Three Projections

03/17/21 • 30 min

urhere

Map Links

Mercator 1569 World Map [2:26]

Equal Earth Political Wall Map [9:58]

Double-sided Princeton, Gott, et al Revolutionary [18:30]

Want to visualize a 3D globe on a flat piece of paper? You have to project it first. And when you project you distort someway somehow. The three maps we discuss handily represent three different projections: Mercator, Equal-Earth, and what we're going to call "Double-Sided" in these show notes.

Mercator

Is Greenland really the same size as Africa? Mercator created his projection for a single purpose: navigation on the high seas and in particular, across the Atlantic, and this projection worked very well in getting captains and their crews from point A to point B. However, this projection is now used in online maps because of its computational ease--latitude and longitude lines form rectangles in this projection--and it isn't always good for online maps depending on their purpose.

Ever the cartographers, we also pose the question: did Mercator like or loathe writing a copyright statement on his map?

Equal-Earth

Now here's a projection that was developed just a few years ago and works well for world-scale map data. We discuss why its good--Greenland and Africa are their actual size, for one. We bring up a few other projections like Gall-Peters [13:09], Robinson [14:53], and Winkel-Tripel [15:19] too. Wet laundry is hung up to dry metaphorically as well [16:20]. Two of these have been standards at National Geographic at varying times and we believe this will probably not be the last time that National Geographic is brought up, seeing as how they make beautiful maps.

Every projection is just trying to find the perfect accuracy and remove as much bias as possible for a particular use case but it is hard because any kind of flatting of the Earth will create some kind of distortion. A bad pun occurs at [15:52].

Double-Sided

This one is also called variously "The Princeton Projection" or the "Revolutionary Projection" but it does not have a standard name as of yet. If you want to read the paper that goes with this projection, as opposed to the general audience article linked to above, click here (pdf). The article refers to this projection as revolutionary and so we discuss not only what this new projection is all about but also our opinions on whether or not it is truly revolutionary. This projection is azimuthal and typically azimuthal maps, which are distorted at the equator as that is where the most stretching occurs, are set side by side but this double-sided projection--you guessed it--they are placed on top of one another.

This was the talk of the spatial world for at least a week. Two azimuthals of the poles are not revolutionary [22:00] but technically, putting them together in this way is revolutionary [22:22]. Boundary cut off problem [23:00] is solved with this projection. A ball of clay analogy [23:20] is used to explain azimuthal projections and a party store paper lantern [26:40] analogy happens.

With maps, geography and shape really matter!

Map Links

Mercator 1569 World Map [2:26]

Equal Earth Political Wall Map [9:58]

Double-sided Princeton, Gott, et al Revolutionary [18:30]

Mercator

Ever the cartographers, we also pose the question: did Mercator like or loathe writing a copyright statement on his map?

Equal-Earth

Double-Sided

With maps, geography and shape really matter!

Previous Episode

Three Historic Maps

Babylonian Map of the World 0:21

Hereford Mappa Mundi 14:20

Catawba Deerskin Map 21:40

Babylonian Map of the World

What does this map have to do with unicorns, mermaids, Ikea, and Sharpies? Incredibly we weave it all in.

Babylon is the center of the universe in this map. It’s one of the oldest known maps, it’s a copy of an earlier map that has since gone missing, and it features a large circle that represents the Bitter River (ocean). We talk about cartographic symbology then vs. now. Do the triangles represent mountains? Did the Babylonians invent the Sharpie? Have you ever seen a mythological being that is a cross between a unicorn and a mermaid on a map? Might this be the first story map?

Hereford Mappa Mundi (T and O Maps in general)

Ptolemy, in and around 150 AD, as well as many other philosophers, showed the Earth was round. In the middle ages, T and O maps ignored this and showed the Earth as flat. T and O maps aren’t geographically accurate but the T shape we find on them usually represents the Mediterranean Sea and the Nile River, the O usually represents the Earth, and the three segments created by the T inside the O represent the three major known regions, with the center being Jerusalem.

The Hereford Mappa Mundi, a T and O map, is from 1300 AD and is notable for being printed on a very large vellum (animal skin). It survived bombings so it is nice that we still have it. The materials that maps are made on are important and scholars believe we’ve probably lost a lot of maps due to the ephemerality of those materials.

Catawba Deerskin Map

This is a fairly simple map that uses squares and circles, a symbology that we find interesting in that the squares represent European settlements and the circles represent Native Nations, connected with paths to show trade routes between the two. This map is what we would call a world view, meaning that it doesn't represent exact locations but rather a view of how those locations relate to one another for a specific purpose, in this case trade. The beautiful symbology on the map that denotes, for example, a hunting ground, is worthy of attention. Native Americans have a long mapping tradition and we are lucky that a few historic pieces, including this map, have survived to today.

Next Episode

Three Political Maps and Ethics

How do map data and map design affect bias? Does it matter if the bias is intentional or not? Honesty is the cornerstone virtue of ethics. These considerations are discussed with respect to three specific political maps but the concepts are widely applicable to most mapping endeavors.

Maps and Links

USA 2016 MTC Election Map [3:21]

Gerrymandering - The Atlas of Redistricting Article [12:24]

Victory Through Airpower 1943 Video [25:18]

USA 2016 MTC Election Map

Election time in the U.S. tends to be a fun and exciting time to watch newscasters point to maps on TV as they show election results. This particular election map shows counties in either a solid red or a solid blue color depending on the results of the 2016 presidential election. But counties vary in size greatly across the U.S. and herein lies the issue: a county that is quite large-in-size might have a few thousand people in it whereas a small-in-size county, on the East Coast for example, might have 40,000 people in it. The larger county carries more visual weight than the small one even though this does not reflect the number of voters in those counties. Historically, U.S. presidential maps were often shown this way, except for the occasional bulbous-looking cartogram, which is a type of map that distorts geography depending on numeric values within the geographic units [7:18].

Modern-day elections maps have been getting a lot better at showing the data in a more accurate way. In 2020, in particular, the U.S. election maps were highly varied. We saw some attempts at more diagrammatic maps like grids of states where each state was an equally sized square, which at least equalizes the geography. But some of the maps go further. For example, value by alpha maps use the correct geography but vary the alpha-channel, or transparency, of the blues and reds such that the color is more transparent where there are less people and more opaque where there are more people [8:50]. You can take the value by alpha map style even further by displaying the colors as a mixture of red and blue so that a place that is, for example, shown as purple, would indicate that there is more of a 50/50 mixture of votes for each party in that location.

Gerrymandering - The Atlas of Redistricting Article

Gerrymandering is the act of drawing a voting district boundary such that it includes just the right proportion of voters for a particular party to enable that party to benefit [14:34]. The Supreme Court ruled that both parties are at fault with respect to gerrymandering [15:22].

There is a concept in mapping called the Modifiable Areal Unit Problem (MAUP), where you have point data (in our case, with gerrymandering, these are really people points, or where those people live) that you are aggregating, and depending on where you draw your aggregation lines, you may get vastly different statistics out of the data [17:00]. In mapping, if the cartographer decides to re-draw aggregation units in order to make the map look a certain way that is inconsistent with the data, this would be an intentionally biased map [19:26]. Maps are authoritative documents, with the implication being that cartographers have a responsibility to ensure maps are designed as correctly as possible [21:10].

Note that the example at [23:22] would have been better if it had been laid out as splitting the Denver area into the same number of districts in both cases. If a party has a lot of rural voters it could be tempted to create districts that have small portions of the city and larger portions of rural areas (probably resulting in elongated districts) whereas a party that has a lot of city voters could be tempted to draw districts that included enough city dwellers to skew them toward that party.

Victory Through Airpower 1943 Video

This is an animated persuasive movie trailer that has a lot of visuals depicting dangerous things happening with respect to war. It evokes feelings via dramatic sounds and visuals. Maps have the power to persuade and do indeed do so in this video. The map that starts 12 seconds in on the trailer is animated in the sense that the Ken Burns effect is used to sweep the camera across an image. There are also animations on the map in the more traditional sense of the word animation; the edges of polygons move in order to draw attention to them. Note that it was incorrectly asserted in this segment that the map only animates once the camera gets to Japan, whereas in actuality it also is animated at the beginning of the camera sweep.

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