Reading notes: Edwin A Abbott — Flatland

Reading motivation

Like an amuse-bouche, the first 5–10 pages of a book can reveal much, if not about the book itself, then about the author’s state of mind when they began writing. This isn’t to say the rest of the book will maintain the same quality — quite the opposite, actually. Often, the author’s mindset changes as they write, especially for longer works, and not always for the better. This is wonderful in itself for those who enjoy the journey. Sometimes it’s like riding Charon’s boat, with your attention as the fare. With all this, the first pages, our figurative amuse-bouche, offer insight into the author’s motivation, that final kick that pushed them to start writing. It’s a subtle touch, and like an amuse-bouche, it often goes unnoticed by less discerning readers.

Since childhood, I’ve wondered what life in 2-dimensional (or 1-dimensional, 30-dimensional, etc.) space would be like. It was a sort of introspective thought about how our 3-dimensional world might appear to those of higher dimensions (since it would be largely invisible to lower-dimensional worlds), if at all. It seemed obvious we wouldn’t treat a 2-dimensional world like we do ants in their glass colonies — firstly because that world might be more advanced than ours, but more importantly because its z-dimension equals zero. Hence, the seemingly lower dimension is simply inaccessible to us, much like, or even more than, a higher-dimensional world. I never expected to share these thoughts with others, let alone read a bona fide novel on the topic. Yet here I am, ready to soak in musings on the same subject written in the Victorian era, of all times.

2024-07-17

Initial impressions (chapters 1–4):

I was half-expecting this to turn into a sort of sequel to the Three-Body Problem trilogy, where low-entropy civilisations almost mindlessly destroy the universe based on past fears, transforming into mindless protocols of self-preservation with the meanings of preservation lost in rigid processes. In a way, it is, and the fact that it was written in and about Victorian England well over a century before Cixin Liu’s great work of modern sci-fi makes for a very nice ironic meta-commentary on what we consider “progress” based on a society’s temporal existence.

Overall, the didactic narrative creates a Brechtian distancing effect, allowing for a nuanced examination of the narrator’s evolving perspective on his society and himself within it.

In fact, the main narrator has almost immediately situated himself within the society, not without a certain pride, giving full justification to the existing social system. Ironically, from his own description, it becomes obvious that his character is a second-generation nobility — a mere square. This yields additional flexibility to the narrator’s position as a source of societal critique both up and down the social hierarchy.

The existing society is described from the beginning as authoritarian, with strong class stratification, and with women basically treated as almost subhuman. In fact, the treatment of women, justified as deeds “for their own safety,” is painfully reminiscent of many current societies where women’s bodies and agency are controlled by patriarchal structures. In that respect, the initial thought that pops into the reader’s mind is that the settings are quite modern, only to be hit with the realisation of how archaic these oppressive gender structures are, and how we find them “normal” and even relevant to our times.

This irony in the radical suppression of women in the 2D world lies in the fact that the attempts at suppressing women are futile and women do let the men know their own opinions regardless of the class, sometimes even with the use of extreme violence. Considering this almost a century away from Second Wave feminism, the notions of the women’s conditions and resistance in the book are quite progressive.

The social structure of the 2D world is oppressive not only towards women but also the lower classes — the Isosceles. The automatic advancements in status of all classes except the lowest ones both continuously devalue the simpler shapes and widen the division between the lower and middle-cum-upper classes even further, despite the rare possibilities of vertical social mobility for those lower classes to become equilateral triangles. Furthermore, any possible upward social mobility is followed by complete and total isolation of the “evolved” character from their lower origins for fear of possible hereditary regression. It is clear that very little has changed from the Victorian era, besides the terminology we use.

Quite like in the Spacelands (our domain) the upper classes are very much worried about the possible uprising of the proletariat, and are actively working to undermine the revolts, by co-opting the revolt leaders, as well as by instilling cultural hegemony, as per Gramsci and Marx. In that respect, I wouldn’t be surprised if the author has read, or has been a part of discussions on, the works of Marx and Engels, as the theme of class struggle is very evident in the first several chapters.

Finally, early in the story, we get a glimpse of the epistemological shift, possibly fuelled by the power structure, through the explanation of attempts to find the source of light and the act of suppressing knowledge-seeking activities, not only by legal means but also by labelling the knowledge-seekers as insane in the best Foucauldian tradition of the social construction of madness.

2024-07-20

Chapter 7

Chapter 7 is talking about Regularity and Equality of Angles. It is ironic that the term Equality is used as a measure and justification for rejection, opression and destruction non-conforming entities. This is of course done in the name of convenience and safety of the majority. This rhetoric has not changed much since the Victorian England and is still actively used by those, who are willing to deny the equal rights to minorities, LGBTIQ+ or anyone who does not conform to the arbitrary standards set by the society.

2024-07-21

Chromatistes

The narrator’s account of the colour reform — a measure that would ostensibly render the society more egalitarian — serves as a potent illustration of ideological manipulation by the ruling class. This episode vividly demonstrates the reinforcement of hegemonic cultural norms and values, effectively manufacturing consent among the Isosceles. These chapters present a rudimentary yet accurate depiction of cultural hegemony, remarkably predating Gramsci’s Prison Notebooks by some four decades. The narrative thus offers a prescient critique of power structures and social control mechanisms that would later be formally articulated in critical theory.

Of course the last part of the chapter that has described the ruthless suppression of the uprising by extreme and prolonged violence, the anti-colour terror, is especially noteworthy. Only 30 years later Russian Czar has attempted to violently suppress protests (Bloody Sunday), which led to further protests (including Potemkin Mutiny), which eventually led to the Red(!) Revolution. The status of aristocracy has changed forever after that.

The later chapter brings up the notion of the higher classes treading the matters of personal relationships, traditions and marriage with far lower care than the middle ones, not only ignoring the history of their chosen women’s lineage, but even specifically opting for the ones with deficiencies in the recent history, choosing them on the account of their immediate attractiveness. Our narrator seems to be oblivious to the fact upper class hypocrisy towards morality — it is merely the arbitrary set of rules specifically made for the middle classes in order to keep them in line. This is valid in 2D world, in Victorian England, and today anywhere.

2024-07-22

Lineland king

The interaction between the Square and the Line king is both clever and hilarious. The attempts at communication between beings of different dimensional levels produce some truly memorable expressions, such as:

excess of approximation

Aside from all the cleverness I am not sure why the protagonist didn’t explain to the Lineland king his universe in king’s own terms, as an infinite number of lines adjoined to each other creating plane.

Finally, I’ve found it funny how the protagonist is flexing that he can infer shapes, while we, the readers, can actually see shapes. Moreover, the fact that we are reading this text, i.e. seeing shapes makes it particularly ironic.

Spaceland and conclusion

The last third of the book a starts showing a clear decline in the quality of writing. Over-flowery monologues with no purpose, predictable outcomes, weak motivations, it feels like the author was rushing to finish the book, while still ditching the last attempt to make it not as short as it turned out to be (the book is just over 100 pages). The change of the dialogue format to speaker-labeled form serves no purpose and breaks stylistic continuity. Additionally the quality of the narrative has deteriorated. Gone are the strong social systemic commentaries, replaced with implausible focus on individuals as a narrative drivers. Gone is the vivid description of the society and how their 2-dimensional existence affects it. Most of the very interesting themes stayed unresolved. The piece has failed to fulfill its full potential, and has transformed an exciting (for the time) topic into arguably entertaining school material that explains some abstract basics in epistolary form — the conclusion certainly does not deliver on the full potential of the subject. 6/10

Inaccuracies

With all the mathematical precision and very novel at the time social commentary, I am bothered immensely by the fact that the 2D characters’s visual perception of each other and their world is described as seeing lines, black with gradient (with sufficient training) or coloured during the Chromatistes era. These are volumetric expressions, that are ontologically impossible in the universe with no z-dimension. The same issue is, of course stands in the 1D universe — the Lineland. Even if the inhabitants of those universes would perceive each other somehow (I think the author was quite careful as to hint that some terminology the 2D narrator is using is borrowed from 3D world, but it does not necessarily mean exactly the same thing in their universe), it would be quite impossible for the representatives of the higher dimension to see them. This means the Sphere would not be able to see the Triangle, and the Triangle would not be able to see the Line, and of course neither of them could see the Point — an entity of a single dimension, a mere positional indicator, rather than an entity, with no width, height or length.

The author, clearly fluent in Euclidian geometry, seems to have compromised quite a bit of mathematical sense for the sake of a fun story. Was the sacrifice of accuracy worth the convenience of the narrative?