Coping with Minard’s non-Euclidean cartography

Charles-Joseph Minard (1781-1870) was a French civil engineer, visualization designer, and all-purpose nerd. He’s best remembered for the invention of flow maps, which show the quantities of materials, people, or traffic moving from one place to another. He also didn’t think much of North Africa, South America, or the existence of Ireland:


(Ireland added for emphasis.)

As Sandra Rendgen wrote in The Minard System,

“Minard quite deliberately and continually transgressed every idea of cartographic precision… his ‘non-Euclidean cartography’ is not the result of coincidence, incompetence, or mere negligence. On the contrary, we must consider it a clear decision on Minard’s part to treat cartography as an ‘auxiliary canvas’ on which his main story (i.e., the drama of the statistical numbers) unfolds.”

It’s easy to be appalled by Minard’s fast-and-loose approach to world geography. See this map of English coal exports in 1860:


However, if I pick up a map titled “English Coal Exports in 1860,” my goal is presumably to understand English coal exported in 1860.

I’m in design school now, and one of the first lessons I learned was the difference between activities, tasks, and goals. To paraphrase About Face, tasks and activities are what people actually do, while goals are the end condition they are trying to reach. If my goal is to soothe negative emotions, I could pick many different activities: exercise, talking to a friend, eating ice cream, and so on. If I decided to address my feelings via ice cream, I could perform the tasks of making ice cream myself, going to the grocery store, or convincing my girlfriend to bring me a pint of Ben & Jerry’s.

The (presumed) goal of this chart’s audience is to understand coal exports. The map is great for activities like seeing the wide reach of English coal, and comparing coal exports to different countries. But the shape of the world is distorted to convey that information. The map is very bad for activities like determining the location of Algeria, finding the distance between Denmark and Sweden, or figuring out the easiest way to travel between Morocco and Spain. However, those activities aren’t actually related to the goal of understanding coal exports. So did Minard really need to worry about facilitating activities unrelated to that goal?

If I focus on activities, tasks, and goals, Minard’s changes to the coastline make sense. But the idea of deliberately distorting a map makes me break into a cold sweat. Once a map is released into the wild, no one really knows what readers will try to accomplish with it. I don’t actually know my reader’s goals, and neither did Minard.

Are visualization designers responsible for background information that wayward readers might take away from our graphics? I would argue that we should take every opportunity for accuracy. If I want readers to trust some of the information I provide, I must expect them to trust all the information I provide. However, every map involves some degree of distortion, and labelling anything means obscuring something. So how can designers signal the appropriate goals for a map, without stamping COAL ANALYSIS ONLY on top?

I see three potential techniques in Minard’s work that might be useful for modern-day designers:

  • Erase the details. Take away any information that is irrelevant to the goal you’re trying to facilitate. Make it extremely difficult to even try and accomplish tasks irrelevant to the goal you have in mind.

    Consider the famous graphic of Napoleon’s Russian campaign:

    The width of the flows show the number of men in Napoleon’s army during the campaign. The brown flow shows the army during the invasion into Russia, while the black flow shows the army during its retreat. The shape of the flows correspond to the army’s route through Russia, and the labels show the places that they passed. The contrast between the widths of the flows illustrate the disastrous loss of life over the course of the campaign.

    The graphic floats in near-empty space, and is useful for a limited number of activities. It would be impossible to use the map to study Russian geography or find a route between Smolensk and Moscow. However, the modern popularity of this graphic suggests that modern readers can see the dwindling army without any greater geographic detail.

    As Rendgen points out, the Napoleon map was originally published with a map of Hannibal’s march over the alps, which did include a background map:

    It’s unclear why the Hannibal graphic is so much more detailed than the Napoleon graphic. Elsewhere in The Minard System, Rendgen suggests that Minard generally relied on his reader’s mental models of the world to correct his maps. Perhaps Minard expected that his readers would have a mental model of Spain, France, and Italy, but would not be able to fill in the details of the Russian countryside. If that was the case, he matched his erasure to the presumed knowledge of his audience.

  • Absurdity. Make the distortion so wild that the reader will discount all related information. For instance, Florida is weird, but I know it’s not this weird:
    minard_florida-01As soon as I saw Florida, I knew that I shouldn’t trust any of the geography on any of these maps. However, this tactic assumes a lot about readers: first, that they know what any given map should look like, and second, that they are paying close enough attention to catch the absurdity. I assume most people know that Africa and South America aren’t shaped like this:

    However, Africa and South America are far from the focus of this map about cotton imports before, during, and after the American Civil War. What if readers miss the absurdity cue because they are focused on the flows themselves?

  • Annotation. Add a lot of notes and labels related to the goal you’re trying to facilitate, and and leave the rest a mystery to signal your priorities. Note the (lack of) labels on this map of immigration:

    The precise number of migrants is noted on each flow, but the only geographic labels are arrival and departure points.

    Labels weren’t the only source of annotation. Minard sometimes added additional charts and tables about the focus of his maps, such as the area chart in the coal export map above. He also left narrative captions and notes about data sources and manipulation, but only for the information related to his audience’s presumed goal. His annotation indicates his priorities, and a keen-eyed reader would likely catch on.

As a designer, my first choice would be to use an accurate map. Of these three techniques, though, I lean towards erasure. Annotation and absurdity assume that the reader is paying a lot of attention to detail–an assumption I don’t feel comfortable making when I post a graphic on Twitter. Fortunately, I have access to digital world maps, opacity sliders, and an entire Internet of people ready to point out my errors. But erasure, absurdity, and annotation can highlight the intended purpose of any visualization, and help match a map to a reader’s goals.

Image sources:
Library of Congress (coal, cotton, migration), Edward Tufte (Hannibal), Wikimedia Commons (Napoleon), The Minard System (Florida).

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