When Edwin Abbott Abbott wrote his little masterpiece over one hundred years ago, he did it for several reasons. Some of these were obvious to his readers and remain obvious today. Others had to be explained by Abbott himself in the introduction to the second edition, which followed one month after the first, at the end of 1884. Still others were immediately clear to Victorian readers but need some clarification for readers in our day. Fortunately, there is enough evidence, direct and indirect, in this remarkable author's forty-five books and other writings to give us answers to many questions, though not all, since the subject itself continues to encourage us to raise new ones.
The first subject that has to be addressed is the treatment of women in Flatland. Abbott was a social reformer who criticized a great many aspects of the limitations of Victorian society. He was a firm believer in equality of educational opportunity, across social classes and in particular for women. He participated actively in the efforts to bring about changes, and the frustration he felt from the resistance of the educational establishment is mirrored in the satire of Flatland. This was the first generation in which women were permitted to attend classes at Oxford and Cambridge, but their access was stiII quite limited. Although there were many schools where a boy could be trained for the demanding university entrance examinations, there were few comparable opportunities for girls, and many of the young women who gained entrance to universities, like Abbott's daughter, had received much of their education at home, often from private tutors. It was partially to aid in this effort that Abbott composed his Hints for Home Teaching, directed at parents who wished to help their children prepare for higher education. Abbott was also a vocal leader in the Teachers' Training Syndicate, formed and primarily supported by the major female educators of Victorian England, who extensively praised Abbott for his efforts on behalf of education reform, in particular for proposing alternate wavs of qualifying for entrance into university studies. The narrow-minded attitudes that blocked these efforts show up quite clearly in Flatland, where females are presented as incapable of comprehending the education given to males. Many people ignored one whole dimension of women's existence, as symbolized by the representation of women in Flatland as straight line segments. Under the guise of protecting women, they kept them away from the means by which they might better their station. Abbott's sentiments in this matter are clear by the end of Flattand, where the narrator comes to realize that the very (female) virtues his society has been putting down are the ones that are to be most prized.
Abbott was one of the first to recognize the implications of a "two cultures" society. The men in Flattand epitomize the rational, emphasizing the importance of that which can be measured empirically and described in precise scientific language. Qualitative properties not susceptible to such quantification are relegated to the world of women, who have an absolute corner on not only the intuitive aspects of knowledge but also the abstract concepts such as loyalty and love which are difficult to translate into a strictly utilitarian construct. A Square, the two-dimensional narrator of Flattand, considers himself enlightened when he propounds the view that the strain of maintaining two separate languages, one for conversation among men and one for talking with women, exacts too great a toll on young minds. There is always the danger that the language of men will be revealed to women, reminiscent of the prohibitions in earlier societies against teaching slaves to read.
As a religious man with a well-developed traditional sense of morality, Abbott clearly did not subscribe to the prevailing scientistic view of knowledge, and he more than once pointed out the dangers of letting one side of the personality completely dominate the other. Abbott was a teacher who extolled balance, and Flatland reduces to an absurdity the single-minded tendency of choosing either the totally rationalistic or the totally intuitive.
Another aspect of the satire in Flatland is the treatment of those who did not fit in. In the rigid society of Victorian England, there was little tolerance for irregularity. It was often associated with criminal tendency, and some theories blamed deviant behavior on an abnormal shape in the frame or the skull. Frequently, the unusual were segregated from the rest of society in asylums. The rest of society maintained a fascination with the freakish element, and asylums often had viewing gaileries so ordinary people could observe the activities and antics of the inmates. Abbott's suggestion that irregulars be eliminated is a Swiftian exaggeration, especially when coupled with the cruel plan of keeping a number of these unfortunates available as object lessons, an expendable supply of individuals with no rights at all, to be studied by the regular Flatland pupils. Especially pointed are his remarks about the appearance of irregularlties among the upper classes. His readers could certaintly supply their own examples of men destined for high station who had failed to fulfill the prerequisites for completing a university education, Such people are not fit for lower employment, and so they simply cause trouble within society. Abbott's solution is worthy of Jonathan Swift's A Modest Proposal: anyone who fails the final examinations of the university will be incarcerated for life or subjected to a painless death. No reader should miss the satirical intent of such a paragraph.
Abbott definitely saw education as a means for students to transcend the social class into which they were born, and he was particularly censorious of the efforts of those who used education to perpetuate class distinctions. A basic liberal education should be provided to all students, so that some of them might go on to higher education and others might go into business from a more enlightened perspective. Abbott's students at the City of London School learned practical science and art as well as theoretical subjects. Abbott resigned from the headmastership just seven years after the writing of Flatland, during a crisis over the splitting of the curriculum into separate "modern" and classical sides. In Flatland, Abbott echoes this crisis as he satirically contrasts the "feeling" of the lower classes with the more refined "seeing" of the educated part of society. By preferring the more remote way of sensing, the higher classes built a barrier between themselves and the lower strata.
Several of Abbott's students who broke societal barriers were only too happy to thank their old master. Most famous was the Prime Minister of England, H. H. Asquith, Lord Oxford, a man from humble background who gained entrance to Oxford as a result of his classical education under Abbott. Bramwell Booth, the second director general of the Salvation Army, also thanked Abbott for his encouragement and for promoting the development of his self-worth. Sir Israel Gollancz went on from the City of London School to study at the University of London at a time when educational opportunities for Jewish students were meager. He always sent his Shakespearean volumes to his old teacher, and induced him to accept tiiembership in the British Academy, which Gollancz had helped to found. It is evident that Abbott was proud of his former pupils and that he preferred the kind of education that allowed people to rise on the basis of merit rather than of the social class into which they were born. The prevailing system is the target of his satire in Flatland.
Mathematics Awareness Month is sponsored each year by the Joint Policy Board for Mathematics to recognize the importance of mathematics through written materials and an accompanying poster that highlight mathematical developments and applications in a particular area.