Edwin Abbott Abbott (1992)
Genre
Fiction
Reading Time
120 min
Key Themes
See below
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A humble square's encounter with a sphere in a two-dimensional world shatters his reality, revealing the humorous limits of his flat existence.
A Square, the narrator, describes Flatland, a two-dimensional world of geometric shapes. He explains the social hierarchy: women are lines (the lowest order), soldiers and workers are Isosceles triangles, middle-class professionals are Equilateral triangles, and the upper classes are Squares and Pentagons. Nobility consists of Hexagons and higher polygons, approaching a Circle. A Square details the challenges of perception in Flatland, where objects appear as lines, and recognition relies on touch, sound, and subtle changes in observed length as shapes move. He also introduces 'Irregulars'—shapes with unequal sides—who are often shunned or removed.
A Square describes the unique and dangerous nature of women in Flatland. As mere lines, they appear as points from certain angles, making them almost invisible and able to cause fatal injury by accidentally piercing another shape. To prevent this, women must emit a constant, shrill warning cry in public. They must also use specific, narrow doors to enter and exit buildings, ensuring they are seen. This rule highlights the dangers and limits of a two-dimensional existence, where thinness can mean invisibility and threat. The narrator notes that women are also thought to be less intelligent and emotional.
Since Flatlanders see each other as lines, A Square explains their recognition system. This includes a refined sense of touch to feel other shapes' angles. Sounds, like specific voice tones and pitches, are also important. The main method is 'sight-recognition,' which involves guessing a shape by watching its apparent length change as it moves. A skilled observer can deduce angles and sides from these subtle changes. This needs significant practice and education, especially for recognizing higher polygons and Circles, whose sides seem to blend into a continuous curve.
A Square tells of a dream where he visits Lineland, a one-dimensional world of points and lines. He tries to explain the concept of a second dimension to the King of Lineland, a long line segment. The King, confined to his single line, sees others only as points or line ends. He finds A Square's descriptions of 'upward' and 'downward' impossible to understand, dismissing them as madness or divine revelation. This dream is a parallel, hinting at A Square's later struggles to understand and explain a higher dimension, showing how hard it is to imagine realities beyond one's own perception.
On the eve of the new millennium (the year 2000), A Square is visited by a mysterious entity. At first, he sees it as a small, growing circle. This entity, a Sphere from Spaceland (a three-dimensional world), tries to explain the third dimension to A Square. The Sphere shows its nature by passing through A Square's house, appearing as a circle that changes size, then vanishing. A Square, initially confused and skeptical, struggles with the idea of 'upward, not Northward' and the Sphere's ability to see inside Flatland objects. The Sphere's patient explanations slowly change A Square's two-dimensional view.
Frustrated by A Square's inability to grasp the third dimension through words, the Sphere takes a direct approach. It lifts A Square out of Flatland and into Spaceland. From this new view, A Square sees Flatland spread below him, perceiving all house interiors and the true shapes of its inhabitants at once—something impossible from within Flatland. This experience is deeply disorienting yet revealing for A Square. He sees the Sphere's true form and begins to understand 'up' and 'down' in a new way, realizing the limits of his former perception.
After his experience in Spaceland, A Square returns to Flatland. He is convinced of the third dimension's existence and feels he must share this truth. He tries to explain his journey and Spaceland's reality to his brother, a fellow Square, but is met with disbelief and ridicule. His brother dismisses his accounts as dreams or madness, unable to imagine anything beyond their two-dimensional reality. This initial rejection foreshadows A Square's greater challenges in his mission to enlighten his world, reflecting his own earlier skepticism when the Sphere confronted him.
A Square, not discouraged by his brother's skepticism, decides to preach the 'Gospel of Three Dimensions' to the highest classes in Flatland: the Circles, who are the Priests and leaders. He believes their advanced intelligence and near-perfect shape might make them more open to new ideas. However, he finds them even more rigid in their adherence to Flatland doctrines. The Circles, proud of their circularity and intellect, feel threatened by the idea of a dimension beyond their own, as it would undermine their authority and worldview. They dismiss his claims as rebellion and heresy.
Because of his persistent 'subversive' preaching about the third dimension, A Square is arrested and imprisoned. The Council of Flatland, led by the Circles, sees his claims as a dangerous threat to social order. They declare his ideas seditious heresy, punishable by permanent confinement. A Square is confined to a cell, where he continues to ponder dimensions and his society's closed-mindedness. Despite imprisonment, his belief in Spaceland remains firm. His isolation shows society's resistance to new truths and the fate of those who challenge established beliefs, even with evidence.
Confined to his cell, A Square continues his intellectual journey. He reflects on his experiences and Spaceland's implications. He considers the possibility of even higher dimensions, a 'Fourth Dimension' or 'Thoughtland,' building on the Sphere's earlier hint that Spaceland might not be the ultimate reality. He imagines a being from this Fourth Dimension visiting Spaceland, just as the Sphere visited Flatland, and how such a being would be incomprehensible to the Sphere. Despite the futility of convincing his fellow Flatlanders, A Square finds comfort and intellectual stimulation in these advanced thoughts, maintaining hope for future understanding, even if it is beyond his world's grasp.
Years pass in A Square's imprisonment. He continues to write and reflect, regretting his mission's failure. He sees the irony: he, who once struggled to understand the third dimension, now cannot make his peers understand it. He feels like a prophet whose message is ignored, condemned by those he tries to enlighten. He understands that their two-dimensional existence stops them from imagining a 'height' that is not also a 'length' or 'breadth.' This deep frustration highlights the book's main theme: the difficulty of breaking free from ingrained perceptual and intellectual limits, and the resistance to truths that challenge basic assumptions.
The Protagonist
A Square transforms from a conventional Flatlander into an enlightened prophet, experiencing a higher dimension and striving to share its truth, ultimately facing persecution.
The Supporting
The Sphere serves as a catalyst for A Square's transformation, revealing the existence of a higher dimension and challenging the protagonist's worldview.
The Supporting
Remains unchanged, symbolizing the static nature of Flatland's limited understanding.
The Mentioned
Remains unchanged, serving as a symbolic representation of dimensional limitations.
The Antagonist
They remain entrenched in their two-dimensional worldview, acting as the primary antagonists to A Square's message.
The Supporting
Their societal role and perception remain static throughout the narrative, reflecting the rigid social structure of Flatland.
This theme explores how one's environment shapes perception and makes it hard to imagine realities beyond one's own. Flatlanders, including A Square, struggle greatly to grasp the third dimension, much like the King of Lineland cannot imagine a second. This is clear when A Square cannot tell 'up' from 'North' until the Sphere physically removes him from Flatland. The Circles' rejection of A Square's teachings shows how deep-seated perceptual limits can lead to rigid beliefs and the refusal of new truths, even with evidence.
“To talk of 'upward, not Northward,' was to us an absurdity, as if a man should talk of 'eastward, not Northward.'”
Flatland shows a strict social hierarchy based on the number of sides a shape has, with Circles at the top and Lines (women) at the bottom. This structure controls everything from housing to education and political power. The novel criticizes the unfairness and prejudice in such systems, especially regarding women, who are seen as dangerous and inferior due to their geometric form. The Circles' refusal to accept A Square's message is partly to maintain this order, as a higher dimension would challenge their supreme status and the basis of their societal beliefs.
“Our women are of the lowest order. Our Soldiers and lower classes of workmen are Triangles. Our Middle Class are Equilateral Triangles. Our Professional men and gentlemen are Squares and Pentagons. Our Nobility are Hexagons, Heptagons, and so on up to Dodecagons.”
The book shows humanity's (represented by Flatlanders) natural resistance to ideas that challenge strong beliefs or established ways of thinking. A Square's attempts to teach about the third dimension are met with ridicule, disbelief, and imprisonment. The Circles, especially, show this rigidity, clinging to their two-dimensional worldview because it supports their authority and understanding of the universe. Their fear of 'sedition' and 'heresy' reflects how powerful groups can suppress new knowledge to keep control, rather than accepting potentially transformative truths. This theme echoes historical conflicts between scientific discovery and religious dogma.
“I was called to a Council of the Chief Circles, and there heard my sentence pronounced: that I should be imprisoned for life, and every day receive a certain number of lashes.”
At its core, Flatland examines the philosophical implications of dimensions. It uses lower and higher dimensions as an allegory to make readers question their own understanding of reality. By showing how a third dimension is incomprehensible to a Flatlander, and a second dimension to a Linelander, the book implicitly asks if humans might also be limited in their perception of a 'Fourth Dimension' or beyond. The story challenges the idea that our perceived reality is the only or ultimate reality, encouraging an open mind toward the unknown aspects of existence.
“And now, you ask me, what of the Fourth Dimension? I answer, I do not know. I cannot even conceive it. I can only imagine that it must be even more wonderful than Spaceland.”
The entire narrative functions as an allegory for human society and scientific/philosophical thought.
Flatland is a profound allegory. The two-dimensional world serves as a metaphor for human society, with its rigid class structures, prejudices, and intellectual limitations. The struggle of A Square to comprehend and then communicate the third dimension allegorically represents the challenges faced by scientists, philosophers, or prophets who attempt to introduce revolutionary ideas that challenge established paradigms. The resistance of the Flatlanders to the Sphere's and A Square's teachings mirrors historical and ongoing societal resistance to new scientific discoveries or philosophical concepts, particularly those that undermine existing power structures or traditional beliefs.
A Square's dream of Lineland serves as a parallel and foreshadowing device.
A Square's dream of Lineland is a crucial plot device. It functions as a direct parallel to his later encounter with the Sphere and his own struggle to comprehend a higher dimension. By experiencing the frustration of trying to explain a second dimension to the King of Lineland, A Square gains an empathetic understanding of the Sphere's challenge. This dream foreshadows the incredulity and rejection A Square will face when he attempts to explain Spaceland to his fellow Flatlanders. It effectively primes the reader and the protagonist for the central conflict regarding dimensional understanding, highlighting the universal difficulty of transcending one's own perceptual limits.
The story is told from the limited perspective of A Square, emphasizing his personal journey and the subjective nature of reality.
The use of first-person narration by A Square is essential to the novel's themes. It grounds the fantastical concepts of dimensions in a relatable, individual experience. The reader experiences A Square's initial skepticism, his awe, and his subsequent frustration directly through his eyes. This perspective emphasizes the subjective nature of reality and how profoundly one's environment shapes understanding. It allows the reader to empathize with his struggle to grasp the third dimension and his subsequent isolation as a 'prophet' in his own world, making the philosophical ideas more accessible and emotionally impactful.
The portrayal of Flatland society subtly critiques Victorian social structures and prejudices.
Flatland functions as a subtle social satire, particularly of Victorian England's rigid class system and gender roles. The strict hierarchy based on the number of sides (from Lines to Circles) directly satirizes class distinctions, where birthright or perceived 'perfection' dictates status and power. The description of women as dangerous, intellectually inferior lines who must constantly cry out to avoid collision is a sharp critique of the patriarchal views and restrictive roles imposed on women during the period. The dogmatism of the Circles, who suppress new ideas to maintain their authority, also satirizes the resistance to scientific progress and social reform found in established institutions.
“I am, however, permitted to retrace my steps and to describe the more difficult and more eventful period of my life, which followed my escape from the Land of Three Dimensions.”
— The narrator, A. Square, reflects on his journey and the challenges after experiencing a higher dimension.
“We of Flatland, who have not the eyes of a Man, are yet not without our own mental vision.”
— A. Square explains the limitations and compensatory abilities of Flatlanders.
“Every human being, and therefore every Flatlander, is a creature of habit.”
— A general observation about the nature of beings, including those in Flatland.
“To be able to see a line, and to know that it is a line, and to measure its length, is to possess some of the elements of a higher knowledge.”
— A. Square ponders the concept of dimensions and how even a simple line can hint at more complex realities.
“The Sphere, I am told, is a being of such vast dimensions as to be almost beyond our comprehension.”
— A. Square recounts his initial understanding and awe of the Sphere from a Flatland perspective.
“Ignorance is bliss, they say; but for us, in Flatland, ignorance is the very breath of our being.”
— A. Square reflects on the societal acceptance of limited knowledge in Flatland.
“The principle of our nature is to be content with our limitations, and to seek no further.”
— Describing the general mindset and societal norm within Flatland.
“To talk of a Third Dimension seems to me little short of madness.”
— A. Square's initial incredulity when first introduced to the concept of a higher dimension.
“I will not waste time in describing the sensations of a being who has just discovered a new dimension.”
— A. Square, having experienced a higher dimension, chooses to focus on the implications rather than the immediate sensory overload.
“Prejudice is a two-edged sword; it cuts him who wields it and him against whom it is wielded.”
— A. Square reflects on the nature and impact of prejudice in society.
“To be brief, I was a Square, and had the good fortune to be a member of the professional class.”
— A. Square introduces himself and his social standing in Flatland.
“The Law of Nature in Flatland is that a straight line may be drawn from any one point to any other point.”
— Explaining a fundamental geometric principle that governs Flatland.
“The greater the number of sides, the more perfect is the individual.”
— Describing the social hierarchy in Flatland, where polygons with more sides are considered superior.
“I tried to explain to them the wonders of the Third Dimension, but they could not understand.”
— A. Square's frustration in trying to convey his newfound knowledge to the inhabitants of Flatland.
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Edwin Abbott Abbott was an English schoolmaster, theologian, and Anglican priest, best known as the author of the novella Flatland (1884).
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