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Flatland | Study Guide

Edwin Abbott Abbott

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Flatland | Themes

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Oppressive Hierarchy

Flatland is full of oppressive hierarchies that bind women and the lower classes in submission and necessitate the destruction of "irregular figures." This leads to massacres to quell revolution and stifles the human mind and imagination. These hierarchies are explicitly modeled after and intended to satirize the rigid social systems of Victorian England, including class systems, racial hierarchies, gender hierarchies, and the burgeoning eugenics movement. Class systems manifest as the physical differences between men who are Isosceles Triangles at the lowest end of society, Squares and Pentagons in the middle, complex Polygons as nobility, and "circular" priest kings at the top. Below all of these men are women, who are straight lines, reflecting the legal, social, and often absurd medical restrictions on Victorian women.

The Circles preach a doctrine that shape is the true source of morality and that anyone with very acute angles—or, worse, irregular ones—is morally and intellectually deficient. These shapes are subject to outright destruction, carefully monitored imprisonment, or a tithe where they are given to schools to be slowly starved to death while they are used as teaching subjects. This is modeled on Victorian pseudosciences such as phrenology and early "race science" intended to prove the superiority of white Victorians over the people they colonized. The Circles and those who imitate them are constantly concerned with making sure the sharper and more numerous Triangles never succeed in rebellion. They stifle useful innovations and truths they cannot understand, such as color and the secret of the Sphere, because it threatens their power and prestige.

The hierarchies in Flatland are at once purported to be natural and intuitive but also rigidly reinforced, much as Victorians used supposedly scientific rationale to reinforce their ideas about the order of the world. Women are said not to have any mental capacity, but laws prohibit their education and constrain how and where they can move. They are prevented from improving themselves and can be legally put to death for even accidental misbehavior. Isosceles Triangles are assumed to be too intellectually inferior to be capable of organization or strategy, but they are also monitored closely on account of their cunning. They are denied the expensive education the Polygons receive, the results of which the Polygons use to justify their superiority over the Triangles. The thirst for advancement among the nobility is so strong that they routinely risk their children's lives to break their sides to create a greater number of sides.

Flatland follows A Square's journey from being a relatively orthodox member of the society to being imprisoned for trying to share the truth that there are more than two dimensions. In his initial description of Flatland, he echoes all the prejudices of his society, and it is difficult for him to conceive that it could be any other way. While he is able to see some hypocrisy, it is not until he is shown the truth of three-dimensional space that he comes into conflict with his society. Unfortunately, the hierarchy is much stronger than he is as an individual.

Limited Perspective

All of the characters in Flatland view the world from a limited perspective, and what they are able to perceive determines how much they can understand of the world. For characters living their entire lives in a single dimension, it is nearly impossible to conceive of a second dimension, and so on. Even Sphere reacts with anger to the suggestion that there are dimensions beyond those he understands.

The book's characters see the world and others in it in one less dimension than they understand themselves. They must use reason and sensory evidence to understand the world and others in their proper configurations. The King of Lineland, for example, sees others as single points along his line and uses sound to survey them. A Square sees others as single lines and determines their angles using fog and mathematics. Sphere sees the outlines of shapes and uses light and shadow to infer their volume. Even within their native plane, perspective is incomplete, and the characters' senses provide an incomplete picture. While other dimensions and perspectives exist outside of those they know, they lack the vocabulary to think about or explain them. The Point's perspective is in fact so limited that it cannot perceive anything outside itself. This is also true of the characters' cultural touchstones. The apology for A Square in the preface speaks directly to how much of the Circles' view of Flatland he has absorbed and how it colors all of his judgments in the first half of the book. Likewise the King and the Point are so absorbed by ideas of their own superior culture that they cannot clearly perceive or even acknowledge A Square. This self-importance and limited perspective satirizes a Victorian Britain so deeply assured in its belief in its own superiority in the natural order of the world that it was capable of cruel oppression and devastating errors in understanding.

A Square experiences a radical shift in perspective when he travels into Spaceland. From above he can see clearly everything that cost him tremendous mental energy in his world. With this new perspective and his rational understanding of math, he is able to extrapolate even higher dimensions. This is, ultimately, the point of Flatland as a text: to inspire readers to strive to look beyond a narrow perspective.

Modesty and Aspiration

In Flatland's dedication, A Square hopes to inspire his readers to aspire beyond their own current understanding of the world and cultivate a sense of modesty. By this Edwin A. Abbott means to strive for greater scientific and spiritual understanding without ever growing complacent enough to assume that readers already know all the answers there are to be had. Aspiration and modesty are the chief moral virtues of the book, and readers see both a positive example of these virtues and their antitheses.

The King of Lineland and the Point, with their more limited perspectives and greater assurance of their own superiority, are the most pointed examples of characters who lack modesty and aspiration. However, even Sphere falls short in this respect, as he lacks the humility as a teacher to accept A Square's questions about the fourth dimension. Eventually he apologizes and concedes their scientific plausibility. The Circles who rule Flatland also have a deadly sort of intellectual immodesty, as they do not care about truth as much as they care about maintaining their power. Their doctrines and teachings promote themselves at the expense of others. They are self-serving rather than truth-seeking. These critiques apply, by extension, to Abbott's audience and the society they were a part of. Unorthodox opinions and behaviors were often viewed very dimly by Victorian culture, which assumed itself the height of morality and human evolution. Flatland argues that immodest conviction in one's own superiority culturally, physically, or mentally limits one's ability to perceive and pursue what is actually true.

By the end, A Square provides the best example of a modest and aspiring character. He is moved by the beauty of a new perspective and willing to endure humiliation and imprisonment in service of the truth. He speaks of his efforts in terms of imagination and rebellion. His greatest desire is to free the human mind from its constraints.

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