MAY 16, 2025 IN REVIEW GROUNDCOVER NEWS A world of sharp angles and sharper opinions Book review: Flatland — A Romance of Many Dimensions geometric regularity. Triangles form the laboring class, with their sharp angles signifying their low status. Squares and Pentagons enjoy middle-class respectability, while the ruling elite consists of multi-sided Polygons who, through generations of refinement, gradually evolve into Circles, the highest class, divine beings of Flatland, the priests. This strict classification is upheld with absolute rigidity. Any deviation from ‘perfection’ of regularity, any irregularity in angles, is seen not as an individual characteristic but as a dangerous anomaly. Such individuals are not merely excluded, they are eradicated. Order must be preserved at all costs. Women in Flatland are paradoxically DIDEM KOCHAN Groundcover contributor Step right up and enter Flatland, a world where you do not need an elevator! Imagine living in a place where up and down do not exist, where all the inhabitants are geometric figures, your social status is determined by the number of sides you have, and where women are, well … sharp and dangerous. This bizarre, two-dimensional world was brought to life in Flatland, a novel by Edwin A. Abbott — and it is much more than a geometry lesson. At first glance, the book seems like a whimsical mathematical fairy tale, but soon you realize it is also a satire, a social commentary, and a mind-blowing exploration of what lies beyond the limits. It is a book that makes you laugh at its absurdities until you realize it is holding up a mirror to your own world and challenges your understanding of what is real. To fully appreciate Flatland, we must understand that the author lived in Britain during the Victorian era. It is a period where industrialization reshaped British society, but the class separations not only remained but deepened. This was an era of progress and inequality, reflected in events such as the Titanic disaster. Meanwhile, mathematics was undergoing its own revolution. The field of non-Euclidean geometry was gaining interest among mathematicians, challenging traditional approaches, just like Flatland does. The protagonist and narrator of this story is A. Square, an inhabitant of the two-dimensional world of Flatland. In Flatland, social hierarchy is not built upon wealth, wisdom or virtue but on both feared and ignored. As razor-thin straight lines, they are seen as physically dangerous yet intellectually inferior, too emotional and unfit for education. Their exclusion from intellectual life is not a matter of oversight but of deliberate design. Women cannot reason, learn and worst of all, they cannot evolve. Men in Flatland, on the other hand, are the rational ones, the philosophers. Male figures can pass on their sides to future generations, increasing their status over time, while women remain as single lines, never progressing in shape or standing. The Color Revolt, a brief but significant episode in Flatland’s history, underscores the anxieties of its society. When color was introduced, it initially promised individuality and progress, but its dangers soon became apparent. The issue arose when women could manipulate their appearance by shading their sharp edges, allowing them to imitate the esteemed Circles. This was intolerable, not just a threat to the ruling class, but a dangerous hint that women, given the chance, might get an education, learn politics or even seize power. In response, the ruling class quickly declared color to be a dangerous threat to social order and banned this brief experiment in individual expression. The world returned to its proper, boring and obedient state. After introducing us to Flatland and its social organization, our narrator, A. Square, shares his own journey of discovery. As a middle-class resident in Flatland, he considers himself a rational and enlightened thinker. When he visits Lineland, a one-dimensional world where inhabitants can only perceive forward and backward, he attempts to explain the wonders of two-dimensional existence. The poor Linelanders are incapable of comprehending his words. With no concept of left or right how could they possibly understand a second dimension? Their existence is so deeply limited to their singular way of perceiving reality that any alternative is considered as insanity. Our A. Square, observing their ignorance, views himself as superior to Linelanders. But here is a twist – he soon finds himself in an analogous situation when his grandson dares to suggest the possibility of a third dimension. Just as the Linelanders rejected his ideas, he rejects his grandson’s. They have forward and backward, left and right, but how about up and down? There is no evidence of such a thing, so it cannot exist. However, this belief has to change when our A. Square encounters a character from Spaceland, a three-dimensional realm. The Sphere attempts to reveal the existence of a higher dimension. At first, A. Square is in complete denial. His perception is limited to the two-dimensional plane, and he cannot conceive of a reality beyond it. But when the Sphere lifts him out of Flatland, he experiences a revelation. For the first time, he sees his world from above and perceives it in a way that was previously unimaginable. He now understands what he once thought impossible: the third dimension is real! Just when he is ready to embrace the idea of the third dimension, he makes a critical mistake and asks, “Could there be a fourth dimension?” Well, that is a big no. The Sphere, despite being regarded as superior in the Square’s eyes, reacts with the same dismissal that our Square once exhibited toward his grandson. The cycle repeats itself. Even the Sphere, supposedly enlightened, balks at the next step. Even those who consider themselves enlightened often fail to see beyond their own limitations. This realization shakes our Square to his core; now that he has tasted the truth, he cannot go back to being ignorant. He realizes how small Flatland really is, how much more there is to the universe that he once assumed was impossible. He begins to reflect on the nature of existence, the limits of their knowledge, and the possibility that reality is far greater than what is immediately perceivable. In the words of the Monarch of Spaceland, “the joy of thought, the joy of being.” What a revelation! Abbott’s novel, despite being written in 1884, feels as relevant today as ever. It is about us, about how our society resists change, how those in power cling to their authority and how new ideas are often neglected until they become undeniable. This book is not just a mathematical curiosity or a social critique, it is an intellectual adventure. In this adventure, we find an invitation to explore, to question, and to embrace the unknown. Much like episodes of TV show Black Mirror, Flatland forces us to expand our limits. It reminds us that the greatest barriers to understanding are often the ones we create for ourselves. As we turn the final pages, we are left with a challenge: just as the Flatlanders could not see beyond their two-dimensional existence, could we, trapped in three-dimensions, be blind to a reality beyond our comprehension? So, whether you love mathematics or philosophy or simply enjoy imaginative storytelling, dare to enter Flatland. Let your mind stretch beyond its familiar edges. You might just discover new dimensions, both in the book and within yourself. 7
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