Flatland: A Romance Of Many Dimensions Summary

Edwin Abbott Abbott

Flatland: A Romance Of Many Dimensions

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Flatland: A Romance Of Many Dimensions Summary

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Flatland: A Romance of Many Dimensions is a literary hybrid. It is a math- and science-based novella that creates a fictional land while at the same time satirizing Victorian culture and introducing theories of space’s multi-dimensional nature. Flatland is a two-dimensional world chronicling the adventures of A. Square (a pseudonym originally given as the author of the book), a mathematician who lives there. Women are straight lines and are considered the lowest of shapes. Men are polygons and the number of sides they have is dependent on their ranking in the social hierarchy. Odd and unexpected incidents bring A. Square together with numerous other geometric shapes. Some of the places he ventures into are Spaceland, which has three dimensions, Lineland, which is one-dimensional, and Pointland, which does not have any dimensions. A. Square also imagines a land with four dimensions, which is considered a subversive concept. The actual author of the 1884 book is Edwin Abbott Abbott, an English schoolteacher.

The narrator, A. Square, is a member of the professional caste in society and begins the story leading his life in a two-dimensional world. That women are but simple line-segments and men are polygons with many sides gives the book a symbolic and metaphoric slant right from the start. It is New Year’s Eve and Square dreams of visiting Lineland, a one-dimensional world where “lustrous points” live. In the dream, he imagines killing the monarch ruling the realm but is unsuccessful. The monarch in turn tries to kill Square rather than put up with him. After this, Square receives a visitor.

A three-dimensional sphere, named appropriately, A. Sphere, appears to Square. Square does not know what to make of this until he sees the three-dimensional Spaceland firsthand. It turns out that Sphere appears in Flatland at the beginning of each millennium and teaches a new follower about the concept of a third dimension hoping to one day educate everyone in Flatland. From Spaceland, they can see the leaders of Flatland as they talk of knowing there is a third dimension and threating anyone who spreads word of its existence. Many witnesses to this announcement are killed or put in prison including B, who is the brother of Square.

At this point in the narrative, Square has become open to the idea of additional dimensions. He attempts to persuade Sphere that there could be fourth and fifth dimensions and even beyond. Sphere does not pursue this line of discussion and returns Square to Flatland. Square has another dream. In this one, Sphere appears to him again, this time taking him to Pointland where the point is the only resident and is the universe and the monarch. Any communication that takes place, Point believes, is from his own mind, implying that he lacks the ability to imagine anyone but himself. Sphere tells Square that there is nothing to be done to save Point from his omniscient view of himself.

Square comes to realize the ignorance of the Pointland and Lineland monarchs. He acknowledges his own ignorance he had to overcome with respect to the existence of higher dimensions. He is, however, not able to try to convince anyone in Flatland that Spaceland does in fact exist because of the rules that were passed prohibiting any talk of other dimensions. Eventually, he is imprisoned like his brother before him. He sees his brother from time to time, having been placed in the same prison, although in spite of all they have both experienced, he cannot convince even his brother of other dimensions. Square then writes a book, Flatland, as a memoir, hoping it will preserve the ideas he wants to spread, and that it will serve to help future generations see beyond the limits of a two-dimensional world.

Within Flatland, the society is strictly separated into classes. There are harsh rules, strict control of rights and privileges, and the extermination of lower class members as deemed necessary. The book takes on a level of social satire symbolically representing the Victorian view of the role of women in society and the hierarchy in which men are classified. In dealing with such concepts, particularly the view of women he presents, Abbott has been accused of being a misogynist, but others have countered, saying that Square is used as an historical narrative voice that sheds light on the history of women that had previously been largely ignored in historical writings. The book also goes beyond the mathematical concepts it contains, and addresses the more universal need to overcome fear of new ideas and be more open minded. While other Victorian literature may be turned to more frequently as “classic” examples of time and genre, Flatland remains intellectually challenging given that it prompts an examination of the elements of society without needing to adhere to a firm delineation between fact and fiction.