Flatland: Synopsis

"Flatland: A Romance of Many Dimensions", by a Square (pseudonym for Edwin A. Abbott) is not a romance in the modern sense of the word. There are no torn bodices, nor longing looks. The book was written at the tail end of the Romantic Period in Europe. It is rather a fanciful view of what a universe might look like should it contain only two dimensions. The book is "illustrated" with two dimensional drawings by the author himself.

The story of flatland begins with a description of the world in two dimensions. People in this world have no concept of depth, only length and width. Nevertheless the world appears to be vertical because the rain simply falls from north to south, so that the houses, made in the shape of a pentagon, serve to keep the inhabitants dry. Fog is fairly common in this world and is one of the means of distinguishing the various inhabitants.

In Flatland, the men are all polygons, and the women are lines. The fewer equal sides a person contains, the lower the class in society. Isosceles triangles are the lowest order and form the working class and the soldiers. Equilateral triangles, because they are more regular form the merchant class. Squares are lawyers (as is the proclaimed author of this work - A Square). Pentagons are doctors and progressive numbers of sides, up to virtual circles, move up higher in leadership and governance. The circles form a sort of nobility. The more sides there happen to be, the more intelligent and educated they are supposed to be.

Women are among the most dangerous beings in Flatland, as their shape can easily pierce most any polygon. However, in the view of Flatlanders, they do lack intelligence and are mainly ruled by their feelings. Females are controlled by their husbands, but because of their supposed lack of intelligence will occasionally go berserk, killing all about them and twenty-minutes later not even realizing what they have done. Women have a separate entrance into homes and are forced to make certain noises and to move in a certain fashion (continuously moving their backside) in order to indicate their presence (because end-on they appear to be just a point, which is very difficult to see).

Recognition of the degree of a polygon in Flatland is an art-form and one of the major things taught in schools. Recognition is by sound (as in the forced peace-cry of the women), by feeling the point of a polygon, or noting the different hues of a polygon as it approaches. Although there are no true circles among the polygons, with the high number of sides, they approach circular-ness, and are called circles as a complement and in recognition of their power. It should be noted that the more sides a polygon attains, the more physically vulnerable he becomes. However, the society, the customs of Flatland, as well as the status and intelligence of circles serve to protect them from attacks from the lower classes.

Deformed or irregular figures are immediately destroyed when found out. Nevertheless, some are found among the criminal class. Advancement is possible within flatland society, but only in a generational manner. Typically, the son of an isosceles will be equilateral, the son of an equilateral will be a square, whose son is most often a pentagon, and so forth adding a side every generation.

At one point in the history of Flatland, painting was discovered. It had the unfortunate consequence of upsetting the social order because it allowed every polygon or triangle to look like another. In this way the various stratifications of society were erased. The rule of the "circles" seemed to be coming to the end. But a reaction occurred and the use of colors and paints was outlawed. The social structure was ratcheted back to its previous state.

The lower orders in Flatland are treated rather callously. They can be summarily executed for knowing things they should not. Some obtuse people are used in schools, tied into place merely for the purpose of teaching young polygons about angles.

The Square, the narrator, has a vision of yet another land, which he calls Lineland. It is the land of one dimension where the king lives on a line, controlling his people by sound. The women are dots and the children are short line segments. When Square attempts to make a second dimension known to him, the king of Lineland is uncomprehending and reacts violently. Square then goes to Pointland where there are no dimensions. When he attempts to converse with the king, who is the only being in Pointland, he finds the king to be completely self-centered. This being of Pointland does not even acknowledge that the square can possibly exist.

When the year 2000 comes about, Square is visited by a sphere which tries to explain the fact that there are actually three dimensions. Square reacts as violently to this news as the king of Lineland did to the idea of two dimensions. The result of a tussle causes Square to be lifted into Spaceland (the land of three dimensions). He sees for himself that there is depth. The sphere exhorts him to spread the "gospel of the three dimensions". Square realizes that if there is a land of one dimension, a land of two dimensions, and a land of three dimensions, there must be an infinite number of lands in an infinite number of dimensions. When he tells the sphere of his realization, the sphere is perplexed. He can only conceive of three dimensions.

Square is returned to his own world and encouraged to preach the new gospel. However, the government is prepared for him as every thousand years there is a visitation by the sphere. At a general meeting of the representatives of the states of Flatland the sphere appears. His amazing appearance is called a mere trick and all of the witnesses who are not higher level polygons are either imprisoned or destroyed. When Square attempts to spread the "gospel of the three dimensions", he is arrested for telling the truth the way he sees it. He is imprisoned along with his brother, who had been a clerk present at the appearance of the sphere at the meeting of the states.

As the story closes, the two brothers have been imprisoned for seven years. They are allowed to communicate once per week. When square attempts to convince his brother of the third dimension, the brother is unbelieving as he had only seen two dimensions of the sphere. Square sets down his account of his experiences and hopes that someday it will convince someone of his belief in the many dimensions.

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