Curvature of Glorantha

[Lordabdul]

Glorantha is supposed to be a flat world, so in theory it doesn't have any curvature, but this week-end I was wondering what that means for visibility distances and horizons and all that. It looks like it was briefly touched upon in a discussion in the old forums, but it wasn't really conclusive, and it was more of a meta question about whether the whole "the earth is flat and gods exist!" was an in-character or out-of-character "truth" about Glorantha, which frankly doesn't matter that much and will make your head hurt pretty quickly.

So here I'm just noodling around with some basic math and figuring out what a Gloranthan character might expect about a few practical things. It's as serious as it is tongue in cheek -- I'm mostly thinking about how long I should let players debate how far away can they spot a pirate ship at sea before I get Water Lizards to sink their boat because I'm bored. But also, I don't like the idea that Glorantha is perfectly flat. The text box in Strangers in Prax (p36) about crow's nests being useless in ships, for instance, highlights how a flat world kills some cool adventure tropes. Flat worlds suck. So I wondered: how much curve can I get away with?

(since this involves some math, I might have made a mistake, so if you feel like something is off, feel free to ask for details or correct me!)

The first thing that I did was figuring out what Glorantha would look like if it had the same curvature as Earth. I took Pamaltela, which is roughly 4200 miles long (GtG, p540), and eyeballed the space around it from the general Glorantha map. That looks to me like roughly a quarter of its length on each side, which gives me a rough distance of 6300 miles from one side of the Gloranthan cube to the other side. With a radius equivalent to Earth's (6371 km), that actually gives an angle of only around 91 degrees... which means that the Gloranthan "cube", as viewed from the side, would look like this:

Not too bad, I think! You could frankly almost go with that and have Earth-like visibility, which means you don't need to argue about useless things with your players! Yay! I'm frankly tempted to do it (although I don't need to tell them, I can still say "as far as you know, it's flat... I mean, can you see the curve? Shut up and listen to your priests!"). Glorantha is described (RQG, p16) as "a slightly bulging, squarish lozenge". That's more that "slightly bulging" but it can do!

Now, to make it a bit flatter, what if we double the "radius"? That ends up pretty much halving the angle (to around 45 degrees), and now our Gloranthan cube looks better (and definitely "slightly bulging"):

Ok so what does that mean for visibility? I took the Quivin Mountains, in Sartar, for reference. Their peak is around 6500 ft (GtG, p187), so around 2000 m. Let's see how far south we can see those mountains... of course, other things like atmospheric interference (haze, clouds, etc.) will have to be taken into account on top of everything else, but let's put that aside for now.

• Whitewall (70 miles/110 km away) looks like it's maybe 3000 ft high (900 m).
• The centre of Beast Valley (Creek-Stream River, 100 miles/160 km away) is maybe around 2000 ft high (600 m).

These elevations are based on the very loose colour coding in S:KoH (p8).

At Earth's curvature, the Quivin Mountains seen from Whitewall's elevation will disappear from view around 130 km (80 miles) away... so you can barely spot the top of the peak from Whitewall at best. Beast Valley is too far away, however, with the Quivin mountains out of view, at that elevation, at around 140 km (87 miles) away.

At the half-curvature (twice Earth's radius), the Quivin Mountains seen from Whitewall's elevation can be seen as far as 180 km (110 miles) away. At Beast Valley's elevation, it's 200 km (125 miles). This means that the area around Whitewall probably has a few nice viewpoints, while Beast Valley can get a glimpse of the peaks on a very good day sometimes.

Here's a rough comparison of how far you can see the Quivin peaks from a Sartarite elevation (900 m, like Whitewall) at Earth's curvature (orange) and at half-curvature (blue).

Doesn't make too much difference, so I might fudge it here and there for dramatic purposes, and keep in mind the Gloranthan cube is bulgy.

Am I overthinking this and do I have too much free time? Yes, possibly. But hey, this is what passes for fun around here

 

 

[Bill the barbarian]

5 minutes ago, lordabdul said:

Am I overthinking this and do I have too much free time? Yes, possibly. But hey, this is what passes for fun around here

 

Yes, yes, and certainly. Fascinating none the less. May you continue to have to much time on your hands...

Cheers

[g33k]

Interesting!

But why are you presuming any Gloranthan curvature (if it even exists) will be smooth and regular?  Maybe the curve gets less toward the edges, or more; maybe the oceans are more-curved, or less; maybe it follows some inobvious rule(s) only hinted-at in a few obscure God Learner texts...

[Lordabdul]

40 minutes ago, g33k said:

But why are you presuming any Gloranthan curvature (if it even exists) will be smooth and regular?

Because the math is a LOT easier to write when you're dealing with a sphere

Even for a, ahem (checks notes) oblate spheroidal like Earth, approximating it to a sphere gets you pretty close to what we need, given that we just want to know if you can see this mountain or this castle from a distance -- not setup a laser with a precise target. And AFAICT, it's not necessarily useful to go into more precise shapes because at some point, atmospheric light refraction will affect visibility more than the rest.

But yes, if I was to make the Gloranthan cube into a funnier shape, I would probably make the edges more round, i.e. make the curvature increase exponentially until it ends up vertical on the face of the cube. In Glorantha, the recession of glaciers is not caused by climate change, but is actually Valind's Glacier slowly sliding off the top and falling down the North face

Edited June 11, 2019 by lordabdul

[Joerg]

I would expect some concave curvature of sea level towards Magasta's Pool rather than the convex one you showed.

The optical properties may still be similar to your convex model due to the non-straight curvature of the visiual beams your eyes emit when you look at the landscape.

Still, visibility from sufficiently high places is strongly dependent on haze rather than curvature. A good example is the visibility of the Alps from Munich. When there is Fön (an inversion weather situation pouring warm air over the Alps from the south), haze is strongly reduced, and you get an excellent look at the mountain range. Under normal conditions, you have to drive at least halfway towards Garmisch to begin to see the mountains (only to find them obscured much of the time by the foothills, except across Lake Murnau). Or, in another example, a vantage point on the Laboe memorial (about 200 feet above sea level) allows to see the Danish island coast some 30 miles away - but only on rare days with non-existent haze. Days with slightly above average haze will make it hard to see the Kiel broadcast tower about 12 miles away.

 

5 hours ago, lordabdul said:

In Glorantha, the recession of glaciers is not caused by climate change, but is actually Valind's Glacier slowly sliding off the top and falling down the North face

Cute, but no. The glacier does cover significant parts of the Hudaro ocean, but it doesn't stand a chance to remain cohesive on Sramak's River which surrounds the Earth Cube. At least in summer there are ice-free fjords (if you disregard the occasional huge iceberg calved off the ice wall) that allow the stone-hulled Sendereven ships access to the city of the Altinae.

One of the two version of the Kalikos myth have that entity shake or melt off the frost on the edge of the summer sky, pushing the dome back south, but given the daily rotation of the sky dome, that myth doesn't conform to Gloranthan stellar mechanics in the least.

 

Edited June 11, 2019 by Joerg

[Lordabdul]

2 hours ago, Joerg said:

I would expect some concave curvature of sea level towards Magasta's Pool rather than the convex one you showed.

Oh yeah good point -- although in my Glorantha it might just be very local, i.e. the curvature inverses only, say, 200 km from the edge of the whirlpool (Magasta's Pool itself seems to be less than 500 km in diameter). When you go "over the bump" and see it, it's too late!

2 hours ago, Joerg said:

Still, visibility from sufficiently high places is strongly dependent on haze rather than curvature.

Yeah I mentioned that atmospheric effects play a big role. As far as I understand, there are even light refraction effects that commonly let you see things that are technically just behind the horizon? I haven't looked too much into that.

2 hours ago, Joerg said:

Cute, but no. The glacier does cover significant parts of the Hudaro ocean, but it doesn't stand a chance to remain cohesive on Sramak's River which surrounds the Earth Cube.

Ah right I forgot Sramak's River. I still stand by my joke  

[PhilHibbs]

24 minutes ago, lordabdul said:

Yeah I mentioned that atmospheric effects play a big role. As far as I understand, there are even light refraction effects that commonly let you see things that are technically just behind the horizon? I haven't looked too much into that.

Getting somewhat off topic here, but this Flat Earth debunk video mentions the difference due to refraction, and this shot shows that the lower parts of the building are squished due to atmospheric lensing.

[Julian Lord]

I've always preferred the (false) old RW theory that vision is provided by rays from the eyes that bend upwards into the Sky and towards the source of light that's the Sun.

 

[Lordabdul]

Oh yeah, that reminds me that one super-hand-wavy way of explaining a horizon in a fantasy flat world is to just say that light doesn't work the same way it does in the real world, and that it bends in a way that makes ships disappear behind the water in the distance and so you still need someone in a crow's nest to spot them better.

At that point, it's really about choosing whether things appear to behave more or less like on Earth (and then you can hand wave the explanation if needed), or whether they perceivably differ, in which case I'm afraid to end up in debates about night-sky navigation with my players, which is why I'm leaning towards "it's the same as on Earth as far as you can tell" (especially since the players will already have enough stuff to deal with, like magic and spirits and traditions and whatever).

[PhilHibbs]

37 minutes ago, Julian Lord said:

I've always preferred the (false) old RW theory that vision is provided by rays from the eyes that bend upwards into the Sky and towards the source of light that's the Sun.

And of course Farsee makes those rays go more straight so you can see further.

[JonL]

This post on flat-world visibility from the Dormal thread seems relevant:
 

On 2/11/2019 at 4:08 AM, Brootse said:

 

Yeah, in my Glorantha, I've used the meteorogical visibility ratings, and for the human visibility acuity 1 arc minute.

Visibility ratings:

Very poor: less than 1,000 metres

Poor: between 1,000 metres and 2 nautical miles

Moderate: between 2 and 5 nautical miles

Good: more than 5 nautical miles

And in really good conditions, you can see tens of kilometers on sea, or even over hundred on mountains.

1 arc minute means that you can see 1 m tall object at 3.5 km in perfect conditions, which means that you could on really clear days see a trireme at 50 km distance.

A single arc minute is also very low definition. Legibility of text drops off below 18 arc minutes, and more basic symbols' detail falls off below 16. That's perhaps less relevant to the Closing, but meaningful for spotting distances generally. For example, a 5m high emblem on a sail or large flag will have details visible at around a kilometer, and basic shape and contrast at about double that. Context might still let you reasonably infer more information from less detail, such as in cases where only a certain group used big red circle designs, or similar.

Crows' nests are still useful on an uncurved sea, as you can see over the swells, fog, or other nearby ships.

Edited June 11, 2019 by JonL

[Joerg]

33 minutes ago, lordabdul said:

At that point, it's really about choosing whether things appear to behave more or less like on Earth (and then you can hand wave the explanation if needed), or whether they perceivably differ, in which case I'm afraid to end up in debates about night-sky navigation with my players, which is why I'm leaning towards "it's the same as on Earth as far as you can tell" (especially since the players will already have enough stuff to deal with, like magic and spirits and traditions and whatever).

Night Sky navigation is difficult. There are easy indicators for the east-west direction, but you don't get parallax to aid you with triangulation, as the Sun Path goes more or less right overhead, and the Polar Star sits right overhead, too, wherever you are on the surface world. There are no good ways to get latitude or longitude from watching the sky, although you get a very precise clock if you have a clear sky and good reference charts. That tells you zilch about longitude, though, as the sun rises at the same moment in all of Glorantha (despite those curvature effects - Yelm's gaze is straight). It also rises due east and sets due west, whether you are on Ygg's Isles or in the Sea of Worms. Only in the Outer World you may tell whether you are south or north of the Gates of Dusk and Dawn, or inside or outside some of the sky domes. But then, distances in the Outer World become different.

The Red Moon may be the only object in the sky that changes its position depending on where you are in the world, but only the angular position - it always appears at the same elevation angle as long as you are outside the Glowline, and at a different one inside the Glowline. That means you can calculate the Lunar radiate you are on, but not where on that radiate you are. You would have to guess whether you're north-northwest or south-southeast of Teleos, for instance.

[Lordabdul]

It's a bit ironic that I'm basically saying "I don't want to have to debate star-based navigation with my players because I want to get on with the adventure" but then I end up debating it here anyway

4 minutes ago, Joerg said:

the Sun Path goes more or less right overhead

I thought I read somewhere that the sun path was actually varying between seasons... something about the trajectory arching northward in the cold seasons, and back towards the centre of the sky dome in the hot seasons? (which sounded to me like basically the mirror of what we get on Earth's northern hemisphere). Did I misunderstand that?

Edited June 11, 2019 by lordabdul

[Ali the Helering]

MGDV - from time to time I play around with the idea that the lozenge is a 'map' in a Great Ocean on a Ringworld. Some interesting celestial ramifications and the possibility of Pierson's Puppeteers and Kzinti on the plains of Pamaltela! 

What's not to love???? 😇

[Bill the barbarian]

16 minutes ago, Joerg said:

and the Polar Star sits right overhead, too,

Worth a mention although it is only a niggling detail, unless this has changed (oh it's so hard to keep up) the pole star has not been at  zenith since the world broke.

Cheers

[Joerg]

57 minutes ago, Ali the Helering said:

MGDV - from time to time I play around with the idea that the lozenge is a 'map' in a Great Ocean on a Ringworld. Some interesting celestial ramifications and the possibility of Pierson's Puppeteers and Kzinti on the plains of Pamaltela! 

How are you going to get sunrises and sunsets on a Ringworld? Against a sky rotating on you once a day?

Ringworld has eternal noon, switched off by the shades.

Quote

What's not to love???? 😇

The problems with the workings of the Gloranthan sky. For a normal space solution, you'd need to have a rotating flat surface always pointing towards Pole Star. That surface would have to orbit or be orbited by Yelm while keeping its orientation towards Pole Star. And the other Sunpath and southpath planets, too. Then you need a way to insert Orlanth's Ring on the same rotation speed as the surface, against the stars in the background. And you need a stationary Red Moon, and after 1624 a Boat Planet that follows the Celestial River (avoiding the celestial city, otherwise running up from Lorian and down on the opposite side, with a period I cannot recall having read in a canonical publication).

Something like this cold be engineered, but not as part of a Ringworld. A Culture torus might have something like this as a gimmick.

 

1 hour ago, lordabdul said:

It's a bit ironic that I'm basically saying "I don't want to have to debate star-based navigation with my players because I want to get on with the adventure" but then I end up debating it here anyway

That's the nature of this list. But then, we aren't your players, and this isn't cutting into your facetime with your players.

Quote

I thought I read somewhere that the sun path was actually varying between seasons... something about the trajectory arching northward in the cold seasons, and back towards the centre of the sky dome in the hot seasons? (which sounded to me like basically the mirror of what we get on Earth's northern hemisphere). Did I misunderstand that?

Yes, there is the Kalikos wobble in the Sky Dome axis which drags along all the stellar objects except the Red Moon (and possibly Zenith and Stormgate). The effect could be up to 17 degrees in either direction, IIRC. In a first approximation, that's directly overhead, you'd need to measure this against a perpendicular lead to see this. The incline is the same throughout the Inner World, whether you are in North Pent or the Nargan Desert. That means this doesn't help you with navigation, although it will tell you whether it is summer or winter regardless of temperatures.

You will never experience a noon with the sun fairly low in the sky - Glorantha is a tropical world in this regard, regardless of climate.

 

44 minutes ago, Bill the barbarian said:

Worth a mention although it is only a niggling detail, unless this has changed (oh it's so hard to keep up) the pole star has not been at  zenith since the world broke.

Well, "Zenith" is a different stellar body, and it is not in the highest point of the sky dome.

Pole Star passes trough the highest point of the sky dome on the equinoxes in his slow wobble north- amd southward. It has started to wobble since Umath lifted the Sky Dome off its hinge on the Spike, but the real wobble started when Jagrekriand smashed Umath into the northern Pillar, starting a northward tilt that was reversed by Kalikos at some point, then went into the other direction until  the Skyspill into the Nargan put the balance the other way. Or something like that. In the Grey Age/Silver Age, the sky wobbled like this above the patchwork ruins of the Gods War, and continued to do so with the birth of Time.

Over the course of a year, the sky dome makes either 293 or 295 rotations around Pole Star, approximately one per night, but with an annually repeating precession.

 

Edit: Since Glorantha is a goddess, I expect the usual curvaceous illustrations of Kalin Kadiev to apply. Ample bosom and buttocks, etc...

Edited June 11, 2019 by Joerg

[Ali the Helering]

1 hour ago, Joerg said:

How are you going to get sunrises and sunsets on a Ringworld? Against a sky rotating on you once a day?

Ringworld has eternal noon, switched off by the shades.

The problems with the workings of the Gloranthan sky. For a normal space solution, you'd need to have a rotating flat surface always pointing towards Pole Star. That surface would have to orbit or be orbited by Yelm while keeping its orientation towards Pole Star. And the other Sunpath and southpath planets, too. Then you need a way to insert Orlanth's Ring on the same rotation speed as the surface, against the stars in the background. And you need a stationary Red Moon, and after 1624 a Boat Planet that follows the Celestial River (avoiding the celestial city, otherwise running up from Lorian and down on the opposite side, with a period I cannot recall having read in a canonical publication).

Something like this cold be engineered, but not as part of a Ringworld. A Culture torus might have something like this as a gimmick.

 

That's the nature of this list. But then, we aren't your players, and this isn't cutting into your facetime with your players.

Yes, there is the Kalikos wobble in the Sky Dome axis which drags along all the stellar objects except the Red Moon (and possibly Zenith and Stormgate). The effect could be up to 17 degrees in either direction, IIRC. In a first approximation, that's directly overhead, you'd need to measure this against a perpendicular lead to see this. The incline is the same throughout the Inner World, whether you are in North Pent or the Nargan Desert. That means this doesn't help you with navigation, although it will tell you whether it is summer or winter regardless of temperatures.

You will never experience a noon with the sun fairly low in the sky - Glorantha is a tropical world in this regard, regardless of climate.

 

Well, "Zenith" is a different stellar body, and it is not in the highest point of the sky dome.

Pole Star passes trough the highest point of the sky dome on the equinoxes in his slow wobble north- amd southward. It has started to wobble since Umath lifted the Sky Dome off its hinge on the Spike, but the real wobble started when Jagrekriand smashed Umath into the northern Pillar, starting a northward tilt that was reversed by Kalikos at some point, then went into the other direction until  the Skyspill into the Nargan put the balance the other way. Or something like that. In the Grey Age/Silver Age, the sky wobbled like this above the patchwork ruins of the Gods War, and continued to do so with the birth of Time.

Over the course of a year, the sky dome makes either 293 or 295 rotations around Pole Star, approximately one per night, but with an annually repeating precession.

 

Edit: Since Glorantha is a goddess, I expect the usual curvaceous illustrations of Kalin Kadiev to apply. Ample bosom and buttocks, etc...

Wrt Ringworld, I did say that the celestial ramifications were interesting, not simple.  It requires a Realist rather than Mythicist analysis, and relies upon the idea that Glorantha has suffered many impacts both from outside the Ring (eg the Crater, Kero Fin) and from inside its plane (eg Magasta's Whirlpool). The Darkness is the result of secondary impacts triggering forest fires across the local arc etc. 

As so often with Glorantha the mental reward is not from the initial theory but rather from calculating possible outcomes and then seeing how it integrates with the wider mythology. 🤔

[Sir_Godspeed]

1 hour ago, Joerg said:

Edit: Since Glorantha is a goddess, I expect the usual curvaceous illustrations of Kalin Kadiev to apply. Ample bosom and buttocks, etc...

This is really neither here nor there, but Kadiev's illustration in the Glorantha Sourcebook features an illustration of the Celestial Court that includes Glorantha, and she appears as a Lotus-positioned ascetic with hair radiating out above the Spike. I believe the flavor text of that illustration says something about it being from the City of Wonders or something, so make if it what you will. Maybe Belintar's view is an outlier.

Gata, however, is both represented as (iconographically) square and (anthropomorphically) *very* curvaceous.

[Julian Lord]

4 hours ago, lordabdul said:

I thought I read somewhere that the sun path was actually varying between seasons... something about the trajectory arching northward in the cold seasons, and back towards the centre of the sky dome in the hot seasons? (which sounded to me like basically the mirror of what we get on Earth's northern hemisphere). Did I misunderstand that?

The Sky Dome wobbles back and forth seasonally.

Annoys the heck out of every single Mostali trying to fix the World Machine ...

[Bill the barbarian]

4 hours ago, Joerg said:

Well, "Zenith" is a different stellar body, and it is not in the highest point of the sky dome.

Pole Star passes trough the highest point of the sky dome on the equinoxes in his slow wobble north- amd southward. It has started to wobble since Umath lifted the Sky Dome off its hinge on the Spike, but the real wobble started when Jagrekriand smashed Umath into the northern Pillar, starting a northward tilt that was reversed by Kalikos at some point, then went into the other direction until  the Skyspill into the Nargan put the balance the other way. Or something like that. In the Grey Age/Silver Age, the sky wobbled like this above the patchwork ruins of the Gods War, and continued to do so with the birth of Time.

 Over the course of a year, the sky dome makes either 293 or 295 rotations around Pole Star, approximately one per night, but with an annually repeating precession.

 

Edit: Since Glorantha is a goddess, I expect the usual curvaceous illustrations of Kalin Kadiev to apply. Ample bosom and buttocks, etc...

Is that Joerg's way of saying"Gee Mr. Barbarian, you were right*? :)

* (mostly)

Cheers

[Lordabdul]

Here's the 2 proposed "bulging cubes" with magasta's pool inserted at rough scale! (what I inserted is actually around 700 km wide... 500 km for the whirlpool itself, plus a 100 km "margin")

As before, Earth is curvature first, double curvature second.

 

Edited June 12, 2019 by lordabdul

[Joerg]

4 hours ago, Bill the barbarian said:

Is that Joerg's way of saying"Gee Mr. Barbarian, you were right*?

* (mostly)

Cheers

On the rumor scale, you earned a B for "basically true, but wrong in the specifics." I took some exception against "since the world broke" - while Umath's birth changed the workings of the World Machine and maybe broke Mostal, the world remained pretty much unbroken.

Also, if the Copper Tablets are correct, the stars emerged at the same event Umath crashed into the northern pillar, which means that Pole Star never sat immobile in the top spot of the Sky Dome.

[Bill the barbarian]

37 minutes ago, Joerg said:

On the rumor scale, you earned a B for "basically true, but wrong in the specifics." I took some exception against "since the world broke" - while Umath's birth changed the workings of the World Machine and maybe broke Mostal, the world remained pretty much unbroken.

 

I do believe I have been Joerged!

Is this statement:

A Too awful to contemplate?
B basically true but wrong in the specifics?

Cheers

 

[Joerg]

20 minutes ago, Bill the barbarian said:

I do believe I have been Joerged!

BTW, that rhymes to "irked"

20 minutes ago, Bill the barbarian said:

Is this statement:

A Too awful to contemplate?
B basically true but wrong in the specifics?

I'd give it a M. Yeah, you got the Joerg experience.

Don't you hate it when multiple choice questions don't contain any right answers?

[Ali the Helering]

When it comes to the ridiculous Dara Happan claims as to the original and unmoving centricity of Yelm, I always go back to Zerel Fan. 

Their sun god had three early manifestations, Early Light, Rising Orb and Victorious Zenith. The sun had to rise before it reached its zenith. QED. 

Thanks Greg.

YOUR Glorantha Really Did Vary!