Plot and Major Characters
In Flatland, Abbott created a fictional world, called Flatland, of only two dimensions inhabited by two-dimensional beings. The narrator, A. Square, begins by introducing readers to his two-dimensional world, including its different types of life and its social order. A male's position in this social order is determined by angles and sides; the square narrator, a lawyer, is higher in the social hierarchy than triangles (who tend to be laborers, soldiers, and merchants) but lower than more complex regular figures. The highest figures in Flatland are those with so many sides and angles that they are close to being circles. Parents aspire to have children who possess more sides and angles than themselves. In addition, figures with irregular angles are considered outcasts and criminals. Females in Flatland possess no angles or complexity of form whatsoever; rather, they are simply line segments, representing, for Abbott, the second-class status of women in Victorian society. Women in Flatland are, however, powerful figures, since their sharp forms can puncture and deflate the males. Given this fact and their emotionally volatile natures, females in Flatland are governed by sets of rules that limit their full participation in society. The second part of the novel concerns the narrator's vision of a one-dimensional world called Lineland. More fantastic and less satiric than the first part of Flatland, this section describes what life might be like in such a world. This dream of Lineland is both highly imaginative and mathematically intriguing. The tables are turned on the narrator in the last third of the novel, in which the two-dimensional being encounters a being from Spaceland—in other words, a being from a three-dimensional world. The Spacelander, Lord Sphere, tries valiantly to explain the concept of three dimensions to someone who knows only two, but A. Square cannot understand and feels threatened by the Spacelander's seemingly supernatural view of events in Flatland granted by his three-dimensional perspective. As the Flatlander was attacked by the Linelanders, so the Flatlander here attacks the Spacelander—a sharp commentary on how people tend to respond to things beyond their understanding. The Spacelander then lifts A. Square to three-dimensional space, from which he can see Flatland from above. The narrator finally accepts the notion of space and ascribes divinity to its inhabitants, which the Spacelander appropriately denies. Any notions of more than two dimensions are considered heretical in Flatland, so the narrator's experiences with the sphere cause him trouble with the Flatland Council. Still, despite persecution and imprisonment, he continues to insist on the reality of a three-dimensional world, worlds of more than three dimensions, and a world revealed by the sphere called Pointland, inhabited by a single being satisfied with its own existence and unaware of the existence of others.
Primary among Abbott's themes in Flatland is his satire of Victorian social structure and mores. Abbott's portrayal of women is sharply critical of traditional women's roles in his society. Additionally, since Flatland is a two-dimensional world, its inhabitants see each other as line segments or, if facing a female directly, a point. Thus, distinctions between people, though they exist, are difficult to perceive. Significantly, the ability to judge another's shape, and with that another's status, comes mainly with education. Given Abbott's position as a cleric and his deep interest in spiritual issues, religion is also a topic of concern in Flatland. Some readers have seen A. Square's encounter with Lord Sphere as a metaphor for humanity's limited understanding of its encounters with the divine. Though Abbott never clarified these issues in subsequent editions of Flatland, he defined his religious views in his many theological works, especially in his late entry into the Tractarian controversy. In his religious writings Abbott also distinguished between the miraculous, which he dismissed as untrue, and the supernatural, which he thought was different from the miraculous in being both above nature yet linked to nature. In light of this, one might see a connection between Abbott's fanciful novel and his theological beliefs.
Reviewers at the time of its publication were mixed in their opinions of Flatland. Some appreciated its imagination and satire, while others found the book tedious and didactic. Many readers were puzzled by what they took to be the metaphorical intent of the novel, unsure whether Abbott was suggesting that God occupies a higher dimension and can become partially manifest on the human plane just as Lord Sphere can appear in Flatland as a cross-section, or whether the divine is more vaguely related to the natural world, as a three-dimensional world would be related to one of two dimensions. Nevertheless, Flatland acquired an eccentric but loyal following in the twentieth century. Later critics noted that Abbott explored issues of scientific relativity a half-century before Albert Einstein would develop his world-changing theory. Flatland's champions include scientists, mathematicians, and fantasy and science-fiction fans, and the novel has inspired several tributes and sequels by twentieth-century authors. A 2002 edition annotated by noted mathematician Ian Stewart has once again renewed interest in the novel.