Developing the Cosmic Compass System

[Patrick-Leigh]

For the flintlock fantasy story setting I’m developing, I’ve decided that the way people travel between planets is by taking “shortcuts” through other planes. Where I’m having some issues is coming up with a way for people to navigate these other planes, since each one has its own structure and obstacles. I’ve settled on the idea of some kind of magical compass that people can use to at least determine which way they're facing and how far they are from the center of these planes. But, I need help figuring out if my ideas would actually work and if there would be problems with these compasses within certain parts of the planes, i.e. being too close or too far from a particular pole to get accurate readings on the compass and stuff like that.

Since I have a limit on how much I can write in a post, I'm going to only give you certain key details about these planes and how they work. The most important detail is that people are using magical compasses to determine their location inside of a sphere. These other planes are three-dimensional and pretty large. Ignoring the specifics of what they're like and how people traverse them, the concept is that these planes are spherical. You're not traveling on the surface of a planet, you're traveling around inside a ball the size of a solar system. (Which is still smaller than the much longer distances between planets that are set in separate galaxies, so, yeah, no point in complaining about that.)

The point is that my characters can't use a regular compass that points north and south. They having to use a spherical coordinate system. And that... is not something that's easy to explain to readers. It also lacks a certain, shall we say, organic quality. When people give directions, they don't usually specify things like latitude and longitude. You don't give the exact GPS coordinates for the corner grocery story, you say something like, "Head west on Main Street then take the third right after Market Street." There's also the issue of how my characters could figure out their coordinates inside of these very, very big spheres.

What I've settled on is that these planes have seven poles, of sorts, that are detectable by a magical compass, called a Wayfinder's Compass. Further, those poles aren't a result of some kind of magnetic field. I don't know what causes them, yet, but each pole only affects a certain type of material. So you have some kind of compass which tells you exactly which direction the poles are in relation to your position. Using the image below as a reference, the poles are North and South (along the X axis,) East and West (along the Y axis,) Up and Down (along the Z axis,) and Center, which is the point where all three axes intersect.

​

So, let's say that a character is at the location marked P. His Wayfinder's Compass will somehow be able to indicate which direction the seven poles are in relation to his position. With those, he can figure out (by doing a lot of math, no doubt,) his coordinates, as well as which ways is "up" and "down," at least in navigational terms. (Given the way gravity works on these planes and their size, up and down can be a matter of perspective a lot of the time, so instruments that give you definite directions are kind of essential.)

Yet I need a means for my characters to discuss their locations and headings without leaving the readers utterly mystified. This is where I really need some help. I think I might have a system, but there are two issues. First, I need to be sure that my idea for the Wayfinder's Compass actually works in terms of someone getting their bearings by knowing the direction of the seven poles. There's no point in coming up with this whole compass system if it wouldn't actually work for navigating these planes. So, I need confirmation on that. I can tell you that the people using a Wayfinder's Compass are usually aware of the size of these planes. They have a diameter of 20 billion kilometers and are perfect spheres. (Still figuring out how they determined this, but that's another topic entirely.) Would that information, plus the directions of the poles, be enough information for someone to determine his coordinates?

Second, I need some terminology for my characters to use that makes sense to the readers. Terms like north, south, east, west, up, and down are easy enough to grasp, but how to I have my characters say they're facing both north and a certain angle up or down in relation to the X,Y axes? I know they could just say, "We're bearing north and up thirty-seven degrees," but I feel like that lacks a certain flare to it and might still be confusing.

Presently, my thinking is that on the X,Y axes, the cardinal directions are the same as a conventional compass rose. (North: 0° = 360°, East: 90°, South: 180°, West: 270°) The Z axis has two points of simply called "Up" (0° = 360°) and "Down" (180°.) When characters describe specific degrees on the up-down Z axis, they don't use terms like "north" or "south." Instead, 45° is "Upward" while 135° is "Downward." Thus, going north on a 45° angle is going "Upward North" while going north and down at a 135° angle is "Downward North." The same applies to all the other cardinal and intercardinal points on the compass, i.e. "Upward South," "Downward East," "Upward Northwest," "Downward Southeast," etc.

As for the points of 22.5° and 67.5° on the Z axis, the equivalents of North-Northeast and East-Northeast on a horizontal compass rose, the terms "High" and "Low" are used. So, going north at a 22.5° is going "High Upward North." Going north at a 67.5° angle is going "Low Upward North." The same applies to the points of 112.5° and 157.5° from "Up" on the Z axis, which would be the equivalents of East-Southeast and South-Southeast on a horizontal compass rose. Thus, going North on a 112.5° angle is "High Downward North" and going North on a 157.4° angle is "Low Downward North."

I've gotten some positive feedback on this system on another forum, but I wanted to see if folks on other forums thought it worked. Having a few people on one site say it does really isn't a sure way to know if it would work for most of my readers, after all. And, once again, I'm trying to get confirmation from multiple sources that a compass pointing to fixed points on the perimeter of a sphere would actually work for navigation. If the Wayfinder's Compass can't do that, I need to figure out some other way for my characters to tell which way they're going.

A second aspect to this system that I want to confirm is the use of a changing frequency to indicate how far people are from the center pole of these planes. Since I want my characters to be able to determine their range from the center without having to do a ton of math (especially when they're pressed for time,) I figured that the cores of these planes gave off some kind of signal that could be detected by the Wayfinder's Compass. For each kilometer closer or further away from the core, the frequency would increase or decrease by 1 Hz.

Since these planes have a 10 billion km radius, I decided that the frequency of the signal would be 1 Hz at the edge. Thus, it would be 10 GHz at the center. So, a character could tell exactly how far he was from the core simply by the number of Hz the signal is. That would not give him any other coordinates, however, just his range from the center. The directions of the six other poles would be necessary to figure out the rest. Whatever this signal is (I'm calling it the Cosmic Pulse at the moment,) it is not affected by any physical matter or forces, so the changes in frequency are consistent no matter what. The only thing the signal does is affect some kind of detection mechanism in a Wayfinder's Compass.

So, do my ideas hold up? Do you think a reader would be able to follow them with minimal amount of exposition? Let me know what you think!

Keep moving forward!

Patrick Leigh​

 

[Riva]

Hello,

to me the way you decided to convey directions seems okay, so I'd leave it at that.

As for how to determine the characters' position in the sphere I'd have a question: are the seven poles always in the same positions relative to one another? (hence same angles between them)?

 

[Patrick-Leigh]

Hello,

to me the way you decided to convey directions seems okay, so I'd leave it at that.

As for how to determine the characters' position in the sphere I'd have a question: are the seven poles always in the same positions relative to one another? (hence same angles between them)?

The seven poles are fixed in their positions. They don't shift around, like the poles of our magnetic field do. So, if you drew lines between them, you'd have a perfect set of X,Y,Z axes with the center pole being the origin point of each axis.

 

[Riva]

If that's the case I don't even think that you would require maths. You could roughly figure out where you are just by looking at the tilt of the compasses' rods.
If you really need precision you could pick three poles and the centre to serve as the base of your reference system.
I'm gonna assume you can measure the angles between the indivdual rods, so for example your compasses could be partly transparent and you can mark the direction of the rod on a sheet of paper with a sort of goniometric cricle on it.
You can represent your position with a three-component vector, we can call it (x y z).
Since we know our distance from the centre it's better to express our coordinates in polar form, so we take away one variable.

(x y z) = (r*cos(lat)*cos(long) + r*cos(lat)*sin(long) + r*sin(lat))
Where "r" is the distance from the centre (given by the frequency and "lat" and "long" are the latitude and longitude in radians.

Now we have only two variables to find. I'm imagining that your travelers could use an instrument that is kind of like a glass ball with a fixed marble in the center to which are attached seven threads with seven rods at the end of them. That would be handy because you could setup some kind of angle measuring station (you know, goniometers on the sides ecc) and look at angles in space.

Ok finding the actual latitudes was kind of tricky lol, I spent a fair bit of time in these days trying to see if you could actually find the lat and long of your position knowing only the angles between the rods.
You can, at least if my trigonometry didn't fail me hahaha.
It is a bit of a lengthy process and to explain it it would be far far easier with drawings, so I'll leave that to you. If you can't do it just ask, I can try to explain.
Hope it helped, cheers.

 

[Patrick-Leigh]

I think an explanation would be useful, just so I'm sure I'm doing it right. I need this system to be pretty solid, since navigating these planes correctly is imperative. In one of my other threads, I went into detail about the scale of these places and the recurring structure they tend to follow. There are some regions where my characters DO NOT want to end up. In fact, I'm planning a short story where my protagonist, Perdita Nightshade, goes into a cave with a portal to the Plane of Earth while exploring a deserted island. She takes out her Wayfinder's Compass to determine which part of the Plane of Earth she's entered and realizes she's about 9 billion kilometres from the Core. That's almost to the outer edge of the Plane of Earth, which is were the biggest, baddest Abominations are found. I think she's going to refer to the instant where she saw the readings on her Wayfinder's Compass as, "the most butt-puckering moment of my life."

 

[Riva]

There you go. I think it's right but if you find a mistake let me know.

I'm a tad curious on how you would implement this in your story, I think that I woud've just said something like "She took out her compass, did her calculations, and for the love of god..."
Just wondering.

 

[Patrick-Leigh]

I’m thinking she’s exploring the island, finds a cave, goes inside, finds an opening to a side passage that her Wayfinder’s Compass determines is actually an earth portal, and goes through it to determine where it leads on the Plane of Earth. Once she is in far enough, she activates the compass again, and can tell by the angles that she’s closer to one of the outer poles than she should be. She does the math and can’t believe the results, so she checks the frequency of the Cosmic Pulse. It confirms she’s really deep into eldritch territory. After that, she backs out of the earth portal very slowly and quietly. Not sure what else to do with the idea, so far; I just know it’s going to be a really scary moment for her.

 

[Riva]

A scary moment for sure.
Just one thing, before doing the math you have to check the Pulse, not the other way around. At least, that's my understanding.

Anyways good luck with the writing, hope that helped.

 

[Vaporo]

How do your travellers know how the "flat" XY plane is oriented? I'm assuming that the planes are mostly empty voids with no gravity. When they first arrive in a plane, how will they know how to orient themselves?

To me, trying base your system on a "neutral" plane in such a space seems like trying to fit a square peg into a round hole. If I were designing a navigational system for these spheres, I'd probably repurpose latitude and longitude along with an "altitude" value, since those are all things that most readers will be familiar with and won't require a lot of explanation.

How did this system come to be? Was it developed ad-hoc by early explorers, or by scientists and engineers (or equivalent). The system you have makes more sense if it was invented by explorers, since a (modern) scientist would probably come up with something based on radial, Cartesian, or latitude/longitude coordinates.

A second aspect to this system that I want to confirm is the use of a changing frequency to indicate how far people are from the center pole of these planes. Since I want my characters to be able to determine their range from the center without having to do a ton of math (especially when they're pressed for time,) I figured that the cores of these planes gave off some kind of signal that could be detected by the Wayfinder's Compass. For each kilometer closer or further away from the core, the frequency would increase or decrease by 1 Hz.

This doesn't make a lot of sense. Imagine ripples in a pond. The ripples move away from their source at a constant speed. They don't speed up or slow down no matter how far away they get. Thus, the frequency would also remain the same.

However, maybe your waves do slow down for some reason. In that case, depending on how slow they get you could risk another phenomenon called "aliasing," AKA the Doppler effect. Basically, unless your measurement device is perfectly stationary relative to the emitter, you will read a higher or lower frequency than reality. You can observe this in real life with things like the apparent change in pitch from the horn of an oncoming train.

A better method, I think, would just be to read the magnitude of whatever force the core is emitting, since presumably the signal would be weaker farther from the core.

However, if these planes have landmarks such as stars and planets, you can pretty easily determine your exact location based on where they appear in the sky. Perhaps, if your characters are good enough at it, they don't even need any sort of coordinate system to navigate. Maybe they just know "The gate to Morbheim is located 400 miles above the big green splotch on that planet close to the core" and just work with that.

While it's good to develop this sort of thing as background information for yourself, I think that you'll find that it's difficult to write about this sort of thing with any real detail without grinding the story to a halt. If it's not perfect, to fret overly much about it. Most of the time you'll just be able to say "oh, my destination is above me and in the coreward direction" and that will be it.

 

[psychotick]

Hi,

The whole poles thing confuses me, mostly because I have no idea what they are. What are they pointing to? I'd probably go back to the basics. So the compass points always to the sun - it's a problem if your sphere doesn't have a sun or else has more than one, but there you are. That's your true north. Then a level on it crossing the north south line. This level isn't affected by gravity but rather by the direction of spin of the sun and the solar system. And if you use your hertz bit to get distance, your compass tells you how far out you are from the sun and which way is "spinwards, and which way is anti-spinwards. Now the only other thing you need to know is on which degree of the planetary system you are. So that's like a clock laid flat on the direction of spin with the sun at it's centre and you look for what way the hour hands pointing as it points at you. It points at you because your compass carries something on it that attracts the energy of the sun and causes the clock to spin until it points at true solar north, while an hour hand points at you.

Put simply, your compass is in two parts. The top half points at the sun and gives you distance and the orientation of the planets. And when you've got that you turn the compass over, making sure that it's still parallel to the spin disc and facing the sun, get the clock face with the sun at it's centre and work out what time it is.

So your hero arrives in a new sphere and pulls out his compass. He reads the top half which gives him the direction of the sun and the plane of the ecliptic, then turns it over. And he works out he's fifteen units from the sun at seven thirty O'clock! The only other direction he might need is the angle above or below the ecliptic, but unless he has space ships and so can arrive at points a long way above or below the planets that's not likely to be an issue. The planets will mostly be on the ecliptic, so up and down don't really matter - mostly.

Hope that helps. Not sure I'm explaining it well.

Cheers, Greg.

 

[Patrick-Leigh]

How do your travellers know how the "flat" XY plane is oriented? I'm assuming that the planes are mostly empty voids with no gravity. When they first arrive in a plane, how will they know how to orient themselves?

To me, trying base your system on a "neutral" plane in such a space seems like trying to fit a square peg into a round hole. If I were designing a navigational system for these spheres, I'd probably repurpose latitude and longitude along with an "altitude" value, since those are all things that most readers will be familiar with and won't require a lot of explanation.

How did this system come to be? Was it developed ad-hoc by early explorers, or by scientists and engineers (or equivalent). The system you have makes more sense if it was invented by explorers, since a (modern) scientist would probably come up with something based on radial, Cartesian, or latitude/longitude coordinates.

Firstly, none of these planes are empty. They are:

The Plane of Earth - Big ball of rock with tunnels going through it
The Plane of Water - Big ball of water with vortexes and air pockets in it
The Plane of Air - A big ball of air with lots of clouds and occasional floating islands and dwarf planets floating around in it
The Plane of Fire - Still figuring this one out, but it's probably not a place most people like to go
The Plane of Mirrors - Similar to the Plane of Air in that it's a big ball of gas, but there are countless mirror portals floating in it
The World Tree - Still figuring this out, but I'm thinking it's another ball of gas but with some kind of giant, tree-like thing spreading its branches all over the place

There are going to be two more, but I haven't figured them out just yet.

As for the compass system itself, it came about partly by explorers noticing that certain materials would tug in specific directions and using that the make the original Wayfinder's Compasses, partly through the observation that portals to specific galaxies were generally clustered together in specific directions (i.e., portals to the "north" galaxy were always opposite of the Core from portals to the "south" galaxy,) and partly in reference to certain scriptural passages in holy texts with lines like, "And the Elves came from the Cosmic North" or something to that effect. Thus, the pole which would lead you toward the portals to the galaxy occupied by the Elves was deemed the North Cosmic Pole, the pole that would lead you to the galaxy occupied by the Orcs was dubbed the South Cosmic Pole, the pole that would lead you to the galaxy occupied by the Faeries was called the "West Cosmic Pole" and so on. (The Upper and Lower Cosmic Poles were therefore given their designations once the East and West Cosmic Poles were designated.)

As to your point about the system being invented by more modern scientists, that's largely a result of the Dwarves. In my setting, they're really big on mathematics and geometry. Platonic solids, for example, are considered divine polyhedrons. The Dwarves developed stuff like Algebra, Calculus, Trigonometry, etc., thousands of years before the current era in my story setting. (Which, by the way, is a flintlock fantasy heavily inspired by the 18th century, the Golden Age of Piracy, and the First Industrial Revolution.)

I'm glad you pointed out the Doppler effect movement would have on the readings for the Cosmic Pulse. I overlooked that when researching frequencies. The Cosmic Pulse is not, however, going to be an electromagnetic wave. It's some kind of Arcane energy the Core of the Transitory Planes emits. I figured since gravity can work differently on these planes, it wouldn't be that big of a stretch to think that the frequency of a magical energy wave would go down as it spread out. The reason I decided the Cosmic Pulse was necessary is because the Transitory Planes each have the same diameter: 20 billion kilometres. This, combined with the fact that some of them are made of stone, water, or fire, is why using landmarks to navigate the Transitory Planes is not usually a reliable method.

(Granted, my characters are usually staying within a 100,000 km radius of the Cores, since that's where most of the portals to the galaxies they live in are clustered, but not all portals connect to those inner regions of the Transitory Planes.)

Even if I'm not going into a tremendous amount of detail about this stuff in the narration or dialogue of the books I'm planning, I still need to have a good sense of how my characters can navigate these places with their Wayfinder's Compasses. I'm not content to hand-wave the details and say that it just works "because magic," especially since Arcane Magic is going to be very science based. It doesn't break the laws of physics, but it does let you bend them. You can't turn someone into a frog with Arcane Magic, but you can manipulate temperature, momentum, light, electricity, etc., and the more you understand about how the laws of physics work, the more precise your Arcane Spells become. Since the Cosmic Compass and the Cosmic Pulse are both Arcane in nature, having this stuff figured out is kind of important for me. Plus, I suspect some people would just find it cool to read about the details even if it's just in some kind of lore book about the story setting and not in the actual stories themselves.

 

[Vaporo]

All right. But without any consistent landmarks in each plane, the question still remains: How do people orient themselves relative to find the XY plane when they first enter a plane, particularly if they were to enter through a previously unexplored portal?

Actually, you know what? The way I described it before, where the speed of the wave determines the frequency, isn't right. Even if the waves slowed down near the edge of the sphere, the frequency, the time between the peaks of each wave, would remain the same. So the idea of this "cosmic pulse" being emanated from the core still doesn't make sense. It doesn't matter if it's an electromagnetic wave, mechanical wave, a hydraulic wave, or otherwise, the core properties of a wave remain the same. If the core is emanating a repeated pulse, its frequency will be the same no matter how much the waves accelerate or slow down.

If you're dead-set on the idea of your compass measuring some sort of waveform, perhaps instead it contains some sort of crystal that vibrates when exposed to the "radiation" from the cores of the planes. The frequency of the vibration depends on how much radiation it is receiving, so it vibrates faster near the core and slower near the edge.

Or, maybe instead the pulse is actually a constant frequency, but time speeds up the further you get from the core making it appear slower.

If you take that along with the Doppler effect, then I can imagine a scene where your characters get out near the edge of a sphere and their compass stops working since even the slight motion caused by their heartbeat is enough to throw the reading off by millions of miles.

Incidentally, what happens when something reaches the edge of a plane's sphere?

 

[Patrick-Leigh]

The way people orient themselves is with the Wayfinder's Compass. It doesn't just point to the XY plane (north,south,east,west,) it also indicates the Z plane (up,down.) Alternatively, they can use a particular type of spell to get their bearings. Without either of those, it is very easy to get hopelessly lost on the Transitory Planes. I'm thinking the ancient ancestors of the various races might have had an innate ability to sense the directions of the Cosmic Poles, but that ability has mostly been lost by subsequent generations. Now, you either need a spell or a device like a Wayfinder's Compass to get your bearings.

As to the Cosmic Pulse, you're point about a crystal that vibrates in response to it is actually the main thing I'm considering, actually. If the Cosmic Pulse itself isn't what changes in frequency, then the resonance of the crystal in the Wayfinder's Compass is what changes in frequency. Either way, the frequency is 1 Hz at the edge of the Transitory Planes and 10 GHz at the very center of the Core. (Not that anyone with a Wayfinder's Compass has actually reached either of those points, but they've figured out those are the limits of the frequency range through various experiments and other research.)

Regarding what happens when you get to the edge of the Transitory Planes, the answer is... I don't have an answer to that, yet. My current thinking is that you if you reach the end and try to go past it, you'll just end up on the opposite side of the same plane. That is, if you try to go past the East Cosmic Pole, you end up at the West Cosmic Pole and vice versa. The only way to leave these planes is through portals. But, again, nobody has actually been able to confirm if this is the case. The further from the Core you go on any Transitory Plane, the more Lovecraftian the creatures get. (See my post on the regions at this convenient link.)

The point is that, with the right device or spell, you can determine what they XYZ axes of the Transitory Planes are, the directions of the different poles, and your distance from the Core. That will give you your coordinates and your heading. I'm just trying to make sure that this could actually work since I'm against simply hand-waving the explanation and saying something like, "It works because magic." Plus, it's just fun to consider the ramifications of what one or two small changes to a law of physics or the way technology works would be. In this case, it's a compass that lets you navigate the inside of a sphere. A really, really, really big sphere. (Seriously, 20 billion km is beyond the orbit of Neptune, but not quite to the hypothesized distance of the heliosheath.)

 

[Vaporo]

The way people orient themselves is with the Wayfinder's Compass. It doesn't just point to the XY plane (north,south,east,west,) it also indicates the Z plane (up,down.) Alternatively, they can use a particular type of spell to get their bearings. Without either of those, it is very easy to get hopelessly lost on the Transitory Planes. I'm thinking the ancient ancestors of the various races might have had an innate ability to sense the directions of the Cosmic Poles, but that ability has mostly been lost by subsequent generations. Now, you either need a spell or a device like a Wayfinder's Compass to get your bearings.

So how does the compass know how to orient itself? It only has one consistent point of reference: the core. To define a plane, you need at least a point and a vector, while here you only seem to have a single point.

 

[Riva]

Oh if you were going to do something more like actual waves with the pulse then I'd go with Vaporo's suggestion of the force field. You could have your crystal vibrate in response to being affected by the field or something like that, if you want to have a frequency. The ratio of force and distance might not be linear though, but that I don't think is a problem, and you can simply say that the force isn't inversely proprtional to the distance squared for whatever reason.
Anyway my take is that you just need to put in some phenomenon which is dependent on the distance from the core, and it doesn't have to be a frequency, nor it needs to be a linear dependency.
If you really want to have waves propagating from the core it would be interesting if they would be reflected by the outer edge of the sphere, so you could have stationary waves (though I don't know how they work in 3D, AND a stationary wave alone would not give you information about the distance from the core, so you'd still got that. I might suggest you to do so that the motion gets damped the more you go outward, but we haven't done the dampened armonic motion in school so I'm not sure that would result in a lower frequency near the edge).
I'm gonna throw this out there: the pulse could really be particles that similarly to photons have a frequency that's proportional to their (in this case) "arcane" energy. While they're traveling they give out some other particles which detract energy from the original particle. This happens in a manner that would result in a linear function between the distance and the frequency (for example our imaginary arcane photon could lose X joules of energy each meter). The detecting device would then measure the frequency of these particles.
Note that at the edge of the sphere they might get sparse.

Vaporo the way I assumed they did it is that since each pole attracts different materials and they are always at 90 deg angles between eachother (I think op said that at some point) they would have seven points of reference and seven associated vectors (whose components are initially unknown though).

By the way, maybe I'm stupid but don't you need a point and two vectors to define a plane?

 

[Vaporo]

Anyway my take is that you just need to put in some phenomenon which is dependent on the distance from the core, and it doesn't have to be a frequency, nor it needs to be a linear dependency.

It doesn't even have to be a linear dependency. In fact, it makes more sense if the dependency weren't linear, and it reduced with the inverse of the distance or the square of the distance from the core. E.g. if you triple the distance, the frequency is reduced by a factor of 3 or 9. Perhaps the 1Hz/km metric is actually just a convenient an approximation that only works near the core, and the further you get from the core the more you need to actually need to back-calculate to find the actual distance. Or maybe the compass has some sort of built-in "computer" that handles distance calculation automatically.

the way I assumed they did it is that since each pole attracts different materials and they are always at 90 deg angles between eachother (I think op said that at some point) they would have seven points of reference and seven associated vectors (whose components are initially unknown though).

Ahhh. Ok, that bit confused me in the original post. Well, if that is the case, it immediately brings up another question: What holds the poles in place? Why do they exist? Why do they attract different materials? A configuration like that doesn't usually exist in nature. It feels a little bit contrived to have these "attractors" placed so conveniently.

By the way, maybe I'm stupid but don't you need a point and two vectors to define a plane?

Nope. The minimum information needed to define a plane is a point and a normal vector:

 

[Vaporo]

Perhaps instead of "poles" you could borrow from astrophysics and instead have some sort of "jet" emitted from the core to give you your normal vector:

If you also know where the portal you just came from is, you then should know precisely where you are in the plane, how you're oriented, and what direction you need to go.

 

[Riva]

It doesn't even have to be a linear dependency. In fact, it makes more sense if the dependency weren't linear, and it reduced with the inverse of the distance or the square of the distance from the core.

Yep, that's what I said mate , just anything that gives you information on your radial distance from the core.

Nope. The minimum information needed to define a plane is a point and a normal vector:

Oh right, silly me, but that is if the vector is normal. In this case I understand that there is indeed a normal vector to the x,y plane but we cannot initially know its components from our point of view (at least I believe, you could try to get it by connecting the head of the core rod to an imaginary extension of the rod that points either up or down, but you still wouldn't know by how much you have to extend it)... aaaand I got lost lol.
Why did you bring that up?

Perhaps the 1Hz/km metric is actually just a convenient an approximation that only works near the core

I like that

 

[Vaporo]

Yep, that's what I said mate , just anything that gives you information on your radial distance from the core.

Well, you did word it kind of weird...

Technically, in order to constrain orientation of coordinate system of the plane itself, you do need a third point or vector. However, if the traveler comes through a known gate then the coordinates of the gate itself can provide the third point. If the gate they came through isn't know, they'd have to figure out something else. Or perhaps people have constructed beacons of some sort at commonly used portals, so if they get lost they just need to locate a beacon and use it to reorient themselves.

 

[Riva]

Ah ok got it.

Well, you did word it kind of weird...

Well, yeah, that "radial" was kind of redundant.