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Picture cover: Flatland cover. You can purchase Flatland from Amazon US here: https://www.amazon.com/Flatland-Romance-Dimensions-Edwin-Abbott/dp/B0875SRH84

Flatland is a satirical novella by Edwin Abbott Abbott and was first published in 1884. This in itself is incredible given the thought process and analysis of one dimensional, two dimensional, three dimensional and even four-dimensional concepts and ideas in this book. Flatland is also classified as a science fiction book.

The protagonist and narrator of this story is A Square who lives in the fictional two-dimensional world of Flatland. All the inhabitants of Flatland are geometric figures (called Flatlanders). The women are line segments, and the men are polygons with various numbers of sides.

To fully appreciate Flatland, the reader must understand that the author lived in Britain during the Victorian era. This was a period of rapid change in British society due to industrialisation. It was also a time of intense social and cultural tensions and changes. Victorian society was strictly divided into the upper, middle, and working classes. These social distinctions were exacerbated by the progress and development taking place at the time (The story of the sinking of the Titanic is very informative about British and American social classes at the time). At the same time, the field of non-Euclidean geometry in mathematics was gaining a lot of interest from prominent mathematicians.

Overview of Flatland

Flatland is a two-dimensional world inhabited by Flatlanders who live in a highly structured society organised into strict classes based on the number of sides of the men. Irregularity is not tolerated as, to quote A Square: “irregularity is not only immoral but criminal.”

The women don’t count at all as they are merely straight lines and are not considered worthy of education. They are only considered at all for their reproductive purposes and role as homemakers but are described as being capable of destruction of their families if angered.

The societal attitude towards women in Victorian England is illustrated by this quote from John Ruskin, Sesame and Lilies, 1865:

The man’s power is active, progressive, defensive. He is eminently the doer, the creator, the discoverer, the defender. His intellect is for speculation, and invention; his energy for adventure war, and for conquest.. but the woman’s power is for rule, not for battle – and her intellect is not for invention or creation, but for sweet ordering, arrangement, and decision… she must be enduringly, incorruptibly good; instinctively, infallibly wise, wise not for self development, but for self-renunciation: wise, not that she may set herself above her husband, but that she may never fail from his side.’

This stereotypical attitude comes through strongly in Flatland with regards to women.

A Square writes his story from prison and details the social organisation of Flatland and the revelations he received about a three-dimensional land called Spaceland from the Sphere who visits A Square on the eve of the new millennium. The purpose of the Sphere’s visit is to find an apostle in Flatland who he can teach about the Third Dimension.

A Square does not understand the Sphere’s teachings which are uncomfortable and unbelievable to a two-dimensional shape who lives under the strict doctrine of social order dictated by the Circles, Flatland priests who make up the highest class. Even though A Square is a member of the caste of gentlemen and professionals, the concept of a three-dimensional world is outside his experience and contradictory to the laws and views of the Circles which makes his speculations with the Sphere heretical and punishable by imprisonment or even death. The Sphere responds to A Square’s rejection of his teachings by taking him to Spaceland to experience 3D for himself.

In advance of the visit from the Sphere, A Square has a dream where he visits a one-dimensional world, Lineland. Lineland is inhabited by men who consist of lines and women who are lustrous points. During the course of this dream, A Square has a conversation with the monarch of Lineland and attempts to convince him of the existence of his two-dimensional land of Flatland. He meets with the same resistance from the monarch that he exhibits to the Sphere when introduced to the idea of Spaceland. A Square has this dream-state experience under his belt when he visits Spaceland.

A Square is convinced about the existence of other dimensions, and he tries to convince the Sphere of the theoretical possibility of the existence of a fourth dimension and higher spatial dimensions. The Sphere is horrified by A Square’s ideas and returns him to Flatland in disgrace.

A Square has another dream during which the Sphere takes him to a zero-dimensional space called Pointland. The single occupant of Pointland, a Point, is its monarch and universe in one, and he perceives any communication as a thought originating from himself as he can’t conceive of any other forms of life.

This experience with the Point further opens A Square’s mind to the ignorance of the monarchs of both Pointland and Lineland and even the ruling Circles in Flatland. He is so inspired and excited by his newfound knowledge; he can’t help sharing his ideas despite such talk being against the law. A Square is ultimately imprisoned and decides to write the book, Flatland, as his memoir, in the hope that future generations might appreciate its content.

In addition to its mathematical concepts and ideas, the first half of Flatland is a social satire which examines the inflexibility of Victorian society through the fictional Flatland. In Flatland, society is rigidly divided into classes and freedoms are few for the working classes. Even the middle classes must live by the rules dished out by the upper classes. Anyone who goes against the rules and promotes any change is either killed or promoted to a higher class, depending on the situation. Promotion is a way of collaborating with any valuable intellect coming from the working class. Any deviant thinking or attempts at changed are considered dangerous and harmful.

This was a fascinating and insightful book and one I will definitely revisit.

Quotes from Flatland

“Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality, for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn this lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy.”

“Either this is madness or it is Hell.” “It is neither,” calmly replied the voice of the Sphere, “it is Knowledge; it is Three Dimensions: open your eye once again and try to look steadily.”

“All this very plausible reasoning does not convince me, as it has not convinced the wisest of our Statesmen, that our ancestors erred in laying it down as an axiom of policy that the toleration of Irregularity is incompatible with the safety of the State.”