Introduction

In his introduction to Flatland: a Romance of Many Dimensions (1884), British mathematician Banesh Hoffmann describes the novel as “a stirring adventure in pure mathematics” and emphasizes the fundamentally fantastical nature of the story (iii). He also says that author Edwin A. Abbott intended the novel to be instructional. Both the surreal nature of Flatland and its didactic elements are plain, but there is disagreement among scholars and readers on the question of exactly what the novel aims to teach. Abbott, a professional mathematician, waded into late 19th-century debates about the nature of dimensionality, and he seems to have been resistant to the idea that Euclidean geometry provides the only reliable mathematical map of the universe. However, he also uses Flatland to level harsh—if often humorous—critiques against the Victorian system, the British Empire, and toxic perspectives on gender roles and women’s rights. Finally, the novel theorizes about religious revelations. In addition to working as a mathematician, Abbott was a theologian, and a central concern throughout his career was how to reconcile empirical scientific exploration with a more abstract understanding of religious truths. In its attention to the various relationships between perception, inference, knowledge, and physical proof, Flatland gives voice to Abbott’s belief that while materialism is important to our experience of the world, it is not necessarily central to our spiritual, emotional, and interpersonal lives. Ultimately, Flatland brings the sense of infinite possibility common to travel and adventure narratives together with specifically 19th-century concerns about knowledge, surveillance, governmental overreach, and what happens when civil rights are neglected or quashed.

This guide refers to the Dover Thrift Edition of Flatland (1992).

Content Warning: The novel contains references to rape and death by suicide that this guide discusses.

Plot Summary

Flatland is divided into two main sections. In the first section, the narrator, identified only as the Square, describes his life in Flatland and provides details about its social structure and recent history. Flatland is a two-dimensional world in which all inhabitants take a multi-sided shape that indicates the social class to which they belong. Women are an exception to this rule, as they are all straight lines. The higher classes, which include professionals, nobles, and priests, exercise total control over the lower classes, which consist of middling tradesmen, laborers, soldiers, and the deeply hated Irregular Triangles, who are treated like common criminals and have no rights. Flatlanders have developed complex ways of recognizing each other, since each inhabitant appears to the others as a straight line: these methods include touching or feeling each other and using the perpetual fog that floats through Flatland to detect variations in each other’s shapes. The Square describes a historical event known as the Colour Revolt, which began after a polygonal Flatlander known as Chromatistes found a way to create color and began to paint objects and people. The development of color gradually led the lower classes to rebel against the upper classes by introducing the Universal Colour Bill, a law that would erase all social and political distinctions. However, the priests and nobles manipulated the women and soldiers to turn against the bill’s supporters and the revolt was violently suppressed.

In the second part of the novel, the Square relates his adventures in various dimensions. The adventures begin with a dream in which he visits a place called Lineland. In Lineland, all the inhabitants live on the same straight line and have an extremely limited vision of the world; however, they do not understand this limitation and believe they can see everything that could possibly exist. The Square argues unsuccessfully with the King of Lineland, trying to convince him that Flatland is a real place. He wakes up right before the enraged king and his followers attack him. Soon after, the Square is visited by an otherworldly being known as the Sphere. The Sphere has arrived to spread the gospel of three dimensions and transports the Square to Spaceland, a three-dimensional world in which considerably more is perceptible to the Square than in Flatland. The Square realizes how limited his own vision has been and feels as though he has had a religious experience. He expresses a fervent desire to visit the fourth dimension, and then the fifth, and so on into infinity. The Sphere denies that such places exist and pushes the Square back to Flatland.

The Square feels compelled to share his new knowledge with his fellow Flatlanders, but the government has recently passed a law requiring anyone who claims to have received otherworldly revelations to be imprisoned for life. He slowly loses his grip on reality, unsure whether his memories of Spaceland are accurate but still motivated to enlighten others about the true nature of the universe. He eventually has a public outburst in which he recounts his trip to Spaceland in detail, leading to his imprisonment. The Square reveals that he is still in prison as he writes the story, and while he remains uncertain about the factual truth of his visit to the third dimension, he feels the emotional truth of what he saw there in his heart.