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Original post on worldbuilding.stackexchange by user 86462
I have a magical childrenâs fantasy land, which is bordered by mountains on its northern side. I want to make it so that anyone travelling too far north is likely to enter one of many trap pocket dimensions which are easy to walk into but extremely difficult to exit; once youâre inside, the outside edges wrap around and you find yourself back where you started if you keep travelling. This is likely to be fatal, unless the traveller happens to be in a pocket with a stream and a food supply and shelter and enough supplies to survive.
Now, itâs a magical kingdom, and things donât have to obey the laws of physics, or be 100% coherent. But I do want it to be conceptually coherent enough that I can give narrative explanations for plot events and give magical locations rules that are applied relatively consistently, locally if not globally. You could say (correctly) that I have local ad hoc physical laws specific to individual locations.
So, what Iâm wondering is, is there a geometry or geometric analogy that can explain/model the rules of a location where you can enter in on foot but not enter out (except at one point, if travelling in one specific direction or with a particular velocity/acceleration), while being able to continue to travel in one direction for a long time or indefinitely?
EDIT: The first comment here is quite possibly a sound suggestion: A fish trap (I had the inside of a plastic bottle in mind, which I think is the same). Itâs easy enough to analogise the situation as, "You feel like youâre walking straight ahead, but youâre actually walking around the inside of the walls". The problem for me with this suggestion is that so far I donât know what using the exit looks like in-universe, as opposed to walking across the exit without actually going through it.
A childrenâs book needs an illustrator, and thatâs not me. But letâs try:
At the lower right (east), we have one far upper fringe of âThe Normal Worldâ. It is already decidedly abnormal, because itâs gotten separate from other regions east or west that go to their own, similar, traps. The person following the blue trail at bottom moves off the east edge to the west, keeps going ... eventually (question mark) notices heâs going due east. The system tried to save him! Yet he persisted, going once again true north. Eventually he reaches the "hole" of the fish trap â a place where there is only a short distance east to west before youâre back at yourself. Donât shoot your bow and arrow at things in the bushes or you might hit yourself! Eventually though, heâs out to the point where the right side connects to the left side of the pocket world. He keeps going for some time, then turns back again south at the exclamation point â which is justified when he reaches it again!
The dotted line at the south of the pocket universe connects to the dotted line at the north. To borrow Sean OâConnorâs comment â âthe area on the left is the pocket, the area on the right is the distorted near pocket area, the traveller starts by the question mark and is being wrapped east to west each time he touches a green border line.â
But for fun, letâs add a mismatch: the north edge of the wrap-around is higher. That means that â!â might actually be on a stream, down which you might take a raft until you reach your starting point again. The constant downward flow of water might be an energy source for heating the pocket dimension if the Sun never makes it there. All material eroded away simply comes back again above, so the stream never digs a canyon downward. Which is convenient for the story, since I imagine that downward must pinch inward, with less and less distance across from east to west, until there is no where left to dig down at all â your pick axe would hit itself, striking from another angle! The gravity is frozen in the shape of space, emerging from the bottom point without needing to have an actual source.
The sky, however, is open â there is some âoutâ from this pocket dimension by going upward. Whatever you like could be up and out there. The sky is dark, and the darkness allows the landscape to radiate the heat produced by perpetual motion.
Hyperbolic geometry grows exponentially with respect to radius. This means that itâs very easy to get lost. Anyone who has played HyperRogue is familiar with this: the final boss is the challenge of back tracing a mere 100 steps accurately. Itâs only really feasible if the player has a way to create a trail, since there are trillions of destinations you can get to in 100 steps.
So in a sense, the world you want already exists; itâs HyperRogue.
Spheres.
A sphere is a 3 dimensonal object. We can walk on a sphere and we will eventually wind up where we started. That is how our Earth is.
In your world, other 3d spaces intersect with ours through the 4th dimension. These spaces contain spheres and humans can move around on these spheres. When 3d spaces intersect / overlap one can move from one to the other.
The trick is that the intersection points are in motion through the 4th dimension. The place where they overlapped and you came thru is not there any more. The overlap might not exist, or might be somewhere different in the respective planes. Or might be with yet another 3d plane. I like the idea of the character unwittingly moving on to successively smaller spheres with the same terrain. Finally she sees someone in the distance, facing away. She shouts but the person does not turn around. She runs after the person but the person runs away, then stops when she stops. She is looking at her own back.
For the childrens book, the analogy is walking off the train platform onto the train. The 3d spaces of the station and the train temporarily interect. When you are on the train and turn around the door you came through is closed. It will open again but it now connects somewhere else because the train moved. You can wait on the train until you come back around to the station they got on.
Your characters will need something to orient themselves. Maybe a map like for a subway system? I could see that being an excellent cover art. Or something like a 4d compass that will show the direction of large 3d masses nearby through the 4th dimension. That will lead them to where the planes might overlap enough for them to move through to somewhere different.
I am reminded of the map from Time Bandits.
If youâre willing to give up "once youâre inside, the outside edges wrap around and you find yourself back where you started if you keep travelling", then you can satisfy the rest of your questionâs requirements by having your travelers end up in a dimension with hyperbolic geometry, which is much "bigger" in some sense than Euclidean geometry is (e.g., the circumference and area of circles both grow exponentially with radius, unlike in Euclidean geometry where theyâre linear and quadratic, respectively). In hyperbolic geometry, itâs basically hopeless to ever end up somewhere you were before unless you retrace your steps almost exactly (youâll instead just keep ending up in new places).
You can get a feel for this firsthand by downloading the game HyperRogue and venturing into the Haunted Woods. The only way out of that land is the way you went in, and once youâre far enough in that you canât see the exit anymore, youâll find that itâs basically impossible to return unless you somehow marked your path.
Möbius strip
A möbius strip is an object with just a single side. However you move over the edge,you will move along the strip on both the âbackâ and âfrontâ of the strip to end up in the same place.
An excellent example is shown here: By Sketchplanations
There are many more complex shapes possible for such a strip, but this is the easiest way to show it.
Now imagine there is one tiny strip leading to the Möbius dimension from your main dimension. Much like a fish trap you can have the entrance become smaller. Then they arrive unknowingly on the Möbius dimension. They can move around and will end up in the same place if they walk straight. There is a chance to find the tiny strip leading to and from it, but as the Möbius strip can be much wider it might be hard to stumble upon the small entrance/exit.
Itâs like a circular railroad track, just in all compass directions
With one inbound track. As soon as the train is on the circle, it wonât ever find the way out because a train is always going forward.
Yeah, itâs an incomplete analogy. Trains can go backwards after all.
The full story is: Thereâs an additional direction that humans canât perceive; letâs call it âfeywardâ. Entering a circle happens if you go âfeywardâ, to leave them you need to go âanti-feywardâ. Thing is, humans simply cannot go anti-feyward, just as they canât go back in time.
+1 for "Feyward" as a good term for an extradimensional direction. âRuadhan
The term was inspired by (or stolen from) the writings of Jack Vance, I believe. âtoolforger
