Flatland as social satire: Women’s status in Victorian times and the push for educational reform By Xiang Fu

This blog post was written by our summer research student Xiang Fu, who was supervised by Andrew Potter and June Barrow-Green. This blog post focuses on the status of women in mathematics in Victorian times, and today.

Xiang Fu completed her Open University mathematics with statistics bachelor degree with first class class honours this July. She has commented that she absolutely enjoyed the study and appreciated the opportunity of the summer research project.

Flatland: A Romance of Many Dimensions by Edwin A. Abbott was first published under the pseudonym of A. Square, in 1884. It quickly gained popularity as a science fiction story for the introduction of higher dimensions; but also it is a satire criticising social inequality in Victorian Britain. The description by Square, the protagonist from Flatland, that women were regarded inferior to men was so vivid that the author was denounced by contemporary book reviewers as a misogynist. Abbott, writing in defence of A. Square in the preface to the second edition in 1885, had to explain that, as a historian, he had “identified himself (perhaps too closely) with the views generally adopted in Flatland and […] even by Spaceland Historians” (Abbott, 1884a, p.9), and in fact he believed that the straight lines (women) were superior to circles (the priests forming the top of the social caste) in many respects.  This essay will focus on how Abbott, using Flatland as a satire, exposed the injustice of women’s situations in Victorian times and Abbott’s effort to improve education, especially that for women.

Edwin A. Abbott (1838—1926) was a graduate of Cambridge, and worked as the headmaster of the City of London School (MacTutor, 2005).   Abbott’s written works covered various topics. Flatland was inspired by mathematician and science fiction writer Charles Howard Hinton (1853—1907), who was interested in the fourth dimension, and coined a word – tesseract – for the four-dimensional hypercube. Hinton, who was married to Mary Boole, the eldest of the five daughters of the renowned mathematician George Boole, taught Mary’s sister Alicia about tesseracts; and Alicia edited one of Hinton’s books about the fourth dimension (Chas, 2019). The fourth-dimension concept offered a great stage for drama and art in the late 19th century and first two decades of the 20th century (Ibanez, 2017).

Since women were viewed as disadvantaged in their intelligence level, they were excluded from Oxford or Cambridge until the 1860s to 1870s, and could not earn a degree from these two privileged universities until 1920 and 1948 respectively (BBC, 2019).  Female German mathematician Emmy Noether (1882—1935), who made a significant contribution to invariant theory, was discriminated against at different stages of her career due to her gender and Jewish origin. Like Alicia Boole, Russian mathematician Sofia Kovalevskaya (1850—1891) had to be tutored privately (Flood & Wilson, 2011, p.167).

In addition, the diminishing of women in the 19th century was supported by the widespread idea of the ‘missing five ounces’ of the female brain, though modern science has not found any significant difference in the functions of the brains of different genders (Eliot, 2019). In Flatland, one’s geometric properties decides one’s intelligence.  This can be understood as an analogy with the widespread idea of biological characteristics, such as the circumference of the head (measured with cephalometer) being supposedly linked with brainpower. French psychologist Gustave Le Bon (1841—1931) allegedly believed that women were the “most inferior forms of human evolution”, hence they “excel in fickleness inconstancy, absence of thought and logic and incapacity to reason” (Quotefancy, n.d.). Gustave Le Bon’s evolutionary theory about genders echoes Darwin’s conclusion that a man can attain “a higher eminence, in whatever he takes up, than women — whether requiring deep thought, reason, or imagination, or merely the use of the senses and hands” (Darwin, 1896, p.12).

That women held lower social status in Victorian Britain is mirrored in the narration about the social hierarchical system in Flatland by Square:  in Flatland each resident is a polygon; and one’s social status and intelligence are positively correlated with one’s number of sides and the equalness of one’s angles. The more sides one has, the higher one is positioned in the social pyramid. As a square, the protagonist is a middle-class mathematician. However, women are put in such a low rank that they are excluded from the two-dimensional hierarchy: women are nothing but “straight lines” (Abbott, 1884a, p.21); hence they are “needles” (p.25) from sideways and shrink to a point from the very front or back. Since women “have no pretensions to an angle”, they “are devoid of brain-power, and have neither reflection, judgement, nor forethought and hardly any memory” (p.27). Therefore, women have no “hope to elevate from the caste”; and “the very laws of Evolution seem suspended” (p.29) in their disfavour. Women are subject to emotions, not logic, and they identify others by feeling.

The “romance” narrative in Flatland develops with the key action in the second part of the book: Square is enlightened by a sphere from Spaceland, a higher dimensional world than the 2-dimensional Flatland. The sphere embarks upon a mission to Flatland to explain to Square about the existence of Spaceland. Square extrapolates his new knowledge of dimensions and insists that there must be a 4-dimensional terrain. However, this is rebuked by Sphere. The square offends both the sphere and the noble class in Flatland by challenging their superiority and privileges derived from the hierarchical system. The ruling class in Flatland sends Square to jail for his heretical proclamations about Spaceland.

The resistance from Sphere or from the governing class in Flatland to the acknowledgement of the existence of a higher dimension is assumed to come from their fear – the fear that the hierarchical system may be undermined, or even overthrown – leading to the loss of their social supremacy. It is the same kind of fear that drives the priests in Flatland to suppress the Colour Bill, an historical event detailed in the first part of the book. Starting from an unknown pentagon, a ‘chromatist’ – he painted himself and the new fashion spread quickly and widely in Flatland. When the lower-classed polygons begin to colour themselves too, the new colour culture in Flatland blurs the clear-cut social status based on being able to recognise by sight one’s number of sides and the equalness of one’s angles. The belief flies from mouth to mouth that “Distinction of sides is intended by nature to imply distinction of colours” (Abbott, 1884a, p.47). The lower-class polygons put forward the concept of social equality and asserted that there was not much difference between them and higher-class polygons. The Colour Bill was presented at the all-state assembly of Flatland, proposing that Priests would be painted in the same way as Women. The Colour Bill movement led to civil war and was ultimately suppressed.  The existence of the fourth dimension and the events of the Colour Bill revolt ridiculed Flatland’s (and therefore Victorian society’s) stiff social pyramid by exposing it as unjustified and illogical, which had been ingrained for generations as ‘natural’. The democratic movements in Flatland echo the fights for equality in the French Revolution, campaigns for political rights for working-class men in the 1840s, and fight for women’s rights  and the suffrage movement from the 1860s (Jann, 2008).

Flatland attracted attention from contemporary critics immediately after it was published. It was reviewed, in the journal Science in 1885, as “an amazing story” based on the “transcendental mathematical concept” of higher dimensions (Comment and Criticism, 1884). Robert Tucker in Nature recommended this humorous book for readers when they had a “leisure hour from their severer studies” (Tucker, 1884, p.77). Though puzzled and distressed with the “geometrical romance” of Flatland, (estimating only six or seven people in the US and Canada would enjoy reading it), the author of a review in the New York Times admitted that it made some apparent sense “in an appeal for a better education for women” (New York Times, 1885).

Though, as described in Flatland, women were confined by domestic duties and excluded from formal academic education, change involving women’s social status was happening in the 19th century. In 1846, the British government launched a teacher training program to take people older than thirteen years old into a teaching apprenticeship (Intriguing History, 2011). The paid teacher training scheme allowed women to enter the teaching profession, though female teachers received lower payment than their male colleagues. The suffragette movement, which fought for women’s voting rights, started in the 1860s. The Manchester Society for Women’s suffrage was established in January 1867. In 1866 and 1867, petitions promoting women’s suffrage were presented to the parliament by John Stuart Mill MP (1806—1873), who supported equality between the genders. However, all these petitions were turned down and women’s suffrage was not secured until August 1928, when Parliament passed the Representation of the People Act 1928 and British women won suffrage on the same terms as men.

In 1884, Abbott had his book Hints for Home Training and Teaching published to help parents who did home schooling with their children: boys and especially girls, since girls had much less chance to be admitted to the universities.  In the preface of the book, Abbott claimed that more educational opportunities then available for women “justifies the belief that in the next generation mothers will take a large part in the teaching and training of the young” (Abbott 1884b, p.12).  Abbott was one of the leaders of the local teacher training organisation. His effort in education reform was praised by the major female educators in Victorian times (Banchoff, 1991).  Thomas Banchoff (b. 1938) Professor Emeritus of Mathematics at Brown University argued that Abbottt was a strong believer in the equality of rights between men and women, especially in education (1991).

Flatland was written in the genre of science fiction (then called a ‘scientific romance’), introducing the mathematical concept of higher dimensions. By belittling women as one-dimensional line segments while the men were two-dimensional polygons, Abbott revealed the unfair adversity Victorian women were born into and had to live with. It is important to remember, however, that Flatland is a social satire. With his books and efforts in pushing female’s education reform, Abbott contributed to the fight against the social inequalities between men and women.  More than one hundred years on, the struggle for gender equality continues. For example, there still persists a gender wage gap (Advani et al., 2021); and in 2019, only 24% of the STEM professionals in the UK were women (Dossi, 2022). When reading Flatland today, enjoy the mysteries of the fourth dimension, but don’t forget the hidden message which strives for gender equality which is still as relevant today as it was in 1884.

 

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