Flatland

flatland

Flatland: A Romance of Many Dimensions’ is an 1884 satirical novella by the English schoolmaster Edwin Abbott Abbott. Writing pseudonymously as ‘A Square,’ Abbott used the fictional two-dimensional world of Flatland to offer pointed observations on the social hierarchy of Victorian culture.

However, the novella’s more enduring contribution is its examination of dimensions, for which the novella is still popular amongst mathematics, physics, and computer science students.

The story is about a two-dimensional world referred to as Flatland which is occupied by geometric figures. Women are simple line-segments, while men are regular polygons with various numbers of sides. The narrator is a humble square, a member of the social caste of gentlemen and professionals in a society of geometric figures, who guides us through some of the implications of life in two dimensions. The square has a dream about a visit to a one-dimensional world (Lineland) which is inhabited by ‘lustrous points.’

He attempts to convince the realm’s ignorant monarch of a second dimension but finds that it is essentially impossible to make him see outside of his eternally straight line. He is then visited by a three-dimensional sphere, which he cannot comprehend until he sees Spaceland for himself. This sphere, who remains nameless, visits Flatland at the turn of each millennium to introduce a new apostle to the idea of a third dimension in the hopes of eventually educating the population of Flatland of the existence of Spaceland.

From the safety of Spaceland, they are able to observe the leaders of Flatland secretly acknowledging the existence of the sphere and prescribing the silencing of anyone found preaching the truth of Spaceland and the third dimension. After this proclamation is made, many witnesses are massacred or imprisoned (according to caste).

After the Square’s mind is opened to new dimensions, he tries to convince the Sphere of the theoretical possibility of the existence of a fourth (and fifth, and sixth …) spatial dimension. Offended by this presumption and incapable of comprehending other dimensions, the Sphere returns his student to Flatland in disgrace.

The Square then has a dream in which the Sphere visits him again, this time to introduce him to Pointland. The point (sole inhabitant, monarch, and universe in one) perceives any attempt at communicating with him as simply being a thought originating in his own mind (cf. Solipsism): ”You see,’ said my Teacher, ‘how little your words have done. So far as the Monarch understand them at all, he accepts them as his own – for he cannot conceive of any other except himself – and plumes himself upon the variety of Its Thought as an instance of creative Power. Let us leave this God of Pointland to the ignorant fruition of his omnipresence and omniscience: nothing that you or I can do can rescue him from his self-satisfaction.’

The Square recognizes the connection between the ignorance of the monarchs of Pointland and Lineland with his own (and the Sphere’s) previous ignorance of the existence of other, higher dimensions. Once returned to Flatland, the Square finds it difficult to convince anyone of Spaceland’s existence, especially after official decrees are announced – anyone preaching the lies of three dimensions will be imprisoned (or executed, depending on caste). Eventually the Square himself is imprisoned for just this reason, where he spends the rest of his days attempting to explain the third dimension to his brother.

Men are portrayed as polygons whose social status is determined by their regularity and the number of their sides; a Circle is considered to be the ‘perfect’ shape. On the other hand, females consist only of lines and are required by law to sound a ‘peace-cry’ as they walk, because when a line is coming towards an observer in a 2-D world, her body appears merely as a point. The Square talks of accounts where men have been stabbed to death (both accidentally and on purpose) by women. This explains the need for separate doors for women and men in buildings.

In the world of Flatland, classes are distinguished using the ‘Art of Hearing,’ the ‘Art of Feeling’ and the ‘Art of Sight Recognition.’ Classes can be distinguished by the sound of one’s voice, but the lower classes have more developed vocal organs, enabling them to feign the voice of a polygon or even a circle. Feeling, practiced by the lower classes and women, determines the configuration of a person by feeling one of their angles. The ‘Art of Sight Recognition,’ practiced by the upper classes, is aided by ‘Fog,’ which allows an observer to determine the depth of an object. With this, polygons with sharp angles relative to the observer will fade out more rapidly than polygons with more gradual angles. Color of any kind was banned in Flatland after Isosceles workers painted themselves to impersonate noble Polygons. The Square describes these events and the ensuing war of reaction at length.

The population of Flatland can ‘evolve’ through the ‘Law of Nature,’ which states: ‘a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility. Thus the son of a Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on.’

This rule is not the case when dealing with isosceles triangles (Soldiers and Workmen). The smallest angle of an isosceles triangle gains thirty arcminutes (half a degree) each generation. Additionally, the rule does not seem to apply to many-sided polygons; the sons of several hundred-sided polygons will often develop fifty or more sides more than their parents.

An equilateral Triangle is a member of the craftsman class. Squares and Pentagons are the ‘gentlemen’ class, as doctors, lawyers, and other professions. Hexagons are the lowest rank of nobility, all the way up to (near) circles, who make up the priest class. The higher-order polygons have much less of a chance of producing sons, preventing Flatland from being overcrowded with noblemen.

Regular polygons were considered in isolation until the issue of irregularity, or physical deformity, became considered. In a two dimensional world a regular polygon can be identified by a single angle and/or vertex. In order to maintain social cohesion, irregularity is to be abhorred, with moral irregularity and criminality cited, ‘by some,’ as inevitable additional deformities, a sentiment concurred by the author, a Square. If the error of deviation is above a stated amount, the irregular polygon faces euthanasia; if below, he becomes the lowest rank of civil servant. In this study of what was to later to become known as eugenics, an irregular polygon should not be destroyed at birth, but rather allowed to develop in order to see if its irregularity could be ‘cured’ or reduced to within society’s level of tolerance. If the deformity could not be corrected then the irregular should be ‘painlessly and mercifully consumed.’

In Flatland Abbott describes a society rigidly divided in classes. Social ascent is the main aspiration of its inhabitants, apparently granted to everyone but in reality strictly controlled by the few that are already positioned at the top of the hierarchy. Freedom is despised, laws are cruel. Innovators are either imprisoned or suppressed, members of lower classes who are intellectually valuable and potential leaders of riots are either killed or corrupted by being promoted to the upper classes. The organization and government of ‘Flatland’ is so self-satisfied and perfect that every attempt or change is considered dangerous and harmful. This world, as ours, is not prepared to receive ‘Revelations from another world.’

The satirical part is mainly concentrated in the first part of the book, ‘This World,’ which describes Flatland. The main points of interest are the Victorian concept on women’s roles in the society and in the class-based hierarchy of men.

Abbott has been accused of misogyny due to his portrait of women in ‘Flatland.’ In his ‘Preface to the Second and Revised Edition,’ 1884, he answers to such critics by stating that A Square: ‘was writing as a Historian, he has identified himself (perhaps too closely) with the views generally adopted by Flatland and (as he has been informed) even by Spaceland, Historians; in whose pages (until very recent times) the destinies of Women and of the masses of mankind have seldom been deemed worthy of mention and never of careful consideration.’

Although ‘Flatland’ was not ignored when it was published, it did not obtain a great success. The book was discovered again after Einstein’s General theory of Relativity, which introduced the concept of a fourth dimension. ‘Flatland’ was mentioned in a letter entitled ‘Euclid, Newton and Einstein’ published in ‘Nature’ in 1920. In this letter Abbott is depicted, in a sense, as a prophet due to his intuition of the importance of time to explain certain phenomena: ‘Some thirty or more years ago a little jeu d’esprit was written by Dr. Edwin Abbott entitled ‘Flatland.’ At the time of its publication it did not attract as much attention as it deserved… If there is motion of our three-dimensional space relative to the fourth dimension, all the changes we experience and assign to the flow of time will be due simply to this movement, the whole of the future as well as the past always existing in the fourth dimension.’

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2 Responses to “Flatland”

  1. If the Pentagon above was the “Pentagon”, then the bottom right-hand corner would be my home.

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