***** Warning: Rhythm of War spoilers below *****

While working on some updates to our "Interactive Map and Timeline of Roshar" I came across something that intrigued me regarding Rosharan units for distance.

EDIT: I'm coming back to this a few months later because I've just received my 2021 TWoK leatherbound and, to my surprise, the scale on the Alethkar map (referenced below) is gone. That's right. The original Alethkar map had a north arrow and a scale. The 2020 TWoK leatherbounds have the north arrow removed but the scale remains. Apparently they made some kind of last minute change that wasn't included in the 2020 printings because in the 2021 TWoK leatherbounds both the north arrow and the scale have been removed. Weird! (there's also a white shadow behind the text on the map, making the blue font stand out much brighter--that's actually the more noticeable difference)

I'm leaving this entire post as-is. That scale was really the heart of my speculation below, but I'm not surprised it was apparently wrong. Turns out my first "final thought" below (I think the scale on the Alethkar map is probably just an oversight, and that it's wrong...) was dead on. The scale was our best reference to what a Rosharan mile might be, without that there's much less substance here.

That said, I quoted a lot of references to miles in the text. So perhaps when I have some time I'll circle back and make some fresh guesses!

Some background info first

@Paleo was working on a tool to measure distance on the map by clicking two points. In the process, we realized that the grid overlay we were using was not correct. @Otto Didact was the first to realize that our world map of Roshar is a "azimuthal equidistant projection", which is an interesting globe projection where all points are at a consistently proportional distance from a chosen center point. It is perhaps best well known for it's use in the United Nations emblem, where the North Pole is used as the center point. You don't have to use one of the poles as your center point, though that's the most common use. For example, the one on the right, centered on Taipei. It's a great projection to use for Roshar because the the central area of the map looks accurate, as if seen from space. The distortion is worse along the edges. Roshar conveniently has all of it's land in one corner of the globe, so the distorted parts (of the full map) are off in the middle of the sea on the other side of the planet. The map we get in the books of course is just a cropped portion of the full projection.

Anyways... We were looking into this distance measurement tool and realized the calculated coordinates for points toward the edges of the map didn't match up with the grid we were using. Oops! Conveniently, Oathbringer came with a beautiful map of Roshar that included the planet's grid. We just need to adjust things to match this map. And come to find out not only was our grid wrong, but the calculations weren't quite matching the Oathbringer grid either. We never did figure out what was wrong with the grid, so we'll have to make a new one from scratch. As for the calculations, it turns out we needed to pick a better center point. It's hard to say precisely what the center point of the projection should be. The IDEA behind the projection, is that a great circle passing through the center coordinate will appear on the projection as a straight line. We know the center point must be on the "prime meridian" of the map, because it's the meridian that appears as a straight line, but we don't know the right latitude. I used my globe of Roshar to draw great circles through different latitudes on the "prime meridian", and then sketched horizontal lines across the map looking for a match. Through this I found that the center point must be somewhere around 16 or 17 Rosharan degrees south of the equator. Paleo realized that 16 Rosharan degrees is the center point of the image file, so we went with that.

Distance Discrepancy

I've used my globe, linked above, to measure distances in the past... But I was never entirely sure of how accurate my projection for the globe was. (plus we realized the globe website wasn't quite calculating distance right through this) After working through everything above, I was quite confident with what we had. Our new grid, calculated mathematically was a pretty solid match to the one used on the Oathbringer map. We know the circumference of the planet is about 22,110 miles. So we should have distance measurements that are as accurate as possible.

With that done, I wanted to check something that I've always wondered about.... The Map of Alethkar in The Way of Kings has a scale on it. So I was curious if our measurements would match this scale. I wasn't expecting it to match actually, because I've been under the impression that the scale was wrong. There is a new version of this same map in Oathbringer, and it has the scale removed. That has given me the impression the last few years that they were retconning some map details. Indeed, the TWoK version also includes a "North" compass heading that conflicts with the Oathbringer world map, and which the OB Alethkar map also removed. Curiously, however, the 10th Anniversary TWoK leatherbounds DID remove the compass but DID NOT remove the scale. So I was curious about what's going on there... Is it right or wrong? An oversight? Something else?

One problem right off the bat is that it's not clear how the scale is meant to be used. Alethkar covers a sizeable chunk of the planet's surface, so a single linear scale can't really be highly accurate for the entire map. So we have to realize there's some margin of error built in. But I did find that the map of Alethkar overlays quite nicely onto the Oathbringer map of Roshar. From there, it was very easy to count pixels on the world map and compare them to known distances. For the azimuthal equidistant projection that we have, any line radiating from the center point as a constant scale. So given the circumference of the planet, we know the distance from the center point at 16 Rdeg South to the intersection of the prime meridian and the equator. If we count the number of pixels on the image, we have our distance/pixel relationship. Now I can draw a straight line (or line segment) at any angle through the center point, count the number of pixels to figure what the distance is. Meanwhile I can overlay the Alethkar map and count the number of pixels for the scale (in the same map). Here's what I got:

So the Alethkar map's scale was for a total distance of 300 units. Presumably miles. Presumably Rosharan miles I should say, because it's an in-world document, which I'll refer to as "Rmiles" from here on out for clarity. Note also my use off Rdeg for Rosharan degrees--they use 200 Rdeg in a circle.I should also note that the "22,110 mile circumference" that we have is NOT entirely clear whether that's Rosharan miles or "real" miles. I tend to get the feeling that they use real miles, internally, and so it's probably that. But we don't know. For all we know, the two are equivalent.

Anyways, what I've done in the image above is mark 300 mile long line segments. We know these are accurate because that's simply how the projection works. And they DO NOT match the scale on the Alethkar map by a significant margin. In fact, I found the scale to be 95% longer. Almost double in length. So what do we make of this?

The very first thing I should say is that this could simply be an error. There are WoBs which clearly indicate that Brandon and his team had NOT entirely nailed down the details of the world map at the time The Way of Kings was written. Isaac notes in that particular one that the continent is 4000 miles across. It's currently at ~6400 miles across if measured through the center point. Depends where you measure from exactly, but it's definitely more than 4000 miles now. The scale WAS included in the leatherbound... but this could simply be an oversight. An error seems highly plausible to me.

Rosharan Units of Distance

But what if it's not an error? Then what do we make of this? You COULD take it as the discrepancy between "real" miles and Rosharan miles. What if the Alethkar map approximates 300 Rmiles while the segments I've drawn are just 300 real miles? Remember that the scale is... a bit ambiguous... The trick of measuring pixels like I did only works along lines radiating from the map's center point. The scale's pixel measurement that I did is not quite a radial line segment, and any measurements on the Alethkar map that are perpendicular to these radial lines will vary in consistency from left to right. That is to say, the scale of vertical measurements distorts as you move across the page from left to right. Where does the 300 mile scale apply? Unclear. But the margin of error shouldn't be SO far off. I'd be surprised if it's more than +/- 5%.

So let's run with this notion that Rosharan miles are about 1.95 times the length of a real mile...

1 Rmile = 1.95 miles = 1.95 x 5280 feet = 10,296 feet.

I can't help but notice how close this is to a metric-like multiple of 10 as we would expect from Rosharans. Indeed, we know that they use ten inches per foot. Or rather, I should say they use 10 Rinches per Rfoot. And for the number of feet per mile we're really more interested in Rfeet per Rmile. BUT we know that Rosharan feet are just a BIT longer than real feet, and Brandon's use of the word isn't meant to imply something highly unintuitive. This is pretty straight forward though. If we imagine 10,000 Rfeet per Rmile we get:

1 Rmile = 1.95 miles = 1.95 x 5280 feet = 10,296 feet = 10,000 Rfeet

1 Rfoot = 1.03 feet = 12.36 inches = 10 Rinches

1 Rinch = 1.24 inches

In Khriss's essay on Roshar she DOES say that their units of measurement are larger than the cosmere standard equivalent units. And with these assumptions it's precisely what we get. Miles that are about twice as long as "normal". Feet that are perhaps something like 5% longer than "normal". (which matches this WoB--5% on top of 6'-4" adds 4 inches) Inches that are ~25% longer than "normal". (emphasizing once again that this is all very approximate, based on me measuring pixels on a world map... There's room for some variance.

Textual Issues

Unfortunately, there are a few references in the text that conflict a bit with this interpretation. BUT there is one that, in my opinion, affirms it. And it's possible that these references could be adjusted in future leatherbound versions as none of them are in TWoK.

Quote

TWoK Interlude I-1

The Purelake extended in all directions, hundreds of miles wide, its glassy surface perfectly transparent.

The Purelake is a little over 1000 miles across and 400 miles wide. For 2X long Rmiles, that would be 500 and 200, so this fits nicely.

Quote

WoR 69

“Actually, I’m wondering how the trunk of a stumpweight tree got here,” she confessed. “They can’t possibly be native to this area of the Shattered Plains. Too cold out here. It might have grown along the coast, but a highstorm really carried it that far? Four hundred miles?”

For 2X Rmiles, it looks like the eastern coast is only 150 Rmiles away. Could say Shallan's sense of geography is off... but with her photographic memory I think this is pretty unlikely.

Quote

OB 5

Perhaps he could have flown all the way to Hearthstone if he'd been more practiced with his powers. As it was, he’d traveled over a thousand miles in half a day, but this last bit—ninety or so miles—had taken an excruciating three days.

The distance from Narak to "not quite Hearthstone" looks to be about 1700 miles. That would only be about 850 Rmiles. Though maybe Kaladin's judge of distance just isn't quite right. Or maybe with error it's just barely over 1000 Rmiles.

Quote

OB 55

Soon after he left through the Oathgate, everyone would slowly start to lose their powers. They’d be gone in an hour or two. Kaladin had to be relatively near—Sigzil had placed their maximum distance from him at around fifty miles, though their abilities started to fade somewhere around thirty miles.

This one actually AFFIRMS the idea of 2X Rmiles in my opinion.

I'm measuring the diameter of the Shattered Plains as about 170... The exact edges aren't clear, so it depends where you measure from. But it's definitely over 150 miles. That means the radius is 75 miles minimum. In the Words of Radiance finale, we see Lopen's arm heal back in the warcamps while Kaladin is presumably somewhere around Narak. Lopen was easily more than 50 miles away, and certainly more than the 30-mile limit where their powers supposedly diminish.

But for 2X Rmiles, the Shattered Plains has a radius of perhaps about 40 Rmiles, give or take. That fits MUCH better with Lopen's healing. I'd go so far as to say that if this "theory" about Rosharan miles is wrong, this reference is an error.

Quote

OB 64

“If you’ll all excuse me, I have to prepare for an appointment with an emperor a thousand miles away.”

This is Dalinar going to visit Azir.

Azir is less than 800 miles from Urithiru, so he's just plain wrong about that distance regardless. Though I suppose overestimating 800 miles would be more reasonable than for him to say "a thousand" when it's only ~400.

Quote

OB 83

“The Shattered Plains ?” Yokska asked, aghast. “But Brightlord, that’s hundreds and hundreds of miles!”

This is correct either way.

Quote

OB 93

“I didn’t know of those until Kal told me about them. I used a portal between realms. Cultivation’s Perpendicularity, they call it. On your side, it’s in the Horneater Peaks.”

“That’s hundreds of miles from here,” Adolin said.

This is correct either way. (spoken from Shadesmar in the vicinity of Kholinar)

Quote

OB 108

He looked back at her map and pointed. “Thaylen City,” he said. “If we continue this direction, we’ll eventually pass just north of it.”

“ ‘Just north’ in this case meaning more than three hundred miles away from it, in the middle of a bead ocean.”

[...]

And the fact that they had to somehow escape from a ship in the middle of a sea of beads, reach the shore, then hike two hundred miles to reach Thaylen City.

These distances seem to refer to real miles. The distance from Thaylen City to the coast of the bead ocean where they landed is about 200-300 miles. So this doesn't jive with 2X Rmiles.

Quote

DS 1

Seeing him left her speechless. He lived thousands of miles away from her. How was he here? She stammered, searching for what to say.

Reshi Isles is thousands of miles either way... Well, for 2X Rmiles it's not quite 2000 miles I think, but seems reasonable enough for her to say.

Quote

RoW 3

Flying. It had worked. Not just in maneuvers and tests on the Shattered Plains, but on a real mission, flying hundreds of miles.

Works either way.

Quote

RoW 27

A thousand men at a time stood for their turn at the Oathgate, where Radiants transferred them to Azir. With a flash—a ring of light rising around the plateau—both men and banners were off, sent hundreds of miles in a heartbeat.

Works either way.

Quote

RoW 111

He was flying. Covering a hundred miles in less than half an hour.

This is Dalinar flying from their base in Emul to Ishar. It's not entirely clear where teir base was (or precisely where Ishar was). I think this works either way though, eyeballing the area.

Final Thoughts

I think the scale on the Alethkar map is probably just an oversight, and that it's wrong...

BUT I really like this idea for the units. I think it's safe to assume that a Rosharan foot must be similar in length to a foot. If Rosharan miles are supposed to be closer in length to miles, there's not a great way for Rmiles to be a 10X power of Rfeet. Again, assuming feet are fairly similar, using 1000 Rfeet per Rmile gives an unreasonably short Rmile. I think the best alternative idea is that they use 5000 Rfeet per Rmile. That means you just need Rfeet at 6% longer than a real foot to give Rmiles the length of miles. Increasing the foot size a bit more gives Rmiles a bit longer as well. Using a multiple of 5 like this has precedence in their units. We know that there are 50 Rosharan minutes in a Rosharan hour, rather than 100. So this seems reasonable... But using 10,000 Rfeet per Rmile is a really nice alternative that seems to fit with the scale on the Alethkar map!

That said, there ARE definitely some quotes (mostly in Oathbringer) that would need some revisions if this is the intent. (and one that needs to be revised if it's not)