This is a summary of the book Flatland: A Romance of Many Dimensions, by Edwin Abbot Abbot, published in 1884.
The goal is to summarize everything from the original novel to make it easier for people to understand, if they don’t want to read the original novel or the 2024 translation, or would like a quick(er) reminder.
You can read and download this from the Internet Archive in multiple formats, including editable documents.
You can also buy a physical copy here, or purchase the files from Itch.io.
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Flatland: A Romance of Many Dimensions, is a political satire as well as an introduction to the concept of different dimensions. The author, Edwin Abbot Abbot, wrote it to criticize the systems of oppression he saw around him in Victorian England: Misogyny, racism, ableism, classism, intersexism, and more.
(This is a very long post, don't click the read-more willy nilly)
(Archived read-more link)
He wrote his narrator to be a bigot who is very self-centered and proud of his own bigotry, to make fun of actual bigots. Everything the narrator believes in is exaggeratedly and blatantly evil, to showcase the evil of society's bigotry towards women, people of color, disabled people, intersex people, poor people, and more.
Section 1: About the Narrator of Flatland
The Narrator of the original book does not have any confirmed name that we know, because he chose to hide his identity with the fake name of “A Square”, the same way that people will call themselves “J Doe” or “M Smith” when they don’t want to reveal their true identity.
Many fans enjoy calling him “Abbot Square”, affectionately naming him after the author, Edwin Abbot Abbot, or give him other names that start with A, and base their own original characters for the setting's last names on their shape in a similar style. For example, “B Line”, or "K Polygon".
Despite this, the narrator's name is not actually A Square, so you can call him anything you want, and you won’t be wrong. The Sphere who visited him also has no confirmed name, and can again be called anything.
We do not know what kind of family names exist in Flatland, or if they even use them at all.
The only character from the book whose name we know for certain is Pantocyclus, a historical dictator Circle.
Another historical figure is usually called Chromatistes, but even within the story, there is some debate by historians about whether or not that’s accurate.
Both Pantocyclus and Chromatistes lived thousands of years before the story takes places, so the only things we know about them is what the Circles decided to tell people afterward. If it makes it easier to think about the scale of time, they can safely be considered as far back in history as Jesus, or even earlier.
The narrator of Flatland has a wife, and they have had at least six children together: 5 Pentagons, and 1 Straight Line.
We do not know any of their names, or their personalities.
We do know that one of the adult Pentagon sons died, presumably along with his wife, leaving behind two orphaned Hexagons, the narrator’s grandsons, who now live with the narrator and the rest of his adult children and wife.
They live in a surprisingly rich neighborhood near a large theater. We know that the roof of their house was recently repaired, though we do not know how it was damaged.
We know that the narrator is considered a gentleman, a respected lawyer, with money and social status. We also know he's a bigot, and that he likes the idea of color (which you'll learn more about later), and he enjoys doing math for fun in his free time, including going to conventions for it.
But that's pretty much all we know about him. The original Flatland novel's first half is a general overview of Flatland society, with the second half being the narrator's personal journey to different dimensions. We do not learn much more about him than I have described above.
If you want to write your own version or continuation of the story, you can build on all of the above, or throw it out completely. Just remember to keep the morals of the original story firmly in sight.
Section 2: About Flatland, and the people and societies that the Narrator was familiar with
The people of Flatland are different geometric figures: Circles, Hexagons, Pentagons, Squares, Triangles, Lines, and more.
They have no arms, legs, feet, or hands, but are still able to move about and move things in a way that is not explained to us. Since they have no legs, they can't "sit" or "run" the way we do, but still use these words to mean different levels of activity: staying in one place calmly is called sitting or lying down, moving quickly is calling running, and suddenly surging in a direction is called jumping.
People in Flatland don't actually call their world “Flatland” among themselves, that is just a name the Narrator came up with to make what it's like more obvious for the audience. Flatland is a very easy way to make it clear that Flatland is a land that is very flat.
We do not know the names of any countries in Flatland, or what any of them actually refer to their world as.
We do not know how many countries there are, or how big or small they are, or where they are in relation to one another.
We just know that there are multiple countries that are ruled by a council of Circles, which is then ruled by the supreme Chief Circle. None of these Circles are elected, instead they are chosen for their physical form. In these areas of Flatland, wider angles and more sides equals higher social status. And the Circles were the highest ranked of them all.
It might be helpful to think of them as structured similarly to the United States of America, but we don’t know for sure, since we aren't given any details.
There are almost certainly countries outside of this arrangement, but none were spoken of. It's extremely likely that it would be illegal for anyone within the Circle-controlled countries to speak of countries where things are done differently.
Flatlanders refer to themselves as human beings. Nothing is told to us about any other specific species in Flatland, though the narrator does take the time to assure us that just because he doesn’t mention something doesn’t mean it doesn’t exist. (Just like how most authors don't tell us when the characters go on bathroom breaks, but those are still a thing that exists, that the characters are doing at some point)
We know that vegetables and trees exist in Flatland, but we don’t know the details, besides that tree trunks somehow aid in determining North and South.
You should imagine the inhabitants of Flatland as very thin shapes that swim through the top layer of a large ocean. They can't leave this single layer, either by going up or down, and they’re not aware of anything outside it. They’re not even aware that they’re inside a liquid at all, or aware of any movement of this liquid. They cannot look up or down. They have no inherent concept of up or down at all.
They categorize the directions as North, South, East, and West.
They can look forwards, and from side to side. They cannot look up or down as we define them.
[Image description start: A diagram showing a triangle with a purple inside and simple pink blobs for organs, labeled, “Flatlanders can look forward, and side to side. To look behind themselves, they have to spin around entirely.” The Triangle is shown at the bottom of the image and pointing upward, with their eye first looking to the left, then turning to the right, then they are shown at the top of the image looking down and straight ahead. Next to this is a much smaller, black and white diagram showing the triangle turning to face back the way they’d come. Image description end.]
Unlike our compass directions, which are indicated by magnetic north, the Flatland compass is defined by the "Southern pull", an affect like a magnet or gravity that is noticeable in most parts of Flatland.
The strength of this pull is increased the further South along the flat plane you go, and weakens the further North you travel.
We do not know for sure what causes it, because the narrator did not know, but it could be some sort of magnet, or a dense core of some sort creating a kind of gravity.Whether or not there is a special 2D gravity is up to you to decide.
Moving on from the compass, the houses in Flatland are shaped like pentagons, because it was decided that the angle of a pentagon was the sharpest angle that should be allowed on a building for the sake of public safety, because running into the sharp corner of a more pointed building could be very dangerous.
The pentagonal houses face north so that rain, which always comes from the north on a predictable schedule, does not come in either of the doors, which are on lower sides that are angled inward.
On the western side is a large door for men, on the east a much smaller door for women.
Buildings in Flatland have no windows, because light is always visible no matter where you are or if you are in a building or not.
Unknown to them, light comes from the Third Dimension above them. Scholars used to try to figure out where light came from, until the Circles made it illegal to ask those sorts of questions.
If not for the fascist society they live in, it can be assumed that Flatlanders would naturally come to theorize about other mathematical dimensions just like we have.
The only buildings allowed to have sharper corners than pentagons are ammunition warehouses and other military and government buildings that are not meant to be used by just any random person. It can be safely assumed that jails and asylums also have sharp corners to keep unwanted visitors away.
When seen from above or below, the internal organs of these geometric Flatlanders are clearly visible.
But they are not aware that their insides are visible from another angle, because, and I cannot stress this enough, they have no idea that the directions of “up” or “down” exist at all.
As far as they are concerned, they’re completely solid, just like you and me.
[Image description start: A Square Flatlander first shown as seen “from above or below”, with the square shape clear, and the purple and pink insides visible. The square then warps as the point of view is lowered, until they are visible only as a black straight line, labeled, “From Flatland”. Image description end.]
What exactly their insides look like is up for you and I to speculate on, because the narrator didn’t feel like giving a lecture on anatomy.
But we do know that Flatlanders each have a single eye, which, in some way that is never explained to us, doubles as their mouth. This eye-mouth will always found on one of the Flatlander’s angles or points, where two sides meet.
[Image description start: A black and white collection of different square Flatlanders, with their eyemouths at different parts. At the top of the image is one with the eyemouth on the upper corner, labeled, “Eyemouth on corner equals canon compliant”. Below this are three more, one with an eyemouth in the center, seeming to look towards the camera, one with it on the middle of one side, and the last one has an eye on the side above a separate smiling mouth. Image description end.]
For Isosceles triangles, we know that their eye-mouth is on one of the points of their base, rather than their longer sharp point. For Straight Lines, just pick an end. For other Irregular Figures, go wild, pick whatever angle you want.
There is no such thing as a true Circle in Flatland, only Figures with many small sides, so you can just pick any part of a Circular character to put their eye, even if you’re just simplifying them as a Circle. (I doubt anyone wants to sit there and figure out how to draw a shape with 600+ perfectly equal sides)
When in their natural habitat (Flatland) a Flatlander only ever sees anything they are looking at from its side, so that everything appears as a straight line, just at different lengths, levels of brightness, and distances.
You can see how this would work yourself by taking a coin, or a shape cut out in cardboard or paper, and putting it on a table.
When you look down on it from above, you see the shape it really is. But if you put your eye on the level with the table it sits on, it will appear as a straight line.
[Image description start: First we have a square labeled, “A Flatlander seen from above or below has visible insides”. The square has a purple interior, with simple pink blobs for organs. Text after this reads, “We do not actually now what the insides of a Flatlander look like because A Square didn’t tell us.” Below is a straight line, labeled, “A Flatlander seen from the side in Flatland appears to be a solid line.”. Image description end.]
That straight line is how Flatlanders see everything when they are inside Flatland. Only from above can their true shape (and internal organs) be seen.
Everything, to a Flatlander, looks like a straight line. When someone or something is closer to them, the line appears longer from side to side, and when further away, it is smaller from side to side.
[Image description start: A diagram labeled, “Simulated Flatlander field of view with added height for visibility. Imagine this bar to be very flat.”. In the center of the diagram is a large bar, with one half colored in black, and the other half mostly grey, with a thin black stripe towards the right. At the bottom of the diagram are three small triangles, one labeled, “You”, one labeled, “the friend standing right in front of your face”, and the last is labeled, “the friend standing across the field”. Grey lines radiate out from the front point on “You” to show how the friend in front of “you” blocks most of your vision, creating the large black section on the bar, while the friend across the field only blocks a smaller part, representing the thin black stripe on the other side of the bar. Image description end.]
This is why their eye-mouths are on their edges, because that is the only direction they can ever look, and everything looks solid from that angle.
If they had an eye-mouth on their upper or lower side, they wouldn’t be able to see or eat anything inside Flatland, and they would only see what is above or below them.
[Image description start: A drawing of multiple Flatlanders of different shapes arranged around the edges of the image, all looking at text in the middle that reads, "The eye-mouth is on the outside of the Flatlander, otherwise they wouldn't be able to see or eat." The shapes looking at the center consist of a square, an irregular polygon, a circle, an isosceles triangle, an equilateral triangle, and a straight line, who is a very thin trapezoid. There is also a very small pentagon child who instead has an eye in the center of their body, looking towards the camera with a questionmark, labeled in smaller text: "If a Flatlander were born with their eyemouth in their center, they wouldn't be able to see or eat anything in Flatland, and would most likely starve to death in childhood without immediate medical intervention of a feeding tube directly to their stomach.". Image description end.]
If you're planning to draw characters from Flatland, like with everything else about it, you can break this rule for stylization purposes, or you could do a story where a character is born with their eye out of the usual place, and is considered Irregular because of it. (They would also neccessarily be blind and would need to find other ways to navigate and interact within Flatland, no matter what they can see above and below, unless it happened to be a mirrored surface.)
But when speaking of the original novel, this is how it works. Eyes are on the edges, not the upper or lower surfaces.
We do not have any details of what above and below Flatland look like, so it is up for any interpretation.
Despite everything they look at appearing as a straight line, Flatlanders are still able to navigate and recognize one another by sight, because the edges of Flatlanders, and other living things, all glow with automatic bioluminescence, and because in many places there is usually a dense "fog" in the air.
This means that when one Flatlander looks at another in an area with fog, the areas that are closer to them appear brighter, and the parts that are further away are darker.
Three Figures will help us demonstrate this idea so you can understand: Billie the Straight Line, Bob the Circle, and Joe the Hexagon.
[Image description start. A diagram labeled, “Billie, Bob, and Joe seen from above”. Billie is a Straight Line, who is a very thin diamond shape. Bob is a Circle. Joe is a Hexagon. Image description end.]
If Bob the Circle looks at Joe the Hexagon so that one of Joe’s flat sections is facing him, Bob the Circle will see a bright line in the center of his vision, with a darker gradient on either side.
The bright line is the flat section of Joe that is closest to Bob. The gradient on either side is what is visible of Joe’s other angles from this perspective.
And if Billie the Straight Line looks at Joe from another angle, so that one of Joe’s points is facing her instead of one of his larger flat sections, then Billie will see a small point of light, with a larger gradient from light to dark around it, because the closest thing to Billie is one of Joe’s points.
[Image description start: Another drawing, now zoomed back, with Joe in the middle of Billie and Bob, who look at him from different angles. Billie looks at one of Joe's angles, and Bob looks at one of his flat sides. A bar at the top is labeled, "Billie's view of Joe", and has a thin white stripe in the center, with a slow gradient to grey on either side. At the bottom of the image is another bar showing Bob's view of Joe, which has a large white stripe in the center, with a faster gradient to grey on either side. Image description end.]
By using the different levels and gradients between brightness and darkness when looking at one another, Flatlanders whose families are rich enough to send them to specialized private rich kid schools can learn to recognize different shapes from sight alone.
This is known as The Art of Sight Recognition, and it is very difficult to master, so difficult in fact that most Flatlanders rely instead upon The Art of Feeling – where Flatlanders gently and carefully feel along the angles of one another to figure out what shape they are. This is treated as a formal introduction (The difference between shaking hands while trading names, and simply saying 'hi').
But the Art of Feeling can be dangerous if you’re not careful, because some shapes have very sharp angles that can cut, stab, or even outright kill someone if hit with enough force.
The Narrator tells us that one of his ancestors, who was an Isosceles triangle (A triangle with two sides the same, and another different), accidentally killed a man while he was being Felt, by accidentally moving too quickly because of pain from his arthritis, and ended up cutting the man who’d been Feeling him in half.
We are told that the “moral shock” of this action degraded the angles of the narrator's male ancestors for generations, but it is much, much more likely that the people doing the measuring simply lied about their angles to punish them.
Higher class citizens look down on the Art of Feeling, not only because it's dangerous, but because they think it's "vulgar" simply because the poor people do it too. Instead, rich families spend a whole lot of money and time having their sons trained to use Sight Recognition alone, so they can feel special and more intelligent than the poor people.
Fun fact: The word "vulgar" literally means...anything done by the common poor people. It's used to mean "digusting" today literally because rich people think literally anything poor people do is disgusting, gross, and shameful. Because they hate poor people. (This is also why there's some species with a scientific name ending in "vulgaris" if they're very common and easy to find)
To make sure that their male children aren't "contaminated" by the poor people, noblemen do not allow their sons to be taught the Art of Feeling at all, and must rely on Sight Recognition forever.
If, when they go to one of their fancy rich people collages, they’re caught using the art of Feeling despite the rules, they will be given a warning the first time, along with some sort of punishment, and expelled completely the second time. And once you get kicked out of one of these private schools, you can't go back.
Any nobleman who fails to learn the art of Sight Recognition, even after years in university being taught it, is completely shunned from the society of their fellow rich people, and no longer has the right to get married, for fear that they’d pass their inability to learn Sight Recognition down to their kids.
Why, you ask? Because fascism and eugenics go hand in hand. They literally want to "breed out" undesirable traits, so if you have some kind of disability preventing you from leaning Sight Recognition, they don't want you to be able to have kids.
Since these “trash of the rich” (as the narrator calls them) don’t know how to use Sight Recognition or the Art of Feeling, they’re unable to interact with larger society at all, and lead miserable lives.
If given enough time, they could probably learn the Art of Feeling, if they were willing to get past the idea that it's "vulgar" and beneath them, but even then, the society of Flatland is so strictly separated by caste determined by your shape that there are no jobs that would, or even legally could, hire them.
There is another kind of Recognition used to tell people’s classes apart, and it is done simply by listening to someone speak, and judging what class they’re from based on their accent.
This isn’t very helpful, though, because while poor people are easily able to mimic the accents of rich people, the rich people, who only ever hang out with other rich people, and only notice poor people's existence when they're thinking of how disgusting they are, cannot do the same in reverse, since they have no idea what poor people actually talk like.
And since all the rich people hang out together, and more importantly are desperate to fit in with one another and not stand out, they all speak in the same general way, so you can’t tell from their Rich Person Accent alone whether they’re an eight-sided Octagon, or a twenty-sided Icosagon.
When A Square wrote his autobiography, the societies he spoke of accepted only specific shapes as worthy of being called human beings with basic civil rights, insisting that humans could only be "Regular" Figures, meaning that all of their angles and sides had to match.
This meant that when the Art of Feeling or Sight Recognition were used for identification, only a single angle needed to be felt or looked at to figure out the whole shape.
These societies also considered all “Straight Lines” to be female, and every Figure that was not a “Straight Line” to be male.
Because Joe and Bob are, for the sake of this summary, “shapes” with multiple angles, so they would be considered Male, or Men, and Billie, being a “Straight Line”, and having “no angles” would be considered a Female, or a Woman.
But despite the fact that they are referred to as “Straight Lines”, Flatlanders who care about basic mathmatics are in fact aware that so-called “Straight Lines” are actually all very thin parallelograms, a term that includes squares, rectangles, diamonds, and more.
Straight Lines are shapes too, with their own angles, just like everyone else, they just happen to be much thinner. And the people in charge of society are very aware of this fact, but spread the lies anyways.
[Image description start. A digital drawing captioned, "Despite their name, Straight Lines are actually very, very thin parallelograms rather than true lines.". Next to this are three examples of Straight Lines from Flatland: A rectangle, a diamond or kite, and a trapezoid. All of them are very thin. Image description end.]
Knowing this fact did nothing to change the bigotted insistence that Straight Lines lacked angles, and therefore literally lacked brains.
Because actual facts don’t convince bigots to change their minds, because bigotry isn’t logical, it just claims to be for a false sense of legitimacy. They benefit from the bigotry they're spouting, and they don't care if it doesn't actually make sense or not, that doesn't matter, the only thing that matters is what they have to gain from spreading the lies.
Section 3: Irregular Figures and the Systems of Oppression in Flatland
The lowest status members of Flatland society at the time the narrator was alive were “Irregulars”, which were shapes whose angles and sides did not all match, and, we can assume, Lines that were not straight, though the original book does not actually mention Irregular Lines.
It can be assumed that Irregular Lines existed just as much as other Irregular Figures, and they would be categorized as Lines depending on how thin they were compared to other figures.
The very obvious implication of Women being called “Straight Lines” in particular very clearly implies the existence of non-straight or Irregular Lines, otherwise they wouldn't need to specify that they're straight.
Irregular figures were not considered human at all in the countries the narrator knew of, and, in these countries, most of them were killed as soon as they were born if doctors decided that medical intervention couldn’t “fix” the Irregularity.
In the original novel, Irregularity is used as a metaphor for oppressed people of all kinds depending on the situation, including intersex people, disabled people, people of color, Queer people, and more, depending on the situation.
The act of surgically altering infants who are considered “Irregular” to "fix" is a very clear parallel to the physical violence intersex people face in reality, along with some disabled people.
This system of Regular-Superiority meant that Equilateral (also known as Equal-sided) Triangles were the lowest class of Figures acknowledged to be human, because they had the lowest number of equal sides and angles possible, which is three. Any less than that, and you can't get equal sides or angles.
These societies had a very strict caste system, where your shape determined everything about your life, from the kind of jobs you would be allowed to work, who you could marry or even speak to, and where you could live.
Isosceles are triangles who have exactly two angles and sides that do match, with a third side and angle that are not matching.
These are not to be confused with Scalene triangles, who have no matching angles at all.
Neither Isosceles, or Scalene triangles were considered human, and they had no civil rights at all, though Scalene triangles were not mentioned by that name. They would simply be referred to as Irregular Triangles.
Isosceles were the lowest class of Figure allowed to exist within the narrator's society without being murdered on sight in most cases, because, while they were still Irregular, they were the least amount of Irregular as a Man could get, with only a single side/angle not being equal.
Triangles with no matching sides at all, meaning Scalene triangles, were not tolerated within any of the societies the narrator was familiar with, and would presumably be murdered on sight, or as soon as they were born, if their Irregularity could not be surgically “fixed” to make them either an Isosceles or an Equal-sided triangle.
To reiterate again, Isosceles triangles were not considered human beings, due to being Irregular.
They were considered property, and were bought and sold as such, often being inherited from family lines along with the land they labored on.
Isosceles were forced to perform all of the most dangerous, difficult, degrading, and tedious jobs, while also serving as expendable soldiers for the military, and private armies.
They were were also used as cleaning and serving staff for middle and upper-class families, working as butlers, errand-boys, dishwashers, and more, and would be inherited along with the house they were attached to, if they weren't sold or gifted separately.
Also known as: they were enslaved. They were slaves. A person who is property is a slave.
The measurement of an Isosceles’ unequal angle would determine their social status among other Isosceles. The closer your angle was to 60 degrees, the higher your comparative status, which would give you access to better and safer work assignments than those with lower angles.
Instead of being used to clean the disease-ridden, clogged sewers, for example, or working in a mine, you might instead be washing dishes in a rich guy’s mansion.
Isosceles with very small angles were, among other things, regularly used as expendable executioners; they would be brought in to kill prisoners who were involved with state secrets, only to then be killed themselves to avoid being able to reveal those state secrets to others, even if they hadn’t actually heard the prisoner say anything.
Isosceles were treated as completely disposable non-human things barely worthy of being considered people.
In these fascist societies, Irregularity was conflated with moral bankruptcy, meaning anyone who was born anything except perfectly Regular was considered to be inherently evil, which was the excuse given for murdering and inflicting other cruelties on these people at every opportunity.
But even during the narrator’s lifetime, there were people trying to fight back against this idea, spreading pamphlets pointing out that if a child was born Irregular, and he had to face abuse, hatred, and bullying from his nurse, siblings, and even parents for as long as he could remember, and was constantly told that he was inherently a bad person no matter what he did, and then was shoved out into the world where he was constantly followed by the police under the assumption that he was going to commit a crime, and he was not allowed to have a job or get married, and had no friends to speak of.
If you deny someone literally every opportunity to do good, what other choice do you give him except to be bad?
If you will not let him honestly work for his food, where do you expect him to get it besides from stealing?
In other words, treating people like they're inherently immoral, untrustworthy, and dangerous, and refusing to let them have any opportunities for “honest work”...literally means they have no choice but to become the criminals you’ve told them they are since they were born.
The narrator was not convinced by these pamphlets, even though he admits they are “very plausible”, because he insists that he’s never met an Irregular who wasn’t a horrible person who deserved everything he got.
He admits that the lives of Irregulars are horrific, but says that’s just too bad, because their lives just have to be horrible to make sure everyone else’s are good.
We do not know the details about any specific Irregular characters, because they were only ever mentioned as hypothetical.
Any shape that does not have all equal sides and angles would be considered Irregular, regardless of any other equality or symetry about the shape.
A perfectly symmetrical five-pointed star, for example, would still be considered Irregular even though it’s symmetrical, because the wider angles on the inside do not match the sharper angles on the five points.
[Image description start. A black and white diagram showing a five pointed star, with text reading, “Symetrical, yes…but still considered Irregular, because the angles aren’t all equal to each other”, with arrows pointing to show that the acute angles on the outer points do not match the obtuse angles on the inner sections. End image description.]
The same would be true of many other shapes as well. The eugenicist goals of Flatland were incredibly specific and restrictive.
If all three of your angles were measured at 60 degrees, you weren’t considered an Isosceles, but an Equal-sided triangle, and you would have basic human rights.
[Image description start. A diagram captioned, "A variety of Isosceles triangles. The closer your third angle is to 60 degrees, the higher your comparative social status, though none of them have any civil rights, and are literally not considered human at all due to being Irregular.". Below this is a line of Isosceles triangles, starting with the widest angle on the left, then getting narrower towards the right, until the last almost appears as a straight line. Image description end.]
Isosceles with angles approaching 60 were regularly put into arranged marriages by Circles in an attempt to “breed” children who would be born Equilateral triangles. More eugenics.
If an Equilateral triangle were born to any Isosceles family, whether through the explicit eugenicist program run by the Circles, or by random chance, the infant would be immediately taken away from their Isosceles family, and given to an Equilateral family that did not have any children.
The adoptive parents are then sworn to never reveal the child’s true birth parents, and never to let the child anywhere near them, with the fear that their Irregularity might be contagious and infect the child with proximity.
The birth of an Equilateral triangles from the Isosceles class is celebrated for miles around, because it is used as “proof” to the Isosceles slaves that if they just work hard enough, they can win a better future for their children. They are told that hard work, frugality, and self-control will increase their chances of having Equilateral children.
This is patently not true, but it is a helpful lie for the Circles to spread, because it means their force of free labor works harder and doesn’t complain as much when they don’t have enough to eat. It is the same myth that is spread today, of the “self-made millionaire”.
The rich will always tell you that simply working hard and being a good person is what got them where they are today. The truth is that they were just born to rich parents, and maintain and increase that wealth through exploitation of the working classes, just like the Isosceles of Flatland are exploited for the benefit of the higher classes.
The angles of Isosceles were categorized in a range from 0.5 to 59.5 degrees.
This meant that their angles could be useful for learning the Art of Feeling, because they could be used to learn different angle measurements, which would then help you learn to tell different shapes apart.
Because of this, a huge number of Isosceles, especially those with smaller angles and thus lower status, were sold to elementary schools for middle and upper class children to learn the Art of Feeling.
The children would continually Feel the Isosceles, using them as a human guinea pig for learning angles.
Yes, this is exactly as horrifying as it sounds. Imagine being chained up so that you can't move a muscle, while children grab and poke at you all day, every day, until you die from starvation.
Yes, starvation. Expensive schools with higher budgets would allow the Isosceles prisoners to literally starve to death while being tortured every day by probably hundreds of children.
A Flatlander going without food or water could survive for around a month, which meant these prisoners spent their last month of life being tortured to death not only from the starvation and dehydration, but constant poking, prodding, and, since kids also have sharp angles, probably also many cuts and bruises.
When they died, the rich school would simply buy a new slave to replace them with.
We do not know how they disposed of the bodies, or what exactly happens when a Flatlander dies.
Schools that could not afford to keep buying new slaves every month would provide the ones they did have with food and water, keeping them alive for years on end, before eventually replacing them with “fresh specimens” when they eventually died, or became too scarred from constant feeling to be “useful” anymore.
The narrator of the book originally advocated for allowing these enslaved people to starve, specifically in the hopes of “thinning their numbers”, which he made sure to tell us was a goal every politician agreed on.
In universe, after the narrator was imprisoned for seven years, thinking about what the Sphere had said to him, he became much more progressive in regards to the treatment of Women and Isosceles, though we don't actually know if he'd now want to abolish slavery.
From an out of universe perspective, the entire point of him being such a blatant bigot in the first place is, I feel the need to remind people, specifically done to make the bigotry absolutely clear and make people think of how reprehensible it is.
You are supposed to look at the narrator casually and happily advocating to let people starve to death while being tortured and think “holy crap what is wrong with this guy and the rest of his society?”. And then you’re supposed to take that idea and look at what is going on in the world around you and see if that outrage has a target in the real world, because it probably does.
In the United States, slavery is still literally legal, as long as it’s imposed as a punishment for a crime. That’s literally what’s written in the constitution as of 2024, and has been since slavery was supposedly “abolished”.
Prisoners in the United States as of 2024 are literally, by law, enslaved. They are forced to fight wildfires. They are forced to labor without pay, or for just pennies an hour doing difficult and dangerous work. And this is literally slavery as defined by the Constitution of the United States, which say it’s fine actually, because slavery as punishment for a crime is good.
Many people are explicitly arrested and sent to jail for the purpose of serving as slave labor, and most of these people are Black and brown. Minor crimes that a white person wouldn't think twice of comitting can ruin your life and make you into a literal slave if you've got the wrong skin color.
And yes, this was implimented literally to keep American Slavery going even after pretending to end it. All the slaveowners had to do was arrest their former slaves on fake charges, and wow, would you look at that, they're enslaved again, and no one's gonna start another civil war over it!
Even though they should.
Flatland was written to criticize the systems of oppression in Victorian England, but the criticisms themselves are timeless, and can apply to bigotry anywhere.
Back to the summary.
Isosceles triangles made up the majority of the non-Straight Line population in the narrator’s country.
Next in the social order of recognized classes in Flatland would be Straight Lines, who are considered Women.
Like Isosceles, they have no civil rights, but unlike Isosceles, they are not all enslaved, nor are they casually tortured to death inside elementary schools. They are not allowed have a job outside the home, or get an education, but they are still much better off than any Isosceles, who is not only denied an education, but is also, and I cannot stress this enough, literally enslaved, and regularly tortured to death. Especially if they are part of a higher class of shape – the daughters and wives of Equilaterals and up have many more privileges than the daughters and wives of Isosceles.
Many bigoted people read Flatland and pretend that high-class Straight Lines are the most oppressed people in the setting, because they’ve decided to ignore the fact that Isosceles are literally enslaved and tortured to death in elementary schools, along with all of the other dangerous and degrading labor they're forced to perform.
You, my dear reader, will not ignore this, will you?
You will not make me or anyone else suffer through essays and fan-sequels that pretend it’s good that the Isosceles are literally enslaved and tortured while you pretend that they are treated better than every single Straight Line in the world, will you? Because if you do I will be absolutely ashamed that you ever read this summary and still came away with such a horrible understanding of the systems of oppression in Flatland.
Look up White Feminism and why it’s bad. Ignoring the oppression of marginalized men to pretend that women are the only oppressed people who exist will always be racist, ableist, and more.
The Flatland version, you might say, could be called Straight Line Feminism. And I do not want to have to deal with any more people pretending it’s good and true.
Do not pretend that Straight Lines are the most oppressed people in Flatland, and are all equally as oppressed as one another, as though there’s no difference in the life of the wife of a Circle and the wife of an Isoceles. Just don’t do it. Do not brush the treatment of Isosceles and Irregulars under the rug because you think no one besides the metaphors for rich white women can really be oppressed or has rights worth fighting for.
Straight Lines are oppressed. But you cannot pretend they’re the Most Oppressed people in Flatland when the other oppressed people are literally being enslaved and regularly tortured to death, or just flat out murdered on sight.
If you are writing stories where the characters are fighting back against the injustice in Flatland, they need to be fighting back for the rights of everyone, not just the Straight Lines whose husbands and fathers are Circles and Hexagons and Squares.
Now let’s get back to the summary. Again.
Straight Lines are in some countries of Flatland required by law to constantly move their back end from side to side to make them easily visible to anyone who might be standing behind them.
This is for two reasons: 1: to let Edwin Abbot Abbot reference the bustles on dresses that were in fashion during the era the book was written.
[Image description start. A simple digital scribble of a stick figure wearing a dress with a large bustle in the back making the person look like they have a big butt, with dotted lines showing where the legs are under the fabric. There is an arrow pointing at the bustle, labeled, “A bustle was attached to a dress using different styles of frames which were then covered in fabric.”. Image description end.]
2: To make Straight Lines easier to see.
Flatlanders are bioluminescent on their their edges their eyemouths. The level of brightness from their eyemouth is even used to indicate mood.
From the sides, a Straight Line appears as a glowing line, which is easy to see. Billie, Bob, and Joe, will demonstrate again:
[Image description start. Another diagram like the one above, but now Billie is turned to the side so that her flat sides face her friends instead of her points. Now there is a single bar showing Bob’s perspective, labeled, “Bob’s view of Billie from the side:”, and shows a single white line, with no gradient. End image description.]
From the front, they appear as a glowing point. This is a bit harder to see than a full line, but still visible.
But from behind, their end point does not glow as brightly, and because of this it’s hard to see them, because of how tiny their end point is compared to everything else you might be looking at.
[Image description start. A digital diagram with a black border showing three shapes: Joe, a hexagon, Billie, a straight line, and Bob, a circle. Billie stands between Joe and Bob, with both of her ends pointed towards her friends. There are two bars in the upper corner showing what Bob sees. The first is labeled, “Bob’s view when Billie faces him:”, and shows Billie’s face as a thin stripe of white, in the center of Joe, who appears as a large grey bar, which then fades to the background.
The second is labeled, “Bob’s view when Billie faces away:” and shows the same gradient as before, but instead of the thin stripe of white in the center, it is now a grey just a few shades lighter than the grey of Joe behind it, making Billie very hard to see in comparison. End image description.]
By moving their rear end back and forth, that dim speck becomes easier to notice, so you’re less likely to run into them. Something which could be very dangerous if you were moving quickly, because of how sharp they are.
They are also expected to keep up a constant “Peace-Cry”, or a humming noise, so that anyone can hear when they are near.
It should also be noted that Straight Lines are also used to represent Women as another reference to ongoing social issues at the time the book was written.
At the time, fancy hats were very fashionable for women, and to keep them in place, people would use a long sharp pin to stick through the hat and through their hair, holding everything together.
This wasn’t a problem for anyone, until women who were harassed or attacked realized they could use these hat pins to defend themselves.
And then of course everyone got all up in arms – not because these women were being attacked, but because they dared to defend themselves and their boundaries.
Instead of punishing the men who were harassing women, the women were punished for defending themselves.
Laws were passed to regulate the length that hat pins could be, and anyone wearing one longer than the limit would be, in some places, fined over a thousand dollars in 2024’s money.
Straight Lines are categorized as Women in Flatland because if they weren’t treated horribly, they’d have less reason to kill people.
No one in Victorian England woke up in the morning and thought to themselves, "I'm gonna stab someone with my hat pin literally just for fun".
And the Straight Lines did kill people, especially in areas where they were forced to endure harsher restrictions, like in some countries of Flatland where they were not allowed to leave the house at all except during religious holidays, or had to always be escorted by a male relative.
Men who abused their wives were likely to end up dead at the end of their sharp stingers, and this led to many laws being passed with the goal of preventing this. No, before you get excited, the laws were not designed to protect these wives from abusive husbands. Just like with the hatpins, the laws were passed to punish the wives and allow the husband to abuse them in safety.
Straight Line’s apartments within their home (Think of it as a hotel room if you're unfamiliar with the concept of apartments being inside a larger family house) were required to be built very narrowly, so that Straight Lines couldn’t get in or out quickly. If they wanted to move from one room to another, they'd have to carefully back up, move forward, back up, and move forward again in very small, slow increments to avoid getting stuck or hitting walls.
This was explicitly done to prevent them from murdering anyone who upset them while they were in their room, which Multi-Angled Figures took full advantage of.
There were also the specific, separate, narrow doors that Straight Lines had to use at all times, as I mentioned in the description of their houses.
Straight Lines were not allowed to have an education, and were lied to almost every moment of every day by the other Figures around them, who would say one thing within their earshot, and then say something completely different when they left the room.
The narrator tells us that the way things are spoken among only “Men” versus in the earshot of “Women” are so different that they may as well be separate languages. They lie to Straight Lines and claim to love and care for them, and pretend they think they are the most beautiful and amazing things ever created. But in reality they think they are nothing more than mindless creatures who hardly even deserve the label of person.
This double-language becomes a problem for younger non-Straight Line Figures, who spend their first three years of their life being raised by their mother or nursemaid, or any older sisters, learning the language of emotions and kindness, only to then suddenly be ripped away and told to forget all of that and think only in terms of calculation and efficiency, and to despise and look down upon the very person who’s shaped their whole life so far.
The narrator was worried about the strain this sudden revelation puts on the minds of young male children, and worried that one day, one of them might reveal to their mother exactly what her husband and his friends thinks of her.
This concern has, surprisingly enough, made the narrator advocate for Straight Lines to be allowed to receive an education.
He isn’t thinking of their welfare, of course, he frames it as concern for the male children, who aren’t being taught as much as they should be at younger ages, and who, he thinks, shouldn’t have to struggle to keep the truth of the world secret from their mother and sisters at such a young age. He thinks it's unecessarily stressful to force a little kid to have to unlearn and relearn so many things, while keeping up a double life.
His solution to this problem is to allow women to be educated, as they were ages ago in history.
Onto family lineages.
In the narrator's country, the family lines of all Figures are kept careful track of for the purpose of eugenics, and this includes Straight Lines.
Lower class Figures who are really into the whole eugenics thing and excited and hopeful about giving their kids a better life will carefully pick out a Straight Line to marry who has no history of Irregularity for thousands of generations back in her family tree.
Higher class shapes, though, are lazier with their commitment to the eugenics project, since they think they’re already so far ahead. They will be less careful to pick a wife with “good genes”.
The narrator mentions that a Circle has been known to marry a Straight Line whose grandfather was Irregular, simply because he liked her.
The narrator blamed these "lazy" tendancies as one of the reasons that higher classes tend to have fewer children.
Since the narrator had six kids himself, it can be assumed that he went to great lengths to choose his wife based on her "good genes", and says this is why they've managed to have so many Regular kids together.
When referring to a Straight Line's family history, it is refereed to as a "pedigree", exactly like a dog or a show horse, because Straight Lines are not considered human, and referring to them like animals is a way of reinforcing that.
Straight Lines who are diagnosed with any illness that causes sudden, uncontrollable movements like seizures, chronic colds, or other diseases, are immediately murdered upon diagnosis.
In the level of status in Flatland society, after Straight Lines we have the Equilateral triangles, who were the Middle Class, and were the owners and managers of shops and stores, overseeing a workforce of Isosceles slaves.
Above the Equal-sided triangles were the Squares with four equal sides and the Pentagons with five sides. This was the only class made up of two different Configurations. They were considered “gentlemen”, and had jobs such as lawyers (like the narrator), doctors, and other high-class, well paying jobs.
Next came the Hexagons with six equal sides, who were the lowest section of the nobility class.
After this, the narrator stopped bothering to list out specific shape names, but the level of social status continued to increase with the number of sides. When you reached some unnamed point, you were given the title of Polygon, or many-sided, and were part of the higher nobility.
The final and most powerful class were the Circles, shapes who had so many sides that it was no longer worth the effort of counting to keep track. This was also helped along by the fact that Circles were encouraged from a young age to refuse to let anyone properly measure them, so there was no real telling how many sides they actually had or didn't' have. After a certain number of sides, Sight Recognition stopped being helpful, so Circles were able to keep their exact measurements a secret.
The Chief Circle was supposedly chosen because he had the most number of sides in the country, and was assumed to have ten thousand sides to be polite.
The Chief Circle was the supreme leader of all the allied countries in Flatland that the narrator knew of. Also known as a dictator.
The Circles created this system to give themselves all of the power they could get. They held all of the political offices, and controlled everything.
The “Circularchy” is similar to both the Patriarchy of our own world, along with other systems of oppression, like white supremacy, racism, ableism, intersexism, queermisia, and more.
The Circles are called “Priests” in Flatland, but they use the word differently. They are the administrators of all businesses and government. They don’t do any work themselves, they only direct the workers on what to do.
Circles hold themselves up as the ideal human being. They tell everyone they are the smartest, the only shapes fit to rule.
They tell everyone below them that it should be their entire life’s goal to become as much like a Circle as possible.
It isn’t actually possible for a Flatlander to naturally gain sides over the course of their lifetime, but the Circles have been in power for over two thousand years, and spread constant propaganda telling people that, if you just work hard and don’t complain, and do everything in your power to uphold the Circularchy, your efforts will someday be rewarded in your children, or your children’s children, having a larger angle than you, if you’re an Isosceles, or one more side than you, if you’re an Equilateral, and so on and so forth.
So, this propaganda said, if you just work hard enough and don't complain, maybe, eventually, someday, if you're lucky one of your descendants might be a Circle, and that will make all your suffering be worthwhile.
The narrator tells us that this generational evolution from one shape to another is just a natural law of nature, that every figure’s son is guaranteed to have one more side than his father.
And then since this is just blatantly not true, he has to immediately admit that it doesn’t actually apply to the Isosceles, or any other shape, for that matter.
Yes, multi-angled figures can be born with another side, or even many, in the case of “Circles”, who can at times be born with 50 more sides than their father, but it’s not a guarantee, and it is in no way “a law of nature”.
If that were true, there wouldn't be any non-Circle shapes left, because everyone’s ancestors would have become Circles long before anyone’s records of history.
The fact that the propaganda is objectively untrue doesn’t stop it from working, though, because as I said before and must reiterate again: Bigotry is not actually logical. It just pretends to be to. But it’s literally not.
This is a metaphor for classism. The rich tell you that if you just work hard enough, and don't complain about how little you're getting paid, then your kids can have a better life for themselves, and someday your family's name might belong to billionaires.
The Circles have invented a saying – “Attend to your configuration”, which they use to reinforce this propaganda.
This Configurationist bullcrap is used to justify enslaving the Isosceles, murdering other Irregulars, repressing Straight Lines, and elevating Figures with higher numbers of sides to better social status.
They claim that if your configuration is Irregular, then you are just inherently either violently immoral, or worthless. So they claim that an Isosceles, if not enslaved for the good of society, is just destined to go on to become a violent criminal, and that Straight Lines need to be kept in the home as much as possible, where they can't hurt anyone.
And on the other side of the coin, a Hexagon is just inherently going to be a better person than any “lesser” shape, and any time they do something wrong, well, ~obviously~ it means that something happened to temporarily change their configuration – like a sudden change of temperature, running into someone in a crowd, not exercising enough, or exercising too much, or even what kinds of food they've recently eaten.
The narrator admits that this idea is great in theory, but makes it very difficult to parent young children in reality, because when one of his Hexagonal grandsons misbehaves, and then blames it on the temperature, and insists that instead of being punished, he should be given his favorite desserts to “strengthen his Configuration”, there’s no way for the narrator to deal with this that doesn’t lead to violating the ruling of the Circles in some way.
The Circularchyy has been a problem in Flatland for as long as anyone in the Narrator’s country and remember, but the specifics of this brand Configurationism were invented several thousand years before the story takes place. Most likely exactly two thousand years ago, during the period of time known as the Color Revolt.
During this time, a Pentagon whose exact name is debated by historians, but is usually called Chromatistes, came across various pigments to create basic colors, and figured out how to turn them into paint.
First he decorated his house, then his slaves, then his father, and his sons, and his grandsons, and finally himself.
The results were both beautiful and very convenient, because now everyone could recognize these painted figures by their colors from a distance, and could easily tell which way they were facing. No one ran into them or got in their way.
By the end of the first week, all of the triangles and squares in the town had painted themselves. A month or two later, and the 12-sided dodecagons had started painting themselves. By the time a year had passed, all but the highest nobility of the town were painted, and then the trend began spreading outward to other towns and cities, spread by the saying, "Distinction of sides is intended by Nature to imply distinction of colours". AKA, “Nature gave us sides so we would paint them”.
Two generations later, everyone in the known lands of Flatland wore paint, except for Straight Lines and Circles, because it was argued that Straight Lines had “only one side”, and thus, no sides, plural, and Circles also had “only one side” and therefore no sides, plural. (If you pretend that Circles were true Circles and not just polygons with too many sides for anyone to bother counting).
The Straight Lines were made to be ashamed of their supposed lack of sides. The Circles on the other hand bragged about it.
It seemed at first glance that it would be impossible to paint a Figure that had “no sides”.
And while that was being argued with, massive social progress was unfolding.
Because anyone could simply look at use someone’s colors to tell what shape they were, it was easy for everyone to move in crowded areas without bumping into anyone, instead of the Art of Sight Recognition being given to only the rich people.
Different shapes were painted with different colors on each side, making them easy to recognize.
We do not know all the combinations, but we do know that Isosceles were painted black, purple, and orange, Equilateral triangles were red, white, and blue, and Squares were purple, dark blue, gold, and reddish brown.
For the rest of the possible shapes, you just have to make it up yourself. We just don’t know.
This color-coding made it easy for everyone to learn to recognize different shapes, not just the rich people.
The Isosceles were able to use this fact, and others, to successfully argue that they deserved equal rights as everyone else, and should no longer be forced to literally be tortured to death in elementary schools to teach rich kids the Art of Feeling, since no one needed to bother with it anymore when you could just look at people instead.
The Arts of Sight Recognition and Feeling were being used less and less, because they were no longer needed. Only the Circles still practiced and trained themselves in Sight Recognition, because they refused to be painted.
But eventually people figured out that you could, in fact, paint a Straight Line and a Circle. They decided to pass a law saying that since both had no sides, then both would be painted with the same two colors: Red on their front half, and green on their back half, so that everyone could recognize them and see which direction they were facing. This bill also demanded complete equal rights for everyone, protected by law.
This was known as the Universal Color Bill.
This news delighted the Straight Lines, and horrified the Circles. Because if they were both painted the same colors, it would be so easy for someone to mistake the two.
This brought almost all of the Straight Lines over to the side of the Chromatic Innovation, as the Color Revolt was called in those days.
At least twenty-three Circles were murdered by their wives when they refused to support the proposed law that would give them equal rights.
And since the Circles desperately did not want to pass a law that would give everyone the same rights and privileges as they had, and because they knew that if they let this go on much longer they’d probably have to deal with a violent uprising instead of a peaceful protest, they had to come up with a plan to ruin the reputation of the Chromatic Innovation, and make people hate it instead.
So they made up a story about a poor orphaned Straight Line princess from a noble family, who killed herself on her wedding night after being tricked into marrying an Isosceles stalker who painted himself like a twelve-sided Dodecagon to make himself seem like a nobleman instead of a slave.
The Circles spread this fake story and convinced everyone it was true, and used this to convince the Straight Lines that the Chromatic Innovation was dangerous for them and that they shouldn’t trust anyone who was painted, because the same thing could happen to them, or to their daughters.
AKA: They convinced all the white women that they were better off being property of their husband as long as it meant that Black men were still enslaved.
Just like all the racist white women in history who’ve fought to uphold white supremacy even when that also means upholding the same patriarchy that oppresses them and keeps them locked into abusive marriages with no escape.
And again, please note the fact that the people who claimed an Isosceles not only figured out how to perfectly paint himself in twelve different colors in the exact pattern required to fake being a Decagon, are also the exact same people who claim Isosceles have no brains.
Imagine how difficult every single step of that plan that would be to pull off. Imagine you have only three sides, one of which is shorter than the others, and you have to figure out the Exact Pattern to paint yourself in to make you look Exactly like a Dodecagon.
And then you have to make connections with this Straight Line’s family and court her through all the proper channels for months on end, without ever making a mistake, and you’d have to keep reapplying the paint and keeping up a perfect fake accent the entire time, and you can never let anyone get close enough to feel you, or even accidentally bump into you.
Think about exactly how difficult that would be. You’d have to be both a master actor, and a master painter, a trained mathematician, and have the best luck in the entire world.
Really think about how difficult it would be.
[Image description start: A thin Isosceles triangle next to a much wider, Regular thirteen-sided shape. Image description end.]
And then remember that the same people claiming an Isosceles did all these that would require an absolute master of disguise, acting, and planning, are also the exact same people who insist that Isosceles are literally brainless things that shouldn’t even be considered human.
Because bigotry is not actually based in logic. It is not based in reality. And bigots know this. They know they’re lying.
They will tell you in one breath that the oppressed people are all-powerful dangerous masters of disguise and cunning able to trick dozens of "inherently superior" rich people for months on end without getting caught. And then in the next they’ll tell you that Isosceles are actually just completely mindless creatures only good for hard labor because they aren’t even smart enough to count their own angles.
It doesn’t make sense because bigotry doesn’t make sense. Bigots will lie to you and insist that it does, but they’re liars and they know it.
So the bigots of Flatland didn’t think twice about how impossible and contradictory this story of the Circles was. They didn't care that if it was true (which it wasn’t) it would mean they were completely wrong about the capabilities of Isosceles.
All they cared about was that it gave them an excuse to destroy all the strides towards equality their society had made in the last few years, as long as those who had privilege in the status quo could keep those privileges, even if it meant they’d also be losing their opportunity to get actual equal rights.
The Chief Circle of that time was known as Pantocyclus, and he called together a meeting of all the allied countries to meet and discuss the Universal Color Bill.
Hundreds of thousands showed up to the meeting, where Pantocyclus announced that the Circles had finally seen the error of their ways, and were prepared to pass the Universal Color Bill.
But first, before they signed it, he just wanted to make sure that everyone understood both the pros, and the cons of the bill.
And then he gave a speech first telling the Equilateral triangles, Squares, and Pentagons that if the Isosceles were given the same rights as them and every other shape, that all the hard work they and their families had put in for generations would all for nothing.
Then he addressed the Isosceles with the widest angles that were the closest to 60 degrees, telling them that many of them had been about to be let into the Equilateral class, and for others, their children could have been born Equilaterals. But if the lower-angled Isosceles below them were given equal rights to everyone else, then that distinction would be meaningless, and, again, all their hard work would be for nothing.
Pantocyclus told these higher status Isosceles that if the Universal Color Bill passed, then all the power in the country would go to those with the most numbers, and that would be the Criminal classes of Isosceles with the smallest angles, almost impossible to tell apart from Straight Lines.
Chromatistes tried to protest in defense of the lower class Isosceles, but was silenced by guards who forced him to remain silent. These guards were Isosceles prisoners controlled by Pantocyclus himself.
Then Pantocyclus spoke to the Straight Lines, and told them that if the Color Bill passed, no Straight Line would ever be safe again, because anyone with multiple angles could pretend to be something they weren’t.
He shouted that death would be a better alternative, and this was the pre-planned signal for all of the Straight Lines — in this instance, very clear metaphors for privileged white women — to sneak up invisibly and start murdering the lowest-classed Isosceles, while Chromatistes was murdered by the same guards who had silenced him before. Every door was guarded by more of these Isosceles prisoners who now acted as assassins along the murderous Straight Lines.
All of the lower-angled Isosceles in the area were murdered. Over a hundred and forty thousand of them had attended the meeting, thinking they were finally about to be given their freedom and equal rights for the first time in their lives.
The higher-angles Isosceles were decimated, in the original meaning of the word – one in every ten was murdered, as a punishment for them all.
Every Equilateral triangle so much as suspected of any Irregularity was murdered on the spot.
Any triangles who survived the massacre spent the next several years under close monitoring by the government, with their homes being regularly raided to make sure they weren’t thinking of rebelling again.
Every town and city was ransacked, and all of the members of the lower-angled Isosceles who had avoided the first massacre were rounded up and slaughtered.
The use of color was banned. Even saying a word simply referencing color was made illegal and severely punished, with only Circles and some of the most highly trained scientific teachers allowed to use them.
There are rumors that in the most expensive courses at the most expensive collages, people sometimes use color to demonstrate complicated mathematical theories, but the narrator isn’t that rich, and cannot confirm or deny the rumors.
There is exactly one factory left that produces color in all of known Flatland, owned by the Chief Circle. It is run entirely by Isosceles of the lowest angularity, and each year the workers are slaughtered, and new ones brought in, so that none of them can ever share the secret of how it is made.
It has been at least two thousand years since the Color Revolt was violently ended.
Color, and anything to do with it, is still illegal, and punishable by death.
Section 4: How the Narrator went to Lineland
The narrator’s story begins on the night before New Year’s Eve, two days before the new year.
It is the Flatland year of 1999. In two days it will be 2000.
In terms of calendar year, you can imagine that Flatland is about 116 years “ahead” of us, though this of course is not a reflection at all on how “advanced” either of us are in comparison. Calendar years are just made up. Anyone could sit down and start considering it year 0 and it wouldn’t change anything.
For the narrator, this was the first day of his long holiday vacation, and he stayed up late enjoying himself thinking about his favorite math problems. When he finally went to bed, he was still thinking about a math problem that he hadn’t solved yet.
In his dream he found himself looking at a long line of people in the distance. Some of them were short Straight Lines, others appeared to be glowing Points. All of them were lined up, and moving from left to right, making chirping noises like crickets. Some times they all stopped moving, and when they stopped, the noises stopped too.
In the “center” of this line were Straight Lines, and on the "edges" of it, as far as the narrator could see, were Points, which he'd never seen behaving like people before, but, since this was a dream, he didn't question any of it.
In the very “center” of the moving line of people was the longest Straight Line the narrator could see anywhere nearby, though he still considered the length to be short compared to the Straight Lines he was familiar with; more like a young girl than an adult woman.
He decided to approach this Straight Line, asking “her” why everyone was standing in a line, making chirping noises and moving from left to right like that.
He asked three times without getting any answer, getting more annoyed each time, thinking the “woman” was just ignoring him to be rude.
Finally he shoved himself forward, putting his face in front of “her” to stop “her” from moving forward again, and repeated himself again, now very angry and offended.
To his surprise the line replied that he wasn’t a woman, he was the King of Lineland, and where in the world had the narrator suddenly appeared from?
The narrator attempted to explain that he’d simply approached from the side, but the King of Lineland didn’t believe him.
This was the realm of the First Dimension, or Lineland, consisting of only a single line that ran from East to West, with no concept of North or South. The only movements possible for Linelanders were from Left to Right, or West to East, along that single line.
You can imagine Lineland as being very long, but only a single pixel wide.
In Lineland, we are told that there are two shapes people can take: Straight Lines, which were were classified as Men, and Points, which were classified as Women.
Straight Lines like the King had two pairs of eye-mouths, one on either end, each with a different voice. Points had only one voice each, though we are not explicitly told that they have only one eye-mouth.
We are told that two (2) Points and one (1) Straight Line are required to produce children, which was done through singing once a week until all four of their voices (One voice for each Point, two for the Straight Line) perfectly harmonized, which always created two new Points and one new Straight Line.
It usually took years of practice to harmonize with partners, and when this finally happened, the three became officially married.
Because Linelanders existed only in a single straight line which you can imagine one pixel wide, and took up all of the single-pixel width of that line, they could not move or see past one another.
To work around this, their sense of hearing was extremely sensitive and well-trained, allowing them to quickly calculate distances and shapes based on sound alone, similar to echolocation.
The King of Lineland demonstrated this by calling out to his two wives, who were both over six thousand miles away from him on either side, and they called back.
Using the time that it took for his voice closest to reach them versus the voice further away, his wives could tell that he had a total length of 6.457 inches, and called this answer back to him.
This is the Lineland method for recognizing other shapes, in place of both Sight Recognition and the Art of Feeling.
Sight Recognition would be useless in Lineland, because you can only ever see two people in your whole life – whoever was born next to you on either side. And even with those two people, you can only ever seen them as a Point, or if it's easier to imagine, a pixel.
(Notice how this is one dimension lower than the straight lines that a Flatlander sees everything as. A Flatlander sees everything as a line, and a Linelander sees everything as a point.)
The Art of Feeling would also be useless in Lineland, because again, a Linelander would only ever be able to use it on their two immediate neighbors to the left and right, and when you literally spend your whole life next to the same two people, they’re not exactly strangers.
The King of Lineland also tells us that the act of touching another is illegal in Lineland because Points are supposedly extremely fragile, and could be accidentally killed by running into someone else, and since it’s impossible for a Linelander to see the difference between anyone, because everyone looks like the exact same single point or pixel, it is illegal for anyone to touch another altogether, to prevent accidental deaths.
The King of Lineland at one point says that he thinks the narrator’s some kind of mutant woman, because he only has one voice, and does not believe the narrator at all when tries to argue, and explain that he’s a Square.
Because the King of Lineland can only see a point, and can only imagine a Straight Line, he has no clue what a “square” is supposed to be, and does not believe the narrator when he says he’s from the Second Dimension.
He does not believe that there is more to space than the simple Straight Line he can imagine.
So the narrator attempts to prove the existence of the Second Dimension.
First he attempts this by telling the narrator all of the people that he could see before he entered Lineland itself, and lists them out in order. The King scoffs at this, because it doesn’t prove anything; anyone in Lineland could get this information in half a second just by listening – and the narrator had to have hallucinated that he’d seen people, because it was impossible to see the different between a point and a line. No, it was either a lie, or a dream. Either way, it proved nothing.
So the narrator tried again, this time by slowly moving himself backwards out of Lineland, trying to show that he was moving Southward, until he was outside of Lineland altogether.
But this didn't work, because Lineland is so thin that there was no way for the narrator to be partly in it. He was either inside of Lineland, or he wasn't.
You can’t have half of a pixel, there will either be a pixel, or there won’t be. A 2D figure will either be inside of Lineland, or it won’t be.
Imagine you lived inside that pixel-wide line. All you can see, when you look to the left or the right, is a single pixel.
Now imagine that there is an orange square intersecting that line. What do you see when you look at him?
You just see a single orange pixel. No matter what position he’s in, or how far in or out of Lineland he is, or if he’s spinning circles, you will only ever see him as a single orange pixel, sometimes moving closer to you, sometimes further away.
[Image description start. A diagram where the Square narrator is represented by an orange square, facing one point towards Lineland, which is a very thin black line only a single pixel tall. First we see the narrator “As far into Lineland as he can get”, with Lineland intersecting his middle. Next he is “Less than halfway through Lineland”, then “Even less in Lineland,”, then finally, “Only a single pixel left in Lineland”. Text below reads, “The length of the sections in Lineland may change, but the width will always be a single pixel. From inside Lineland, when you can only see from left to right, your view will be of the same apparently unchanging orange pixel, no matter what position the square is in.” At the very bottom is the black line of Lineland again, showing pixel-tall sections of orange where the Square intersects, but not showing anything outside of it. Image description end.]
The only thing the King saw was the narrator suddenly seeming to vanish. He saw no movement at all, just one moment “she” was there, and then “she” was gone. (The King kept up insisting that the narrator was actually some sort of mutant woman despite his protests).
The narrator spent probably half of this conversation purposefully antagonizing the King out of spite, and eventually gave up all pretense of civility, and just started, pun intended, flat out insulting the King, saying that the so-called King could only see a Point and imagine a line, but he, the narrator, could see a line for real, and imagine figures.
He went on this whole rant about how the King was worthless compared to him, and especially compared to any higher class Figures in Flatland, and that he’d come here intending to teach him some common sense from a higher being to a lesser one.
(We can assume that he said he’d come to Lineland on purpose because he was dreaming, and sometimes dreams are just like that. You think, do, or say things that don’t make sense, but feel perfectly natural while you’re dreaming.)
The King’s reaction to this insult was to attempt to kill the narrator by charging at him to stab him to death, while the rest of his subjects gave a deafeningly loud battle cry that literally froze the narrator in place.
Right before the King hit him, the narrator woke up, and found himself in normal Flatland once again.
Section 5: How the Narrator met the Sphere, and was brought to the Third Dimension
Now the story skips ahead to the next night, New Year’s Eve.
It’s late at night, and the narrator tells us that the only ones still awake in the house are him, his wife, and the youngest grandson, a Hexagon.
We're told that earlier, the narrator and his adult sons had started teaching this young hexagon the basics of Sight Recognition, and because he was so talented at it, the narrator decided to reward him by letting him stay up late to give him a special private lesson on geometry.
(The narrator is a lawyer who does math purely for the fun of it, so he saw this as a very cool reward)
He explains to his grandson the basics of geometry, showing him with small toy squares that if you take nine squares who are each 1 inch by one inch, and stack them in three rows to create a larger square, then, even though you couldn’t see the inside of the square, you could calculate the total amount of space it took up by “squaring” the length of a single side.
Because the smaller toy squares were 1 inch by 1 inch, each side of this square was 3 inches.
It was then possible to calculate how much total space the square took up by taking 3, the length of the side, to the 2nd power, which meant doing 3×3, which equals nine.
This showed that the square took up 9 square inches of space.
Do you see the parallel with the Linelanders singing to calculate how much space one of them takes up? Flatlanders cannot see a square, but they can calculate and imagine it. The same way Linelanders cannot see a line, but they can calculate and imagine it.
His grandson thought about this information for a little while, and then told him that it was clear he was planning to teach him how to raise things to the third power, which clearly meant something in geometry, so what did that mean?
The narrator responded that it didn’t mean anything, because there were only two dimensions in geometry – so he explained the basics of geometry to make sure his grandson understood:
First you have a point, with zero dimensions.
Then you move that point parallel to itself, and get a line, which has one dimension. This can be represented by 3.
Then you move that line parallel to itself, and you get a square, with two dimensions. This can be represented by 3², or three squared—
This time his grandson suddenly exclaimed that this obviously meant that the next step would be to somehow move a square parallel to itself, to create some shape he didn’t know the name of, which would be represented by 3³! (or three to the third power).
The narrator angrily told him to go to bed, saying that he was speaking nonsense.
His grandson sadly went off to his room.
Then the narrator sat up in the living room with his wife, still annoyed by what he thought was his grandson’s foolishness wasting his time when he'd been trying to teach him about his favorite subject.
He complained about this out loud to his wife in frustration – and immediately felt a cold chill sweep through him, and sensed a Presence™ in the room, though when he stood up and looked around, he couldn't see anything.
Creeped out and trying not to show it, he said again that his grandson was a fool, because 3 to the third power meant nothing in geometry!
And a voice from nowhere replied that his grandson was not a fool, and 3 to the third power had a very obvious meaning in geometry.
The narrator and his wife both leapt to their feet, and were shocked to see a stranger suddenly appear before them, as if from nowhere.
Because they were in their dry living room, there was no fog, so the stranger before them appeared as simply a white line, with no gradient. But strangely, that white line seemed to be growing smaller and larger with every passing moment, in a way the narrator had never seen before.
The narrator’s wife thought the stranger was a woman who had somehow gotten into their house, and when the narrator tried to argue that he thought the stranger might be a Circle, his wife insisted that Feeling was more trustworthy than Sight Recognition, and approached the stranger to Feel what kind of shape they were.
To her shock, it wasn’t a Straight Line at all – it seemed to be a Circle, but with no sides that she could feel, not even tiny ones. Horrified at how rude she’d been, she wondered aloud if she could have just dishonored a Perfect Circle, something unheard of.
The stranger replied that they could be considered a Circle in a certain sense of the word, and they were definitely a more Perfect Circle than anyone in Flatland could ever be, but to be more accurate, they were many Circles in one.
Then they politely asked the narrator’s wife if they could borrow her husband for a few minutes to speak privately in another room — but the narrator’s wife was so flustered and embarrassed at the thought of forcing a Perfect Circle to leave the room just for her sake that she backed out of the room herself, apologizing many times and saying it was way past her bedtime.
This left the narrator and the stranger alone together. When the narrator checked the time, he realized it was now past midnight, which meant it was now officially the year 2000.
Alone together, the narrator intended to approach the stranger and ask them to be seated, but he found himself frozen in place with fear. He could only see the stranger as a straight line, with no gradient to show any angles, but still the shape and size of the stranger was changing with every passing moment, in a way no Regular shape should be able to move.
Suddenly afraid that the stranger was some kind of mutated Irregular burglar, he rushed forward to Feel them…
And was shocked when what his wife had said was true – he couldn’t feel a single angle or side, not one. The stranger seemed to really be a Perfect Circle. He ran full around them, just to be sure there was no mistake. And there was none.
After spending several minutes apologizing for being so rude, he asked the stranger where they’d appeared from.
And the stranger replied that they’d come from space.
Which confused the narrator, because weren’t they in space right in his living room? So saying you’d come from space was meaningless.
The stranger scoffed, and said the narrator had no idea what space really was, and asked him to define it.
The narrator replied that space was length and width, stretching on forever.
The stranger told him that he was wrong, he was here to tell him that there were really three dimensions – length, width, and height.
The narrator responded that he also sometimes used the word “height” interchangeably with “length”, and sometimes said “breadth”, or “thickness” instead of “width”, so he already knew multiple words to describe the two dimensions.
This wasn’t what the stranger meant, obviously, so they tried again to explain that when they said “height”, they didn’t just mean “length” by another name, they meant something else entirely — A different dimension, both up and down.
They’d come from above, from “Upwards, not Northwards”.
None of this made sense to the narrator, who asked the stranger to show him which way was “up”. But the stranger told him that he would need to have an eye on his side in order to see upwards.
The narrator was offended, and pointed out that he did have a perfectly good eye on one of his points.
The stranger specified that they didn’t mean one of his edges, they meant his side – or, as he thought if it, his insides.
The narrator thought this had to be a joke, but the stranger insisted that from “above”, in the Land of Three Dimensions, they could look down and see inside of all the things the narrator considered solid.
They listed out the occupants of the narrator’s house in an attempt to prove this to him, explaining where everyone in the house was, and what they’d been doing just before they came down into Flatland.
The narrator responded that this didn’t prove anything, because they could have just asked any of his neighbors for that kind of information and gotten it easily, especially if they were a Perfect Circle like the stranger seemed to be. It’s not like any of it was a secret.
So the stranger tried something new and asked him how many dimensions he thought he was seeing when he looked at a Straight Line.
Their intention was to get him to say three, because the line had to be long, and wide, and tall, in order to be visible. If it had only length and width, but no height, you wouldn’t be able to see it from the side, and it wouldn’t really exist.
But the narrator told them that he knew that Straight Lines were really just very thin parallelograms, so the trick question wasn’t going to work on him – he knew that Straight Lines existed in two dimensions just like everyone else.
The narrator asked the stranger if they were calling brightness “height” and saying it was a dimension, because yes, if you took away a line’s brightness, then you wouldn’t be able to see it any more, and if a line stopped glowing, it meant she was dead, so in that way she wouldn’t exist anymore.
Again the stranger told him this wasn’t what they were talking about. They didn’t mean brightness, they meant height.
The narrator said that if height really existed as a third dimension, then it should be easy to prove. All they had to do was demonstrate which way it went. And if they couldn’t do that, then they didn’t have the right to be upset with him for not believing it. He asked them to measure his height to prove it existed.
But the stranger couldn’t measure the narrator or physically point out to him the direction they meant, so they tried to demonstrate it themselves, by slowly lifting themselves out of Flatland, to prove, through their movement, the direction of upwards.
First they explained that because they were a 3D Solid instead of a 2D figure, they couldn’t fit all of themselves into Flatland at once, only a single cross-section at a time. They were a Sphere, which meant that each of their cross-sections in Flatland appeared to be a perfect Circle.
The narrator didn’t believe any of this, but the stranger insisted he just wait – they would show him. He might not be able to see their whole body in 2D, but he would be able to see their circular sections growing smaller as they lifted themselves out of Flatland. All he had to do was watch.
And while the narrator watched, the Sphere lifted themselves slowly out of Flatland, sure that this would prove the existence of the Third Dimension.
But the only thing the narrator could see was that the stranger appeared to be shrinking, until finally they disappeared.
Like the King of Lineland, he didn’t see any evidence of the stranger moving out of space as he knew it, they just seemed to be pulling some sort of party trick.
The Sphere, from above, asked the narrator if he believed them yet. He did not. So the Sphere came slowly back down, their sections expanding this time rather than contracting.
[Image description start. A diagram showing the sphere intersecting a thin black line that represents Flatland, first “Fully in Flatland”, with grey dotted lines inside to show the circular cross section visible to Flatlanders, then they lift up so they are only partly in Flatland, with a smaller circular cross section visible. End image description.]
The narrator was now convinced that the stranger wasn’t a Circle at all, but some sort of stage magician pulling tricks.
It was either that, or the old wives’ tales were true, and there were such things as tricksters who could use real magic.
The Sphere, on the verge of giving up entirely, decided to try one last approach: Analogy.
They explained that a point, moving parallel to itself, became a line. The line had two “terminal points”.
That same line, moving parallel to itself, then became a square, with four “terminal points”.
A line could be described as having two sides, and a square had four.
The Sphere said, Zero, two, four. And what kind of progression do you call that?
The narrator replied that it was a mathematical one.
And what number came next?
Six.
The Sphere was pleased, sure that now the narrator would understand that, purely by following the analogy, the square in the example would move parallel to itself, creating a new shape with eight sides and eight terminal points.
Surely, it was obvious? Surely this would prove that everything they’d said was true?
Nope.
The narrator charged them and attempted to kill them.
But they managed to slip upward and away to safety, and then told the narrator they would prove it to him for sure this time – by going to one of his cupboards from above, and removing one of the books. He would see that the door didn’t open, and was still locked, because he still had the key. From above, the things the narrator thought were “solid” were open to the Sphere for the taking.
The Sphere narrated as they went above a cupboard and took one of the books out, while the narrator, in horror, ran to open the cupboard to see for himself. Behind him, the Sphere reappeared, and the book appeared on the floor in front of them.
The narrator was now terrified that he was losing his mind.
The Sphere lifted back up out of Flatland, and kept moving higher, voice growing fainter, and told the narrator that they could see all of the surrounding neighborhood – a theater ten houses away, the people leaving it, and even a Circle sitting in his home on the other side of the theater. Then the Sphere began to come closer again, and reiterated that they could even see inside the narrator’s own body.
In fact, the Sphere decided to poke the narrator, gently, in his stomach, just to prove that they weren’t lying, saying that the moment of pain it would cause would be worth it in return for the knowledge it would bring him.
The Sphere touched the narrator on his insides, which caused the narrator a shooting pain that lasted a moment, before fading to a dull ache. The Sphere laughed, and then began to lower themselves back into Flatland, saying that if the narrator wasn’t convinced by that, then they didn’t know what would convince him.
The narrator hesitated for a moment, and then charged again with intent to kill, and this time managed to ram them against a wall, while yelling loudly for everyone else to wake up and help him deal with the intruder.
The Sphere had fallen slightly too far into Flatland this time, sinking partly below the surface, and with the wall above and behind them, and the narrator shoving them into it, they couldn’t escape without drastic measures.
[Image description start. An MS Paint diagram with a thin grey line going horizontally across the center. There is a pale green circle almost fully below they grey line, and above it holding it in place are two black lines, one larger one labeled, “The narrator, shoving forward”, with arrows to show the aggressive movement. On the other side is a smaller line labeled, “the wall”. The circle is labeled, “The Sphere, trapped partly below Flatland”. End image description.]
They didn’t want any of the narrator’s family to learn about the secrets of the Third Dimension, so tried to convince the narrator to let them go before his wife entered the room and saw what was happening, but the narrator refused.
They begged him to let go, but without success. Finally they warned him that unless he let them go, he would have to come with them, because they couldn’t stay here and let his wife see them like this.
The narrator refused to let them go, so they had no choice but to surge upward and out of Flatland – knocking the narrator up into space along with them.
Section 6: In Spaceland
At first the narrator couldn’t understand what he was seeing, and thought he’d either gone insane, or was in hell. The Sphere told him that neither was true, he just needed to calm down, and open his eye again and try to look again.
And when he opened his eye again, he was looking down on Flatland, just as the Sphere had described. He could see into every house, every box and cabinet in that house, and see all the people, and inside them too. He was in the Third Dimension — in Spaceland.
When he looked at the Sphere, he thought he was looking at their inside, because from the new angle, he could see all of them, and they appeared as a Circle like he’d imagined, but he couldn’t see their insides. Instead, he saw their solid, spherical surface, which was something he’d never conceived of before.
He’d been imagining the Sphere as a strange kind of Circle, and still didn’t understand why this was happening. So he asked why he couldn’t see their internal organs, if he was looking at their inside?
The Sphere explained that he wasn’t actually seeing their inside. If they were a Circle, he would be able to, but they were a 3D Sphere, a Solid, and their insides couldn’t be seen the way a Flatlander’s could be.
The narrator didn’t understand anything the Sphere was saying, but instead of being annoyed by it, was now happy to just float there and adore them.
The Sphere reassured him that it was okay if he didn’t immediately understand, since he had a lot to learn. For now, they were going to look at Flatland.
The Sphere showed the narrator his own house as seen from above, where his wife was still awake, looking for him in worry.
The narrator wanted to go back down to reassure her that he was safe, but the Sphere told him that she wouldn’t have to worry for long, and for now he had a lot to learn.
The Sphere lifted him higher above Flatland, and began to fly away from the narrator’s house.
An hour passed, and during this time the narrator exclaimed that he’d been given the powers of a god, because he could see so much.
The Sphere told him that was a ridiculous idea, because everyone from the Third Dimension could see this much all the time, including murderers and thieves.
The narrator asked if that meant that the power to see everything, which he called “omnividence” was a power given to people besides Gods.
The Sphere replied that they didn’t know, but if even murderers and thieves could see all of Flatland, then that obviously wasn’t a good enough reason to treat them as Gods.
They pointed out that being able to see so much didn’t make you more kind, or compassionate, or loving, so how, exactly, did it make you more like a God?
The narrator was shocked by this, because kindness, compassion, and love where things the Circles attributed to women as insults, they weren’t supposed to be traits anyone worthy of respect would have! Clearly, knowledge and wisdom were more important than caring about people!
When he told them this, the Sphere told him that it wasn’t their place to tell him what kind of people he should respect, but the people of the Third Dimension that he wanted to worship so much were much more like the Straight Lines of Flatland than their Circles.
The Sphere changed the subject, pointing out a large building they were approaching. This was the General Assembly Hall where the leaders of the allied countries of Flatland met.
The Sphere began to lower them both down towards this Hall, and the narrator realized that it was now one o'clock in the morning.
The highest Circles of the states were meeting, following a tradition several thousand years old. On the newest millenium, or every thousand years, they would hold this same meeting.
The scribe for the meeting was someone the narrator recognized – it was his own brother.
While the narrator and the Sphere hovered above, the narrator's brother read out the agreement that the highest Circles of the last meeting had come to, stating that every thousand years, many people would suddenly claim to have met visitors from another world, and would cause chaos in the streets as they claimed to be able to prove the existence of another world.
The highest Circles had decided to punish anyone found making such claims, based on their shape:
Isosceles would be killed immediately.
Equilaterals would be whipped, and then imprisoned for life.
Any Square or Pentagon would be sent to an asylum.
Anyone of higher rank would be arrested, and immediately brought to this same council for personal judgment.
The Sphere warned the narrator that this would be his fate when he was returned to Flatland. The only reward for the Apostle of the Three Dimensions would be imprisonment or death.
The narrator wasn’t worried though, he thought he understood it so well that if the Sphere would just let him go down now he could convince all of them. He tried to move to do so, but the Sphere held him in place in some mysterious way, and said it wasn’t his turn to preach yet.
Instead, the Sphere went down by themself, appearing to the Circles, and the narrator’s brother, as a Circle that grew and shrank in size. They declared that they were there to proclaim the truth of the Three Dimensions, and then came back above again.
The younger Circles in the council were afraid, but the Chief Circle assured them that this had been expected, because he had the secret records of the first Millenial meetings. Everything was going as expected – they should just, obviously, not tell anyone else what they’d seen.
Then he summoned his own personal guards from outside, and ordered them to first arrest, and then kill the Isosceles guards that had been in the room, to prevent them from sharing the secret of the Sphere's appearance with anyone.
Then the Circles agreed to pass the law forbidding speaking of the Third Dimension again, and went home to enjoy their holiday.
The narrator’s brother was told that because he’d witnessed the Sphere’s visit, he would also be arrested, but as long as he kept his mouth shut and behaved well, he would be allowed to stay alive, living out the rest of his life in a jail cell.
The narrator wanted to rescue his brother, or at least say goodbye, but the Sphere stopped him, sadly, and said that soon enough they’d probably have all the time in the world to speak.
The Sphere lifted the narrator back up above Flatland, and began the flight back to the narrator’s house.
The Sphere then taught the narrator how to tell the difference between 2D Figures, and 3D Solids. They demonstrate this using a stack of square cards, slowly stacking on on top of the other to reinforce the idea of “upwards” and “above”, and showing the narrator how, by stacking the square cards one on top of the other, they built up a Solid, that, when all the cards were used, formed a Cube.
Because he’d only ever seen anything in Flatland, the narrator started out not noticing or understanding shading and lighting, so when he looked at the Cube made of cards, he at first saw it as an Irregular Hexagon Flatlander seen from above, the same way he'd confused the Sphere for a flat Circle when he first saw them in 3D.
[Image description start: Two images, the first is a white cube with black outlines, labeled, “A Cube as seen by one trained in the Art of Perspective”. Next to this is the same cube now colored in solid black, so that looks like an irregular, stretched out octagon, labeled, “A Cube as seen by one untrained:”. Image description end.]
The Sphere taught the narrator how to understand perspective, using movable lights and allowing the narrator to feel around the sides of both the cubical card stack, and their own spherical body, until he could easily tell the difference between a Sphere and a Circle, a 3D Solid and a 2D Figure.
The Sphere would have then taught him about other regular 3D shapes like pyramids, cones, cylinders, but the narrator interrupted him, saying that he was ready now to see the Sphere’s insides.
The Sphere was, understandably, bewildered, and asked what he meant.
The narrator explained that it was clear from everything the Sphere had taught him so far that they were preparing him to learn about the Fourth Dimension, the obvious next step in the analogy, where they would go beyond the Third Dimension, and look down and be able to see the insides of all the 3D Solids he had just learned about. He wanted to skip past other information about the Third Dimension, and go right to the Fourth.
The Sphere told him that was ridiculous, there was no such place.
The two argued back and forth, with the narrator insisting that it was clear from the analogy the Sphere had originally used on him, that there was a next step in the pattern: 0, 2, 4, 8, 16. In a Fourth Dimension, you would, according to the analogy, be able to find a shape with 16 points.
The narrator went back over the analogy from the start, insisting that it clearly continued into a dimension beyond the Third.
He argued that if his logic was correct, then the Sphere needed to admit that and show him the Fourth Dimension already — but if he turned out to be wrong, he would drop the subject and never annoy them with it again.
He asked the Sphere if people of Spaceland had ever reported visits from other worlds, or claimed to be able to see inside things, the same way Flatlanders who had been visited by Spacelanders did.
The Sphere admitted that yes, people did claim that, but they were never able to provide proof, and they didn’t all say the same things. And none of them claimed to have visited the Fourth Dimension.
The Sphere tried to tell the narrator to drop the subject and stop wasting time, because there were still things he needed to be taught about the Third Dimension, but the narrator got caught up in his imagination, and went on a rambling tirade about how they would visit the Fourth Dimension, and then the Fifth, and the Sixth, and the Seventh, and the Eighth—
This went on for a very long time, and a massive paragraph. The Sphere tried multiple times to shut the narrator up, but he was too caught up in the excitement, and didn’t hear them.
Finally the Sphere could take it no more, and without another word sent the narrator falling back to Flatland with a crash that he felt both inside him and out.
He fell downwards towards his house in Flatland, and got a final glimpse of his world from above.
Then there was darkness, and a crash like thunder, and when he regained awareness, he was back in Flatland, in his study room, hearing his wife approaching with her Peace-cry.
Section 7: The return to Flatland, and the second visit from the Sphere
The narrator decided that he couldn’t tell his wife what had happened, because it wouldn’t make any sense to her at all, since she didn’t even know enough math to count to four.
So he lied to her, and told her that he’d fainted and fallen into the cellar on the southern half of the house, and lain there all night.
His wife wasn’t very convinced by this story, but didn’t argue, just said that he seemed sick, so he should go to sleep and get some rest.
He was happy to do so, and went to his bed to sleep. Before he fell asleep, he repeated the phrase, “Upwards, not Northwards” to himself, and tried to imagine again the cube he’d seen. He was already starting to be less sure than he had been.
But he fell asleep quickly, and he dreampt.
He was back with the Sphere again, who glowed so brightly that he knew they weren’t upset with him anymore, and had completely forgiven him.
The Sphere was showing him the way through a dark, silent area, towards a bright but impossibly tiny Point of light. As they got closer, the narrator heard a quiet voice speaking to itself.
The Sphere explained that the narrator had spent his whole life in Flatland’s 2D, he’d visited the 1D Lineland, and had been brought by the Sphere into the 3D Spaceland. This would be his last lesson in the Dimensions: 0D, Pointland, the land of Nothing, the Land of Zero Dimensions.
The Sphere explained that the tiny Point of light in front of them was a person like they were, but a being of Zero Dimensions, with no length, width, or height. It didn’t know that anything existed in the world outside of its own mind, and was completely happy with this arrangement, since it didn’t know anything else.
This was the narrator’s final lesson: To never be happy in ignorance, and to always strive to learn more and know more about the world.
The Sphere told the narrator to listen, and when the Sphere stopped talking, the quiet voice the narrator had heard before started speaking again, referring to itself in the third person as “It”, saying happily that it was the only thing in the world and that this was beautiful.
The Sphere explained that the Point referred to itself in the third person because it was too simple to even be aware of the concept of More Than One. It was the only thing in the world as far as it was concerned. Anything it heard them say, it would assume it had thought itself, because it couldn’t tell the difference between its thoughts and what they said.
The Sphere told the narrator to try telling the Monarch of Pointland that it wasn’t the only thing in the world, to see for himself.
The narrator immediately began insulting it, saying that it thought it was the greatest thing in existence, but it was really nothing, because it was only a tiny fraction of a line, and a line was just a shadow of how magnificent a square was—
—and the Sphere told him that was enough, and to listen again.
The Monarch of Pointland still couldn’t tell the difference between itself and the narrator’s words to it, and actually thought that the insults and concepts it had just heard had been a random spark of creativity, which it congratulated itself for.
The Sphere told the narrator that there was nothing either of them could do to convince the Point that it wasn’t alone in the universe, and then they floated gently back up towards Flatland, with the Sphere once more reminding the narrator to always strive for knowledge, and never become complacent in happy ignorance.
As they went, the Sphere apologized for being angry with the narrator when he’d asked about the Fourth Dimension, and explained that they had been taught their own lessons, and they weren’t too proud to admit they’d been wrong to their student.
Then they taught the narrator how a 3D Cube, moving parallel to itself, created a 4D Extra-Solid with 16 points, and that that Extra-Solid, moving parallel to itself, created a 5D Double Extra-Solid with 32 points.
All of it Strictly According to Analogy, and so simply done that even the narrator’s wife would have been able to understand it.
Section 8: The narrator’s attempts to teach his grandson about the Third Dimension, and what happened after that
When the narrator next woke up, he was filled with joy and excitement, ready to tell the world about the Third Dimension. He would teach everyone, even the Straight Lines and the Isosceles. Everyone deserved to know the truth of their world!
He decided he would start with his wife.
But then he heard a voice outside announcing the law the Circles had re-passed the night before, demanding the execution or arrest of anyone who claimed to have been given knowledge of other worlds.
This dampened his spirits, since he knew that if he was found out, he wouldn't be able to avoid the punishment of death or life imprisonment.
His wife came into the room, and they shared some casual small talk, but he decided he wouldn’t tell her first after all.
He needed to figure out some way to physically demonstrate the existence of the Third Dimension, hoping that if he could simply show people without too many words, he could weasel his way out of obviously breaking the law. He decided that the phrase, “Upwards, but not Northwards”, would be his basic guideline.
He thought about who he would try to teach first. He decided that his sons would probably just turn him in immediately, but why not his grandson, who’d come up with the idea of the Third Dimension all on his own, just the night before?
It seemed like a perfect plan. He reasoned that his grandson was just a small child, so he wouldn’t know anything about the new law, and wouldn’t bother telling anyone.
The narrator had his grandson come to his study, and locked the door.
He went over the traditional 2D geometry like he had the night before, but when he got to the part after a line makes a square, he attempted to casually, but actually very awkwardly and nervously, ask his grandson to repeat what he’d said the night before, about the Third Dimension, and “Upwards, not Northwards”.
But before his grandson could respond, the herald outside came around again and once again announced the new law, and the crimes and the punishment for anyone caught doing it.
And the narrator’s grandson, who he’d thought of as simply a young child who was too young to know anything about anything, listened in silence until the sound of the herald faded away.
Then the little Hexagon burst into tears, begging his grandfather not to turn him in, because no one had known about the new law last night, and he’d just been joking and being silly, and he was sure he’d never said anything about a Third Dimension, or said the words, “Upwards, not Northwards”, those were ridiculous ideas, and only a little baby would believe them, and he wasn’t a baby.
The narrator's grandson thought he was in trouble for what he'd said the night before, and that his grandfather was trying to trick him into repeating it to prove he'd broken the new law. He thought his grandfather was going to send him to jail.
The narrator got angry, and insisted that the idea of the Third Dimension wasn’t ridiculous at all, and picked up one of the toy squares, attempting, and failing, to demonstrate moving it upwards.
Because he was only a 2D Figure, even though he knew that the Third Dimension existed, he still couldn’t move in that direction without the help of a Higher Dimensional Being.
His confused attempts to move the toy in a direction that didn’t exist let his grandson claim that his grandfather was clearly just trying to play some joke on him, and before the narrator could argue that he was serious, his grandson had leapt to his feet, unlocked the door, and ran out of the room.
So the narrator’s first attempt to teach someone else about the Third Dimension had been an absolute failure. It convinced him not to try teaching anyone else in his household the secret, and that he couldn’t simply rely on the catchphrase of “Upwards, not Northwards”. He had to figure out a different way to convince people.
So he decided to try writing.
He spent the next several months writing a detailed description of the Third Dimension, but in an attempt to avoid obviously breaking the law, instead of calling it a physical dimension, he called it “Thoughtland”, a hypothetical place where one could, in theory, look down and see inside all things in the world, and where, in theory, you could meet a creature who had squares for its sides, with eight terminal points. A cube.
It was difficult for him to write this book, because no diagram that he could draw could properly convey the meaning he wanted it to, because the only thing that could be drawn were lines, in books made of lines.
He spent these months depressed over the thought that everything he could see now was only a tiny fraction of what the world really was. He neglected his job as a lawyer, and could hardly stop himself from constantly comparing Flatland to Spaceland every time he spoke.
And every day that passed he found it more and more difficult to accurately and confidently remember the exact shape of a Cube.
If he couldn’t even convince his grandson, how could he convince anyone else?
He was already becoming known for skirting the edges of blasphemy, though he hadn’t done anything blatant enough to deserve being arrested.
And then one day, eleven months after he’d visited Spaceland, he finally made his last mistake.
It was at a meeting for mathematicians, and another member had just read an essay about how Providence had declared that Two Dimensions were all that could ever exist in the world.
And the narrator could not stop himself from immediately launching into his entire story from start to finish of how the Sphere had appeared and brought him to Spaceland, and beyond.
At first he tried to pretend that it was just a fictional story, but he couldn’t keep up the lie for long, and by the time he was done it was clear to everyone that he truly believed everything that he'd just said.
He ended with a rousing speech asking all of his witnesses to stop listening to the lies, and commit themselves to the truth of the Third Dimension.
He was obviously immediately arrested, and brought to the council of Circles for judgement.
He was allowed to repeat his story for them all from start to finish.
He noticed before he’d even started that the Chief Circle saw that higher-class Isosceles guards were in the room, and had them replaced with the thinnest Isosceles available.
The narrator knew what this meant: the Chief Circle intended to kill everyone in the room to prevent his story from being known, and there was no point in wasting better guards.
When the narrator was done telling his story, the Chief Circle asked him two questions:
1: Could he demonstrate the direction of “Upward, not Northward”?
2: Could he show them through a diagram what a “Cube” was supposed to look like?
The narrator said that he couldn’t do either. He couldn’t do anything to prove that he was telling the truth. He would just have to rely on the truth to reveal itself someday.
The Chief Circle responded that if that ever happened, then he would be released from prison. But until that day, he would be kept in a jail cell, and maybe if he behaved, he could be allowed to visit with his brother every now and then.
Seven years passed, and the narrator was still a prisoner. The truth of the Third Dimension had not seen fit to reveal itself to the rest of Flatland.
He has never been able to convince anyone that the Third Dimension is real, not even his brother, who he is allowed to visit once a week, who saw and heard the Sphere for himself so long ago on New Year’s Eve.
The only hope the narrator had left was that his book, the summary of which you are reading right now, might somehow, someday, help another generation of people break out of the cage their mind is in and allow themselves to imagine more than what they can see in front of them.
He spends most of his time depressed and anxious. Aside from his once a week visits with his brother, he spends every day and night completely alone in his jail cell.
He is no longer sure he remembers what a Cube really looks like, and in his darkest moments, he can’t even be sure that the world of Two Dimensions around him is real, or just the figment of some terrible nightmare. He is slowly losing his grasp on reality as a result of the solitary confinement.
Yes, the book does end on the most depressing note possible.
This is the end of the summary of Flatland. I hope you enjoyed it.
Morally obligated addendum: Do not recommend people watch the Ladd Ehlinger Flatland movie on this post. It completely destroys all the moral lessons of the original book, because the creator, Ladd Ehlinger, is so abhorently racist and misogynistic that even other Republicans were embarassed to be associated with him. Do not recommend people watch the Flatland movie that misses literally every point of the original book.
I know it can be a bother, but I think if you place links back to the Table of Contents in each chapter, it can make reading much easier.
Ooh, I didn't think of that! I will definitely do that once I turn my laptop on later. It's definitely not a bother, I can't believe I forgot to do that lol :)
This story is Public Domain. This means you can read it for free, anywhere online, without having to pay for it, unless you’ve chosen to buy it from me as a thank you for making it. This also means that you can take this story, and do anything you want with it! You can make it into a movie, an audiobook, you can edit it to change all the characters’ names and pronouns or turn them into unicorns, you can translate it into different languages, and you can sell anything you make from it, or even just print it yourself and sell it that way.
Why have I chosen to do this after spending so much time and work making this, you ask? Because I’m poor, and I want other poor people to also be able to read books for free, and because I think the world is more fun when people are allowed to be creative without copyright law getting in the way.
You will be able to buy physical copies of this book from me if you want, on Lulu.com, as long as Lulu.com exists, and if you would like to send me money after reading the book for free, as long as Paypal exists and I’m still alive, you can send it to “TinyelFlatland” on Paypal, (and do me the favor of ignoring my deadname. I’m too poor to get a legal name change at the moment.)
If you would like to read the original version of this story, published in 1884, you can look up “Flatland: A Romance of Many Dimensions” online, and read it for free, because that’s also Public Domain, which is how I was able to make this for you to read! Isn’t it great?
If you are reading this online, congrats! If you’re reading it in a physical book and you didn’t know you could also read it for free online, then congrats! You can! It can be found on archive.org, otherwise known as the Internet Archive, unless you’re reading this in 2300 or something and they don’t exist anymore, along with other places too. Just search for the title, and it should show up!
This translation was started on September 15th, 2023, at 7:55PM.
It was rainy today.
I’m writing this so that in the future, when the original story of Flatland: A Romance of Many Dimensions, published in 1884, has become so antiquated that it’s hard for students and other readers to understand the language, there will be at least one more recent stepping stone to aid in understanding.
I am also writing this so that schools who want to teach Flatland may do so with a bit more ease, since it might be hard to get most kids to read the old one.
I will try to keep my translation as accurate to the original Flatland as I can, while making it easier to understand. Sometimes, I may interject if I think extra information will be helpful, with my comments marked by double parenthesis and a note that I’m the one interrupting ((Note from the second editor / end of note from the second editor.))
Flatland: A Romance of Many Adventures was written as satire to criticize the systems of oppression that the author saw around him in Victorian London. Satire is a form of humor where the flaws of something are emphasized to make them more obvious and clear. Many people today, and back then, struggle to understand the satire that Edwin Abbott Abbot had crafted. So I’m making this note in the hopes that more people will understand it properly and look at this book from the right, well, angle. (hehe)
The narrator of this story calls himself A. Square to protect his identity, similar to the way people whose identity is not know will be called things like “J. Doe” or “M. Smith”.
His name is not actually A. Square, but many people enjoy calling him “Abbot Square”, after the author.
A. Square represents bigots of all kind, who are so wrapped up in their own biased world-view that they implicitly trust everything they are told by the people in power without ever taking the time to actually question anything enough torealize that what they’ve been told, and how the world actually works, do not match up at all.
This idea applies both to his ideas of the Dimensions, and systems of social hierarchy and oppression.
You will see many contradictions in A. Square’s testimony of how the world works that he doesn’t realize are contradictions at all. Because to him, actual logic and facts don’t really matter, he just goes along with whatever those higher up tell him.
You will see him thoughtlessly repeat propaganda that conflicts with everything else he has been told to believe, without a single trance of irony or awareness of these conflicts.
You are meant to be shocked and horrified and flabbergasted by A. Square’s ideas about society. That’s the whole point. The point is that he’s wrong, to get you to examine your thoughts about society to see if you are falling into any of the same pitfalls he is. The whole point is to show how absolutely ridiculous his ideas are. You’re supposed to laugh at him. It’s a comedy, and the joke is how ridiculous and absurd bigots are all the time without them even realizing it.
There’s a lot more I could say about this subject, but I’ll stop here and let you get onto the story.
For this version of this book which includes illustrations, I will also be including image descriptions for all of the illustrations so generously provided by the original Author, along with any additional illustrations I created myself, for all my fellow Irregulars out there reading this.
The original Flatland is around 33,000 words long. This version has come out to around 39,000.
This translation was, for this version of the document, completed on July 25th, 2024. This version is meant to be read digitally.
From the river to the sea, Palestine will be free.
If you are reading this a hundred years in the future, I hope the world is a better place than it is today. I hope global warming has been managed, I hope capitalism has ended, I hope that Irregulars of all kinds – Queer people, Black and brown people, disabled people, religious minorities – are treated as equals and that no one has to go without food or shelter. I hope that the word “homeless” seems antiquated and confusing, because everyone has a home. I hope sea turtles aren’t still eating plastic because of nonstop pollution and corruption. I hope the black-footed ferrets and bison recover from endangerment and are thriving in their natural environments again. I hope that white supremacy and colonization have been overthrown, and that the world looks back on the country that called itself “The United States of America” with all due horror, disgust and shame. I hope that slavery has been abolished permenantly, everywhere, with no loopholes saying “except as punishment for a crime”. I hope that slaves are not sent to fight wildfires or build bombs to send overseas to murder Palestinians or any other victims of colonization. I hope that the world has figured out a way to disarm all nuclear bombs, and has agreed to forever forget the knowledge of how to make more. I hope that physical books still exist, and that libraries still exist, and that corporate monopolies have all long since been destroyed. I hope everyone everywhere has access to free, quality healthcare, and that all of the stolen land in this world is given back to its rightful stewards.
If you are reading this in the future, I hope you live in a better world than what we have right now.
And if you are reading this right now, I hope you take every opportunity presented to you to learn more, to question more, and to make this world a better place.
Enjoy.
-signed, Tinyel (tin-yell), a physically disabled and autistic+ADHD nonbinary aroace lesbian who uses it/its/itself and skull/skulls/skullself pronouns. (I mention this because I know bigots in 2050+ will still probably try to pretend that Queer identities are brand new and only invented last year, and so Queer and Questioning people in 2024 can see that others are out there!)
PS. My cat says hi.
This is the end of the preface by the second editor.
To the secrets of four five or even six dimensions
Thereby contributing
To the enlargement of the imagination
And the possible development
Of that most rare and excellent gift of modesty
Among the superior races
Of solid humanity
-
Preface to the Second and Revised Edition, 1884.
By the Original Editor (Also known as Edwin Abbott Abbott)
I am writing this preface for my friend from Flatland, since he has been so mentally devastated by his years spent in prison that he can’t write it himself. Rather than copying his words directly, I am paraphrasing on his behalf so you, my Readers, will understand what he means.
First of all, he wants to thank all of his Readers, both fans and critics, in Spaceland, who’ve enjoyed his book so much that he had to get it reprinted again to meet the demand.
Second of all, also wants to apologize for some errors and misprints in the original edition, though these aren’t actually his fault.
Third of all, he wants to explain a few things that have confused some Readers.
He wanted to respond himself, but he’s not the Square he used to be. The problem is not just that he is a prisoner, it’s that no one believes what he has to say, and do nothing but mock him, and he struggles to tell reality from dream. He’s also an old man now, and his memory is fading. He’s forgotten many of the ideas he learned on his adventure in Spaceland, and the words to describe them.
So he has asked me to reply on his behalf, to explain two points that many confused readers are upset or annoyed by.
The first thing people complain about is that when a Flatlander sees a Line, that means they have to be seeing something that does have Height, not just Width and Length, otherwise it would be invisible from the side. So why doesn’t he admit that his people already exist in Three Dimensions?
I understand that people are going to complain about this, since it’s such an obvious problem, especially to Spacelanders. I must say, I really wasn’t sure how to respond when I first read this comment, because I couldn’t think of any counter argument, but fortunately, my friend was able to answer it in a way that makes sense to me, so I’ll paraphrase his words here for you:
"I admit that what this critic said about us having some height is true, but that doesn’t mean we exist in Three Dimensions the way Spacelanders do. Yes, Flatlanders are Tall as well as Long and Wide, otherwise we would be invisible, but this isn’t something we can measure or recognize on our own – (Remember, I didn’t even know the word “up” before my adventure in Spaceland) -- and you Spacelanders also have a Fourth Dimension you don’t have a name for, that I’ll call ‘Extra-Height’, that you can’t measure or understand on your own either, but that doesn’t mean you’re Fourth Dimensional Beings anymore than I’m a Third Dimensional Being. Even after my adventure, I still can’t measure Height, or “Upwards”, not by seeing it, or even trying to imagine it. But I know it’s there, and I have to rely on pure faith.
Let me try to explain. You can only measure something if it has variation to be measured in the first place. If everyone, and every single thing you see – animals, people, trees, buildings, rocks, even -- is exactly the same Height, then you can’t measure Height, because there’s nothing to compare it to. It’s just the way the world is. Nothing is shorter than anything else, or taller. There’s nothing there to measure. Especially because everything you see is all that you can see. You can’t see above the Height of everything, or below it. It’s just what’s there.
Some Spacelander critics who like to complain too much have suggested we invent a so-called “delicate micrometer” to measure our Height with, but again, that’s impossible for us to do, because we can’t measure Upwards, nor can we compare it to anything else.
When we see a Line from the side, we see something that is Long and Bright, and that’s how we know it’s a Line -- Brightness and Length are both needed for us to understand what we are seeing. If there’s no Brightness, the Line becomes invisible to us, and may as well not exist.
This is why, when I try to explain the concept of Height, or ‘Upwards’ to my fellow Flatlanders, when I try to point out the existence of Height in a Line, the only thing they can see is the Brightness. And when I tell them I mean something else, a different Dimension, they demand I prove that it’s there by measuring it. Which I obviously can’t do, for the reasons I’ve already explained. You can’t measure what has no variation.
It was just yesterday that the Chief Circle – our High Priest, or maybe in your terms better understood as the President or King – came to visit me, the seventh of his yearly visits. And just like the last six times he came to visit me, he asked me the same question: ‘Are you sane yet?’.
And so I tried to explain to him that he was Tall as well as Wide and Long. And you can probably guess his response. ‘You say I am ‘High’, so measure my ‘High-ness’, and then I’ll believe you.’
And how, exactly, am I supposed to do the impossible? I’ve already explained that we can’t measure Height. There was nothing I could do to prove what I said, and we both knew it. So he left the room, just as triumphant as the earlier six visits.
Still confused? Then put yourself in my shoes – imagine a person from the Fourth Dimension decided to visit you, said:
‘Whenever you open your eyes, you see what appears to be a Two Dimensional image, and you understand that these are actually many different Three-Dimensional objects, through shading and light, and because you can reach out and touch them. And you think everything you are seeing is Three-Dimensional, but really, you’re also seeing a Fourth Dimension, and it’s not color, or shadows, or anything like that, but a true, separate Dimension. No, I can’t point it out to you. No, I can’t give you any way of measuring it or seeing it. You’re just gonna have to trust me.’
And how would you respond to someone saying this? Wouldn’t you want him thrown into an asylum too?
Well, that’s what happened to me. I was a Square who tried to convince my countrymen that there was a Third Dimension, and I was locked up, just as you Spacelanders would lock up anyone who tried to tell you there was a Fourth Dimension.
Alas, the family resemblance of ignorance and bigotry runs strong through humanity in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes, it doesn’t matter – we are all just as likely to make the same mistakes, believing only what we can see, and refusing to think beyond that.
As your famous Spaceland playwrite, William Shakespeare once said, 'One touch of Nature makes all worlds akin'."
That was the Author’s answer in reply to the first complaint, and it makes sense to me.
As a further note on this point, the Author also wants me to also tell you that in this updated edition of his story, we have added back in some of the extra details of his conversations with the Sphere that we originally left out, because we assumed you, the audience, would find them boring and unnecessary.
So there is his defense against the first point of complaint. I can’t find anything to argue with about it, it seems like a solid defense.
As for the second point of complaint…I wish I could tell you that his response to the criticism was just as well thought out, but I can’t.
It has been objected that he is a woman-hater, and, because many of the people making this complaint are Women themselves, who feel hurt by this, I want to reassure you to the best of my ability that this is not the case, at least as far as I can tell you that without lying.
The unfortunate fact is that the Square who is the Author of this book is not used to thinking in terms of Morality, let alone the ideas of Morality that we in Spaceland have.
If I were to literally transcribe his response to this complaint, I’d be making him look much worse than he really is, because he doesn’t really understand how to articulate his thoughts on this topic, because Flatland (or at least, his country in Flatland) does not have the words to describe it.
((Note from the second editor: I want to emphasize that when the original Editor here says the Author didn’t have the words for Morality, he means that very literally, as you’ll see later, when the Author is narrating for himself. End of editor’s note.))
So, as I am already doing by paraphrasing the his words for you, I will paraphrase again his response to this allegation of misogyny.
It’s my understanding that in the seven years since he was imprisoned, he has changed many of the personal views he expressed in this book, both in regards to Women, as well as the Isosceles and other Lower Classes, such as Irregulars.
His opinion is now much closer to that of the Sphere who visited him, that Straight Lines are in many ways superior to Circles.
But, because he wrote this book from the perspective of a Historian, he aligned himself (maybe too closely) with the general views held by the Higher Classes of Flatland, and, as I’ve since told him, many among us here in Spaceland.
I don’t think I need to tell you that many of our own Historians, who are mostly Men, have generally thought that the lives of Women and other Oppressed People were not worthy of caring or writing about.
The Author also wishes to deny the idea that he is still a supporter of the Circles and Aristocracy. He has had a long time to think since his imprisonment, and while he doesn’t deny that the Circles are very intelligent – otherwise, he says, they wouldn’t have managed to stay in control for so long – he believes that the facts of Flatland speak for themselves.
Revolution cannot always be suppressed by slaughter, and because the Circles themselves tend to be infertile, he believes that Nature Herself has condemned their actions as a failure in the end.
“And this is where,” He said, “I see the laws of Nature working in all worlds. Man thinks he is doing one thing, and he thinks he knows best, but Nature is wise, and cannot be denied. Her end goal is much different, and better, than what Man plans for.”
For the other complaints, the Author begs the readers not to assume that every detail of daily life in Flatland is a mirror of some other detail in Spaceland.
He hopes that his book, taken as a whole, will be educational as well as amusing to Spacelanders who are willing to suspend their disbelief and not immediately cry, “That can’t happen”, or “No, things only work like this”.
The rest of this book, I leave to him, in his original words, now with the small edition of some clarification in his conversations with the Sphere.
((Note from the second editor: If you would like to read the Author’s original words, as transcribed by the original Editor, please look for Flatland: A Romance of Many Dimensions, online. It is Public Domain and belongs to everyone, so you can read it, or listen to it as an audiobook, completely for free.)
I don’t call our world Flatland because that’s what we call it, but because I want to make what it’s like clearer to you, my happy Readers who are privileged to live in Space.
Imagine a vast sheet of paper on which Straight Lines, Triangles, Squares, Pentagons, Hexagons, and other geometric shapes are alive, and move freely, instead of being drawn in pencil.
They move on, or maybe you’d call it within, the surface of the paper, but do not and cannot rise above or sink below it. Almost like shadows, but hard and solid, with glowing edges.
If you can imagine this, you’ll have a pretty good idea of what my country looks like.
Just a few years ago, I would have said, “my universe” instead of “my country”, but now I know better.
In such a flat land, you Spacelanders will almost immediately assume that it’s impossible for there to be anything you would consider “solid”. And yet, if you look down, you’ll see the Triangles, Squares, and other Figures, just like I said.
We on the other hand, see no such thing, because the only things we can see are Straight Lines.
If this sounds confusing, let me give you an example, which you can follow along with while you read.
Get a small coin or similar thin object, and place it in the middle of one of your tables in Spaceland.
When you stand above it and look down, you see the coin as a circle.
But, if you move back to the edge of the table, and lower yourself partway towards the ground – more like the way we Flatlanders see the world – you’ll see that the coin now looks less like a circle, and more like an oval.
Then, if your eye is level with the edge of the table, you are closest to what you can get to being “on our level”. You’ll see that the penny, seen from above as a circle, now appears to just be a Straight Line.
The same thing would happen if you did this with a Triangle, or Square, or any other Shape you could cut out of cardboard. As soon as you look at it with your eye on the table, it looks like a straight line.
Take for example an equilateral Triangle—who with us is a Tradesman, or Buisnessman, of the respectable class.
Figure 1 below represents the Tradesman as you would see him while you were bending over him from above, as a Triangle with all three sides of equal length.
Figures 2 and 3 represent the Tradesman as you would see him if you began to move your eye closer to the level of the table.
Figure 4 represents what you would see if your eye were level with the table: nothing but a Straight Line, which is how we see him in Flatland.
[Image description start: Figures 1, 2, 3, and 4. Each is a very simple black and white illustrations of an equal-sided triangle seen from different angles, first from above, where he is plainly seen as a triangle, then slowly moving the view down so that he gets flatter and flatter until he is nothing but a straight line. Image description end.]
When I visited Spaceland, among other things not worth talking about in detail, I was told that your sailors have a similar experience when they’re out on the ocean – distant lands might obviously have bays, cliffs, buildings, and all kind of shapes on them from close by, but until you get close enough, or unless the sun’s bright enough to cast clear shadows, all you can see at a distance is a grey line on the horizon.
That’s like what we see when one of our Triangular or other acquaintances comes towards us in Flatland. We have no shadows like you do, and none of the other advantages your vision has in Spaceland.
If our friend comes closer to us, he becomes larger, if he goes away, he becomes smaller, but he is always a straight Line. It doesn’t matter if he’s a Triangle, Square, Pentagon, Hexagon, Circle, or anything else. He always looks like a Straight Line, and nothing else.
You’ll of course be wondering how we tell eachother apart if this is all we can see, and I’ll be able to make you understand better once I finish describing the people who live in Flatland.
But for the moment, let me pause this subject, and instead tell you about our houses, and the environment of Flatland.
Like in your world, we also have four points on our compass: North, South, East, and West.
Since we have no sun or other celestial bodies like you do, we can’t tell where North is in the way you do, but we have our own way.
Similar to your birds, we always know where South is, because for us, we are constantly being pulled in that direction. This pull is very light in our most northern countries, so light that even a reasonably healthy Woman can travel for several hundred yards Northward without difficulty.
But even at its lightest, we can still feel it, and can use this to tell which way is South. As an added bonus, the rain, which always falls on a predictable schedule, always comes from the North.
Because of this, when we are in a town or city, we can tell the direction from the way the houses are built – because the rain comes from the north, the solid roof faces north, so that the water can safely run off and down the sides without getting inside.
When you’re out in the countryside where there are no houses, you can use the trunks of the trees instead.
As you can see, it’s usually pretty easy for us to get our bearings.
But one problem is that when you are so far North that you can barely feel this pull, if you are walking in a deserted plain with no trees or houses in sight, I’ve sometimes gotten so turned around that I had to stand in place for hours straight, waiting for the rain to come so I’d know which way to go.
If you are ill or old, or a delicate Female, this pull to the South weighs heavier than on the healthy members of the Male Sex, so it’s considered polite that, if you meet a Lady in the street, you will move to the South and give her the North side to walk on.
This can be easier said than done in such short notice, if you are in a northern climate where it’s hard to tell which way is south, or if you’re feeling sick yourself.
Unlike your buildings, ours have no windows, because light comes to us everywhere equally, whether you’re inside or out, during the day or night, and where this light comes from, we don’t know.
A long time ago, philosophers and scholars used to ask each other “What is the origin of Light?” and debate the possible answers. Many people have tried to find the answer to this question, and the only result is that our lunatic asylums have precious space taken up by the people who’ve claimed to have solved it.
Our Government tried to persuade people to stop trying to solve this problem by forcing anyone who worked on it to pay heavy taxes, but when it kept being a problem, the Law Makers, not so long ago comparatively speaking, finally made it completely illegal to talk about.
And here I am, the only one in Flatland who knows the truth to where Light comes from. But I can’t explain it to my countrymen, and when I try, they just laugh at me – me! The only one in this World who understands that Light comes from the Third Dimension! They laugh at me like I’m the maddest of the mad.
But I’ve gotten off track and this is a painful topic, so let’s get back to talking about houses.
Most of our houses are five-sided shapes, or as they are commonly called, Pentagons.
Here is an illustration to help you understand:
[Image description start: A black and white digital illustration with the compass in the upper left corner, showing a pentagonal house in Flatland. Each of the five points of the pentagon are with a different letter, with “A” and “B” going left to right on the bottom line, and “R”, “O”, and “F” left to right on the top, with the two diagonal lines marked with their combined points, so that the top two diagonal lines spell out, “roof”. On the Western diagonal side is a large gap marked by a grey line labled, “Men’s door”. On the east is a much smaller gap labled, “Women’s door”. Image description end.]
The two Northern sides of a Pentagon house form the roof, and these normally don’t have any doors. On the eastern side, there is a small door for Women, and across from it on the Western side is a much larger door for Men. The Southern side, or floor, usually doesn’t have any doors.
Square and Triangular houses aren’t allowed, because their angles are much sharper than those of a Pentagon, and since the lines of inanimate objects, like houses, are dimmer than the lines of Men and Women, they are harder to see, so if someone wasn’t paying attention, they could get seriously hurt if they accidentally ran into the corner of a Square or Triangle shaped house.
As far back as the eleventh century of our era, Triangular houses have been illegal to build, with the only exceptions being for military structures like forts, ammunition stores, barracks, or other state buildings that most people aren't allowed to enter without special permission.
At that point in time, you were still allowed to build Square houses, but they were subject to special taxes to discourage people from building more of them.
Three hundred years after Triangular houses were outlawed, the Law finally decided that if a town’s population was above ten thousand, then the angle of a Pentagon was the smallest house-angle allowed to be built, in the interest of public safety.
The general community has common sense, and has agreed with this new law, so now, even out in the country on farms, almost all houses you can find will be pentagons. Now and then, though, in some very remote and poor farming district, an antiquarian might still find an ancient Square house.
Section 03. Concerning the Inhabitants of Flatland
[Table of Contents]
Most adult Flatlanders will reach a length of around eleven of your inches, or twenty-eight centimeters. Twelve inches, or around thirty centimeters, is considered the natural limit.
Our Women are Straight Lines.
Our Expendable Soldiers, and the Lowest Classes of Laborers, are Triangles with two equal sides, each about eleven inches, or twenty-eight centimeters long, with their third side, or base, so short (Usually less than half an inch, or two centimeters), that they form at their vertices an extremely sharp angle, or point.
When these sorts of Triangles have a base of the most degraded type (less than an eighth of an inch, or three millimeters), it’s almost impossible to tell them apart from Straight Lines or Women, so sharp are their needle-like points.
Just like you do in Spaceland, we refer to these kinds of Triangles as Isosceles, which is how I will refer to them from now on.
Our Middle Class consists of Equilateral or Equal-Sided Triangles.
Our Doctors and Lawyers and Gentlemen are Squares (which is the class I belong to) and Five-Sided Figures, otherwise known as Pentagons, as mentioned above.
Above us are the Nobility, with several classes, starting with Six-Sided Figures, or Hexagons. After Hexagons, the numbers of sides increase until one is given the honorable title of “Polygonal”, or many-sided.
When the number of one’s sides become so high, and the sides themselves each so small, that the figure can’t be told apart from a circle, he becomes part of the Circular, or Priestly order. There is no class higher than that of the Circles.
It is a Law of Nature with us that a Male child will have one more side than his father, so that each generation rises in the ranks of nobility, as a rule.
This means that a Square (4 sides) will have Pentagonal sons (5 sides), and his grandsons will be Hexagons (6 sides), and his great-grandsons will be Septagons (7 sides), his great-great-grandsons Octogons (8 sides) and so on and so forth.
But this rule doesn’t always apply to the Tradesmen, the Equillateral Triangles, and it’s even less common in the Isosceles Soldiers and Workers. But, to be fair, they can hardly even be described as human beings, since their sides aren’t all of equal length.
Because they’re subhuman, this Law of Nature doesn’t work on them, and most of the time, the son of an Isosceles is still an Isosceles.
But things aren’t entirely hopeless! Your children’s position in society can always get better, even if you’re one of the most degraded of Isosceles, through hard work, dedication, and many successful military campaigns!
Often, when Workers and Soldiers prove themselves to be smarter than their peers, when they are measured again, the measurements will show that their third side, or base, has grown, while their two longer sides have shrunk, producing a larger angle at the vertex!
The Priests then graciously become involved, arranging the marriage of the lucky Isosceles to a suitable Straight Line, and the sons born to these arranged marriages are almost always born with larger angles than their fathers, much closer to being an Equal-Sided Triangle than others who married for love.
Very, very, very rarely, a true, certifiable Equal-Sided Triangle is born to Isosceles parents.
(And a critic might ask, “But why does he need to be certified? When he eventually gives birth to a Square son, isn’t that a certificate from Nature herself, proving that he’s truly Equal-Sided?” And I tell you that no self-respecting Lady would ever consent to marry an uncertified Triangle.
Square sons are sometimes born to slightly Irregular Triangles, which would seem like cause for celebration, but almost every time, the Triangle’s Irregularity is passed down to his grandson, who either fails to attain the rank of Pentagon by instead being born a Square, or relapses entirely by being born a Triangle.)
If an Equilateral Triangle has any hope of being born to Isosceles parents, there must be a careful plan of arranged marriages for several generations, as well as strict self-control and frugality. Each generation needs to become smarter than their parents, and make sure their children are smarter than they are, for many generations.
When a True Equillateral Triangle is born to Isosceles parents, the birth is celebrated for many miles around.
The Sanitary and Social board performs a strict examination of the newborn, and, if he is certified as Regular, he is, with all due seriousness, conducted into the class of Equilaterals.
He is then immediately take away from his proud, sorrowing Isosceles parents, and adopted by an Equilateral who has no children of his own, who has to promise never to let his adopted child go to the area where he was born, or even look at his biological parents, in case he mimics them without realizing it, and reverts to a degraded Isosceles.
The rare birth of an Equilateral from the masses of slaves is not only welcomed by the slaves themselves, as proof that their hope of their children climbing the social ladder isn’t misplaced, but it also gives them something to be temporarily happy about in their otherwise miserable lives, like a sudden, surprise holiday.
Such an event is also welcomed by the Aristocracy.
The Higher Classes know that their own social status won’t be threatened by these births, because it’s really the exact opposite – these births help maintain their power.
If the acute-angled rabble had been completely, absolutely without hope and ambition, it would have given rise to many leaders to start their rebellious phases, and, with their superior numbers and strength, they would have been too much for even the wisdom of the Circles to handle.
But Nature is even wiser, and has decided that, as the working-classes get smarter, they also get weaker, as their acute angle, which makes them so dangerous and stupid, grows wider, getting closer to the comparatively harmless angle of an Equilateral Triangle.
In the most brutal, acute, and threatening of the Isosceles – creatures almost on the same level of Women with their lack of angle and intelligence – their ability to kill is matched by their inability to plan how to do so efficiently.
And in return, when their descendants have finally become smart enough to plan what would be devastating acts of terrorism, they’re no longer physically capable of carrying them out.
[Image description start: A black and white illustration with a black border, titled, “The Law of Compensation”. In the center of the diagram are five triangles, starting from so acute it’s almost a straight line, until it finally becomes a much wider equal-sided triangle. Above and below are scales. The first, above, is labeled, “Intelligence”, and it increases as the shape gets wider. The second, below, is labled, “Physical threat”, and it decreases as the shape gets wider. Image description end.]
How admirable is this Law of Compensation! It just goes to show how natural, and -- dare I say, divinely inspired? -- the structure of our society is here in Flatland! It is as if Nature herself is helping our great Polygons and Circles to kill rebellion in the cradle!
Art, too, comes to the aid of Law and Order. Our doctors can usually figure out a way – through artificial compression or expansion of the exoskeleton – to make the more intelligent leaders of any given Isosceles rebellion become Equilaterals, allowing them to immediately join the privileged higher classes.
Many more of these rebel leaders, though, are too far below the standard for intelligence to be allowed the surgery, but, bewitched by the promises of becoming Regular through similar treatment, they are tricked into entering the State Hospitals, which they will never be allowed to leave. They spend the rest of their lives honorably confined to these hospitals.
Only a few of the more obstinate, foolish, or highly Irregular of the rebel leaders are actually put to death.
And then the wretched rabble of the Isosceles, without a plan, without leadership, are either killed without resistance by the small group of Isosceles assassins the Chief Circle pays in case of emergencies such as this, or, more often, thanks to the suspicions and in-fighting stirred up by the Circular party, begin attacking and killing each other, until none of them are left alive.
There are a hundred and twenty rebellions recorded in our state records, and a further two hundred and thirty-five minor outbreaks.
Now that you understand how dangerous our highly-pointed Isosceles Triangles are, you can understand how much more dangerous our Women are. Because if an Isosceles is a wedge, a Woman is a needle, made up of, you might say, nothing but points, at least at the two ends.
Add to this sharpness a Woman’s ability to make herself practically invisible at will, and you’ll see that the Females of Flatland are not the kind of Creatures you want to mess with.
But maybe some of my younger Readers are confused, and thinking, “But how can a Woman in Flatland make herself invisible?” I think the answer is pretty obvious, but it won’t take very long to explain, so even those who aren’t paying full attention will understand.
Place a needle, or another long, thin object, like a pencil, on a table. Then, lowering yourself until your eye is level with the surface of the table, look at your line from the side, and you'll see its whole length. But if you turn it so that you are looking straight at it from the front or back, you see nothing but a small point.
This is what happens with our Women. When her side it towards us, we see her as a straight line. When her front or “head” in you terms, the part, containing her eye or mouth (which for us, is the same organ) is pointed at us, we see a bright point.
But when her back is pointed towards us, we see a dim light, so dim it's almost as dark as an inanimate object. And this is how a Woman, by simply turning her back on you, can become practically invisible.
[Image description start: A black and white digital diagram with a white background and black border. On the left is a drawing of an eye as seen from the side, with dotted lines radiating out to show the line of sight. This eye is looking downwards on a straight line, and is labeled, "A Straight Line viewed from the side.". The next is looking to the side at a tiny dot that is marked by a large arrow so you notice it, and this eye is labeled, "A Straight Line viewed from the front or back.". Image description end.]
I need to make it clear to you just how dangerous our Women are. If running into an Equilateral Triangle, whose angle is 60°, will give you a painful gash, then running into an Officer of the military class, an Isosceles, will give you a serious wound. If a mere accidental bump from the vertex of a Private Soldier, one of the lowest of the Isosceles, is life threatening, then what can you expect from running into a Woman, except complete and total annihilation?
And when a Woman is almost invisible like this, imagine how difficult it is, even for the most cautious, to avoid running into them!
Many laws have been put into place in the different countries of Flatland in order to reduce this danger, and in the Southern and less temperate environments where the force of the Southern pull, or gravity, is greater, where human beings are more likely to have sudden and involuntary movements from constantly fighting the gravity, the laws regarding Women are, naturally, much stricter and harsher.
But a general view of the regulations for Women can be understood from the following summary:
1. Every house will have one entrance on the Eastern side, to be used only by Females, and all Females must enter “in a becoming and respectful manner”. Females must never use the Men’s or Western door.
[Note from the Author: When I was in Spaceland, I was told (in a conversation not transcribed in this book, to save my Readers’ valuable time) that some of your Religious buildings have a similar policy, with a separate entrance for the working poor so that they can also "approach in a becoming and respectful manner."]
2. No Female shall walk in any public place without continually keeping up her Peace-cry, under penalty of death.
3. Any Female diagnosed with St. Vitus’s Dance ((A neurological disorder causing sudden, involuntary movements after an illness, usually affecting children)), seizures, a chronic cold accompanied by violent sneezing, or any other disease that causes involuntary movements, shall be destroyed immediately upon diagnosis.
In some countries, there is another Law that forbids Females, under penalty of death, from walking or standing in public spaces without constantly moving their backs from side to side, so that people behind them can see them better.
Other countries will sometimes demand that any Woman in public should be followed by one of her male family members or servants, and still others ban Women from public entirely, confining them to their homes except during religious festivals.
But our wisest of Circles and Politicians have found that having so many restrictions on Women not only leads to the weakening of our society overall, but also to an extremely high number of domestic murders, to the point where the number of Men killed as a result far outnumbers the accidents that the Law was attempting to avoid in the first place.
Because when the temper of a Woman is stoked by being confined to her home, or having to deal with harsh, inconvenient restrictions when in public, they are likely to unleash their fury upon their husbands and children or siblings. Several times, in countries with highly restrictive laws, the entire Male population of a town has sometimes been wiped out in just a few hours as the Females simultaneously and violently succumb to their wrath.
And this is why the first three laws I’ve outlined here are good enough on their own for the better-run countries such as the one I belong to, and can be used as a rough summary of the Female Code.
After all, it’s not the Law itself that protects us so much, as the instinct for self-preservation in the Women themselves.
It I true that they can inflict instant death by simply moving backwards, but it is also true that unless they can immediately remove their stabbing-end, their own fragile bodies can easily be shattered by the death throes of their victim, and the Woman will be killed along with them.
The power of Fashion is also on our side.
I said above that in some less civilized countries, Females are not allowed in public without swaying her back from side to side, but in my country, our high-ranking and ambitious ladies have been doing this of their own free will since as far back as anyone can remember. The idea that a law would have to be passed to guarantee this behavior, (which should be instinctive in ladies of high breeding), is extremely embarrassing.
The rhythmic and, if I may so say, well-modulated undulation of the back in our ladies married to Circles is envied by the wives of Equilaterals, who, trying their best, can only create a regular twitch like the ticking of a clock.
But even that simple ticking is admired by the wife of the ambitious Isosceles, who wishes to raise her family’s status, so that she becomes the first in all her family line to practice the art of back motion.
So you see, in every family worth considering, “back motion” is as old and ingrained as time itself, and the lucky Male members of these families enjoy their immunity from invisible attacks.
But don’t get me wrong, I’m not saying our Women don’t care about their families— it’s just that, unfortunately, their emotions in the moment overpower their other feelings, driving out every other thought until their anger passes.
This, of course, is the result of their unfortunate Configuration as Straight Lines.
They have no Angle to speak of, and thus are mentally and physically inferior to even the very lowest of the Isosceles. They are, as a result of this lack of Angle, completely devoid of brain-power, and are completely incapable of self-reflection, judgment, or planning, and barely any memory at all.
This is why, when they are in a state of fury, they have no idea what they’re doing, or who they’re doing it to. They will not recognize their husband or even their children.
I’ve actually heard of a legal case where a Woman murdered everyone in her whole household, but then half an hour later, when she’d calmed down and the fragmented bodies had been swept away by Police, asked them where her husband and children were. She didn’t remember a thing.
So it should be obvious that you shouldn’t annoy a Woman if she’s able to turn around and stab you. But when you have them in their apartments – which are built so narrowly specifically to prevent them from turning and attacking – you can say or do whatever you want, because they’re incapable of reacting in any way except through speech, and in a few minutes, they won’t even remember whatever it is you’ve said or done that they’re threatening to kill you for, nor will they remember the hasty promises you’ve made (with no intention of keeping) to get them to calm down again.
In general, we get along pretty well with our Women, except in the lower classes of the Isosceles military. These Isosceles, lacking in angle, also lack in tact and discretion, and many times this has caused indescribable disasters.
These Isosceles rely too much on their sharp points as weapons instead of the shield of common sense and knowing how to react to different problems, so these reckless Creatures often fail to properly follow the safety code for building Women’s apartments, or irritate their wives by insulting them when out in public, and then to make matters worse, refuse to immediately apologize.
And, being simple Creatures who are too fond of the literal truth, these Isosceles refuse to make the kinds of lavish, impossible promises that Circles readily deploy to pacify the would-be murderess.
The result of this lack of careful handing is massacre, but you shouldn’t see it as a tragedy – on the contrary, these outbreaks eliminate the more brutal and troublesome of the Isosceles, and many of our Circles view the destructiveness of the Thinner Sex as one of many favors Providence has given us for naturally suppressing the population of Isosceles, and helping to nip Revolution in the bud.
But even within the families that most strictly follow the Female Code, even with our closest-to-true circles Circular families, I have to admit, our idea of “domestic bliss” isn’t as full of affection and comfort as it is with you in Spaceland.
There is peace, (if the absence of slaughter can be called peace) but it is impossible for there to be shared interests or hobbies between Man and Wife, with the Man’s safety paid for by the loss of true comfort and companionship.
Since time immemorial, the Women of our Circular and Polygonal houses have had the habit – which has now become a kind of instinct – of always keeping their eyes and mouths pointed towards their Husband and his Male friends.
If a lady in a high-ranking family turned her back on her Husband, it would be seen as an omen of disaster threatening a huge loss of social status.
But, as I will soon explain, this custom, while insuring safety, is not without its problems.
In the house of the Isosceles Working Man, or the Equilateral Tradesman, where the wife is allowed to turn her back on her husband while performing her household duties, there are moments of peace, where the wife is neither seen nor heard, except the humming sound of her ever-present Peace-cry.
But in the homes of the upper classes, these moments of peace are few and far between. There, the loud and bright face of the Wife are always directed at the Master of the household, and not even the never-changing Light is more persistent than the never-ending Feminine Chatter.
The diplomatic skill required to avoid a Woman’s sting has no power against a Woman’s mouth, and, since the Wife has absolutely nothing meaningful to say, and no intelligence or conscience there to prevent her from speaking anyway, more than a few cynics have been quoted with saying they prefer the death-dealing but mercifully silent sting of a Woman’s back side to the obnoxious volume of her mouth.
To my readers in Spaceland, the condition of our Women may seem truly miserable, and indeed it is, without question. A Male of even the lowest type of Isosceles can look forward to some improvement of his Angle through hard work and dedication, and eventually the increased rank of his entire degraded caste, but no Woman can ever hope for such things for her own Sex.
“Once a Woman, always a Woman” is a Decree of Nature; and the very Laws of Evolution seem to stack misfortunes against her.
But at least we can admire the wise arrangement Evolution and Nature have given us, so that even though the Women have to be miserable for our great society to exist, at least they’ll soon forget it.
Section 05. Of our Methods of Recognizing one another
[Table of Contents]
You, who are blessed with the ability to perceive Shading as well as Light, whose people are gifted with not one, but two eyes, who understand perspective, who get to enjoy all shades of Color without thinking about it, you who can actually See an angle, and see the complete circumference of a Circle from your happy, elevated position in the Third Dimension without a single speck of effort—How can I make you understand how difficult it is for us in Flatland to recognize each other?
Remember what I already explained to you earlier? All things in Flatland, alive or inanimate, no matter what their shape, appear to be, to our view the same as a Straight Line. So then how can we tell one shape from another, when all shapes look the same?
The answer is threefold.
The first way of recognizing different shapes is the sense of Hearing, which with us is much more highly developed with us than it is with you in Spaceland, and not only lets us recognize the voices of our friends, but even to tell which class someone belongs, at least as far as the three lower classes – the Equilateral, Square, and Pentagon – go. As for the Isosceles, well, there’s no telling.
As we rise in social standing it becomes harder and harder to tell people’s classes apart by their voice, partly because the higher classes all speak in similar ways, and partly because using someone accent to judge their class is a poor man’s skill that is looked down upon by the Aristocracy.
And if there’s any danger of offending someone more important than us, we can’t trust this skill, because among the lowest classes, the vocal organs are more strongly developed, so that an Isosceles can easily fake the accent of a Polygon, and, with some training, even a Circle himself. So a second method is more commonly used.
Feeling is, among our Women and lower classes – (I’ll explain shortly about our higher classes) – the main test of Recognition in most cases between strangers, and also when the question is not to the individual’s identity, but his class.
As a result, what you in Spaceland call a “formal introduction” is the equivalent of “Feeling” with us.
For our more old-fashioned gentlemen who live out in the country, “Permit me to ask you to feel and be felt by my friend Mr. Smith”, is still the go-to phrase.
But in the towns, and among businessmen, the words “be felt by” are cut out, and the sentence is shortened to, “Let me ask you to feel Mr. Smith”, and it is just assumed that the “feeling” will go both ways.
Among our younger, more modern, and dashing young gentlemen, who refuse to expend any extra effort than necessary, and don’t care at all about protecting the sanctity of their language, the phrase is shortened even more, using the words “to feel” as a shortcut for “to recommend for the purpose of feeling and being felt”.
At the time this book was written, this “slang” of the newest generation allows such disgraceful barbarism as the sentence, “Mr. Smith, permit me to feel Mr. Jones”, to exist.
But please, my Readers, don’t assume that “Feeling” for us is as awkward and tedious as it would for you, or that we have to go all the way around the person, feeling all his sides, before we can figure out what class he belongs to.
Years of practice and training, started in school and continued in daily life, allow us to immediately tell apart the angles of an Equal-sided Triangle, Square, or Pentagon at a single touch. And I don’t think I need to explain how the brainless vertex of an acute-angled Isosceles is obvious even to the dullest touch.
That is why, as a general rule, we don’t need to feel more than a single angle of an individual, and this by itself can tell us the class this person belongs to, unless he belongs to one of the higher sections of the nobility, where things become much more difficult.
Even a Master of Arts from our University of Wentbridge has gotten a Ten-sided and Twelve-sided Polygon confused, and there is no Doctor of Science, in or out of that university who would pretend to know, without hesitation, the difference between a Twenty-sided (or Icosagon) and a Twenty-four sided (or Icositetragon) member of the Aristocracy.
The Readers who have been paying attention and remember what I said earlier about our Women’s Code should quickly understand that the process of Feeling requires serious caution and self-control, otherwise the angles of the one being Felt might seriously injure the Feeler.
It is essential for the safety of the Feeler that the Felt should stand completely still. A single twitch, any fidgeting, and yes, even something as simple as a violent sneeze can prove fatal. Things like this have ended many promises friendships before they could even begin.
This is especially true with the lower classes of Isosceles. Their eyes are positioned so far from their sharpest point that they can barely see what’s happening at their most dangerous end. These Triangles are also literally insensitive, and can barely feel the much more refined touch of a highly bred Polygon. So no one can really be surprised if a sudden toss of the head deprives the State of a valuable life!
I’ve heard that my honorable Grandfather – (one of the least Irregular of his unhappy Isosceles class, who obtained, shortly before his death, four out of seven votes from the Sanitary and Social Board to let him be certified as an Equal-Sided Triangle) –often bemoaned, with a tear in his venerable eye, an accident of the kind I’ve just described to you, which happened to his great-great-great-Grandfather, a respectable Working Man with an angle, or brain, of 59 degrees 30 minutes.
According to this story, my unfortunate great-great-great-great-great grandfather, who was suffering from rheumatism, and while being felt by a Polygon, with one sudden, unintentional movement, he accidentally transfixed the Great Man in a horrific stabbing straight through the diagonal.
Half because of his long suffering in prison, and half because of the moral shock that swept through all of my ancestor’s relatives, our family’s angle was thrown back by a degree and a half, cutting off their rise to higher status.
This resulted in the next generation of the family brain being measured at only 58 degrees, and it wasn’t until five whole generations passed that the lost ground was recovered, and the full 60 degrees obtained, finally lifting my family out of the class of Isosceles.
And to think this whole series of calamities all came from one little accident in the process of Feeling.
And I think at this point I can hear some of my readers exclaiming, “How can you Flatlanders know anything about angles, degrees, or minutes? We can see an angle from Spaceland, because we can see two straight lines connecting to form an angle, but you Flatlanders can only ever see one line, or just a few pieces of different lines in a bigger line – how can you hope to measure any angle, let alone measure angles of different sizes?”
My answer is that while we can’t see angles, we can infer them, and do so with great accuracy. Our sense of touch, trained through constant use, lets us tell angles apart far more accurately than you can with the naked eye. We have many Natural Advantages that shouldn’t be forgotten.
It is a Law of Nature that the brain of the Isosceles class begins at half a degree of angle, or thirty minutes, and if it increases, it will do so by half a degree for every generation, until the goal of 60 degrees is reached, when the newest, freeman generation leaves behind the condition of slavery, and joins the class of the Regulars.
This means that Nature herself gives us the tools we need, in the form of an ascending scale, or alphabet, of angles for every half a degree, all the way to 60 degrees, giving us all the examples we need, specimens of which are placed in every Elementary School throughout the land.
Due to occasional slip-backs like the kind my family suffered, as well as frequent moral and intellectual stagnation, not to mention the extraordinary ability of the Criminal and Vagabond Classes to breed, there is always a vast pool of individuals with an angle of half a degree or a single degree, and a fair abundance of Specimens up to 10 degrees.
These are absolutely destitute of civic rights; and many of them are too stupid to even be useful in warfare, so they are given from the State and to the schools, to be used for education.
Shackled so tightly they cannot move in any way to remove all possibility of danger, they are placed in our kindergarten classrooms, and are used by the Board of Education to teach the young Equilateral Triangles that have been adopted away from their biological parents the proper tact and intelligence that the wretched Isosceles who produced them are completely lacking in.
In some Countries, these chained Specimens are sometimes given food and water, and as a result, are allowed to suffer through life for several years after their capture; but in better-run areas, we know that the educational interests for the children are better served with saving the cost of the food, and simply getting new Specimens every month – which is about how long a member of the Criminal Class can last before starving to death.
The cheaper schools which choose to prolong the life of the Specimen lose in the long run by the cost of the food and water, and partly in the lessened accuracy of the Specimen’s angles, which, after a few weeks of constant “Feeling”, become damaged.
And when we think of the advantages of the more expensive system of constantly replacing Specimens, lets not forget that it helps, however slightly, to lower the numbers of the Isosceles population, which is a goal that every statesman in Flatland constantly keeps in mind.
This is why I think (even though many of our popularly elected School Boards prefer the cheap system) that the more expensive system is, in this case, the best use of the money.
But I shouldn’t let the politics of School Boards distract me from my real subject. I’ve said enough, I hope, to show that Recognition by Feeling isn’t as tedious or confusing a process as you might assume, and it is also obviously more trustworthy than Recognition by Hearing.
But many argue, rightly, that this method can be very dangerous.
This is why many in the Middle and Lower classes, and almost all of those in the Polygonal or Circular classes, prefer a third method of Recognition that I will explain to you in the section below.
[Table of Contents]
In the previous sections I’ve told you that all things in Flatland appear to us to be nothing but a Straight Line; and it was implied that this makes it impossible to tell people or objects apart by looking at them.
But now I will be explaining to my Spaceland critics how we Flatlanders do recognize one another by our sense of Sight.
If you, the Reader, will take the time to revisit the paragraph where you think I claimed that Recognition by Feeling is universal, you will that I specified “among the lower classes”. Only among the higher classes in our civilized societies is Sight Recognition practiced.
That this skill can be practiced anywhere, for any class, is the result of the Fog that covers the land for most of the year in all parts of Flatland except in deserts. What Spacelanders see as a depressing, evil smog that blots out the landscape and makes you cold and sick, we celebrate and see as a blessing second only to air itself, and is recognized as the Nurse of art and the Parent of science.
But I’ll try to stop singing praise for this generous Element so that I can explain to you what I mean.
If Fog didn’t exist, all Lines would appear just as sharp and clear as every other Line, and this is actually the case in those unhappy desert countries where the atmosphere is perfectly dry and transparent.
But wherever Fog can be found, objects that are at a distance of, for example, three feet, are noticeably dimmer than those at a distance of two feet and eleven inches.
This means that by careful, constant observation, we are able to understand, with very high accuracy, the shape of the object we are looking at.
A specific example will let me make my meaning clear to you without needing many more paragraphs of explanation.
Imagine that I see two strangers approaching me, whose rank I want to learn. Let’s say that they are a Merchant, and a Physician, or in other words, an Equilateral Triangle, and a Pentagon – so how do I tell them apart?
Here is a diagram to illustrate:
[Image description start: A black and white illustration showing an equilateral triangle and a pentagon, with a drawing of an eye seen from the side pointed at each of them. The point facing the eye is labled A, the point below is B, and the point above is C. A thin line traces the peripheral vision of the eye, and a vertical rectangle in front of point A shows what the eye of the Flatlander can see: a straight line, in a gradient of white at the center, and darker at the edges. The triangle’s edges become darker faster than the pentagon’s. Image description end.]
It will immediately be obvious to every child in Spaceland who knows anything about Geometry that if I am facing these two men so that I am looking directly at their front point (A), my view, obviously, lies perfectly between the two points on either side of that (CA, AB), so that both points appear to be the same size.
Now when I look at the Equilateral Merchant, what will I see? I will see a straight line (in reality made up of three points), with the center of the line (which is really point A) being very bright (Because point A is closest to me).
The two seeming-ends of the line, though, will be much darker, with a very sudden shift from the white of the center to almost black. This is because the points (B and c) that make up the ends of this seeming-line are much further away from me, with more Fog covering them.
On the other hand, the line that represents the Pentagon Physician will shift from white to a lighter grey rather than almost black, because the points that make up the ends of the line are not as far away from me than they were on the Triangle.
((Note from the second editor: To simplify further: The closer the point is to you, the brighter it is. The further away, the darker it is. Just remember this, and you’ll be fine.))
The Reader will probably understand from this example how – after a very long course of training aided by constant practical experience – those of us who are well-educated can easily tell strangers apart when it comes to the Equilateral and Isosceles classes by our sense of sight.
If my Spaceland friends have grasped this idea enough that you’re not immediately rejecting it as impossible, I’ll consider my job done in this matter. If I tried to give you any more details, I’d only confuse you hopelessly.
But for the sake of the young and inexperienced, who might assume, from the two examples I gave above of how I would recognize my Father and one of my Sons, that Recognition by Sight is easy to learn, I feel the need to point out that, in reality, the problems posed by Sight Recognition are much more subtle and complex than my simple diagram can convey to those in Spaceland.
For example, if my Father, the Equilateral Triangle pictured above, were to approach me with one of his sides instead of his angle, then, until I’ve asked him to rotate, or until I move around him to another angle, I cannot be certain whether I am looking at my Father, the Equilateral Triangle, or a Straight Line, which in other words means a Woman.
Then, when I am with one of my two Hexagonal Grandsons, looking at one of his sides, it will be clear, I hope, from the diagram below, that I will see a straight line with a large center of brightness (made up by the points A and B), with two small darker sections above and below, which quickly fade away into dimness.
[Image description start: A black and white illustration showing a hexagon being looked at from the side, so that one of the flat sides, created by points A and B, is facing the eye, with points C and D above and below. The Flatlander's eye perceives a straight line with a large, white center, with the very top and bottom sections suddenly turning dark, and fading even darker at the ends. Image description end.]
But I need to resist the temptation to keep explaining about these topics.
Even the best mathematician in Spaceland should believe me when I tell you that when you are at a party or a convention, moving around the room and other people, trying to recognize and keep track of the many high-ranking Polygons around you is not an easy task.
This is why we value our expert mathematicians, Professors of both Static and Kinetic Geometry, from the University of Wentbridge, so highly. They are the ones who teach the elites of the states the complex art of Sight Recognition.
It is only a few of the most promising sons of our most noble and wealthy houses who can afford the time and money necessary for actually Mastering this noble and valuable Art.
If I, a Mathematician of fair skill, and the Grandfather of two very promising and perfectly regular Hexagons, find myself in the middle of a crowd of rotating Polygons of the higher classes, even I sometimes find myself unsure!
And of course, to a common Tradesman Equilateral or Slave Isosceles, such a sight must be as bewildering and meaningless as it would be to you, my dear Reader, if you were suddenly transported to our country.
In a crowd like this, the only thing you would see, wherever you look, is nothing but a Line that seems to be straight, but with different parts in constantly changing light or darkness.
Even if you had graduated from your third year in the University’s classes for Pentagons and Hexagons, and had memorized the theory of the subject, you would quickly find yourself realizing that it will take many years of practical experience before you could confidently move through a high-society crowd without bumping into your betters.
It is impolite in the extreme to ask to “Feel” such superior nobles, and it is without a doubt, due to their superior culture and breeding, that these fashionable crowds know everything of your shape and movements, while you, still inexperienced, know next to nothing about theirs.
In other words, the only way to truly belong in Polygonal society is to be a Polygon yourself. It’s a painful lesson I have had to learn the hard way.
It is astonishing how much the Art (I like call it an instinct) of Sight Recognition is honed simply by constant practice, while avoiding the custom of “Feeling”.
((Note from the second editor: I apologize in advance for the next sentence you are going to read after this interruption is done.
The author here, as you may be able to guess soon enough, thinks he knows more than he does.
I will state now, for the record, that his idea of how Deaf and nonverbal people learn to speak is completely and blatantly false, a myth long since thrown away, but I will still transcribe his words here for the sake of posterity, and to better help you understand his mindset.
Let me make it absolutely clear that denying Deaf, Nonverbal, and Semiverbal children access to sign language or Augmentive and Alternative Communication devices (AAC), and forcing them to lipread or spend years learning to speak perfectly aloud, does not help them learn to communicate better. The only thing it accomplishes is isolating and punishing them and delaying their ability to talk to you.
Let them learn sign language (and you can learn it alongside them!). Get them an AAC device. Stop trying to fit a square through a circular hole! It is a myth that sign language stops Deaf and mute people from speaking – just because you didn’t bother to learn doesn’t mean they’re not talking!
Interruption over now. You may continue.))
Just as with you, if the Deaf and Mute are allowed to gesticulate and to use sign language, will never acquire the more difficult, but far more valuable art of speech and lip-reading, so it is with us as regards "Seeing" and "Feeling".
No one who learns to "Feeling" early in their life will ever learn "Seeing" in perfection.
This is why “Feeling” is either discouraged. or forbidden completely among the families of our Higher Classes.
The children of High-Class Polygons are not sent to the common Public Elementary schools where Feeling is taught. Instead, they are sent to private schools with very strict entrance requirements.
At these schools, to “Feel” is seen as a serious problem, and is punished with Suspension for the first offense, and complete Expulsion for the second.
But the lower classes think of Sight Recognition as an unattainable luxury.
The common Equilateral Tradesman can’t afford to send even just one of his sons away to spend an entire third of his life studying abstract ideas.
So the children of the poor are allowed “feel” as soon as they begin moving, and in doing so become practiced at moving and interacting with others very quickly, which makes them seem, to the untrained eye, much better developed than the comparatively listless, unmoving attitude of young nobles Polygons of the same age.
But don’t let this disparity fool you – once the young Polygons have finally completed their course at the University, and are ready to go out into the world to gain more experience, a change sweeps over them so that they seem to be born for a second time.
In all the skills of art, science, and sociability, they then rapidly catch up to and out-compete their Triangular competitors with ease.
It is rare for any of the Polygonal Class to fail their Final Test at the University, but it does happen, promising a life of pitiable misery to these unsuccessful nobles. Cast out by other Polygons, they can make no friends among the common classes either.
They cannot function in Polygonal society because of their lack of Sight Recognition, but also have no idea how to navigate by Feel, as they’ve been forbidden and shamed out of learning it their whole lives.
There are no jobs they can perform, either professional or common, and though most Countries do not actually ban them from getting married, it is still difficult for them to find any willing partners, since history has shown us that the children of such marriages will be, at best, similarly unfit for the noble life, or, at worst, blatantly Irregular.
This trash of the Nobility is where many of the leaders of the various Tumults and Seditions of the past centuries have risen. So many, in fact, that an increasing number of our progressive Statesmen have decided that either imprisoning these wretched outcasts for life, or at least mercy killing them, would make life easier for everyone.
But I am once again becoming distracted by the subject of Irregularity, which is actually so important for you to understand that it deserves its own separate section.
Since the start of this book I have been assuming that my Readers in Spaceland were already aware of something that I take for granted. I should have made sure to explain to you the most basic, fundamental law of our society, upon which everything else is built:
Every human Being in Flatland is a Regular Figure.
Which means that a Woman is not simply a line, she is also a Straight Line.
An Isosceles Workman or Soldier must have two of his sides equal (being an Isosceles, he is of course defined by his third side being irregular).
A Tradesman must have his three sides equal.
Lawyers, (the group which I, your humble narrator and guide, am apart of), must have four equal sides, and in the higher Polygon class, all sides must be, generally, equal.
The size of these equal sides of course depends on how old this person is. A Female at birth is about an inch long [around 2.5 centimeters], and a tall adult Woman might be more than 12 inches [around 30.5 centimeters] long.
As for the Males of every class, as adults, the length of all their sides, when added together, measures somewhere around two feet, give or take. [around 61 centimeters].
But it is not the length of our sides that is important. I’m talking about the Equality of the sides, and it doesn’t take a stretch of the imagination to see why the whole foundation of civilization in Flatland rests upon the fundamental fact that Nature wills all Figures to have their sides equal.
If our sides were unequal, our angles might be unequal.
Instead of simply being able to judge a single angle by feel or by sight, you’d have to figure out the measurement of every single angle by time-consuming Feeling.
Life is too short for such mind-numbing groping. The whole science and art of Sight Recognition would be killed instantly. Feeling, as much as it can be called an Art, would perish soon after.
Casual interaction would become deathly dangerous or outright impossible – no one would ever be able to interact with any stranger or make even the most basic social arrangements without being in danger.
In a word, civilization would collapse into barbarism.
Am I going too fast for my Readers to understand how I’ve come to these obvious conclusions?
Surely if you think for a moment, and imagine a single instance from our every day life, you’ll be convinced that every part of our society relies on Regularity, or Equality of Angles.
For example, say you meet two or three Tradesmen in the street. You know they are Tradesmen by a single glance: a seemingly straight line, with a bright point in the center, rapidly growing darker towards either end. You ask them to step into your house for lunch while you discuss business.
This is something you can do, right now, without any hesitation, because everyone knows how much space, give or take an inch or two, is taken up by an adult Triangle.
But imagine if one of these Tradesman dragged behind his Regular and respectable angle, not just a straight line, but a parallelogram of twelve or thirteen inches on the diagonal. Now what are you supposed to do with a monster like that stuck in your door?
[ID: A simple digital drawing with a black border around it, showing a Square looking out a doorway at three other shapes. Two are Equilateral Triangles, and the third is an Irregular shape with an Equilateral front, and a very wide parallelogram back. Next to the square is a small bar showing three points of brightness with fading edges, lining up with the points of the Triangles in front of him, as he says: "To my view, they all look like Equilateral Triangles. Just at different distances from my eye." Then there is another bar behind the three shapes, saying, "But from another angle...the Irregularity is revealed.". This bar shows one very large white line, with a smaller grey line next to it, matching up with the backs of the shapes above it. End ID.]
But I am insulting the intelligence of my Readers by explaining things that are clear to anyone who lives in Spaceland.
Obviously the measurement of a single angle wouldn’t help us interact with one another under such circumstances – one’s whole life would be hours upon hours of feeling or visually surveying the entire perimeter of everyone you meet.
It’s already hard enough to avoid running into others in a crowd, even for the trained wisdom of a well-educated Square! But if Regularity flew out the window, and you couldn’t assume anyone around you had logical angles, everything would devolve to chaos and confusion! The smallest panic would cause serious injuries, or – if there happened to be any Women or Soldiers in the crowd – considerable loss of life!
This is why Expediency teams up with Nature in stamping the seal of its approval on Regularity of Configuration, and the Law, of course, seconds their efforts.
To us, “Irregularity of Figure” means a combination of both inherent moral failure and purposeful criminality, and is treated accordingly.
We do, of course, have some distributors of writings that claim there is no inherent connection between geometrical and moral Irregularity.
“The Irregular”, they say, “is, from the moment he’s born, rejected by his parents, bullied by his brothers and sisters, neglected by his nurses, scorned and suspected by society, and excluded from all forms of trust, responsibility, and fulfilling jobs.
“His every movement is openly surveiled by the police until he comes of age, and presents himself for inspection. Then, he is either destroyed if he is found to be Irregular past the set margin of deviation, or imprisoned in a Government Facility as a desk worker of the seventh class.
“Barred from marriage, forced to serve at a tedious job for practically no pay, and with no other choice but to live and eat entirely at this same office, unable even to take a vacation except without a guard escorting him like the prisoner that he is – then is it any wonder that human nature, no matter how pure or benevolent it started out when he was born, becomes bitter and corrupted with a lifetime of this kind of treatment?”
None of this very plausible reasoning has convinced me, nor has it convinced the wisest of our Statesmen, that our ancestors made a mistake when they set down the law that mandated Irregularity as incompatible with the safety of the State.
I have no doubt that the life of an Irregular is hard, but the best interests of the rest of society requires that it be hard.
If a man with a triangular front and polygonal back were allowed to exist, and to father even more Irregular children and grandchildren, what would become of the Arts of life? Are the houses and doors and churches all supposed to be changed to accommodate such monsters? Are the ticket-sellers supposed to measure every man’s perimeter before they let him into a theater, or to take his place in a lecture hall?
Is an Irregular supposed to be exempt from military service? And if not, how is he going to be stopped from killing his comrades by accident?
And just think of the horrible crimes and lies these creatures would be tempted to commit! It’d be so easy for him to enter a shop with his polygonal front forward, and order whatever he likes, on promise of future payment, from a too-trusting salesman!
Let the falsely claimed “Philanthropists” beg all they like for the abolishment of the Irregular Penal Laws, they won’t convince me, because I, for one, have never known an Irregular who wasn’t what Natuer clearly intended him to be – a hypocrite, a misanthrope, and, as far as he can succeed, a perpetrator of all kinds of crime and nuisance.
Not that I would (at the moment) recommend the extreme measures adopted by some Countries, where any infant whose angle deviates by half a degree from the expected angularity is promptly destroyed at birth.
Some of our best Men, Men of real genius, suffered, in their early childhood, deviations as great as – or even greater than – forty-five minutes. The loss of their precious lives would have been an irreparable injury to the State.
We have also achieved many victories in the Art of Healing, allowing most Irregularities to be either partly, or entirely, cured, through the use of medical compressions, extensions, fuses, and more.
I would say there is no point at which we should look at a newborn and decide it is incurably Irregular – but, if the Irregularities cannot be cured before the body begins to form its permanent shape, and the Medical Board has declared that nothing can be done to salvage it, then I would suggest that the Irregular child be mercifully euthanized.
If my Readers have been paying attention to this story so far, you may have realized that life in Flatland can be a little boring.
Obviously, I’m not saying there aren’t the wars, scandals, uphevals and drama that are supposed to make History interesting, or that we don’t enjoy our lives, as strange as they may seem to you in Spaceland. There is something indescribably invigorating about the need for constant calculating of angles, and the usually-instant gratification of knowing you’ve done so correctly.
I mean from the aesthetic, Artistic point of view, that Flatland is, very literally, dull.
It would be difficult for it not to be, when all our lives, ideas, hopes, dreams, even our artistic masterpeices of all kinds, are nothing but a straight line, with no variation at all except for small differences of brightness and shadow.
It wasn’t always like this.
If our Tradition can be trusted, then we know that long ago, Color allowed our ancestors to live in a splendor we can barely imagine.
Long ago, in the remotest ages of history, it is said that a Pentagon whose name we do not know for sure accidentally invented some simple colors, and a method of painting.
It is said that he immediately began decorating his house. Then he painted his slaves, then his Father, his Sons, his Grandsons, and, finally, himself.
The beauty and convenience of the results were admired by everyone.
This Pentagon’s most commonly accepted name among historians is ‘Chromatistes’, and wherever he went, turning his colorful frame, he was the center of attention and respect.
No one needed to take the time to “feel” him anymore, and no one confused his front from his back. Every move he made was easily read by those nearby without any effort on their part or the need for calculation. No one bumped into him, or failed to move out of his way. He did not have to waste his breath exclaiming his rank, as we colorless Squares and Pentagons have to today, to get a crowd of ignorant Isosceles to show us all due respect.
The fashion spread like wildfire.
Before the week was over, every Square and Triangle in the district had copied his example, and only a few of the more conservative Pentagons refused to join in.
After the first month or two, even the twelve-sided Dodecagons had fallen into the trend.
In less than a single year, the habit had spread to all classes in the district except the highest of the Nobility.
Needless to say, it didn’t take long for this trend to make its way out of Chromatistes’ neighborhood and into surrounding regions.
Within two generations, there was no one left colorless except the Women and the Priests.
With these two classes, Nature herself seemed to plant herself as a barrier to stop this infection from spreading further.
For the Innovators, as they were called, having multiple sides was almost a requirement for having color. They would say, “Distinction of sides is intended by Nature to imply distinction of colors”.
These words were popular, flying from neighbor to neighbor, and helped to convert whole towns at a time to the new cultural wave.
But it seemed that this idea could not be applied to Priests and Women. Women, being Straight Lines, have only one side, and thus, in all ways that matter, have No Sides. Women hated to admit this, and were ashamed of it.
On the other hand, Priests, if we are to accept that they are true Circles, and not just very high-ranking Polygons with many small sides, loved to brag and boast that they also had no sides, and were instead being blessed with a perimeter of a single line, or, in other words, a Circumference.
I hope you can see now why these two Classes could not be convinced by the so-called universal truth of “Distinction of Sides implying Distinction of Color”, when it could not, apparently, be applied to them.
Even after everyone else succumbed to the temptation of self-decoration, the Priests and Women alone were still pure and unpolluted by the touch of paint.
Immoral, vulgar, anarchical, unscientific, there are many names used to describe the ancient days of the Color Revolt, but, from an aesthetic point of view, those days were the glorious birth of Art in Flatland. A childhood that, unfortunately, was cut short before it could mature to adulthood, or even enjoy its youth.
To live them was to live in a world of endless delight, because living meant seeing, and even the smallest group of friends was a delight to the eyes, and the richly varied colors in a church or theater are said to have, many times, been so distractingly beautiful that the actors and preachers forgot they had a job to do.
But the most beautiful sight was said to have been the unspeakable magnificence of a military performance.
Imagine it: To see twenty thousand black-painted Isosceles bases suddenly spin to reveal the orange and purple of their two sides at their acute point. The Equilateral Triangles tri-colored in red, white, and blue. The Square artillarymen rapidly rotating to show mauve, ultra-marine, gamboge, and burnt umber, with their vermillion guns.
[Image description start: Three shapes on a grey background, each with their sides in different colors, with rows of matching color boxes below them. The first is an isosceles triangle, with sides of orange and purple, and a base of black. The second is an equilateral triangle, with sides of red, white, and blue. The third is a square, with sides of purple, ultramarine blue, amber, and burnt red. Next to the square is a smaller bar of red-orange. Image description end.]
The dashing and flashing of the five-colored Pentagons and six-colored Hexagons racing across the fields with their doctors, geometricians, and chiefs of staff.
With this fabulous display of color at military parades, its easy to believe the famous story of a powerful Circle king, who found the sight of his army so beautiful that he immediately threw away his royal crown and ceremonial baton, and declared that from that day forward, he was never going to pick up another tool besides the artist’s paintbrush.
The vocabulary alone that they used to express themselves shows how amazingly colorful the times they lived in were. Even the most mundane statements made by the poorest citizens during the Color Revolt seem to be infused with a richness and creativity that is lacking today.
All of our finest poetry, and even the little bit of rhythm and rhyme that can still be found in our scientific statements of today, we owe to the amazing era of the Color Revolt.
But while the beauty of color was thriving, the intellectual Arts were quickly dying out.
No one needed to use Sight Recognition anymore, so they stopped practicing it altogether. Soon, the studies of Geometry, Statics, Kinetics, and other similar subjects became considered pointless as well, and became looked down upon, even at our greatest University!
Not even the inferior Art of Feeling was immune, and stopped being taught at our Elementary Schools.
Then the Isosceles classes, pointing to the fact that the Specimens were no longer needed for teaching, refused to pay up the members from the Criminal class that were owed to the schools, and as a result, their numbers, and their disrespect towards the more Noble classes, increased by the day now that they were no longer subject to the custom that had both thinned their excessive numbers, and removed the most dangerous of them from society.
Year by year, the Soldiers and Workers began to insist more and more often – and with increasing truth to their claim – that there was no real difference between them and the highest ranking Polygons, now that they could deal with all the problems of life just as easily as the nobility by simply using Color Recognition.
And they weren’t happy to just let Sight Recognition naturally die either, they began to actively cause its death by demanding the right to learn it themselves, calling for the law to ban the “monopolization of Aristocratic Arts”, and thus ban the exclusive scholarships that allowed the higher, non-Criminal classes to study Sight Recognition, Mathematics, and even Feeling.
It wasn’t long before they began insisting that Color, which was a second Nature, had now destroyed the need for Aristocratic distinctions at all, and so this meant that the Law should follow the same path, and legally recognize all classes as absolutely equal and entitled to equal rights.
When it became clear that the higher Orders were undecided and wavering in their convictions, the Revolution pushed even harder, demanding, at last, that all classes, including the Priests and Women, should honor Color by allowing themselves to be painted.
When it was argued that Priests and Women had no sides, so couldn’t be painted, the Revoluntionists retorted that Nature and Expediency had worked together to make the solution to this problem simple: that the front half of every human being, containing his eye and mouth, should be easy to tell apart from his back half.
They created a Bill which they showed in front of an extraordinary meeting of all the Countries of Flatland, proposing that all Women should have the front half of her painted red, and her back half painted green. The priests were to be painted the same way – red on the half of their body where their mouth and eye were, and green for the rest.
You can see how devilishly clever this proposal was, and trust me, this plan was not created by any Isosceles – we all know they’re too degraded to understand, let alone think of, such an amazing political move.
No, the creator of this plan was an Irregular Circle who escaped being destroyed in his childhood due to foolish sentimentality, and was now repaying that kindness by bringing down destruction upon his country, and on his countless followers.
The first goal of this ingenious plan was to win over the Women of all classes into joining with the side of Chromatic Innovation. Because by painting Women with the same two Colors as the Priests, the Revolutionaries guarenteed that it would be easy to mistake a Woman standing in a certain pose as a Priest, and treated accordingly. This could not fail to appeal to masses of the Female Sex.
But I understand that some of my Readers might not understand how a Woman and a Priest could be confused even under the new Legislation, so let me explain it to you first, it’s very easy to follow.
Imagine that a Woman – a Straight Line – is decorated according to this new Code: her front half, or head, painted red, and her back end painted green.
Imagine you are looking at her from the side, as we would see her in Flatland – obviously, you will see a straight line, half red, half green.
Now imagine a Priest, a diagram of which will be provided below. His mouth is at M, and his front semicircle is Colored red, and his hind semicircle green.
[Image description start. A diagram showing a circle that is half berry red, and half seafoam green, with an eye looking at it from the side. The top of the circle is marked M, the further side from the eye is marked A, and the side facing the eye is marked B. Grey dotted lines show the direct and peripheral lines of sight for the eye, with a bar drawn to show how the eye sees the circle in only two dimensions: As a straight line forming a gradient from brighter red-purple and green in the center, then growing darker towards the edges. The top of this bar is labeled C, and the bottom is labeled D. Image description end.]
As demonstrated in the diagram above, if you look at this Great Man from the side, you will see a straight line that is half red, and half green.
The line you see may be shorter than a fully-grown Woman would be, and might grow darker at the edges faster than a Woman’s edges would, but the Colors alone would be doing most of the work in identifying this person’s Class to you, allowing you to be lazy and ignore those details, making it easy to confuse a Priest with a Woman if you are not paying strict attention.
Below is another diagram to illustrate the similarities.
[Image description start: An illustration showing a painted line and circle from both a Spaceland and Flatland perspective, with an eye looking at the shapes from either side. The line and circle are both painted half seafoam green, half berry red. The “Spaceland view” shows their actual shape, while the “Flatland view” shows only bars of Color, brighter in the center, and darker at the edges. The bar representing the straight line is almost identical to the circle, except that the straight line appears longer, and the edges do not get dark as quickly as the circle’s do. Image description end.]
Now, don’t forget what I have already told you – that Sight Recognition was dying out as an art at the time of the Color Revolt.
It’s also important to understand that it was guaranteed that Women would figure out how to bend themselves so that their edges would grow dimmer faster, allowing them to imitate the Circles even more closely.
With these facts in mind, it should be obvious to you, my dear Reader, how easy the Color Bill would make it to confuse a Priest with a young Woman.
It’s easy to see why this proposal was so attractive to the Frail Sex; they looked forward to the chaos that would ensue. At home, they might be able to learn political and priestly secrets that were meant for their husbands or brothers, or even give orders in the name of a Circle.
Outside, the striking combination of red and green, without any other identifying Colors, would be sure to confuse commoners into making constant mistakes of who is who, and the Women would always benefit from what the Circles lost.
And this isn’t even mentioning the scandals that would be sure to happen to the Circular Class if the mindless behavior of the Women were attributed to them. It’s clear that the Female Sex couldn’t be expected to understand the consequences their actions would bring.
Even in the households of the Circles, the Women were all in favor of the Universal Color Bill.
The second goal of this Bill was to slowly drag down the Circles themselves.
Amongst the general intellectual decay, they alone still practiced the higher Arts. Kept safely secluded in their childhood growing up in their colorless Circular households, the highest of Nobles were the only ones who still knew how to use the Sacred Art of Sight Recognition, with all of the advantages and higher education that came with it.
Up until the introduction of the Universal Color Bill, the Circles had not only maintained their position, but even gained more distance in the gap between their educational levels and those of the lower classes, all by virtue of refusing to give in to the popular fashion.
This is how the clever Irregular I told you about earlier, the real author of this diabolical Bill, planned, with a single strike, to deal a deathblow to the intelligence of the higher classes by forcing them not only to submit to the pollution of Color, but to make it impossible for them to receive formal training in the Art of Sight Recognition, and destroy their chances of learning even further by not even allowing them to live in their pure and colorless homes anymore.
Once polluted by the chromatic taint, every parent and child Circle would begin to weaken each other’s skills in Sight Recognition.
The only challenge young Circles would have to exorcise their minds with would be the problem of telling apart their Father and Mother, but it’s all too likely that the Mother would corrupt even this test of skills by her deceptions, which would shake the poor child’s faith in the existence of logic and truth itself.
Thus, slowly but surely, the intellectual powers of the Priestly Order would fall, and leave the road open for the complete and total destruction of all Aristocratic Legislature, and the annihilation of our Privileged Classes.
Section 10. Of the Suppression of the Chromatic Sedition
[Table of Contents]
The agitation for the Universal Color Bill continued for three years, and up until the very last minute, it seemed as though Anarchy were going to triumph.
A whole army of Polygons, who came together to fight as private soldiers, was utterly annihilated by a larger force of Isosceles Triangles.
The Squares and Pentagons, meanwhile, remained neutral.
But worst of all, some of our best Circles fell prey to domestic fury.
Infuriated by their political differences, many wives in noble homes tirelessly nagged their lords to give up their opposition to the Color Bill. And some Wives, when they realized their efforts were in vain, became enraged, and slaughtered their innocent children and their husband alike, and died themselves in carrying out the crime.
Our history books record that during this three year agitation, no less than twenty-three Circles were murdered in their own homes.
The threat was very real. It seemed as though the only options left to the Priests were submission or extermination…
But suddenly the course of events was completely changed by one of those perfect events that Statesmen should always take advantage of, try to anticipate, and sometimes, even Create themselves, because they hold so much power over the sympathies of the people.
The story varies a little, but goes generally like this: An Isosceles of a low type, with a brain hardly, (if at all), above four degrees, robbed an Equilateral Tradesman’s shop, stealing several paints.
In some versions of the story, he painted himself. In others, he “caused himself to be painted”, in some unexplained way. But no matter what version of the story it is, the end result is the same: he is now painted in the twelve colors of a Dodecagon.
Going to the Marketplace, he used a false voice to greet the orphaned daughter of a noble Polygon, who he had been in love with for a long time.
With his disguise in place, and with the help of both a long string of perfectly convenient accidents, and an absolutely absurd level of neglect on the part of the girl’s family to prevent just such things from happening, he succeeded in marrying her, and they consummated the marriage on their wedding night.
When the girl realized the fraud she had fallen victim to, she committed suicide.
When the news of this catastrophe spread from Country to Country, the minds of the Women were violently agitated. Sympathy for the miserable victim, and fear that similar deceptions might happen to themselves, their sisters, and their daughters, made them all see the Color Bill in an entirely new light.
Many immediately declared themselves enemies of the Bill, and the rest only needed a slight nudge to do the same.
Seizing this golden opportunity, the Circles hastily called together an extraordinary Assembly of Countries, and, along with the regular guard of Convicts, they made sure that a large number of reactionary Women would be there.
In this unheard of crowd, the Chief Circle of those days, whose name was Pantocyclus, rose to speak, and found himself being hissed and booed at by a hundred and twenty thousand Isosceles.
But he silenced them all by declaring that, from that moment forward, the Circles would begin a new policy of Concession, give in to the wishes of the majority, and accept the Color Bill.
The angry uproar immediately changed into applause, and Pantocyclus invited Chromatistes, the Pentagon who was the original inventor of color and leader of this Sedition, to make his way to the center of the room to receive the surrender of the Circularchy.
And then Pantocyclus began a speech, a masterpiece of talking points, which took nearly the entire day to complete, and cannot be summarized in any way that would do it justice.
With a grave appearance of neutrality, he declared that, because the Circles were finally committing themselves to the Reform, they wanted to take the time to examine the subject in its entirety, its flaws as well as its advantages.
Slowly, they introduced the idea of the dangers this Bill could pose to the Equillateral Tradesmen and the Square and Pentagon gentlemen, and silenced the rising objections of the Isosceles by reminding them that, despite these flaws in their Bill, the Circles would still accept it as long as it was the wish of the majority.
But it became clear that with this part of his speech, he had managed to bring everyone but the Isosceles to be either neutral, or actively against the Bill.
And then he turned to the Workmen, the highest ranking Isosceles, and asserted that their interests should be taken into consideration as well, and if they really wanted to accept the Color Bill, they should only do so with full awareness of the consequences.
Many of them, he said, were on the point of being accepted into the class of Regular Triangles. Others could expect this honor for their children, even if they couldn’t receive it themselves.
If the Color Bill passed, this honor they were so close to achieving would have to be sacrificed.
With the universal adoption of Color, distinctions between Classes would no longer exist – Regularity would be confused with Irregularity, and the social progression they had worked for generations to achieve would begin to slip backwards, and within a few generations the Workmen would be degraded to the level of the Military, or even the Criminal Class altogether. Political power would fall into the hands of those with the greatest numbers, which would be the Criminals, if the regular Compensative Laws of Nature were violated by enacting the Color Bill.
A murmur of agreement ran through the ranks of the Workmen, and Chromatistes, in alarm, tried to step forward to speak to them.
But he found himself surrounded by guards of the Criminal class, and was forced to remain silent while the Chief Circle, with a few passionate words, made his last appeal, this time to the Women, exclaiming that, if the Color Bill passed, no marriage would be safe, no Woman’s honor secure! Fraud, deception, and trickery would invade every household, and their domestic bliss would go the same way as the rest of society, and become a living hell.
“Sooner than this,” he cried, “Come death!”
This was the signal that had been planned in advance, and, at the sound of these words, the Criminals surrounding him transfixed Chromatistes, while the Equilaterals parted their ranks, making way for a band of Reactionary Women who, by the order of the Circles, moved backwards, making them almost invisible to the Isosceles Soldiers they were going to murder. The Workmen, automatically following the example of their betters, also moved to let the Women through without thinking.
At each exit, more bands of Criminals formed an impenetrable phalanx.
The battle, which was more like a massacre, did not last very long. Under the skillful guidance of the Circles, almost every Woman’s first attack resulted in the death of her target, and many of the Women were even able to extract their stingers unharmed, ready for a second round of slaughter.
But there was no need for a second assault; the rabble of the surviving Isosceles did the job for them. Surprised, leaderless, attacked by invisible foes, with all escape routs cut off by the Criminals, they immediately – predictably – lost all pretense of intelligence, and began to shout, “Traitors!”
This sealed their fate.
Every Isosceles now saw every other one as a deadly enemy. Within half an hour, all of them were dead, and the fragments of over a hundred and forty thousand Criminals proved that Order had triumphed over Chaos.
The Circles wasted no time in pushing their victory all the way through. The Workmen were decimate – every tenth man transfixed without mercy or hesitation.
The Militia of the Equilaterals was called forward, and every Triangle reasonably suspected of Irregularity was immediately destroyed by Court Martial, without waiting for any measurements to be taken by the Social Board.
The homes of the Soldiers and Workmen were subject to series of inspections that could continue for more than a year, and during this time, every town, village, and hamlet was purged of all the degenerate Criminals who had been allowed to multiply unchecked thanks to the refusal to pay tribute to the Schools and University, and because of all of the other Laws of the Constitution of Flatland that had been violated since the creation of Color.
This is how the Natural balance of the classes was once again restored.
Needless to say that the use of Color for painting was outlawed, and even owning it became illegal. Even just using any words to describe Colors, except by Circles or sanctioned Scientific Teachers, was punished severely.
There are rumors that, in the very highest and most specialized University classes, color is still used sometimes to illustrate some of the most complex problems of higher mathematics, but I have never had the privilege of attending any of these classes, so this is only rumor.
Aside from these rumors, color is non-existent in Flatland now. The art of making it is only known to one living person at a time: the Chief Circle, and that knowledge is passed down to his Successor only on his death-bed.
Only one factory in all of Flatland still produces Color, and to prevent the secrets of its creation from getting out, the teams of Workmen are executed each year, and a fresh team of workers brought in to continue production, so great is the terror that, to this day, our Aristocracy still feels when looking back to the long-ago days of the Universal Color Bill.
It’s high time that I move on from these explanations of the things of Flatland and get to the main event of this book, which is my introduction to the mysteries of Space. That is my subject; everything that has come before now is simply the preface.
This is why I cannot take the time to explain to you all the things I assume you are extremely interested in, if I may flatter myself.
For example, I will not be going into detail about how we move around despite our lack of feet, or how we construct our buildings of wood, stone, or brick in place despite our lack of hands and our inability to lay foundations as you in Space do, and the fact that we cannot use gravity the way you can.
I also can’t take the time to explain to you how exactly the rain begins in the spaces between our various zones, so that the northern areas don’t stop moisture from falling to the south.
I do not have time to tell you about the nature of our hills and mines, our trees and vegetables, or our Alphabet and method of writing which has been adapted to fit our linear tablets, or books.
These and a hundred other details of our lives I must skip past, and the only reason I mention them at all now is to make it clear to my Readers that I have not forgotten that these things exist, it’s just that I don’t want to waste your valuable time explaining them all.
But before I can really move on to the true subject of this book, I have no doubt my Readers will be demanding some final knowledge about the pillars that uphold the Constitution of Flatland, the controllers of our conduct and the shapers of our destiny, the objects of universal respect and even worship...Do I need to specify that I mean our Circles, or Priests?
When I call them Priests, I want to make sure you understand that the word for us means more for us than you would define it.
To us, Priests are Administrators of all Business, Art, and Science. They are the Directors of Trade, Commerce, Generalship, Architecture, Engineering, Education, Statesmanship, Legislature, Morality, Theology, and many more. They do no work themselves, but ensure that all work that is done is worth doing.
Although the common idea is that everyone who is called a Circle is a Circle, the better educated Classes know that no Circle is really a Circle, he is just a Polygon with a very large number of very small sides.
As the number of sides increases, a Polygon begins to approximate a Circle, and, when the number of sides becomes high enough -- say for example, three or four hundred – then it becomes extremely difficult for even the most delicate touch to feel any polygonal angles, and they are declared a Circle.
Well, I should really say that it would be difficult, because as I’ve said earlier, Recognition by Feeling is unheard of in the highest classes of society, and to attempt Feel a Circle would be considered the most outrageous of insults.
Refusing to allow himself to be Felt enables a Circle to easily maintain the veil of mystery which he wraps himself in from his earliest childhood, preventing others from knowing the exact measure of his Perimeter or Circumference.
But we can still do our own calculations: With three feet being the average Perimeter for an adult, the math shows that, in a Polygon of three hundred sides, each side will be less than a hundredth of a foot, or just barely a tenth of an inch. In a Polygon of six or seven hundred sides, the sides are hardly larger than the diameter of the head on one of your pins.
For the sake of courtesy, it is always assumed that the current Chief Circle has ten thousand sides.
The rise in social status of Male Children of the Circles is not restricted by the same Law of Nature that limits the lower classes to an increase of on side per generation. If it were, the number of sides in a Circle would simply be a question of family pedigree and basic math.
We would easily know that the 497th descendant of an Equilateral Triangle would be a Polygon with five hundred sides, but this is not the case.
Nature’s Law lays down two new and opposing Laws that apply to the Male Children of Circles:
1.As the number of sides of a Circular father increase, his sons’ numbers of sides will increase drastically.
2. As the number of sides quickly increases, the ability to produce male children decreases just as quickly.
In the home of a Polygon of four of five hundred sides, it is rare to find a son, and that child will never have any brothers. But at the same time, that single son may be born with fifty, or even a hundred more sides than his father has.
Art also steps in alongside Nature to help this process of higher Evolution. Our highest doctors have discovered that the small and still tender sides of a newborn Polygon of the higher classes can be fractured, and his whole frame re-built, with such skill that a Polygon born with two or three hundred sides can sometimes – (but not always, because this surgery comes with serious risk) – can sometimes leap ahead what would have taken two or three hundred generations, and, all at once, double the status of himself and his own future sons.
Many promising infants have been sacrificed in this way. Hardly one out of ten survives. But the parental ambition is so strong among those Polygons who live on the fringe of the Circular class that it is very rare to find a Nobleman who has not placed his first-born son into the Circular Neo-Theraputic Gymnasium before he has reached the age of one month.
One year’s treatment determines success or failure. By that time, the child has, in all probability, added one more tombstone to the fields that crowd the Neo-Theraputic Cemetery. But, on rare occasions, a joyful parade escorts the little one back to his exultant parents, no longer a Polygon, but a Circle, at least as much as anyone can be a Circle.
It only takes a single positive result to convince untold numbers of Polygonal parents to perform their own domestic sacrifices, which almost always end, not in the rare Circular child, but the much more common freshly marked gravestone.
The teachings of the Circles can be summed up in a simple statement: “Attend to your Configuration.”
Whether political, religious, or moral, every lesson the Circles teach us has the goal of improving the Configuration, or physical shape, of individuals and society at large, with special importance placed on the Configuration of Circles, which is the most important goal of all.
The Circles are to be praised for how well they’ve suppressed the ancient lies that convinced men to waste their time and energy laboring under the false belief that someone’s behavior was shaped through free will, effort, training, encouragement, praise, or anything else except Configuration.
It was Pantocyclus, the hero mentioned before now as the one who ended the Color Revolt, who first convinced mankind that Configuration is what makes the man – that if, for example, you were born an Isosceles with two Irregular sides, it’s guaranteed you would go down the wrong path in life unless you got them evened out.
This would require a visit to the Isosceles Hospital, or, if you were an Equillateral Triangle or Square, or even a Polygon, if you were born with any Irregularity, you must be brought to one of the Regular Hospitals to be cured. Otherwise, you would inevitably die in the State Prison, or by the sharp angle of the State Executioner.
Pantocyclus declared that every social problem, from the smallest misbehaviors to the most outrageously violent crimes, was caused by physical Irregularity of the body, which could be caused by anything from bumping into someone in a crowd, or not exercising enough, or exercising too much, or even just a sudden change of temperature.
This Illustrious Philosopher concluded from this idea that good behavior deserves no praise, and bad behavior deserves no blame. Why should you praise, for example, the work ethic of a Square lawyer who works hard to defend his clients, when you should instead be admiring the perfect precision of his right angles?
Why should you blame a lying, thieving Isosceles, when instead you should be hating the incurable Irregularity of his sides?
In theory, this doctrine is unquestionable. But in practice, it has some drawbacks.
When dealing with an Isosceles, if the lowlife argues that he can’t stop himself from stealing because of his Irregularity, the judge likewise has no choice but to sentence him to death, because nothing can fix the behavior of the Isosceles, and the case is closed.
But when dealing with your own misbehaving children, when the penalty of death is out of the question, Configuration Theory can make parenting very awkward.
Several times I’ve found myself backed into a metaphorical corner when one of my Hexagonal Grandsons, who is misbehaving, blames his refusal to do what he’s told on a sudden change of temperature that was just too much for his young Perimeter.
He argues that instead of blaming him for something he can’t control, I should be helping him strengthen his Configuration, which, he argues, would be helped along by giving him all of his favorite treats.
When this happens, I can’t argue with him without violating the ruling of the Circles, but I also can’t just give into his demands without question.
Personally, I’ve decided to assume that a good scolding and time out has a positive, and strengthening effect on my Grandsons’ Configuration, though I do have to admit I don’t have any physical proof of this.
But I’m not the only one who uses this loophole to avoid violating the doctrine – I’ve seen many of even the highest Circles, when they are Judges in law courts, placing praise and blame on Regular and Irregular Figures. And in their homes, I’ve seen first hand how, when scolding their own children, they speak of “right” and “wrong” just as passionately as if they believed these words represented real things that a human Figure could choose between.
By constantly enforcing their policy of making Configuration the ultimate goal in every mind, the Circles have reversed the rules that you Spacelanders apply to your own family relationships.
Your children are taught to honor your parents, but with us, after the Circles, a man is taught to honor first his Grandson, if he has one, or his Son if he doesn’t.
But let me make it clear that by “honor” I do not mean “indulge” or “spoil”, but to make them the best they can be. The Circles teach us that the duty of fathers is to always give advantages to their offspring before themselves, which helps increase the status of not only their direct descendants, but the whole State as well.
The weak point in the system of the Circles – if a humble Square may be so bold – seems to me, to be in how they conduct their relationships with Women.
Because reducing the number of Irregular births is such a top priority for the good of Society, it is a logical to conclude that a Woman who has any Irregularity in her ancestry should be considered an unfit partner for anyone who wants his Sons to have increased social mobility through an increase of Regular sides.
Now, Irregularity in Males is a simple matter of measurement, but because all Women are straight, and as far as the eye can see, Regular, one has to figure out another method to measure what I call their “invisible” or “potential” Irregularities that might be passed down onto their offspring.
The State has taken care of this by recording carefully-kept pedigrees showing the family history of all those registered. Without a certified pedigree, a Woman is not allowed to marry.
Now, you might assume that a Circle – proud of his ancestry, and ambitious for descendants, one of whom might even become the Chief Circle some day – would be more careful than any other man to make sure he chooses the wife who will produce the best Sons for him, with no stain of Irregularity in her history.
But you would be wrong.
The care taken to choose a pure-bred Regular wife seems to grow lazier as one rises higher in the social scale.
Nothing could ever convince an aspiring Isosceles, who hopes to produce an Equilateral Son, to take a wife who has ever had a single Irregular member registered in her family tree.
But a Square or Pentagon, who is confidant that his family is on the fast-track to higher status, won’t even bother asking any further back than the five-hundredth generation.
A Hexagon or Decagon is even more careless with his potential wife’s pedigree.
And a Circle has been known to purposefully marry a Woman whose Great-Grandfather was Irregular, all because of the attractive quality of her reflected light, or because of the charm of her deeper voice, something that we Flatlanders find, maybe even more than you do, “an excellent thing in a Woman”.
As you might expect, these badly-judged marriages result in either no offspring at all, offspring who are blatantly Irregular, or who have outright reduced in the number of sides. But none of these disastrous results have ever stopped anyone.
The loss of a few sides in a highly-developed Polygon is easy to dismiss, and is sometimes compensated for by one of those miraculously successful operations from the Neo-Therapeutic Gymnasium which I described earlier. And the Circles are much too willing to submit to infertility as a natural Law of the superior development to do anything to fix it.
But, if this evil is not stopped, the so far slow destruction of the Circular class could accelerate, and the day might come, sooner than anyone expects, when our race will no longer be able to produce a Chief Circle, and Flatland as we know it will be destroyed.
I’m aware of another danger that should be warned against, though with this one I have no easy solutions to offer, and this one is also on the subject of our relationships with Women.
About three hundred years ago, the Chief Circle decided that, because women are lacking in Reason, but have an over abundance of Emotion, they would no longer be treated as rational, and would no longer receive any education.
The consequence of this declaration was that women were no longer taught to read or write, and weren’t even taught enough basic Arithmetic to count the number of sides on their husband or sons. It was inevitable that each following generation would lack more and more intellectual power, and this rule of female non-education still continues to this day.
My fear is that, though made with the best intentions, this policy goes too far, and harms us of the Male Sex.
Because with things the way they are now, we Males have to lead an exhausting bi-lingual and, please don’t think I am exaggerating, bi-mental existence.
With Women, we speak of “love”, “duty”, “right”, “wrong”, “pity”, “hope”, and other completely irrational, emotional concepts which do not actually exist. We pretend these things are real for the sole purpose of controlling Feminine Outbursts.
But among ourselves, and in our books, we have an entirely different vocabulary, and, I might almost say, language. “Love” becomes “the anticipation of benefits”. “Duty” becomes “necessity” or “fitness”, and so on and so forth.
More importantly, when we are among Women, we use language that implies absolute worship for their Sex, and they fully believe that the Chief Circle Himself is less important to us than they are.
But behind their backs, they are both thought of and spoken of, by all except the very young, as little better than, to quote, “mindless organisms".
The matters of Religion are also spoken of completely differently when we are in the Women’s chambers than when we are outside.
My humble fear is that this double training, in both language as well as thought, places too much of a burden upon the young Males, especially when they reach their third year, when they are first removed from the care of their mothers.
They must entirely unlearn their first way of thinking to make way for the new language of science, but then they still have to speak in the old language when in the presence of their Mothers and Nurses and Sisters.
Already I think that children today struggle more to understand basic mathematics than our ancestors did three hundred years ago.
Not to mention the danger that would arise if a Woman ever manages to learn how to read, and tells the rest of her Sex what she’s found in just a single popular book, or the possibility that an very young Male might reveal to his Mother the secrets of the logical language, either by accident, or purposeful disobedience.
Based on the simple fact that the current policies make Men less intelligent, I humbly ask that the highest Authorities rethink the laws forbidding Female education.
