I don't want my world to be infinite, that would be a pain to draw maps for. And I need it to be flat (for a slightly unrelated reason). How would I explain why no one has looked over or seen the edge before? I could always put a giant wall there, but that just makes more questions than answers ( i.e. who built it)?
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1$\begingroup$ How does the sun work? $\endgroup$– JollyJokerCommented Sep 29, 2017 at 10:06
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$\begingroup$ Comments are not for extended discussion; this conversation, including ideas for protecting the edges and the history of flat-earthers, has been moved to chat. $\endgroup$– Monica CellioCommented Oct 1, 2017 at 21:20
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1$\begingroup$ Why would people want to go there ? Here be dragons $\endgroup$– mouvicielCommented Oct 2, 2017 at 9:56
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1$\begingroup$ Would a torus work? Or something topologically a torus, like the old Asteroids game. If you go off one edge, you just come back on the opposite edge. $\endgroup$– Dave XCommented Oct 2, 2017 at 18:47
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3$\begingroup$ the old Asteroids game I just died a little inside. $\endgroup$– John GordonCommented Oct 3, 2017 at 0:06
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28 Answers
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Make your world finite but spatially bounded. This means anyone walking towards where the edge would be will find themselves inexplicably turned around, even though they were still walking in the same direction and to their own minds they didn't turn around. They will arrive back at the place where they started.
The Arthur C Clarke short story "Wall of Darkness" uses this concept. It also has a wall, the existence of which is never explained, but possibly it was built during an earlier time to stop people having the inexplicable experience of finding their world was spatially bounded. I suspect Clarke was putting a science-fictional twist on the sort of flat-earth world that appeared in various fantasy short stories by Lord Dunsany. Clarke was a fan of Dunsany's fiction.
The concept of finite but bounded space appears in certain versions of cosmology. It is quite reasonable to use it for what is essentially a fantasy world. There is no need to explain how and what it is, just show what happens when people reach the "edges" of their world. Effectively they never get there.
This also explains why no-one has looked over the edge. They can't get there to do it.
answered Sep 29, 2017 at 2:32
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$\begingroup$ Comments are not for extended discussion; this conversation about topology has been moved to chat. $\endgroup$ Commented Oct 1, 2017 at 21:24
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3$\begingroup$ How about messing with gravity or other forces a bit? Let's say the gravity gets stronger the further you are from the centre... as you get further out, it becomes more difficult to travel, and eventually impossible. Anyone who's ever tried got a bit further than the last person, but ultimately failed. Another variation is not to call it out as gravity as such, but make it appear like you're travelling up hill when you get to the edges (and infinitely steep at the edge). It's sort of like your wall, but doesn't stand at right angles to the ground. $\endgroup$ Commented Oct 2, 2017 at 15:39
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$\begingroup$ @RalphBolton Nice idea about gravity increasing as you approach the edge. That could stop things falling over the edges. Your second idea could involve gravity changing direction so by the time you reach the edge you would fall horizontally & in a parallel direction to the surface. Congratulations! They're both good ideas for flat-earths. $\endgroup$ Commented Nov 6, 2019 at 3:23
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I can think of at least two reasons.
The physics answer, If your disk is massive enough you get an interesting effect that causes it to behave more like a bowl than a disk even though it is flat, at least as far as gravity is concerned, the closer you get to the edge the steeper the surface feels. to a person on the surface it would feel like climbing a very steep mountain. Try this vsauce video (0:30 to 2:00) for a more visual feel for what I am talking about.
the discworld answer, the edge is entirely one giant ocean waterfall going over the side, anyone who sails too close to the edge gets dragged over the side to their doom. So it is not that no one has ever tried it is just they have never survived the attempt.
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26$\begingroup$ The disc world is an artificial world built on top of giant warp engines disguised to look like a turtle, with the support struts that attach the world platform to the engines disguised as 4 elephants. The control center is in corporate celesti, the central spire that houses the computers and maintenance robots (disguised as gods). $\endgroup$– pojo-guyCommented Sep 29, 2017 at 3:32
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20$\begingroup$ @pojo-guy: That may be the most ridiculous assertion I've ever heard! IT'S MAGIC YOU FOOL :p $\endgroup$ Commented Sep 29, 2017 at 7:39
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4$\begingroup$ Ever read "Strata"? Of course there's times Rincewind bumps into random Creators during his travels (and why the platypus). $\endgroup$– pojo-guyCommented Sep 29, 2017 at 8:45
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1$\begingroup$ @pojo-guy: Strata was Pratchett writing about a disc world, but it wasn't discworld. $\endgroup$ Commented Sep 29, 2017 at 18:25
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2$\begingroup$ Fascinating as that discussion is, it's not going to be definitively answered and is off topic here. $\endgroup$ Commented Sep 30, 2017 at 17:01
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Gravity to the rescue.
If your planet has a disc-shape, gravity will be different towards the edges as compared to the center. The habitable zone on the planet would be near the center (maybe on both sides, that might make for interesting story material...) while the more you go towards the edges, the more everything becomes inhospitable, to the point that the atmosphere is too thin to reach the edge without some kind of space suit, which depending on the time period of your story may be far in the future.
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6$\begingroup$ It would also be a desert, since gravity would pull all fluids (i.e. water) towards the centre... $\endgroup$– komodospCommented Sep 29, 2017 at 8:55
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$\begingroup$ @colmde It would look much like a hill side slowly turning to mountains the further you get from the middle. No plants or soil, eventually no air. $\endgroup$ Commented Sep 29, 2017 at 9:59
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3$\begingroup$ Amusingly, it would have a bulging sea in the middle, like the yolk of a fried egg $\endgroup$ Commented Sep 29, 2017 at 10:02
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10$\begingroup$ Gravity would also pull the edges towards the centre, creating some sort of spherical body . . . oh $\endgroup$ Commented Sep 29, 2017 at 10:12
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1$\begingroup$ The most plausible you could do is a cylinder with about the same diameter and height (still very unlikely in terms of science). Technically you could climb it (max elevation about 45 degrees), but... well... no air... (And what's on the side?...) $\endgroup$ Commented Sep 29, 2017 at 11:51
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the world is so big no one could reach the edges.
And that everything along the way is boring and inhospitable.
Consider that at the boundaries of all known lands, the great sea extends so far that it would take the fastest ship over 3 years to cross. Without sight of a single island or reef.
And the ocean isn't even the worst of it, at least on the ocean one could fish for food. The few explorers who made it to the other side (and returned more than half-mad from deprivation). In every direction they have reported nothing but lifeless desert. (Unlike a real desert), is is completely lifeless. Not a animal nor a blade of grass, or a single spring of fresh-water to be found. And the rains immediately soak into the parched ground. And it seemingly never rains once you get too far from the sea.
The very few explorers sent out from the ships, report than even after months of travel there is nothing insight but more sand -- in truth the desert may be larger than the ocean. The idea of the desert beyond the ocean is to put something even more inhospitable than open ocean out there. (Since oceans can have fish, and rain, and even maybe enough seaweeds etc to live, in theory). A this inhospitable desert could be much worse (You could even do things like the sand being chemically infertile).
of-course this begs the question why the known world is nice, and interesting, but as you go away from it, everything gets boring. * Insert creation myth here. *
So you can do what ever you want with the end of the world. No one is going to see it.
And while yes, where there is a will there is a way, someone could eventually settle on in the desert. Some kind of (literal) fringe group. The prospect of making such a place habitable away from the sea, is basically a teraforming project. And you simply set your story well before it is complete.
answered Sep 29, 2017 at 7:28
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2$\begingroup$ Reminds me of the world view back before Columbus. People had a good idea of the size of the planet but thought everything but Europe/Africa/Asia was empty sea. Imagine Eurasia + Africa on a flat, large sea. $\endgroup$ Commented Sep 29, 2017 at 8:39
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13$\begingroup$ ^Indeed, people had a good idea of the shape and size of the planet -- they knew it was round (as I think you are hinting at). Columbus is the exception to this (as I understand it), he though the world was much smaller than everyone else did. He was wrong. $\endgroup$ Commented Sep 29, 2017 at 8:42
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3$\begingroup$ The idea of traveling for even 1 year without being able to stop anywhere for supplies (especially water) is almost impossible for most levels of technology. This would work for a long time. $\endgroup$– ErikCommented Sep 29, 2017 at 9:33
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$\begingroup$ @LyndonWhite Sure, although my post could technically mean they knew the size but thought it was flat, that really makes no sense. $\endgroup$ Commented Sep 29, 2017 at 9:55
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Requires no exotic dimensional physics.
For the same reasons we humans never visited either the North or South poles, until we developed the technology to do so a few hundred years ago.
It's too cold at the edge, and (like our poles) too cold a hundred miles from the edge. Antarctic temperatures, below -100C. Throw in tornadic winds that could literally lift a herd of elephants, and it is too lethal. The winds prevent any sort of balloon or aircraft from getting close enough.
Of course, if your population develops space flight, they will see the edges eventually; and by science I can know it is not a sphere (one might hypothesize the world is a sphere like Earth but with just one cold pole; however such a sphere has an equator, and you can travel in a straight line due East and reach your starting point: There is no such straight line on the disc world). By science I can know it is a disc (Shadow length and orientation relationships on the habitable part can prove flatness, while mapping of the cold edge, as close as we can get to it, proves circularity).
Actually reaching the edge to peer over it requires some very high tech.
Added: There is another psychological deterrent: Although we can determine the habitable area is a disc (the length of the ice border rules out a small ice cap), we cannot prove there is an edge: The habitable area may be a circular warm spot on an ice plain that could be thousands or millions of times wider than the habitable area itself. With such a possibility, there is no certainty an edge could ever be reached, giving an exploration to find an edge a near certain suicide mission in the eyes of most.
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$\begingroup$ I quite like this. It's theoretically perfectly possible to reach the edge, but practically you'll freeze to death before you make it half way. $\endgroup$ Commented Sep 30, 2017 at 12:15
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$\begingroup$ @JoeBloggs added to my answer, inspired by your comment. $\endgroup$– AmadeusCommented Sep 30, 2017 at 13:46
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$\begingroup$ This is the actual answer most modern Flat-Earthers give... $\endgroup$– G0BLiNCommented Oct 1, 2017 at 15:58
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Looking off the world into the oblivion of whatever lies beyond could simply drive people insane, causing them to leap off the edge, preventing any explorers from returning to civilization with the knowledge of the edge. This is a bit dark, yes, but it makes some sort of sense. I hope I helped.
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1$\begingroup$ Thank you, I really needed somewhere to go off I was Kinda stuck! :P $\endgroup$– Gray9Commented Sep 29, 2017 at 2:32
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There is absolutely no reason why planets have to remain round. There are many scenarios that I can think of that could in theory produce a 'pancake' planet shape. Gravity would be interesting. Or maybe the planet formed like a can, flat on the ends, dumbbell on the sides. Your inhabitants live on the flat ends. Again, gravity would do weird things around the rim. Perhaps you would be walking on a slant to the flat ground, because that would be 'up' (perpendicular to the center of gravity, but not to the flat side), but of course it would be very confusing between the visual, balance, and proprioceptive sensors of the body - probably very nauseating. Especially to a bipedal animal. Like walking into the wind, without the wind. I could imagine it would be extremely unsettling to go near the edge, walking on an angle.
answered Sep 29, 2017 at 2:41
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5$\begingroup$ On any planetary sized body the force of gravity would force all of the mass of the object into a spherical shape. That's part of the definition of what a planet is. $\endgroup$– SlartyCommented Sep 29, 2017 at 2:48
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3$\begingroup$ @Slarty Not if for instance, the planet started as a solid body, and was 'chipped away' by meteor impacts. There are many examples of planetary sized bodies that are not symmetrical. Saturn and Jupiter are squeezed flat by their high rotational speeds. Imagine if Saturn's rings were so dense, they were like a solid surface. If a planet spun really fast, it could flatten like a pizza dough ball. Cosmology loves throwing curves, things we thought were impossible. They just cause us to rethink our theories. CERN physicists have seen so many strange things, it's almost as if nothing is impossible. $\endgroup$ Commented Sep 29, 2017 at 3:21
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6$\begingroup$ @JustinThyme - Saturn and Jupiter are not flat - they are oblate (round, but bulgy around the middle). Once the rotational speed would be fast enough to overcome the circular pull of gravity and flatten "like pizza dough" it would tear itself apart (basically, the flattening trend would continue until destruction). Being bashed by meteors is possible, but a result of that kind of loss of mass is going to be a loss of functional atmosphere. It's also not going to be stable for more than a few hundred thousand years, which puts a damper on the idea of life evolving there. $\endgroup$ Commented Sep 29, 2017 at 3:51
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$\begingroup$ @JustinThyme Well I stand corrected I should have said nearly spherical. But mountains and equatorial bulges aside by definition a planet must be in hydrostatic equilibrium so it must be spherical or nearly so. Jupiter’s Ellipticity is around 6.4%. Saturn’s rings could not form one solid surface as the particles at different heights orbit around the planet at different velocities. Some smaller objects can form very odd shapes but they are not planets. $\endgroup$– SlartyCommented Sep 29, 2017 at 12:09
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$\begingroup$ @Slarty Indeed, just look at many asteroids. Heck, look at Mars' moons Phobos and Deimos (which, last I looked, were believed to be captured asteroids). $\endgroup$– userCommented Sep 29, 2017 at 17:56
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Perhaps the edge is difficult to access as the boundary area consists of difficult terrain such as:
Rings of circular ridges, chasms, cliffs and mountains
A stormy circular shallow sea with lots of reefs and concentric bands of shallow and then deep water
A wide very hot or very cold desert or impenetrable swamp
I assume that you must have introduced some hand waving explanation to make the flat planets gravity work as we would expect on a spherical planet
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Perhaps no one has seen the Edge (and come back to tell of the experience) because the Edgeward Current is too strong and all the daft explorers' ships keep sailing over the Edgefall?
This has the advantage of being both a mythical explanation and also the real fact of geology. Of course, I'm positing an Edgeringing Ocean with no land masses nearby.
So, it's technically untrue that no one has ever seen the Edge. It's just more true that those who háve seen the Edge have really seen it by falling off...
answered Sep 29, 2017 at 2:42
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Haven't you heard the tales? It's said many a dread creature dwells in the Undershadow of the world- fair beyond the likes of normal man, beast, nor weapon. It is said some ancient barrier prevents them from crossing over- a miracle by any other name.
But while they cannot walk on the surface, the Edge is not beyond their reach. Many a brave explorer has dared draw too close to the Edge- one and all they've vanished without a trace. Entire expeditions have been lost- there one day- gone the next. None have ever returned from trying to find the Edge.
And that, my young lad, is why all maps warn against approaching the Edge; why I tell you now to stay far, far away from the unknown, "Here there be monsters."
answered Sep 29, 2017 at 6:08
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Maybe there is no breathable air there and it is too cold for humans to survive more than a few minutes without serious protective gear akin to a spacesuit. Cosmic radiation could also be an issue.
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$\begingroup$ Plausable. On a disk, the gravity would be far less at the rim of the disk. Like climbing up a mountain. You get further away from the center of the planet. Perhaps it gets so scarce, the inhabitants can't breathe. $\endgroup$ Commented Sep 29, 2017 at 13:54
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Your world is flat, so it does not have a horizon (or at least not like we have on earth). Someone on a tall mountain could have a direct line of sight to the edge of the world. The reason they can't see it is because eventually the air would be too thick for light to get through properly, giving the impression of a eternal wall of fog. Like the draw distance in games.
It would be very easy to make it so people are scared of this fog. If the world you want to map is an island and is small enough that they don't see this fog on the land, people would believe it only exists at sea. Since they're the only land they know they won't have boats for crossing oceans and would probably have issues navigating. I don't know how compasses would work in your world, and while they could use the stars, its possible nobody thought of this as it's easier to navigate on land by looking for tall landmarks that are visible from just about everywhere (since the world is flat).
Anyone who does try to find the edge will eventually turn around when they start to lose sight of the shore (as the eternal fog consume it), or they will drift until they sink/run out of fresh water/go mad. Any ships in this situation that do make it back by some miracle will just tell stories of the endless sea and fog, increasing peoples fear and making future attempts even less likely.
Even if they do work out it is caused by light not being able to get through that much air, and that they can use the stars to navigate, it doesn't change much. They don't know if there's land out in the fog so they may just send people to their deaths if they try looking. Everyone knew that if Columbus could keep sailing he would eventually hit Asia, but they knew that he couldn't keep sailing for that long a journey (and he couldn't at the time, he only tried because he thought the journey was shorter than it was).
In your world the people can't be sure they'll hit anything even if they sail forever.
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Giant dome of magic-stuff
Instead of staying in the sky, the sky curves downwards creating an inescapable dome.
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if you make your "end" impossible to reach by more natural means, such as surrounding it by active volcanoes or a lot of very tall mountains, no one will try to reach it.
you also could create a society that deems it unacceptable to try and search for the edge, and even making it punishable.
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$\begingroup$ Would the whole world share this society? Sounds pretty unrealistic. $\endgroup$– pipeCommented Sep 30, 2017 at 11:52
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$\begingroup$ Maybe every society deems it unacceptable separately, imagine like every society deems murder unacceptable $\endgroup$– LavigoCommented Sep 30, 2017 at 16:31
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$\begingroup$ @Lavigo But some have different definitions of murder. $\endgroup$ Commented Oct 1, 2017 at 14:06
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$\begingroup$ @Lavigo Wikipedia states: "Murder is the unlawful killing of another human without justification or valid excuse" so you just need to redefine what is valid "justification" and "valid excuse". $\endgroup$ Commented Oct 1, 2017 at 16:10
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How can you know the edge if nobody has ever returned from it?
People disappear if they venture outwards. They simply do not return.
The geography of this world's hinterlands could be loose and ethereal (maybe like the thin places in the Dark Tower). How do the borderlands know they're on the border, then? Well, their inhabitants don't travel outwards. Because anybody who ever has, beyond a day's journey or so, hasn't returned.
Maybe there's no crisp edge. Maybe the world... disintegrates. Maybe, reality itself gives to the void - slowly, too slowly for mortals to recognize. Maybe nightfall, darkness itself, washes souls out into oblivion. But then again, there could be practical reasons that men do not return. Some may say there's paradise out there. Others say death awaits at the hands of beasts, men, gods... Who knows. Borderland towns often have their own folklore about the edge. It's wise not to look that way.
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How about a society related reason? A religion that sees it sinful to try to look outside of the known world, and anyone who tries would be executed or shunned or deemed insane. Or some extreme fear or belief which makes people utterly uninterested of going outside of the known land. Keep in mind, it wasn't a piece of cake for Columbus to start his voyages, but he was rejected multiple times by kings of different countries when he was looking financial support.
It is not obvious that people would automatically be interested in looking for the edges of the world.
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One of the theories real world flat Earthers have is that some world order captures people who get too close to the edge, drugs them to make them forget they saw it, then send them back to where they came.
Similarly, any plane flights over the "Pacific" actually just release drugs into the ventilation to make you think you went over the Pacific ocean but instead you just went over the Atlantic or other Oceans. A similar thing happens with boats.
Now obviously the time period that your world takes place in will make this more or less feasible.
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What does people see on the edge? You can use the same concept used by video-games which does not allow players to move outside the map. The options includes:
- Some kind of force (like gravity) that increases on the edge, blocking anyone or anything (if only living beings are blocked it can be some kind of gravity associated with biological materials, but if everything is blocked then you have to deal with what people will see: darkness maybe). On GTA V for example, the map is an island and you can try adventure yourself outside but at certain point won't move any centimetre further, having the perception of moving, but you actually don't.
- An invisible magic wall which nothing can pass. Everything that is inside the wall will always be there and the same for what is outside. There's no reason to explain this.
- Darkness or an abyss. There's just nothing there and literally it's an edge.
- An infinite desert. Actually this options isn't a edge, but there's nothing on any direction than flat useless land and everybody that tries to go there dies of dehydration or hunger, or goes back.
- Fog. The more you are far from "world" more fog you get and less you see, forcing you to go back. This option can be extended to have moving sand and dense air, so no one could ever pass using any kind of transportation.
- Temperature change, like becoming very hot or very cold so no one can survive.
- Lack of air to breath.
- Incremental super gravity (making it harder to move and, when far enough, crushing bones and internal organs, killing or doing several damage to people).
So, there are many options, but the one you choose depends on the nature of your world. Is there magic? Is there technology? Is the edge to be a mystery? Is the edge to be forbidden? Does people live close and eventually want to go further the edge? These will help you to decide what kind of force, land type, visibility and explanation you want to give. If this is irrelevant to the story, then a force like gravity would fit nice.
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Cannot believe no one has put this yet.
Just put sketches of dragons and kraken at the edge of your map with sits "here be dragons" Luke hey did for navy flat mayors in the middle ages;)
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1) side-scroller. Keep walking east, you end up on the west end of the map. Just because it isn't round doesn't mean you have to have edges.
2) discworld. Look, you can see the Turtle down there... What's to explain?
3) "Here there be Dragons." If GOD is at the center of the map, the heinous evils of the world would slink to the edges. The further out you go, the more dangerous and insidious and powerful and unreasonable they become. Where's the edge? Nobody knows, because no one has survived to make it that far.
4) No one has looked over the edge? Maybe they have, and are always inducted into the mysterious Illuminati that hide the Great Secrets from the rest of the blithely ignorant world.
5) Holodeck. When you get to the edge, features always make it inconvenient to get all the way to the wall. Unclimbable mountain, impassably raging whitewater, a desert so dry and hot and barren no one would try, and if they do the dunes keep collapsing... and if you do ever make it to the wall, you still can't see it. BUMP! WTF?
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How about a world like Le Guin's Earthsea - a scatter of islands (quite a big scatter) and only ocean anywhere else. She has dragons living in the West, and icy covered land in the North, but nothing is said that I remember of North, South, or East. Given the right level of technology, this is a spatially bounded earth.
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$\begingroup$ There's only ocean on the South and East, West is the land of the dead as I recall, where they visit in the third book The Farthest Shore. There are the rafter tribes to the South, they say the world is only open Ocean any further South, but then they would if they have any to halt the inquisitive. $\endgroup$– AshCommented Oct 1, 2017 at 9:41
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$\begingroup$ Good point about the South. West is the Dragon's Reach, and beyond that the place the dragons live. This isn't described in any detail, but it is implied that they live in the air over the sea. $\endgroup$– astainesCommented Oct 1, 2017 at 19:25
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$\begingroup$ Farthest West beyond the Island chain of Dragon's Reach, and a bit north on most maps, is the Isle of Selador where Erreth-Akbe fought Orm and where there's a wall you can cross between this world and the next. Ged goes there twice, once chasing a dying child and again to stop Cob from destroying the world in The Farthest Shore. $\endgroup$– AshCommented Oct 2, 2017 at 9:15
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Radiation
Because of the flat shape the magnetosphere is only effective at deflecting solar radiation near the middle of the disk.
This means that radiation near the edge is lethal, and causes lots of mutations (mutant beasts?) and sickness in the borderlands. So people avoid the boarder lands and never survive returning from the edge.
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If you use the "pie plate" from Larry Niven's Bigger Than Worlds, described as an intermediate step in Ringworld construction, then the world is for all intents and purposes an Earth-sized, pancake flat circle with a mountain range the whole way around the edge that makes the Himalaya look like a pimple; no-one has gone to The Edge because they die of hypoxia less than halfway there. This does constitute a wall around the world but one that looks natural, I've worked up a weather and geography primer for such a world if you're interested.
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If your world is spinning, then anyone who goes far enough towards the edge will be violently thrown off into the void. Or in opposite, everything is pulled toward the center so it is physically impossible to go to the edge.
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$\begingroup$ I don't think your first sentence is logically consistent. If the world is spinning sufficiently fast that "anyone ... will be violently thrown off into the void", then how is the world itself staying together? You'd seem to need magic for that, but if you're using magic anyway, then you might as well just use magic to explain the edges directly, without needing any intermediary step. $\endgroup$– userCommented Sep 29, 2017 at 20:27
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$\begingroup$ @MichaelKjörling People aren't usually glued to the floor, and it's pretty hard to walk with ice picks constantly. It would be like a slope that gets steeper and steeper towards the edge (so that things fall towards the edge). $\endgroup$ Commented Oct 1, 2017 at 14:11
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Huge mountains that no one can pass. Deserts too dangerous for any life to survive. Oceans with dangerous whirlstreams. Glaciers so cold that nothing can live. Maybe a few well selected spots in between guarded by gods or demons (if it is a fantasy world) with only legends telling what would be beyond.
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Analogous to a "ringworld", you may assume the "disc-world" is a giant "catapult" where a dense planet holds a disc with carbon-nanotubes fibers. The whole structure spins around the barycenter (which is close to the planet) and allows everything to be held on the surface of the disc by centrifuge. The structure works like a slingshot cradle being spun at a constant speed and holding a stone inside it. This will eliminate the need to tackle gravity issues due to the disc's unusual shape.
The rims: There are two ways to tackle the rim issue:
1- A great wall; Similar to Ringworld, a wall will hold-on to the precious atmosphere
2- A slightly concave surface: There may be the need to create high elevations at the rims, and at a high enough altitude there is no atmosphere. There is still a need for a great wall at the rims, but it needs not be as massive as the one around a flat disc. The wall will hold-on to whatever tenuous atmosphere there is for much longer. If that wall did not exist, the upper layer of the atmosphere will spill-over into space, and will be constantly replenished by the lower layers. Over time, the whole atmosphere will escape.
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Religious/mythological reasons: "Mama, what's at the end of the world?" (In dark, forbidding tone) "Oh, we don't talk about that. Only the cursed think about it. Those who go there are cut off forever....." If this world were highly religious, this could be sufficient. (Lots of possible variations: real religion (so the local god(s) do something terrible if you do go there), fake religion (anyone who has tried was prevented, by the religious hierarchy, from returning to society, or was publicly tortured/executed), some interesting combination....
Societal imperative: Something near the edges (some physical or magical power available there) had caused terrible devastation in the past. The only way they saved themselves was putting it so off-limits that the taboo is psychologically just about unbreakable (you can have the occasional person who tries and is viewed with such horror by everyone that they go mad or something). (Careful with this one in terms of copyright issues or some such; a similar ethical imperative (against weapons that kill at a distance) was used quite successfully in Marion Zimmer Bradley's Darkover series. Including books from before and after "The Compact".)
Lack of curiosity:
Especially if this is an alien society. One day humans make contact with them.
Human visitor: "Why, in all the years, has no one gone to look over the edge?"
Alien native: "Never thought about it. What's wrong with right here?"
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Some people do believe our Earth is flat, and, against all possible physics, they believe that for some reason all along the edges we are surrounded by huge walls of ice (they think the North Pole is the center of the disk, and that the South Pole is the circumference all around).
In some extreme cases, some seem to believe that the universe is a huge slab of ice, and here and there there are these circular "hollows", one of which is our (flat) Earth. In other hollows there are other worlds, that are impossible for us to reach due to the millions of kilometers of flat ice between us (and even getting to the top of these ice slab is impossible to begin with, as they're very high. Ok, some conspirationists believe there are military guarding these edges, so that you can't even try to get close).