a formidable eugenics regime. Flatland social status is determined by shape and angle, which usually follows a regular pattern. Since residents of Flatland can only see each other as lines with varying degrees of obscurity, they rely on the regularity of figures to infer the parts of the shape they cannot see. Were angles and sides not such a social fixation, there would likely be no real problem with irregular figures. However, Flatlanders already conceive of intelligence and moral character as dependent on shape, and so irregular figures—which are not predictable, and therefore dangerous in this realm of limited perception—are assumed to be born criminals.

This quote shows an example of Flatland's satirical style. Square is casting about for any justification for his own prejudice against irregular figures and plucks from both the most and least extreme ends of the spectrum.


Immoral, licentious, anarchical, unscientific ... those ancient days of the Color Revolt were the glorious childhood of Art in Flatland.

A Square, Part 1, Chapter 8

In the past, shapes began to distinguish their sides by painting themselves with colors. This threatened the status quo of circular rule and was violently suppressed. While Square is a loyal follower of circular doctrine, he cannot help being moved by the beauty of the mere idea of color. This episode serves to illustrate both the lengths to which the Circles will go to maintain power and Square's unacknowledged dissatisfaction with the doctrine in which he was raised. It also acknowledges the threat of art—and creative individual expression—in a society whose ruling class strives to rigorously impose and maintain conformity in the lower classes.


Doing nothing themselves, they are the Causes of everything worth doing, that is done by others.

A Square, Part 1, Chapter 11

Square is speaking of the circular rulers of Flatland who enjoy lives of luxury and leisure while the lower classes toil and fight on their behalf. The Circles are both priests and kings who may not, it seems, always uphold the moral doctrines they espouse.


Outside his World, or Line, all was a blank to him; nay, not even a blank, for a blank implies Space.

A Square, Part 2, Chapter 13

Square meets the King of Lineland, who cannot conceive of any world existing outside of his one-dimensional line. His perspective is limited by his ideas about dimension. When Square tries to convince him that there is a perpendicular axis to the universe, he becomes so angry he attacks.

Square's talk with the King of Lineland foreshadows his own experience when he is confronted with a three-dimensional being. It also foreshadows the difficulty he will have trying to convince Flatlanders of a third dimension.


What you call Solid things are really superficial; what you call Space is really nothing but a great Plane.

Sphere, Part 2, Chapter 17

The Sphere takes Square on a journey out of two-dimensional Flatland and into three-dimensional Spaceland. From his new perspective above his native plane, Square can easily perceive the interior of figures and buildings. All the angles and shapes he knew only by careful reasoning are easily visible to him from above. The journey is quite literally consciousness-expanding for him.

Though the characters do not visit it, Square also reasons that there must be a fourth dimension, from which three-dimensional things are laid out equally openly.


For why should the thirst for knowledge be aroused, only to be disappointed and punished?

A Square, Part 2, Chapter 19

When Square suggests a fourth dimension, Sphere becomes so angry with him that he puts him back in Flatland. Despite being Square's teacher, Sphere has his own limitations. These include a lack of intellectual modesty that would let him admit that his student has asked a question that he has not himself considered (or is not willing to consider).


To be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy.

Sphere, Part 2, Chapter 20

Sphere delivers this lesson, a summation of the book's central point, as he and Square visit Pointland. Devoid of dimensions, Pointland has only a single inhabitant who believes itself to be the whole of the world. It is so ignorant of the possibility of others that it assumes Square's voice is its own thoughts and congratulates itself on its cleverness.


I ... hope that these memoirs ... may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.

A Square, Part 2, Chapter 22

Square is speaking of the book he is writing from prison, Flatland. Though he has failed to convince anyone in Flatland of the third dimension, he hopes his three-dimensional readers will take his story as an inspiration to be curious and to explore. This is not the only time he phrases the search for knowledge as rebellion. The Circles are keeping him imprisoned to suppress a scientific truth that might undermine their own power and prestige. The book ends on a note of mixed hope and despair. Square still believes in aspiring but is growing weak and forgetting what he saw.

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