New Worlds: The Map Is Not the Terrain

(This post is part of my Patreon-supported New Worlds series.)

Maps come in many shapes, sizes, and colors. But they all share one thing in common: they are, at best, approximations of the thing they represent.

This is inevitable. Even the most high-resolution satellite image is not going to capture square foot of ground, every leaf in that square foot, every cell within a given leaf. Nor is it going to tell us the temperature in that locations, the direction of the prevailing wind, or what polity controls that spot. And we don’t want it to, because there’s a point at which the data becomes too abundant to be useful. A good map is one that serves the purpose at hand, whether that’s helping you navigate to your destination or pinpointing the relative locations of important sites.

The majority of the maps we use nowadays are planimetric, meaning that they show the landscape as if seen from directly overhead, i.e. a bird’s eye view. This isn’t a new thing — there’s a clay map of Nippur from 1400 B.C. that shows a planimetric view — but it’s certainly made easier by modern technology. Surveying equipment lets us measure distances precisely, rather than just eyeballing them like we used to.

selection from the Agas Map of London

Many city maps, though, especially in Europe, tended to show a three-quarter view (as if the site were viewed from a nearby hilltop), or a compromise that disregards the usual rules of perspective. That view can show something left out of most planimetric maps, which is the topography of the landscape: where there are hills and valleys, tall buildings and so forth. A map that focuses on depicting the rise and fall of the terrain is called a relief map. At its most complex, this can be the kind of map table you may have seen in TV and movies, where it’s sculpted to mimic the landscape in three dimensions, but it can also be rendered in 2D with the use of contour lines.

Hoover Dam contour map

For orientation, you’re probably accustomed to the convention that puts north at the top of the map, but that’s far from universal. Medieval European maps sometimes put east at the top — which is why we call this “orientation,” oriens being the Latin word for “east” — while Chinese maps tended to orient toward the south. Artic maps nowadays put the pole at the center, while maps of coastal cities might put the sea at the top, regardless of which way the coastline runs. If a city straddled a river, by contrast, that might be at the bottom of the map, producing an aesthetically pleasing vista.

At larger scales, you run into the problem of distortion. Residents of Discworld have it easy; those of us living on a more or less spherical planet have to grapple with the question of how to project that onto a flat surface. The familiar Mercator projection distorts things rather wildly the further you get from the equator — I used to wonder as a kid why Australia was a continent and Greenland wasn’t, thanks to the warping effect at the edges. On the scale of a city that’s not a problem for day-to-day usage, but it can become a real issue when you need to build precisely-engineered networks of roadways or similar infrastructure.

And you shouldn’t discount the psychological effect of that warping. Mercator’s projection makes European countries look larger than they are relative to equatorial ones, which just so happens to support the political dynamics of colonialism. Nowadays we generally hold the unspoken assumption that a map ought to be geometrically accurate, but maps do many things, and replicating precise spatial relationships is only one of them. They can also represent political ideologies — for example by magnifying the size of the favored land, or by placing it at the center of the image, or both. This even shows up in the question of orientation, for example by arranging text such that it appears right-side-up when a central location (such as a capital or palace) is above that spot.

The question of how to represent locations like capitals or palaces is another major issue in map-making. The modern trend is to go abstract, with simple dots for cities and towns on a road atlas (often with relative size indicating population) or square outlines to depict particular buildings. A service like Google Maps may get more representative, with a fork and knife to mark a restaurant or a tiny plane to mark an airport. Older maps were often very pictorial, drawing whole piles of structures to represent cities, masses of trees to represent forests, and so on.

But of course it depends on what you want your map to depict. As I said before, it can’t possibly contain everything; all maps are made with a purpose in mind, and the most useful ones tend to focus specifically on what’s needed for that purpose. This, for example, is a map from the Marshall Islands that records information about currents and wave patterns, for use in teaching navigation. Sailors still make extensive use of navigational maps that detail the topography of the land under the water. But a political scientist wants a map that will show national boundaries, while an economist wants to visualize the flow of goods and money, and an ornithologist is concerned with bird populations and migration patterns.

Which means that the style of a map will tell you a lot about the person who made it and how it’s intended to be used. A map that puts the capital of a kingdom at the center and depicts every other city as much smaller (regardless of population) might include enough detail about roads to let you know when you need to take the north fork to get to your destination, but its primary purpose is to make a statement about power. A kid’s scribbled map that ignores major landmarks but faithfully records every fruit tree you can scrump from and where the best spots are to catch fish will both express the personality of that kid, and help keep you fed. A military map will concern itself heavily with topography and fortifications, while a climate map that uses a less-distorting projection and puts the south at the top is making a distinct statement about our current world and where it’s headed.

For a while there was a backlash in fantasy against putting maps into books, but I think that’s a very great shame. Because both the style of the map, and what it includes and leaves out, can be a very clear signal of what kind of story you’re getting into.

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New Worlds: The Map Is Not the Terrain — 16 Comments

  1. Pingback: New Worlds: The Map Is Not the Terrain - Swan Tower

  2. I always like maps in books!
    It’s the thing I miss most in ebooks, a map I can read.
    Maps in ebooks are generally not scalable the way the text is – it’s one picture shown at the size of my screen, and when I zoom in to / enlarge the text the map stays the same and doesn’t ‘zoom in’ or enlarge and become scrollable.
    As I read a lot on my phone (since my e-ink screen reader broke), mostly in quite a large font size, that means the map is generally quite unreadable for me, unless a link to a zoomable map on a website is provided.

  3. Your remark about the importance of the type of map in a fantasy novel is fascinating. Now I want to see an epic fantasy use Marshall Island maps at the start of each chapter.

    • My patrons this week got a photo of the Wieliczka Salt Mine’s attempt to solve the problem of mapping a three-dimensional complex in physical media. Which is still Euclidean, but hard enough! The non-Euclidean thing . . . someday I want to do a thing set in a building sort of modeled on the Winchester Mystery House, but with actual Euclid-defying geometry; unfortunately, this has to date run aground on the problem of figuring out how to map it for my own use. 😛

      • Ouch.

        It’s easier when it’s a larger region and saying things such as — this route takes a day when this one takes a month and this one never ends, and if you try to argue they should take the same amount of time, no one will argue back. Or rescue you. (I did that in Madeleine and the Mists. It helps that there’s a trackless forest about the strange paths.)

  4. Other problems with the Mercator projection include the edge/center issues, certainly with early versions. Neither is it a coincidence that Berlin is the visual “golden mean” center… nor that the greatest size/distance distortions were French colonies in Africa.

    Early aviators really, REALLY struggled with “traditional” maps for long journeys, because in one day they could travel much farther than the carefully worked out celestial corrections allowed! (And that might well matter a-dragonback…) One wonders if that affected Amelia Earhart.

    • To be fair to Mercator, apparently he was well aware of the problems and advocated for/used other projections.

      Interesting point about aviators! I hadn’t thought of it, but yeah — if they’re flying over terrain covered by multiple conventional flat maps, then the discrepancies that won’t bother a land traveler very understandably become a problem for them.

      (I do like that something I read — I think it was the Wheel of Time — commented on the characters getting the equivalent of jet lag when they began regularly teleporting around the continent.)

      • In a class about maps, they showed us a map where what looked like a straight line between the US and the UK was longer than the Great Circle flight, which did a big arc, and then showed how a map with the North Pole in the center showed it much more reasonably.

        • Azimuthal projections preserve great circles through their center as straight lines, and I assume a near-center circle is nearly a straight line, too. The gnomonic projection preserves *all* great circles as straight lines, though can’t even represent a whole hemisphere.

    • “Neither is it a coincidence that Berlin is the visual “golden mean” center… nor that the greatest size/distance distortions were French colonies in Africa.”

      I don’t know what most of that sentence even means or refers to. But Wiki:

      “It became the standard map projection for navigation because of its unique property of representing any course of constant bearing as a straight segment.”

      Mercator has a navigational purpose, and is the only map that fulfills that purpose. So any political effects are in fact a coincidence. Looking at the math section, I don’t see any parameters that could be varied, as you might find in some more general projection families. Or, from the page on map projections:

      “North-south stretching equals east-west stretching (sec ?): The east-west scale matches the north-south scale: conformal cylindrical or Mercator… In the first case (Mercator), the east-west scale always equals the north-south scale.”

  5. Fascinating, as all things involving maps tend to be. Will we ever see a map of Lady Trent’s travels, Marie?

    I don’t know if I ever told you this, but a couple of years ago I curated an exhibit of fantasy maps, from our Maps of Imaginary Places Collection (which I *think* is the largest of its kind anywhere). It was really popular, underscoring your point about emotional connections between maps and story.

    https://oaktrust.library.tamu.edu/handle/1969.1/160507

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