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In a two-dimensional world called Flatland populated by living squares, triangles, circles and other two-dimensional shapes, it is three days until the celebration of the year 3000. A Square, attorney at law, struggles to instruct his grandson, A Hexagon, in the art of sight recognition. The lesson is interrupted by A Square's brother B, a clerk to President Circle, warning A to stay home during a meeting at the Senate of the Great Southern Republic of Flatland.
The Senate session has been called to discuss the increasing hostilities between the government and the Chromatist movement, led by Senator Chromatistes, an irregular dodecagon. The movement seeks legalization of the right of Flatlanders to color their sides as they see fit. Traditionally taboo, laws against it had been relaxed; this emboldened the Chromatists to demand legalization. The Great Southern Republic distinguishes itself from its enemy, the Northern Kingdom, by its stances on Chromatism and Irregulars along with a democratic government. Relaxing the laws has already been perceived as weakness by the Northern Kingdom who are massing on the borders.
Against his brotherâs warning, A Square meets his new client, the first female charged as a Chromatist; on his way home he is caught in the melee leaving the Senate. President Circleâs soldiers killed Senator Chromatistes and his supporters, sparking a riot across the city. A Square just gets home safely, then barricades his family against the chaos for the night.
Once asleep, A Square dreams of visiting a one-dimensional world, Lineland, and attempts to convince the realm's ignorant king of a second dimension, but fails to make him see outside of his eternally straight line. A Square awakens to learn that the deadly riots originated in the Senate meeting that B Square was attending. A visit to B Squareâs home confirms that he is missing. A Square scours the city, now under martial law, seeking B Square. At the marketplace, he meets a merchant selling a fascinating "glow point", and buys one for A Hexagon, who has been sulking since being disciplined for coloring one of his sides purple.
The family prepares for another anxious night, only to be terrified by the sudden appearance of A Sphere, CEO of Messiah, Inc. A Sphere declares that A Square is his apostle of the Three Dimensions and privately begins to explain things to him. A Square refuses to entertain the notion of three dimensions, resorting to violence with A Sphere. A Sphere decides the only way to convince A Square of the three dimensions is to show him.
Suddenly and painfully, A Square is plucked out of his dimension and into Spaceland. After the initial shock, the reality of 3 dimensions becomes clear to A Square, along with the possibility of locating his brother from his newfound vantage point. Having business himself at the Great Hall, A Sphere brings A Square to look for his brother there. On their arrival, A Sphere expounds upon three dimensions to President Circle and the Priests who anticipated this event. After rejecting A Sphereâs message and attempting to kill him, the Flatland leaders execute all who have witnessed the event, except B Square, who is imprisoned for life on pain of death in exchange for his silence while his brother watches from high above Flatland.
Realizing that time in Spaceland is short, at least for A Square, A Sphere brings him to Messiah, Inc. to finish his education on the gospel of Three Dimensions. Enthralled by the complex world of Spaceland, A Square posits further about 4 dimensions and so forth to A Sphere who dismisses it as nonsense. Meanwhile, A Squareâs intrusion into Spaceland has become a national emergency, which prompts the Spaceland Senate to call to him to appear for a hearing, to explain this breach of protocol of bringing a Flatlander into their midst. They claim it will be viewed as an act of, and provocation for, war by their enemies, the X-Axis.
During the hearing, A Square also learns that the X-Axis considers the Great Senate as weak because they have allowed the continued existence of his own world, Flatland, which they view as an abomination. As the debate rages, an ailing A Square tries to explain his theory of multiple dimensions to an unsympathetic crowd. Air-raid sirens wail as A Square collapses from the overwhelming effects of gravity on his two-dimensional body and chaos ensues.
A Sphere manages to send his dying apostle back on his way to Flatland via a mailing tube before bombs destroy both Messiah, Inc. and A Sphere himself, but A Squareâs journey back is halted by A Sphere's hovercraft, who attempts to crush A Square to avenge A Sphere's death. But, an X-Axis ship crashes into and destroys the hovercraft, and A Square ends up plunging in freefall toward Flatland and through its surface into unknown regions below, where he experiences a revelation on dimensionality and infinity.
A Square finds himself in his own bed on the eve of the year 3000 and his family informs him that the government has issued orders for the arrest of anyone proclaiming the gospel of three dimensions. Undeterred, A Square hurries to see his brother in Flatland jail to discuss their new shared knowledge of the third dimension. B Square, afraid of execution, denies the experience and in a panic assaults his brother who falls temporarily into an unconscious state where he encounters A HyperSphere along with the Monarch of Pointland who curiously resembles a âglow point.â As the Monarch drones on in his monologue of âbeing the all in all, the one in the one,â A HyperSphere informs his former apostle that time is short and A Square must proclaim the gospel of the three dimensions to his fellow Flatlanders although they, like the Monarch, will probably remain trapped within their own perspectives.
Returning to himself, A Square escapes Flatland prison and outruns the guards. Arriving home, A Square informs his wife that they are going to defect to the Northern Kingdom where he might be able to spread the gospel of three dimensions to a more open minded populace. The soldiers arrive and A Square escapes with the help of Frau A Squareâs âwar cryâ that temporarily stuns them. Before he can reach the border, A Square is cornered by the soldiers whose attempt to dismantle and segment him is thwarted by the Northern Kingdom armyâs attack. In the fracas, things suddenly begin to disappear as though sucked down through the fabric of Flatland until only A Square remains. He too begins to disappear until there is only his eye, then a point of light, a glowing point of light, which welcomes him into another dimension.
Who brings the Square to Messiah, Inc.?
A Sphere