Hmm, I liked the story (both book and movie) largely due to it's having one pervasive theme. One. One theme. Just one. And yes, women being needle shapes who are treated as second or third class citizens, while unfortunate for those characters, *is* relevant to the theme of the book. The very same theme that drives all of the math and extra-dimensionality.
Abbot was not simply teaching advanced geometry here. He did a great job of that, but — like most popular science fiction — that is primarily an allegory to help provide perspective on certain kinds of social inequality. The problem directly being addressed is that of Victorian class hierarchy and social myopia. Socially, (regardless of dimension) these beings are "locked" into a world view they cannot "see" their way out of. In this world view, beings are considered socially acceptable if and only if they are isosceles triangles or near-perfect polygons. Anyone shaped differently are considered abominations or monsters. The movie strays from that slightly but the book drives the point home sternly. Furthermore, those with a greater number of equal sides and angles (approaching practical circularity) are considered to be wiser for some reason (probably due to breeding, as normally polygons gain a side in each generation). Women are seen as inferior due to a social snowball effect beginning with their weaker physiology. Sound familiar?
I hear plenty of people complain about the misogynism inherent in the original work, who obviously don't understand the main theme. This part of the story employs "hostile ideology", much like Jonathon Swift isn't really a cannibal and Stephen Colbert isn't really a republican.
So the idea is to paint this landscape with exaggerated social ills (and curiously lacking a vertical spatial dimension), and then instead of tackling the social ills directly which would merely offend people in 19th century society, he attacks the missing dimension itself which is both an interesting, and a socially benign academic argument. He figures, if a two dimensional being can discover a third dimension and learn to understand it's nature through sheer analogy alone, and the viewer can follow along on this quest, then the viewer might allow their own imagination to take flight to envision a fourth dimension above our own.. which is also fully comprehensible via mathematics and analogy, though we do honestly lack empirical, measurable evidence of what it would be like. EG, you can't just run down to Wal-Mart and buy a genuine Hypercube to study. You have to infer everything about it's nature via mathematics and visual projection.
The viewer is left with this challenge due to A Square trying to explain this next leap to the Sphere and being stubbornly rebuffed. The viewer puts on the shoes of the unexpectedly obtuse Sphere who started the epiphany to begin with, and are thus invited to break out of their own limitations.
And FINALLY, the viewer is encouraged by the sheer magnitude of injustice present in the story to see the roots of the pattern of oppression inherent within Flatland — and how such ignorance can be rendered in any number of dimensions — then to compare that with their own Victorian environment. Lacking in depth, lacking in dimension.. trying to teach a person steeped in tradition that what they are doing is either limiting or even harmful to society is just as frustrating as trying to teach anyone from 1000 AD that the Earth is not flat. You WILL be viewed by most as either a forgettable whackjob, or a dangerous heretic.
It is a fact pervasive of every culture I have studied, past or present, that the general public will collude to suspend certain liberties, much like "flattening" the space in which one may move, in order to avoid unknown and unspeakable threats they prefer to trust companies and governments to protect them from. Such behavior invariably leads to taboo, censorship, and the corruption of power unchecked by a populace who would rather not consider the existence of freedoms employed and then abused by the very people sworn to uphold the strictures. In this movie, President Circle commits mass murder: a crime most flatlanders would consider inconceivable for a being with so many perfectly formed edges. He hides his crime by blaming radical foreign insurgents nobody cares to understand the motives of. He wins doubly by this action. He liquidates the senate, and blames the massacre on his scapegoat enemy. Thus he magnifies his own power via public belief in a maxim by secretly violating that very maxim. Beautiful in it's poetic irony yet grisly in the caution it advises us.
Such social conventions, "prisons you cannot see or smell or taste or touch" are fairly simple to erect in a culture given that once a populace has learned to move through a flat space via complicated ritual, the freedom of an extra dimension of movement becomes terrifying to consider. To that end, any discussion on the matter becomes intolerable, and the assumption goes that none would discuss such "forbidden" freedoms who do not secretly desire greater capacity to abuse them.
In Victorian times, this covered all facets of social etiquette. Cast inequality, gender inequality, racial inequality.. We have since shed much of this ignorant behavior, but we have not yet (and may never) complete such a journey of enlightenment. It is easy for us to look back to the time this book was written as a sphere might look down upon a pitiful flat space, and gloat that our freedoms today are now complete.
However, as A Square might even point out to you, our journey is certainly not finished. The dangerous thing about lacking a dimension is that you cannot easily determine that you are even being limited. You can move in every direction you can see, and you cannot (or reflexively choose not to) see any directions which are closed to you.
Let us consider Gay Marriage as an example, since it is a hot-button topic of the moment. So long as you "define" marriage as needing to involve a man and a woman, you limit your own freedoms (regardless of whether you would ever choose to exercise them) as well as the freedoms of others (who may find such strictures significantly more chafing than you do). So long as you cling to this definition, you cannot see that you are missing anything. Certainly, before the Gay Rights movement any marriage with a "configuration" different than that of one husband and one wife (biblical polygamy notwithstanding) was seen as either ridiculous or an abomination. Anyone who wished to even discuss such an idea was considered either a pervert, a deviant, or perhaps mad.. and you invariably distrusted their motives. Today, it's mostly religious conservatives that still resist the legal endorsement of such arrangements. I suppose they are concerned that once homosexual couples are done fighting for this freedom, they may next move the trenches up to something more genuinely threatening to the religious establishment.
There are countless other examples I will not touch upon here for fear of bristling too many hairs at once (Nudists? Recreational Drug Users? I could do this all day) but one of my favorite Victorian-like, unfair, over complicated, over litigious conventions that is going through it's noisy death throws though no one will publicly admit they want to see it die is Copyright Law.
Hey, settle down! There is no use defending copyright to me on the IMDB boards. This is a topic whose very discussion might get you banned from a forum which gets it's revenue from the very agencies who prefer you know as little as possible about the matter. Because, you see, corporate abuse of copyright law *is* systemic, draconian, and leads to censorship unlike simple Gay Marriage.
Any time an abolitionist speaks out, big content producers need say nothing because an army of alarmed, small or would-be content producers rally to their defense asking stubborn and rhetorical questions like "how will content creators make money?" They don't really want an answer, just to try to make our proposals sound silly. To us this sounds exactly like "Where is this 'up' you speak of? It isn't a direction I can travel in so I call you a liar". Well, I'm sorry, that direction will be challenging for you to comprehend or travel in until after we've released ourselves from the shackles of content monopoly. I could simply name alternatives such as Assurance Contracts or Canned Media as Advertisement for Live Performance, but the people I talk to always try to compare these methods with under-performing or niche experiments already attempted in the copyright-hampered world we live in today, which is much like confusing "up" with "north" and thus arriving at foundationally flawed conclusions.
They also love to bemoan the inevitable loss of movie productions with quarter of a billion dollar price tags. Helpfully, the cost of production drops by magnitudes once you do not have to pay for every second of film and audio to be pristinely and utterly original and hire a team of attorneys to ensure that nobody could somehow interfere with your work by laying claims to any portion of it. It is also needlessly hard to make a buck via honest means in a market distorted by the power of corporations which control every classical content channel (radio, television, Hulu) providing whole copies of their content for free and then charging usurious sums to allow people to view the content again under their own control (for example offline, on their own schedule, or without ads) to say nothing of citing content in an accessible manner or remixing it into your own work.
People tend to demand content that they have either seen before, that their friends have seen, or that is advertised to them to wet their whistles. So long as all such material is copyrighted, the funds gained from fleecing the public to see these canned performances are then re-invested in saturation-marketing the next wave of imaginary property and starting the cycle anew. As a result, today a vast majority of all digital information in the world is under some form of copyright or another, and any access to or use of it is controlled by oftentimes unreachable authors (or more commonly the production houses they've sold out to) whose only commercial interest in allowing you access lies in gouging from you every penny they can get.
When some roads and bridges have tollbooths, you weigh the added convenience of the shortcut against it's cost and drive the long way around if the convenient path is not within your budget. When every road paved has it's own toll booth, all trips become astronomically expensive so you simply stay home or only travel along paths herded by those who control the fees of important routes (such as to or from their own artificially overpriced shopping malls!)
Copyright holders will normally agree to no sum whatsoever (or sums neither you nor they could ever amass in your lifetimes) if you request permission to include their work within your own. This is especially when your enveloping project is intended to be consumed (!) redistributed (!!) or remixed (!!!) freely to encourage wide distribution. This leaves liberal creators no options besides creating or commissioning every molecule of a new work from scratch, and this leaves virtually all human knowledge and parable unavailable to include in situ within discussion. For example, I could not embed a video clip from Flatland the Film on my blog to illustrate a tricky point I intend to make without risking my blog hosting and/or my Youtube channel in the process. Even when it's fair use, I'd have to invest in a court case to defend my blog entry.
So, yes, I had to open a whole can of worms to illustrate an unpopular position regarding copyright. My point is that describing gender equality or interracial marriage so that a Victorian can comprehend it's relevance without tripping over personal offense is as difficult and exhausting as one of many modern day equivalent arguments (such as copyright abolition), which in turn is as challenging as understanding 4 dimensions when all you can perceive are three.
For every action there is an equal and opposite merchandising opportunity
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