Essay: Francis Bacon

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Flatland: A Romance in Many Dimensions

Though written largely as a satirical response to the institutions and beliefs of the Victorian England society to which its author belonged, Edwin Abbot's Flatland: A Romance in Many Dimensions also serves, and has for over a century, as an enjoyable introduction to many different fields of human knowledge. Practically since its first publication, scholar have noted the skill with which Abbot describes complex topics to his readers in such diverse fields as philosophy, mathematics, and even cultural anthropology, though rarely mentioning these fields explicitly (Beidleman, 1973).

Instead, through the main character of the Square and his interactions with other very-humanized characters in the two-dimensional world of Flatland, these concepts are illuminated as logical necessities of the world we live in. Some of the subjects and concepts outlined in the book might have led to some unintentional interpretations; though the author certainly had specific sociological views in mind, he probably did not have any anthropological conclusions he was trying to lead his readers to. Still, the fact that these conclusions can be seen in the work are a testament to its writing and broad appeal.

This broad appeal is also the book's downfall in many ways. Because it illustrates so many concepts -- and does so indirectly -- it doesn't fully or accurately describe any of them. For instance, when the Square is ruminating on the appearance of the three-dimensional Sphere from Spaceland in two-dimensional Flatland, he describes the way the appearance seems to shift: "At the first glance it appeared to be a Woman [who appear as lines in Flatland], seen sideways; but a moment's observation shewed me that the extremities passed into dimness too rapidly...and I should have thought it a Circle, only that it seemed to change its size in a manner impossible for a Circle or for any regular Figure of which I had had experience" (Abbott, 1884).

This description is confusing and, though perhaps accurate for the way a two-dimensional being in a two-dimensional world might see a three-dimensional creature (or object), its difficult for Abbott's three- (or four-) dimensional readers to understand. What Abbot gains in interest by humanizing all aspects of the story, he loses in the clarity of his mathematical discussions. If the purpose of the novel is to educate, and from the depth and breadth of information contained therein it can reasonably assumed that education is at least one of this novel's purposes, then it falls somewhat short in this goal due to the books attempt to maintain a cohesive story. In addition, the breadth of the work makes its educational value limited: "Packing such diverse information into a small space inevitably makes the various sections of the introduction tantalizingly cursory" (Smith, 1992).

Unfortunately for Abbott (and, to a degree, his readers), this same principle works the other way round, too. That is, the book loses much of its possible entertainments value do to the technical nature of many of the discussions. Overall, though, the book is much heavier in satire and entertainment value than it is in philosophical and mathematical information, leading one to believe that the main purpose of the book was not education. Rather, through reliance on logic "satire is here always integrated with a more or less serious depiction of an alternative historical locus" (Suvin, 1983). The satire is made more poignant by the fact that the injustices and silly institutions being satirized occur in this world of seemingly supreme logic. Logic itself, along with other mathematical concepts that can be rationally and logically verified, are not satirized themselves. Rather, Flatland satirizes the misuse, misunderstanding, and misapplication of logic, and calls for a reexamination of certain "logical" principles.

The various social principles discussed in the book go a long way in determining Flatland's purpose and the audience Edwin Abbott had in mind when he wrote it. One of the first issues Abbott brings up in the world of Flatland -- and one of the persistent themes throughout the book -- is the treatment of women, who are simple lines in Flatland. In the scene where the Sphere appears, quoted from above, the Square's wife ends up leaving the room apologizing profusely for her startled reaction when she realizes that the Sphere is not another woman, but some special sort of the very revered Circle class. This illustrates the life of inferiority that women were subjected to in Flatland, which mirrors Victorian England in this regard.

In an earlier chapter, the Square lists the rules of conduct for women supposedly based on the dangers they represent (being "all point"), such as that they must always keep up a cry to let others know of their presence when they are in public, or else they face immediate death (Abbott, 1884). In another passage, the Square reflects the attitude of many of Abbott's contemporaries in saying "unfortunately the passion of the moment predominates, in the Frail Sex, over every other consideration" (Abbott, 1884). Abbott himself was known "as a leading educational reformer," and was also very active in social issues such as women's rights. The book is not meant to represent his views, then, but rather it satirizes the illogical views that others held.

The social arguments that Edwin Abbott makes are at least as important as the mathematical and philosophical principles he outlines, and arguably even more so. Though the premise of the book and the worlds contained within it is completely based in mathematics, the bulk of the story actually has to do with the society that the Square lives in. This society even has an effect on the world of mathematics and science, as the Square is eventually imprisoned for his stories of the Sphere. Even the Sphere ridicules the Square for theorizing dimensions even beyond the third, a concept that modern science and mathematics has shown to be not only probable, but almost certain. In this way, the purpose of the book is at least partially to address the general close-minded attitude that existed in Abbott's Victorian society.

There were certain quasi-revolutionary aspects even to the mathematics of the book, however. Smith cites Banchoff as saying that Abbott's book was both "as both a response to, and a part of, the popularization of non-Euclidean geometry and the corresponding endeavors to visualize higher dimensions" (Smith, 1992). This makes Flatland part of the changing realm of knowledge in Victorian England, which necessarily made it somewhat theological as well. The Victorian period was also the time when Darwin developed his controversial theory of evolution (about which battles are still raging today) and the development of other sciences such as geology and paleontology that seemed to contradict Christian beliefs. This book eschews baseless traditional dogma in the form of preconceived notions of dimension and Euclidian geometry in favor of the world- and mind-expanding concept of taking thought to its logical ends.

The last portion of the novel, after the Sphere ridicules the Square and leaves him, is again highly political, and deals with the justice system in the basically totalitarian state that the Square and his family live in. In order to maintain complete control over the citizens, the government of Flatland outlaws the use of color or "chromatic expression," and also ends up outlawing the discussion or mention of dimensions beyond the second, which carries the death penalty for some.

The Square is not killed, but he is imprisoned for continuing to discuss his ideas about other dimensions (Abbott, 1884). This mirrors the persecution that many scientific figures suffered at the hands of various governments and religious institutions (particularly the Catholic Church) for spreading knowledge that they had verified through repeated observation or mental exercises. In fact, both the mathematics and the politics that appear in Flatland have continued to influence political thinking… [END OF PREVIEW]

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