Sunday, March 12, 2017

Flatland by Edwin Abbott Abbott

Social satire through interdimensional contact
Flatland, a delightfully odd science fiction novel, was originally published in 1884. English author Edwin Abbott Abbott wrote the book under the pseudonym of A. Square. The story is narrated by an actual square, an intelligent geometric figure who lives in a universe of only two dimensions. Speaking to an audience of third-dimensional readers, the Square introduces us to his flat-plane world, describing in detail not only its physical characteristics but also its societal and political structure. The result is a strange combination of geometry lesson, social commentary, and utopian parody.

With no conception of height, only length and width, the inhabitants of Flatland can only see each other as straight lines and must distinguish each other through hearing, touch, and visual techniques acquired through training. This is very important because the society of Flatland is built upon a strict social hierarchy. Circles, or Priests, are the highest social strata, while the lowly workers and soldiers take the form of very acute isosceles triangles. The higher the number of sides and the wider the angles that compose a figure, the greater his intelligence and the higher his social standing. Women, unfortunately, are not even factors in the class struggle, as they always take the form of straight lines. Through his description of this fictional society, Abbott wryly criticizes England’s restrictive class system. When in this satirical mode, the book entertains with an absurdism reminiscent of the sci-fi satire of Voltaire’s story Micromégas. The humor is so dry at times that in some cases, like the extreme chauvinism with which women are discussed, it’s difficult to tell whether Abbott intends to be funny or not.

Flatland is based around an ingenious idea, but the execution is not always all it could be. Though only composed of 155 sparse pages, the book feels long-winded. At times reading through Abbott’s convoluted prose is like trying to run through molasses. Particularly in the first half of the book, he spends a lot of verbiage in making his points and often goes off on annoying digressions. The second half of the novel is much better. The Square describes his visit to the one-dimensional Lineland and his attempts to explain Flatland to the inhabitants there. Then he relates how he originally became aware of the third dimension when he was approached by a sphere from Spaceland. Here the geometry takes precedence over the satire, and the book is better for it, as Abbott illustrates the difficulty in comprehending dimensions above and beyond those which we experience with our senses. The book ends on a high note as Abbott delves deeper and deeper into the philosophical implications of multi-dimensional geometry. On the one hand, the Square and his third-dimensional awakening stands as a sympathetic surrogate for those who claim to have experienced religious revelations. On the other hand, the spirituality of those revelations are called into question as possibly being sensory experiences of geometrical dimensions higher than our own. Once again, how much of such speculation is intended to be serious or humorous is unclear.

For the mathematically minded, the contemplation of fourth-, fifth-, or higher-dimensional worlds is a perplexing but fascinating pursuit. Though the relevance of some of its social satire may have worn off with the end of the Victorian Era, Flatland can still speak to those with an interest in such abstract intellectual exercises, and it does so in a way that is both provocative and amusing.
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