Edwin Abbott Abbott (1838 –1926)
E. A. Abbott was educated at the City of London School and at St John’s College, Cambridge, where he took the highest honours in classics, mathematics and theology, and became a fellow of his college. In 1862 he took orders. Abbott succeeded G. F. Mortimer as headmaster of the City of London School in 1865 at the early age of twenty-six and tutored the education of future Prime Minister H. H. Asquith. He was Hulsean lecturer in 1876. He retired in 1889, and devoted himself to literary and theological pursuits.
Shakespearian Grammar (1870) is a permanent contribution to English philology.
Life of Francis Bacon (1885)
Three anonymously published religious romances – Philochristus (1878), where he tried to raise interest in Gospels reading, Onesimus (1882), and Silanus the Christian (1908).
Theological discussions (anonymous) : The Kernel and the Husk (1886), Philomythus (1891), The Anglican Career of Cardinal Newman (1892), and the article “The Gospels” in the ninth edition of the Encyclopædia Britannica, embodying a critical view which caused considerable stir in the English theological world. He also wrote St Thomas of Canterbury, his Death and Miracles (1898), Johannine Vocabulary (1905), Johannine Grammar (1906).
Abbott also wrote educational text books, one being “Via Latina: First Latin Book” which was published in 1898 and distributed around the world within the education system.
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.
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, like all characters in the novella) 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 Sphere
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 with a Circle 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 evinces accounts of cases where women have accidentally or deliberately stabbed men to death, as evidence of 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, practised by the lower classes and women, determines the configuration of a person by feeling one of their angles. The “Art of Sight Recognition,” practised 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. Colour 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, 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) with only two congruent sides. The smallest angle of an isosceles triangle gains thirty arc minutes (half a degree) each generation. Additionally, the rule does not seem to apply to many-sided polygons. For example, 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 chapter seven of the book when 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” (in the book), as inevitable additional deformities, a sentiment with which the Square concurs. 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. An irregular polygon is not destroyed at birth, but allowed to develop to see if the irregularity could be “cured” or reduced. If the deformity could not be corrected then the irregular should be “painlessly and mercifully consumed.”
Flatland as a social satire
In Flatland Abbott describes a society rigidly divided into 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 and the 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 organisation 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 such critics by stating that the 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. Proof of that can be considered the fact that in the entry on Edwin Abbott Abbott in the Dictionary of National Biography, Flatland is not even mentioned.
The book was discovered again after Albert Einstein’s general theory of relativity was published, which introduced the concept of a fourth dimension. Flatland was mentioned in a letter entitled “Euclid, Newton and Einstein” published in Nature on February 12, 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. —from a “Letter to the Editor” by William Garnett. in Nature on February 12, 1920.
Flatland (2007) animation film directed by Dano Johnson, Jeffrey Travis