Analysis of Flatland

The first half of Flatland reads more like a travelogue than a novelette. Yet its in-depth description is necessary for the reader to understand the amazing two dimensional world created by Edwin A. Abbott. The world is composed of a rigid social structure, which was a satire of the world of Abbott's day (1880s). In the flat world there can only be two dimensional people. These are polygons, which are males, or lines which are females. The social level of each figure is defined by the number of regular sides he possesses. Isosceles triangles are on the lowest rung. They do all of the physical work and comprise the military. They are looked down upon by the higher orders, which are comprised of equilateral triangles, squares, pentagons, etc. No man can hope to advance beyond his station. However, the next generation normally gains at least a side. So a square's son would normally be a pentagon. In the Britain of this period there were indeed social levels or castes, perhaps not as pronounced as in India. Nevertheless, the opportunity for the advancement of the family made men ambitious to get ahead and the progression from proletarian to tradesman to professional to nobility over the course of a few generations was fairly common.

It is interesting to note that Abbot chose to use the pseudonym, "a Square". The story is written in the first-person and this gives it a feeling of immediacy. We feel as though we are getting the description directly from a participant. This man, this narrator, is not of either the lowest or the highest class so he is able to see his world from all perspectives. At the same time, he is so much in the midst of it that he, only with difficulty, can see the whole of it.

Modern sensibility is highly attuned to political correctness. For this reason the description of women, almost off-handedly callous, is quite jarring. Nevertheless, a discerning reader will see that Abbott does this on purpose. As the Square he treats even his own wife disdainfully. Like all women in Flatland, she is merely a line, a one-dimensional being. He believes that she runs totally on emotion. She is kept in her place by the laws of the land which dictate that she must act in a constantly subservient manner by making a "peace cry" and rather humorously, by constantly shaking her nether end in order to remain visible to males. The female lines, because of their shape, are the most dangerous people in Flatland. They can pierce any polygon, even accidently. It is a fascinating conjecture whether this fact arises from the logic of the world Abbott created or whether it reflects his own perception of the latent power of women. The fact remains that Abbott remained a bachelor all of his life.

Some of the history of Flatland as related by the Square reinforces the notion of a society dominated by higher level polygons who have attained their station by birth, but which has sprung and is renewed by entry from the sons of the lower classes. The color revolution, in which all classes, even women could paint themselves to appear like a many sided polygon, threatened the social structure. It was ruthlessly suppressed by the circles. There is no precise parallel in the history of Britain that compares. However, In the late 1700s Europe experienced the rise of a colorful revolution that attempted to create fraternity, equality, and liberty. It was called the French Revolution. It was suppressed by the old order in Europe in a series of bloody wars that lasted for 25 years.

This book is not just about taking left-handed swipes at the Victorian social structure of Britain. While social commentary is an important part of Flatland its two dimensional nature also proves to be highly important. Probably the most important aspect of the book is its hints at the implications of living in a universe where there are multiple dimensions. Our hero, the Square, is granted the good (or perhaps dubious) fortune to see other dimensions. In a dream he sees the world of two dimensions where another rigid social order exists. When he attempts to communicate with the king of Lineland he finds the man to be highly provincial, unwilling to accept the fact that there might even be another dimension. He cannot stretch his mind to see and understand the presence of Square except in cross-section. The square is then allowed to see Pointland, where the solitary inhabitant of no dimensions cannot conceive of anything but his own existence.

These visions only partially prepare Square for a visit from a sphere from the land of three dimensions. At first he rejects the sphere, attacks him for invading his insular world and attempting to change his views by teaching him about the third dimension. Square can no more conceive of three dimensions than the king of Pointland could conceive of one, much less two. Finally, the sphere pulls the square from his plane and allows him to see the world in three dimensions. Square is converted and when he is returned to Flatland he is admonished to proclaim the "gospel of three dimensions". This proves a difficult thing to do in his world where the many sided polygons approaching the perfection of the circle have no interest in a different view of the universe, especially since it might upset the social order where they dominate.

The arrest and persecution of Square takes a tiny step toward Christian allegory. Abbott had taken orders in the Anglican church. He was known to be a devout Christian. It is conjectured that he wrote this work in part to help people to see that within our skeptical world, science, and especially mathematics, leaves room for greater possibilities. Square is locked away. His "gospel" to be suppressed. Perhaps Square was just a little like some of the saints Abbot wrote of in some of his other works, suffering for the cosmic truth.

Though he touches on spirituality, Abbott never makes this aspect of the story explicit. Rather he challenges the reader to use his imagination to try to comprehend that there could be, and probably are more dimensions in our universe. As Shakespeare put into the mouth of Hamlet, "There are more things in heaven and Earth, Horatio, than are dreamt of in your philosophy."

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