Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott (1884)

“Flatland: A Romance of Many Dimensions” by Edwin Abbott Abbott, first published in 1884, is a unique blend of mathematical exploration and social satire. Set in a two-dimensional world inhabited by geometric shapes, the novel introduces readers to a rigidly hierarchical society where social class is determined by the number of sides a shape possesses. Through the protagonist, A Square, the story delves into the limitations of perceiving reality through the lens of one’s dimension, ultimately serving as a critique of Victorian society’s closed-mindedness and class structures.

Plot Summary

In a world as flat as a sheet of paper, there lived beings shaped as lines and polygons. The narrator, A Square, begins by describing his homeland, Flatland. It is a realm of two dimensions where society is rigidly structured by geometry. The number of sides a figure has determines their place in this hierarchy. Triangles, often sharp and lowly soldiers, serve the higher classes, while squares, like the narrator, are professional men. At the top are the Circles, who, with so many sides that they appear smooth, rule as the priests and nobility. Flatland’s strict social order tolerates no deviation. Even the mention of dimensions beyond two is considered heresy.

Women, in Flatland, are straight lines, the lowest of all classes. Their form is dangerous — their sharpness means they can easily kill, and so strict rules govern their behavior. A Square reflects on the dangers women present and the various societal measures imposed to keep them in check, such as the constant sounding of a “peace-cry” to alert others to their presence. While appearing to accept this social structure, there are hints of deeper unease beneath the surface.

As A Square recounts his life, he shares an annual event in Flatland known as the “Color Revolt,” where a brief period of chaos was ignited by a movement to allow figures to paint themselves in colors to distinguish class. The revolt was swiftly suppressed by the Circles, who fear anything that might disrupt their control. The stability of Flatland remains, but only because all ideas that challenge it are eradicated.

One night, A Square experiences a peculiar dream. In his sleep, he visits a one-dimensional world known as Lineland. The inhabitants of this world are simple line segments who can only perceive others as points. He tries to explain the existence of two dimensions to the King of Lineland, but his efforts are in vain. The King cannot fathom anything beyond the straight line of his existence. Upon awakening, A Square is unsettled by the encounter, but quickly dismisses it as mere fantasy.

Soon after, A Square has a life-altering encounter. His reality is disrupted when a being from Spaceland, a three-dimensional world, makes contact with him. A Sphere descends into Flatland, first appearing as a circle that grows and shrinks as it moves through the two-dimensional plane. A Square, bewildered, cannot comprehend what he sees. The Sphere patiently attempts to explain the existence of a third dimension, but A Square resists, stubbornly clinging to his two-dimensional understanding of the world.

As a means of demonstration, the Sphere lifts A Square out of Flatland and into Spaceland. For the first time, A Square perceives depth. He is overwhelmed by this new perspective, marveling at the three-dimensional forms around him. From this vantage point, he sees Flatland as a mere shadow, its citizens moving as lines and shapes on a plane. The experience is transformative, igniting in him a hunger for knowledge beyond the limitations of Flatland.

However, the Sphere’s lesson is not over. A Square, emboldened by his newfound understanding of the third dimension, begins to question the Sphere. If a third dimension exists, might there not also be a fourth or fifth? The Sphere, affronted by such an idea, dismisses A Square’s questions and refuses to entertain the possibility of higher dimensions beyond his own. It becomes clear that even the enlightened are bound by their own limitations.

Despite the Sphere’s rebuke, A Square returns to Flatland with a broadened perspective. However, his attempts to share his revelation with others are met with scorn and disbelief. He tries to convince his fellow shapes, starting with his own family, of the existence of the third dimension, but they mock him as a madman. Even his own grandson, who is particularly intelligent, finds it impossible to grasp the concept of a world beyond two dimensions.

Determined to spread his newfound knowledge, A Square takes his case to the highest authority — the Circles. Surely, he thinks, the ruling class will be able to understand. But the Circles, who maintain their power through suppression of such dangerous ideas, see A Square’s discovery as a threat. They arrest him, condemning him for heresy, and imprison him for daring to challenge the established order.

In the confines of his prison cell, A Square reflects on his journey and the truths he has uncovered. Despite his punishment, he remains steadfast in his belief that the third dimension exists. Though his body is confined, his mind is free, soaring across dimensions and imagining worlds beyond the flat plane of his birth. He holds onto the hope that one day, Flatland will awaken to the reality of dimensions beyond their own. But for now, he is alone in his knowledge, a visionary in a world content with ignorance.

As time passes, A Square grows resigned to his fate, yet the experience of Spaceland lingers in his mind. His imprisonment becomes a metaphor for the limitations imposed by society, not just on physical freedom, but on thought itself. He resolves to continue thinking of the possibilities beyond, knowing that while he may not live to see it, others may one day break free of the flat constraints that define their world. He envisions the day when all of Flatland will rise above the two-dimensional existence and embrace the infinite possibilities that lie beyond.

Main Characters

• A Square: The protagonist and narrator, a mathematician and a member of the professional class (a square). He embarks on a journey of discovery when he learns about the existence of a third dimension (Spaceland), challenging his previously narrow view of reality. His transformation from complacent citizen to enlightened seeker drives the narrative.
• A Sphere: A visitor from Spaceland, the three-dimensional world. The Sphere introduces A Square to the concept of a third dimension, acting as a catalyst for his intellectual awakening. Despite his knowledge, the Sphere is also limited by his inability to imagine dimensions beyond his own.
• The Circles: The ruling class of Flatland, comprised of polygons with so many sides they resemble circles. They maintain strict social order and suppress knowledge of higher dimensions to preserve their power.
• The Women: In Flatland, women are straight lines, the lowest class in society. Their limited intelligence and dangerous sharpness serve as an allegory for the marginalized and oppressed groups in Victorian society.

Theme

• Dimensions and Perception: The novel explores the limitations of perception based on dimensionality. The inhabitants of Flatland cannot conceive of dimensions beyond their own, reflecting humanity’s own struggle to comprehend realities beyond immediate experience.
• Social Hierarchy: Flatland’s rigid class system, where the number of sides determines social status, mirrors Victorian class structures. Abbott critiques the absurdity of rigid societal divisions and the inequality inherent in such systems.
• Ignorance vs. Enlightenment: A central theme is the conflict between ignorance and the pursuit of knowledge. A Square’s journey reflects the struggle to overcome ingrained beliefs and embrace new ideas, despite societal resistance.
• Satire of Victorian Society: Abbott uses the world of Flatland to satirize the complacency and prejudices of Victorian England, especially its treatment of women and resistance to new scientific ideas.

Writing Style and Tone

Edwin Abbott Abbott’s writing in Flatland is characterized by its precise, formal prose, reflective of both his mathematical background and the satirical nature of the novel. His language is methodical, especially when describing the geometric and spatial properties of Flatland, making the world-building feel both logical and immersive. Abbott often adopts a humorous and ironic tone, particularly when critiquing the absurdities of Flatland’s social structure. The blend of satire with mathematical theory allows the narrative to function as both a work of speculative fiction and a philosophical exploration of perception.

The tone shifts throughout the novel, starting with a detached and somewhat authoritarian voice as A Square describes his world and its rules, only to become more introspective and contemplative as the protagonist begins to question his reality. Abbott’s ability to juxtapose the mundane with the profound gives the novel its lasting appeal, as readers are encouraged to reflect on their own dimensional limitations, both literally and metaphorically.