Flatland: A Romance of Many Dimensions

The Square attempts to stop his brother from being imprisoned, but finds he cannot move without help from the Sphere. They then rise back up into Space and the Sphere shows the Square how solids are constructed and how they exist on a given plane. The Square sees these solids as monstrous Irregulars and says it is painful to look at them. The Sphere tells him he is not used to light, shade, and perspective, and will become accustomed to the existence of solid objects by improving his sense of feeling. The Square then asks the Sphere to explain the concepts of light, shade, and perspective, which the Sphere does, but the Square does not repeat his explanations and believes they will be tedious for Spaceland readers.

Once he understands solid objects, the Square feels radically enlightened and declares he wants to help any uprisings against the false Flatland notion that only two dimensions exist. He describes this as the climax of his personal history and foreshadows a dramatic “Fall” that will accompany his new knowledge (70). He begs the Sphere to let him look at his interior, but also says he can no longer describe the Sphere as an example of perfect beauty. When the Sphere indignantly asks why, the Square says that, based upon the Sphere’s own wisdom, many superior beings must exist in many higher dimensions. The Sphere scoffs at this and orders the Square to preach the gospel of three dimensions in Flatland and tells him he cannot reveal his interior. The Square asks to be taken into the fourth dimension, and when the Sphere says there is no such place, The Square uses analogies to argue that such a place must exist. The Sphere finally admits to hearing rumors of a fourth dimension but claims he knows nothing about them and, as they are probably figments of people’s imaginations, their existence cannot be logically defended. Increasingly agitated, the Square exclaims that this place might be called Thoughtland, expressing a strong desire to go there and to keep rising through all possible dimensions.

Frustrated, the Sphere attempts to cut off the Square in the middle of his ecstatic rant, but he cannot. Finally, he simply sends the Square crashing unceremoniously back down into Flatland.

The Square knows by instinct that he must keep his journey to Flatland a secret from his wife, so he invents a story about falling into the cellar. While she is doubtful about this, she does not press him. Before he drifts off to sleep in his study, he tries to draw a mental picture of a cube the Sphere had shown him, but his memory is already fading. He adopts “Upward, yet not Northward” as a mantra to remind him of Spaceland.

The Square dreams that the Sphere takes him to a place called Pointland, the lowest level of existence, “the Abyss of No dimensions” (75). Each being there is simply a point who cannot see beyond himself: he is his own world and has no awareness of concepts like length, breadth, or height. The Square notices that a Point with whom they speak refers to himself in the third person as “it” (76). The Sphere emphasizes how obliviously happy and complacent the tiny, buzzing points are and that they refuse to listen when the Square tries to describe for them the true nature of the universe.

As the two fly back to Flatland, the Sphere says he is no longer angry at the Square for aspiring to soar to higher dimensions. He then reveals to the Square even more mysteries, including things like “Extra-Solids” and “Double Extra-Solids” (77).

The Square awakes joyfully from this dream, determined to share the gospel of three dimensions as far and wide as possible, beginning with his wife. But before he can do so, he hears a herald outside announcing the recent council resolution that will imprison and possibly execute anyone claiming to have received revelations. He decides to omit the fact that he learned these truths from an otherworldly being and instead to simply use scientific practice to demonstrate the existence of three dimensions. He decides not to start with his wife or his sons and instead to share these facts with his brilliant hexagonal grandson. After persuading his wife to return to her household duties and forget about the stranger who had appeared in their home, he sits down with his grandson and uses tablets to illustrate a cube. The boy soon starts crying and says he never meant to suggest that three-dimensional objects might exist; he is now afraid of being imprisoned or executed under the new law. Even after the Square comforts him and insists that three-dimensional objects do exist, the boy refuses to believe him, thinking the entire incident is a joke at his expense.

Discouraged by his failure to convince his grandson, the Square decides he needs to convince the public instead. He spends several months writing a treatise on the “mysteries” of three dimensions; he is careful to speak only in theoretical terms and never claims that an actual third dimension physically exists (79). He is unable to reproduce the diagrams that the Sphere showed to him in Spaceland, as all drawings in Flatland consist only of straight lines. He titles the treatise “Through Flatland to Thoughtland” but is unhappy with the result.

The Square finds that he can no longer enjoy his everyday life now that he is aware of the true structure of the universe; he neglects his professional life, his friends, and his family, obsessed with facts that only he knows. He finds it increasingly difficult to remember the things he witnessed in Spaceland. About eleven months after the Sphere visited him, he tries to envision a cube and realizes he cannot. Meanwhile, he puts himself in greater political danger, unable to prevent himself from having seditious public outbursts about the third dimension. Finally, at a gathering of the Local Speculative Society, he gives an account of his voyage to Spaceland and describes in detail everything he saw there. He is immediately arrested and taken before the Council.

The Council allows him to tell the entire story without interruption, but the Square knows the fate that awaits him. The President demands that he explain clearly what he means by “Upward, not Northward” and orders him to draw a diagram of a cube, but the limitations of Flatland prevent him from doing this. The Square declares that he knows the truth and can say nothing more. The Council imprisons him for life, allowing him to live in some degree of comfort and to receive visits from his brother, who is still in prison.

The Square reveals that seven years have passed since these events. He is grateful to have a good relationship with his brother, who he admires deeply, but he is frustrated that his brother does not believe his story about Spaceland and denies the existence of a third dimension. He says that the Sphere’s revelations were made to him for nothing: because he will never have any Flatland converts, he will never be able to improve life for his countrymen in any meaningful way. He also expresses some level of regret about the entire incident. However, he hopes that his memoirs will perhaps reach humans in some other dimension and may “stir up a race of rebels” who refuse to be “confined to limited Dimensionality” (82). He ends the narrative by admitting that he experiences moments of mental weakness in which even Flatland with all its demonstrable realities seems like a fictional place.