THE VERY FIRST time I watched this, I remember feeling only one thing—Awe. You might be wondering how Flatland: The Movie, a 2D animated film about mathematics and dimensions, can be so unforgettable. Is it the gripping musical score? Perhaps it’s the characters, each one with their own unique and compelling personality. Or maybe it’s the overwhelming sense that something amazing is going to happen, and we simply cannot let it happen without us. When Galileo Galilei first proposed that the Earth is not at the centre of the universe, he was accused of heresy and subsequently punished. Even though he was right, a powerful tide of dispute weighed against him and ensured that his views were kept under lock and key until many years later. The world was not yet ready to accept an idea that challenged the existing status quo, and in Flatland, history is set to repeat itself.
Imagine you live in a world with perfect order. Inside this world, there are a range of different shapes. Every shape has a different level of power, but the almighty circles reign supreme. You are not a circle. You are Arthur Square. You work in a typical office job, doing typical admin duties. You are just another brick in the wall. Even your work colleagues don’t shy away from reminding you of your position: “You’re only a square. Four vertices, Ninety degrees, and no more.” But despite these limitations, despite the rules and regulations that must be obeyed, something within you yearns for more.
Flatland: The Movie was originally released in 2007, co-directed through the creative efforts of Dano Johnson and Jeffrey Travis. The 34 minute film stars the voice talents of Kristen Bell, Tony Hale, Martin Sheen and Michael York, and is based on Edwin A. Abbott’s sci-fi novella, Flatland: A Romance of Many Dimensions, which aimed to explore the existence of higher dimensions and provide a commentary on the social hierarchy of Victorian culture. The film adaptation cleverly adapts both these ideas to the modern audience by layering the novel’s blueprint with a cartoonish art-style and a more personalised cast of characters that have been figuratively brought to life in a colourful, animated world.
—it’s NOT hip to be square—
Sweeping ambient music soars across space, trailing behind an all seeing camera that catches occasional glimpses of pretty constellations before it settles for a bird’s eye view of the flat plains below. You shudder with curiosity. What is this place? Who is this blue square gravitating towards this mysterious six pointed structure? As the blaring sound of the alarm clock pierces your ears, you abruptly awaken, and remember that this is you. Arthur Square, that is. You frown. Even in your sleep the thought pesters you. The one you can’t seem to squash no matter how hard you try: Does another world beyond this one exist? Your wife chooses this moment to remind you that there is “no time for dreams”, because in the real world, more practical things need to be done, such as taking your granddaughter Hex to school.
It is at this point that Flatland embraces the perfect opportunity to explain the basic building blocks that make up this society. Arthur asks Hex about the Flatlandian laws of inheritance, which she is only too happy to recite:
“Isosceles triangles have baby equilateral triangles, equilateral triangles have baby squares, squares have pentagons, pentagons have hexagons…and each new generation gets one new side, until they get so many sides they look like a circle.”
We now have a better understanding of Flatlandian pedigrees, which imply that each generation is different from the last. But then, Arthur asks her a more important question. How does shape affect your place in society? She answers again, but this time with less certainty:
“Triangles work the hard jobs, squares get to work in an office, but the circles just make rules that everybody has to obey.”
Arthur reprimands her for her impudence, reminding her and the audience that ‘the more sides you have, the greater your angles’, and by logical extension, that makes you ‘smarter’. But Hex is right. This is the brilliantly simplistic way in which Flatland uses shapes as a metaphor to make us question the structure of our own societies. Who are the triangles in our lives? Who are the squares and the circles? Are shapes with more sides really ‘smarter’? The word use of the ‘shape’ here is multi-layered, and does not just provide a comment on social hierarchy and intelligence, but also extends to religion, ethnicity, political beliefs, gender roles, physical appearance and so on. Essentially, it is telling us what the linguist Deborah Cameron told us: How we act depends on who we are, and especially in terms of who we are perceived to be by others. Nearly all the residents of Flatland have come to accept these dogmas as law. They do not think, and are not encouraged to think outside these concrete parameters. In The Mask of Zorro, when de la Vega (Anthony Hopkins) spoke to Alejandro (Antonio Banderas) about the training circle, he notably said: This circle will be your world, your whole life. Until I tell you otherwise, there is nothing outside of it. So like Alejandro, these Flatlanders are trapped inside a restricted realm of existence. The difference is, their masters-the circles-are never going to set them free. The circles want to contain the ‘lower-level shapes’ inside the neat little boxes they have created for them, because that is how the circles retain their power. So it is no surprise that when somebody like Hex, a diminutive hexagon, a child, begins to question that indisputable power, Arthur reacts negatively.
As Arthur Square, you are acutely aware of the consequences of even daring to defy authority. And as if someone was reading your thoughts, just moments later there is an impromptu arrest of a baby octagon on the streets. A triangular enforcement team surrounds her in a threatening fashion, oblivious to the pained, desperate cries of her mother, and an official looking circle delivers the final blow, ‘According to Section 2.71828, all irregular shapes must be inspected at the Ministry, for direction or disposal!’ Such is the incredible and fearsome power of the circles to silence anyone who steps out of line. It is swift and without mercy. So when Hex asks you if that’s what happened to her parents, you know better than to discuss it in public.
—a story with many sides—
It is impossible to watch Flatland without experiencing a sense of déjà vu, primarily because of the film’s heavy Galileo undertones. Specifically, that anyone who questions authority will be silenced, and their voices will be erased, just like the mother of the baby octagon. It is this quality that makes the film so intriguing. It is when Miss Helios, Arthur’s circular superior at his job at the Ministry of Regularity, vehemently shouts, “Know your places! You’ll never be more than four sides of mediocrity!” That we are invited to prove her wrong, to prove that squares are more than just four vertices and ninety degrees. The head circle ruler of Flatland, Pantocyclus, adds fuel to the fire at a work meeting when he states that the notion of a third dimension is both ‘absurd’ and ‘illegal’. He goes on to describe anyone supportive of the third dimension as ‘delusional and dangerous individuals’, but the psychological temptation has already been put in place. When somebody tells us we cannot do something, or it is not allowed, it makes us want to do it all the more.
That night at dinner, Hex asks you what a dimension is. You tell her that might be hard to explain, but then she sighs, and has that disappointed face that always makes you sad, so you give in. You take her to the bedroom and pull out a few building blocks. Slowly, you begin to tell her about lines, segments, and powers, but she interrupts you and says she’s seen this before at 33H, a forbidden area. You try to dismiss her claim, and tell her not to believe those ‘conspiracy theories’, but Hex is on a roll. She postulates the existence of a ‘supersquare’, or a square that is 3 to the third power. A cube. Your eyes momentarily sparkle in wonder.
But as if shaken from a trance, you quickly return to your training circle and admonish Hex, especially when she expands the idea of a supersquare to a superhexagon, and ultimately, the unspeakable third dimension. There’s no such thing. There can’t be. The circles are ‘wise’ because of their ‘configuration’, and know better. And you know ‘it’s too dangerous’ to believe in the ‘foolishness’ of the mere possibility of a third dimension. As far as you’re concerned, that is a dream that is best left untouched. So what does this tell us about ourselves, in the real world? It says that as humans, we are really only capable of believing the things we can see or imagine, and that anything which falls outside that domain and is deemed as ‘dangerous’ by those in positions of authority should be rejected. It says that curiosity about the unknown is bad, and like Galileo, we will be reprimanded if we ‘meddle with heresy’. But as we are about to find out, this is only just one side of the story.
When Arthur Square falls asleep that night, he is transported to a dark, eerie world with fluorescent shapes and strange noises. He believes that he is utterly alone, but other creatures exist in this landscape, too. The King of Pointland, for instance, is one of the most bizarre individuals you will ever meet. He is delusional, psychotic, and absolutely hilarious as he blips about his kingdom of zero dimensions.
Voiced by Tony Hale, the King of Pointland represents a comedic interlude to the more serious nature of Arthur’s unconscious investigation, and also shows us the naivety of believing that we are alone in our respective universes. Arthur’s journey takes him to the King of Lineland next, who is also of the mistaken belief that nothing more exists beyond his one dimensional world. When he is presented with the notions of ‘above’ and ‘below’, he scoffs, and replies that even the youngest child in Lineland knows that the only two directions are left and right. What’s interesting, however, is that when Arthur Square enters Lineland in an attempt to convince the King that a two dimensional plane exists, he labels him as an ‘enchanter’ and his actions as ‘mockery’. By now, this should be starting to sound familiar. Arthur departs shortly afterwards, and concludes that the King of Lineland is a ‘simple little fellow’. What he fails to realise, however, is the remarkable similarity to his own situation in Flatland.
—VOICES FROM ABOVE—
Without any warning, Arthur is instantly transported back to the comfort of his home, where he blames Hex for these ‘nightmares’. But his dream isn’t over, not quite yet. The velvety, enigmatic tone of Michael York’s voice permeates the room, and suddenly, Arthur is face to face with Spherius, an omniscient being from above.
And as Spherius explains himself, you listen, quite enraptured. He tells you he is not a circle, but an infinite number of circles. A solid, more perfect than anything in all of Flatland. He also tells you that he comes from space, the third dimension. When he begins to speak of ‘height’, you call it ‘absurd’, echoing the sentiments of the King of Lineland. But everything changes when he plucks you out of your restricted 2D world and catapults you into the unknown. You are suspended in space, floating, tethered to the sky by invisible strings. It’s unimaginable. An angelic chorus begins to sing, intensifying the atmosphere as you experience an unbridled sense of astonishment. All your doubts were in vain. All the circles were wrong. And you can’t believe it. And yet, as Spherius reflects, ‘the evidence was right in front of you, waiting to be discovered’.
Flatland‘s storytelling truly shines in this moment, hinting that even squares like Arthur, or people who are ordinary, are capable of doing and understanding extraordinary things. Put simply, Spherius symbolises the knowledge or creative spark that empowers us to believe that we can accomplish those extraordinary things. Together, Spherius and Arthur travel to the forbidden area of 33H, where he introduces Arthur to the concept of a cube, and reveals that it was left behind to the Flatlanders as a sign so that they would be able to understand the existence of the third dimension without actually having seen it. Arthur asks him whether the circles are aware of this, and Sphereus knowingly reveals that they are, and have been deliberately withholding the information from the Flatlanders. After all, he says sagely, what kind of power would the circles have if everybody knew the truth? This is a prospect that is simultaneously thrilling and terrifying. In Indiana Jones and the Kingdom of the Crystal Skull, we are warned that our minds are not advanced enough to process the colossal streams of knowledge that float around the universe, and we are fools if we try to. But in Flatland, we are shown another perspective, and the distinction is clear: We don’t have to experience something that is beyond our reach to know that it is true; We just have to be aware of it.
—a perfect circle—
Arthur’s joyride eventually comes to an end, and, still in a ponderous state of mind, he questions Spherius about the existence of a fourth dimension. Flatland’s plot comes full circle when Sphereus asserts that he finds the very idea of a fourth dimension ‘utterly inconceivable’, but by now, we have more than enough reason to know that he too is incorrect. Arthur wakes up from his dream a changed man, enlightened by the visions he has seen, and more receptive to his granddaughter’s ideas-a granddaughter who is now busy trying to uncover the secrets of area 33H, and has triggered a wide-scale security breach. Arthur and his brother Abbott rush to her rescue, arriving just in time before the isosceles enforcement teams swarm in and capture her. It is here that Arthur gives Hex the greatest present of all. Something amazing is going to happen, and she is going to be the one to do it. “Never forget what you’re about to see,” He tells her, before he nudges her towards the perpetually rotating cube in the self-sacrificing manner that is unique to parents and grandparents. He knows that she needs to experience the things he saw in his dreams in reality, and the time for her to experience them is now.
Moments later, Arthur is flanked by isosceles triangles, and his circular superior Miss Helios and her self-satisfied laugh make a triumphant comeback. He dares to utter that the existence of the third dimension is true, and as swiftly as the words leave his lips, he is imprisoned in a cage of four walls, a solid reminder of who he is and his shape in the Flatlandian society. But in this case, I think it is safe to say that despite appearances, a square is no longer just a square.
At his trial, Pantocyclus and Miss Helios press Arthur for evidence of this ‘third dimension’ he seems so adamant about. But unfortunately, he is unable to produce anything tangible, and we all know what that means. If you can’t show somebody proof that something exists, it doesn’t exist. And so it goes. Justice is swift. Pantocyclus, the iconic figure of power abuse, delivers the final crushing blow: Arthur Square is condemned to death.
Everything comes crashing down in this moment. All your hopes and dreams, all your theories about space and dimensions, shattered. Perhaps the circles were right. You’re just a square, after all. Four vertices, ninety degrees, and no more. The words echo dimly in your mind. You close your eyes with a heavy heart, utterly defeated. But in the pit of your despair, Sphereus appears in true deus ex machina style, and plucks you straight out of Flatland-this time, in reality. Down below, the circles erupt into cries of outrage. They are demanding that you show yourself, desperate to cling onto the last shreds of the façade they have managed to uphold and beguile the Flatlanders with for the past millennium. Thus, we reach what is perhaps the most climactic few seconds of the entire film: The illustration of the consequences of choosing to oppose authority. At some point in our lives, we have no doubt been in Arthur Square’s position, or known of someone who has. More often than not, the aftermath isn’t rosy. But can you imagine the potential consequences of choosing not to make your voice heard? If, for instance, Galileo had chosen to remain silent about his dispute against the prevailing view of geocentrism? What would that have meant for us today? And what about Flatland? Would the Flatlanders have narrowly missed the window of opportunity to unveil the truth, and been forced to wait another thousand years for a new ‘prophet’ to come forth? We will never know. But we can rest assured in the fact that Arthur Square chose to listen to his granddaughter. He chose to take a leap of faith. Hex eventually descends from above to spread the truth of the third dimension to all the shapes, and Arthur’s sense of pride could not be more evident. The illusionary regime of control pushed forward by the circles suddenly collapses and crumbles into oblivion. Miss Helios accidentally traps herself in Arthur’s cage, and screams at the triangular guards who are now siding with the other shapes, ‘You idiotic isosceles!’, demonstrative of Flatland’s witty, unparalleled humour.
From the vantage point of Spaceland, we hear Sphereus offer Arthur some well deserved acknowledgements for his efforts:
“Your mind has grasped what your eyes could not see. And your imagination has changed your world forever. Not bad for a simple square, Arthur.”
Once upon a time, humans believed that the sun revolved around the Earth. But then somebody dared to question the status quo. For us, that somebody was Galileo. For the Flatlanders, it was Hex, a tiny hexagon whose significance in the discovery of the third dimension was initially overlooked, and a subtle reminder that we should not judge another’s ability or potential based on their ‘shape’. In Flatland‘s closing scene, we see Sphereus dismissing the idea of the fourth dimension, which by now seems to be as foolish as the claims made by the Kings of Pointland and Lineland about the non-existence of anything they could not see with their own eyes. We are left with this insatiable sort of wonder, one that says dimensions greater than the third do exist, and we just have to find them; A wonder that also says despite our substantial progress as a species, we are still simple creatures, striving to understand a complex world, and an even more complex universe. But to strive for something is admirable in itself. Flatland: The Movie is an astounding piece of work that thrills the imagination to the limit. A true feast for the mind that questions, it both validates and intensifies our curiosity for existence, forever urging us to delve deeper. If you haven’t seen it yet, and enjoy films about maths, physics and beyond, you can purchase Flatland from its official website for $24.95 USD (digital download). I wholeheartedly recommend it. Its sequel, Sphereland, picks up where Flatland left off and delivers an impressive conclusion to this electrifying suite of animations.