Saturday, May 18, 2013

The True Size of the North

Map by Tear ©
On the right is the map of Westeros that we are all familiar with. Each time we open a book from the A Song of Ice and Fire Series we are greeted with this immediately recognizable continent. Over this land, conveniently shaped to fit on two consecutive pages, I have enjoyed following the adventures of some of my favorite characters in literature.

With the publication of The Lands of Ice and Fire, us fans have been offered a greater view into the world. As a geographer by training, I quickly snatched it up. Maps are a way that I (and many other readers I know) are able to deeply immerse ourselves in the worlds of fiction, fantasy or otherwise.

As anyone who has taken a cartography class knows, however, maps are never a true representation of the world. Not only can we not include every detail of the world on map, but due to the curvature of the Earth and the flatness of paper/computer screens, no map can accurately display the location of all features. Every map will have either size, distance, direction, and/or shape distorted at least a little bit. (For more information on how this works, check out this ugly but informative page by UC-Boulder.)

This lead me to wonder how the "real" world of A Song of Ice and Fire might be different than they are displayed in the books. This webpage consists of my attempts to explore this question.

Assumptions

I have made the following assumptions regarding the world of ASOIAF in my analysis. I have tried to justify them the best I can, but they are still somewhat arbitrary, and deviation from these assumptions will produce different results.


  1. Westeros is a continent on a spherical globe. I'm not sure how much evidence there is in the book for different shapes of the world (flat vs. round). For all I know, the world in this series might be flat. However, this would make my analysis pointless so I willfully ignore the possibility.
  2. The size of the planet on which the series takes place is roughly the same size as Earth. If we are to take the TV show as canon, then we know the planet has at least the same gravity (and therefore mass) as Earth. 
  3. The Wall is positioned at 60° North Latitude. I chose this latitude because it is roughly where the southern extent of permafrost exists in Canada and continental Asia. We know The Gift is arable land, and areas north of the wall have regular snow even in the summer. 
  4. All canon maps have used the Mercator projection. This projection often gets a bad rap because it exaggerates the size of high latitude features, like Greenland and Canada. However, it is fantastic for one thing: navigation. Which, of course, is exactly what it was invented for, and why I would be used in a fantasy book. If Martin says a character is moving east, then we should be able to assume that she is moving right on the provided map. It is also safe to assume that The Wall runs directly east-west, and would only be shown on a map going left to right. These things are only possible in Mercator-like maps.
Analysis

So lets start with the world as we know and love it, in a Mercator projection.



Note the straight lines of longitude and latitude. This is a characteristic of cylindrical projections like Mercator. We have defined this map's projection, and we know the continents' latitudes. We can can compare the size of this world with our own.


The longitude selected here is arbitrary (in fact these two maps have different longitudes). But from an American perspective, the placement of Westerosi regions is very interesting. The North begins at almost the exact place as the Canadian border. Dorne, which is ethnically and climatically different from the rest of Westeros, sits near the Mexican desert. Kings Landing is at almost the exact same latitude as Washington D.C.

If we know that northern latitudes have exaggerated sizes in Mercator maps, than we should be able to assume that northern Westeros isn't really as big relative to Valyria and Sothoryos as it appears. Generally, mid to high latitude continents are displayed with conical projections. Most maps that show exclusively the US or Europe have this type of projection  This would also be the appropriate choice for displaying Westeros and Essos. The following is a map in an Albers Projection, which distorts shape but keeps area the true.


We can see that this is indeed the case. The North once seemed to be about the same size as the rest of the realm, and now it appears to be closer to a quarter of that size. (I have cut off the eastern part of Essos because this projection was only intended for use in North America. Far east becomes too distorted to be useful.) 

And again, we can see how these changes between projections are analogous to the same on Earth.


While "Up" on the page is no longer directly north, we get a better idea of how the size of land masses compare.

We can make the same comparison between different projections of Westeros exclusively:

 

As you may have guessed, the map on the left is Westeros as we are used to it (in Mercator), and on the right is Westeros in a conical projection.

Let's use this as an opportunity to see how big Westeros really is. I used relatively rudimentary techniques, and I'll try to update these numbers more accurately in the future. But here are following approximations:
  • The North: 415,000 sq. mi/1,070,000 sq. km
  • The Reach: 380,000 sq. mi/984,000 sq. km
  • The Realm: 1.6 million sq. mi/4.1 million sq. km
This means that The North is still the biggest region in the Realm, but not by as much as appeared before.
To compare, The North is roughly the same size as Bolivia. The Reach is roughly the same size as Egypt. And the Realm (Westeros south of The Wall) is a tad bigger than India, and just over a third of the size of the continuous United States. That means it is also roughly the same size as Europe minus Russia.

We now know how big Westeros is, and how its size compares relative to its world. However, we still have not seen a "true" representation of the series' lands. Albers Projection distorts the map like Mercator does, just in a different way.

The follow map attempts to display the continents as they might be seen from space. 


This gives us an even different look at world. We are able to imagine how the continents might wrap around the globe. Interestingly, if I am correct that the wall is at 60°N, then the cartographers of The Lands of Ice and Fire stopped drawing their map right at the equator.

Finally, if you are curious to see how these continents really look on a globe, below I have embedded this map draped over a Google Earth model. You can zoom and fly around to you heart's desire. Currently there is just the outline of the continents, but I would like to add more details in the future.

17 comments:

  1. The size of the world is not necessarily the same as earth to have to same gravity. Size and density determine surface gravity, so the planet could be smaller or larger depending on density. Also since the world of ASoIaF takes place on a world with no regular seasons it must have no axial tilt (though there must be something affecting it).

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    1. GRRM has already said his seasons were magically driven. Little bit of a cop out. However I also read a report stating that if it wasn't magically driven it may just be part of a binary star system.

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  3. The map of Westeros is not a Mercator map.

    Using your analysis, you come to a total size for the North of 415,000 miles. Yet the scale bar of Westeros is in fact the Wall, which is located at the very top of the North, and it is confirmed to be 300 miles in length.

    Using the Wall as measuring stick, it is clear that the North is well in excess of 1 million square miles in size.

    The flaw, I think, in your approach, is the assumption that longtitude and latitude even exist as concepts in Westeros. The more likely answer is that the map of Westeros is simply strung together from hundreds of local maps.

    For example, locals will know that the Dreadfort and Karhold are say 300 miles apart as the crow flies, and draw the local map accordingly. Similarly, locals in the South will know that King's Landing and Storm's End are say 300 miles apart and draw the local map accordingly. Over millenia, all these dozens of local maps were added together to fashion a rough map of Westeros as a whole.

    Again this is shown as valid when Stannis states that Deepwood Motte is 300 miles from Winterfell as the crow flies. This is exactly to the scale of the canon map, where the length of the Wall exactly matches the distance between Deepwood and Winterfell.

    The key principle is that different points on the North/South axis do not align according to a fictional concept known in our world as longtitude. Instead, the map is based on absolute distances.

    What this will mean is that 1000 miles east-west in the North, equates to 1000 miles east-west in the South. But if it was transposed onto a globe, then the North would cover more degrees of longtitude than the South.

    Sure, navigation would be thrown totally haywire, but this would be consistent with the fact that almost no one wants to sail out of sight of land (as depicted by the amazement at Euron's "daring" feat of leaving sight of the shore to strike the Reach by suprise in Feast for Crows).

    To conclude, the canon maps are not Mercator maps, but simply actual depictions of distance that have no relation to consistent longtitude.

    The length of the Wall and the resultant size of the North proves that. 300 miles at the Wall remains 300 miles when measured between Deepwood Motte and Winterfell and remains 300 miles when depicted between King's Landing and Storm's End.

    May 19, 2013 at 2:21 AM

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    1. Yeah, I totally agree that the maps in the book aren't really Mercator. The maps, like you said, are more than likely an amalgamation of local maps. I would argue that these local maps would try to preserve direction at least as much as distance, however. Anyway, 'amalgamation of local maps' isn't a defined projection, so I had to pick something because I thought this would be a fun thought exercise. Mercator seemed (to me) like a good choice, there are other reasonable choices.

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    2. An interesting exercise would be to try and transpose the flat Westeros map onto a globe, but retain the absolute distances as they currently are depicted. In my mind, this would expand the North over a number of extra degrees of longtitude compared to the South.

      This would retain the North's size, which is really beyond dispute. For example, it is 300 miles from Eastwatch to the Shadow Tower. It is also 300 miles as the crow flies from Deepwood Motte to Winterfell.

      These distances are given in the books, repeatedly. Clearly, therefore, the scale of the map remains the same, whether you go North or South. So the North is really as big as they say in the books.

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  4. As Westeros is analogous to Europe, and Essos to the Eurasian continent, would it be possible to get a map projection over that part of the world rather than the US and the Atlantic Ocean? I'd like to see if Dorne stretches down to Morocco, if Essos has overlaps with Turkey and Central Asia, and the like.

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  5. First of all, this was a nice post. The idea is intriguing, and I enjoyed reading through it.

    But I have to bicker :)

    I find the assumption that "the wall is at 60 degrees north" problematic. Change it to a higher latitude, and you end up with bigger continents - which would be more consistent with the often heard "Westeros is about as big as south america".

    Why I think you could (or should) place the wall at a higher latitude: if you take europe and not america for figuring out at which latitude the wall might be, with your argument ("south of it arable, north of it not much so"), you could go about 10 degrees further north - farms exist in Norway as far up as 70 degrees north. Now, an east-west stretch of 300 miles (length of the wall) at 70 degrees latitude on a mercator projection looks much longer than the same stretch at 60 degrees. So if you place the wall at a higher latitude, the continents become bigger. Quite a bit bigger.

    Generally, you could just choose any latitude for the wall so that you end up with a Westeros that is about the same size as south america (these are the only two really good geography clues we have, right?). You can do that because with the weird seasons and such, it doesn't really matter whether you place the "south is arable land, north less so" border at 60 or 65 or 70 degrees latitude.

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  7. Lars Tiede

    The Wall is arguably already too far North at 60 degrees North.

    Your reference to farming at 70 degrees North in Norway is interesting, but consider that the Arctic Treeline mostly ends at 66 degrees North, with some rare trees up to 70 degrees North in certain warmer than normal areas. The Haunted Forest extends 600 miles North of the Wall, and therefore the Arctic Treeline has to be taken as the edge of the Haunted Forest, placing the Wall hundreds of miles south of this line.

    Furthermore, even if there might be farming in northern Norway today, 70 degrees North was most certainly not considered good farmland in the Middle Ages where farming technology was far more primitive. In fact, almost all farming in Medieval Scandinavia was in its extreme southern parts.

    In my view 60 degrees North is the absolute northern limit for the Wall, with 55-58 degrees also possible.

    Regarding the South America comparison, this is to the entire continent of Westeros, including the unknown part of it that lies beyond the Wall. Hence the location of the Wall is irrelevant to the size comparison to South America. Also, this comparison is generally accepted to be to the LENGTH of South America, rather than to its surface area, as Westeros is mostly much narrower than South America, and hence is unlikely to match its surface area.

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  8. You do realize that your main two assumptions are greatly flawed:

    1) The size of the planet on which the series takes place is roughly the same size as Earth. If we are to take the TV show as canon, then we know the planet has at least the same gravity (and therefore mass) as Earth.

    Correctly assumed that gravity & mass of earth are the same, but size and distance from whatever star the planet is orbiting is hugely up for grabs. This planet could be two times further from their star than the Earth is from the Sun. Also the fact that the planet could easily be far more dense or less dense than Earth could greatly change the size of the planet easily.



    2) The Wall is positioned at 60° North Latitude. I chose this latitude because it is roughly where the southern extent of permafrost exists in Canada and continental Asia. We know The Gift is arable land, and areas north of the wall have regular snow even in the summer.

    Following on from the last point, permafrost could potentially exist much further north or much further South. What we do know as canon however is that:

    "The North is the largest region, nearly as large as the rest of the regions combined." - http://bit.ly/19Q1EX8

    This means that these figures need to be tweaked (or adjust the map to give this layout):

    The North: 415,000 sq. mi/1,070,000 sq. km
    The Reach: 380,000 sq. mi/984,000 sq. km
    The Realm: 1.6 million sq. mi/4.1 million sq. km

    This is what you should use as your main assumption. You did great work, don't get me wrong, I just like having great discussions with people I think are equally educated and scientifically precise.

    Basis: Use the ratio of North:Westeros as 2:1 and place Dorne on the equator and you should find the proper size of Westeros & then the rest of Westeros.

    (Nb. go ahead and use the earth as the same size as before, but the line of permafrost leave unknown at the moment)

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    1. Beyenne,

      Yeah, like I said my assumptions are somewhat arbitrary. I chose and Earth sized planet because 1. it would make this analysis way easier and 2. I haven't really seen any evidence that it would be different. If the planet has the same gravity, and it is made out of similar materials to earth (we know iron is plentiful), then we can assume they are at least close to the same size. I'm not sure what distance to the sun has to do with this.

      On to your second point, yeah, again 60N is somewhat arbitrary. I thought that it seemed reasonable though, noting my justifications above. There are good reasons to move it both south and north, but I had to pick something. The concept that the north is as big as everything else combined comes from Robert, was trying to convince Ned and likely exaggerated, if even he knew the actual size of things. Likely not.

      You make fair points, and again, to make this work I had to pick some values for my assumptions. I think the values I chose are reasonable, but reasonably disputable.

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    2. Why do you suppose that the size mentioned by Robert was exaggerated?

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  9. Just a curiosity from a map creation outsider: what method do you use to to make an accurate projection? I mean, how do you adjust proportions? What is your workflow.. do you use fixed mathematical formulae or some kind of geometrical interpretation?

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    1. Thankfully, all of the projection calculations are done by a GIS software, in this case ArcMap. The software comes preloaded with hundreds of different commonly used projections. All I did overlay a map of Westeros onto a map of Earth, at at latitude I deemed appropriate. I told ArcMap that both maps were in the Mercator projection, and that I wanted to see it in a conic projection (in this case, Albers. If your interested, this is what is going on behind the scenes: http://www.epsg.org/guides/docs/g7-2.pdf

      Thankfully, I don't have to bother with that.

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