Flatland: A Romance of Many Dimensions

The Sphere is the Square’s guide to Spaceland, and later in the novel, the figure who represents divinity, holiness, and revelation for the Square. The Sphere appears in the Square’s house suddenly, immediately following a tense moment in which the Square scolds his grandson for arguing that three dimensional objects can theoretically exist. The timing of this occasion implies that the Sphere was somehow summoned to Flatland because of the Square’s grandson’s claim. This also happens on the last day of the 1999th year in Flatland, an event which, according to President, has historical precedents: The Flatland archives, he says, indicate that other otherworldly visitors have arrived on the last two millennial commencements. Thus, the Sphere’s presence in Flatland is part of a longer tradition of third-dimensional revelation.

The text frequently emphasizes the Sphere’s physical beauty and grace. When he initially appears in the Square’s home, the Square is so stunned by the visitor’s perfection that he is rendered motionless: “Without the slightest symptoms of angularity he nevertheless varied every instant with gradations of size and brightness scarcely possible for any Figure within the scope of my existence” (55). When the Square feels the Sphere for the first time, he realizes that “[there] was not the trace of an angle, not the slightest roughness or inequality: never in [his] life had [he] met a more perfect Circle” (55). Later in their relationship, when the Square claims he can no longer consider the Sphere an example of ideal beauty, the Sphere is offended: This suggests he is accustomed to praise for his angleless perfection, at least while in Flatland, and might have become a little vain because of it. While the Sphere is generally patient with the Square and is enthusiastic about showing him the true nature of the universe, he becomes angry when the Square will not stop ranting about the possibility of infinite dimensions and eventually throws him out of Spaceland violently. When he returns, it is in one of the Square’s dreams; he claims to have “fresh insight” into the secrets of the universe and says he is not too proud to admit having made a mistake (77). This humbler version of the Sphere then generously shares facts about extra-dimensional objects with the Square. However, the actual Sphere does not return to the narrative and instead remains a figure whom the Square considers a philosophical guide and quasi-divine teacher.

The novel offers little detail about the Square’s wife outside the context of their marriage, which is fitting, given that in the world of Flatland, women are socially and interpersonally devalued. However, she and the Square have a relatively loving and peaceful relationship and intentionally set aside leisure time for each other; for example, immediately prior to the Sphere’s arrival, they are sitting together and “musing on the events of the past and the prospects of the coming year, the coming century, the coming Millennium” (52). The Square’s wife is dedicated to and fiercely protective of her home, although she is not always capable of handling unexpected events. The Square describes his wife as having “the usual hastiness and unreasoning jealousy of her Sex” and adds that she does not have his worldly experience, all of which leads her to believe the Sphere is another woman intruding upon their household (54). When the Square insists that the Sphere is not a woman, his wife retorts, “Oh, I have no patience with your Sight Recognition” and goes on to quote some proverbs commonly used by women in Flatland (54). However, once she feels the Sphere and realizes it is not a woman, she retreats, apologizing with great embarrassment, to her own apartments.

After his visit to Spaceland, the Square says that he feels, “by a kind of instinct,” that he must keep the experience a secret from his wife (74). He does so by telling her that he had fallen through the trapdoor of the cellar and knocked himself unconscious. But although his wife’s “good sense far exceeds those of the average of her Sex” and she can see that he is unusually agitated, she does not argue with his description of events (75). When he begins his attempt to spread the Gospel of Three Dimensions, he chooses not to start with his wife, and instead persuades her to return to her household duties and not ask any questions. The novel implies that his wife did not go to prison with him, which means that his attempts to protect her were successful; however, we can also assume that she does not appear to visit him there. Rather, she simply disappears from the narrative, presumably remaining—whether by choice or not—in her small domestic world.

The Square meets this figure during his dream visit to Lineland, and importantly, he does not immediately recognize him as a king. Upon seeing a small straight line, he believes it is a woman, as it resembles women in Flatland; however, the figure declares “‘I am no Woman’ [...] ‘I am the Monarch of the world’” (43). The King of Lineland is depicted as pompous, self-centered, and extremely suspicious of his visitor and the new information the Square is attempting to share. He maintains that his vision of the universe is absolutely accurate, a position for which the Square feels some pity: “It seemed that this poor ignorant Monarch—as he called himself—was persuaded that the Straight Line which he called his Kingdom, and in which he passed his existence, constituted the whole of the world” (44). He refuses to accept the possibility that Flatland—or any other dimensions—could exist as he is unable to see them himself. He does not even accept at first that The Square is present and believes instead that the voice he hears is coming from inside his own body.

The King ardently defends the social structure and practices of Lineland, particularly the way marriages are formed and children are born. Of his own family, he says without hesitation that his wives and children “are well and happy” (45). When the Square questions the effectiveness of the “choral dance” that introduces mates to one another, the King scoffs at him, calling his questions “absurd” and “ignorant,” and when the Square attempts to explain the difference between space and length, the King calls him a fool (46, 48). When the Square finally becomes frustrated with him and calls him “the most imperfect and imbecile,” the King reacts violently, advancing towards the Square with “a menacing cry,” although the Square wakes up before any damage can be done (51). Ultimately, the King of Lineland embodies a toxic kind of skepticism that runs throughout Flatland: the kind of skepticism that prevents people from accepting data that conflicts with their preconceived notions of reality.