Why all maps are wrong

At some point, many people realise that the map they have always taken for granted is actually quite distorted in its sizes and proportions. It’s always a big aha moment when I show students that the seemingly solved problem of projecting the world as a globe onto a flat surface is an impossible task. For me, it’s a very good starting point for thinking about how quantification, mathematical models, images and visualisation in general can help us understand the world, but can also cause the most serious problems we have as society.

I have always followed the debate and seen some recurring themes. Every now and then, a piece of work focuses on a different perspective and talks about the problems that arise from it. This living document is an attempt to collect these materials. I hope it will help people find new resources and make some great work more visible.

The most accessible and shareable piece I could find is a 2016 video by Johnny Harris for Vox called “Why all world maps are wrong”:

Using a plastic globe, Harris effectively demonstrates how the “flattening” of the earth is always a trade-off between distances, sizes and utility.

The next piece is also a widely shared video that became iconic for its “Why are we changing maps?”. It’s from the series The West Wing and was broadcast in 2001:

C.J. Gregg, the White House Press Secretary, played by Allison Janney, meets with a group of socially conscious mapmakers who are on a noble mission to persuade the US President to endorse a new world map projection that more accurately represents Third World countries. They argue that traditional world maps are flawed and perpetuate inaccurate perceptions that affect societal views beyond geography. In our society, we unconsciously associate size with importance and even power. If Third World countries are misrepresented, they’re likely to be valued less. In its Don’t Look Up atmosphere, the clip shows how people in power tend to overlook or ignore the interests of an concerned (or affected) group.

The next widely circulated piece is a poster by Kai Krause entitled “The True Size of Africa” (also available on Wikimedia Commons). Krause is concerned about the misjudgement of geography by many people. He demonstrates this by taking the most underestimated continent, Africa, and filling it in with the area of the USA, China, India, Japan and all the European countries. He also coined the term “immappancy”, which he describes as a lack of geographical knowledge.

The poster has inspired many responses, one of which is the interactive version, where you can drag and drop countries into Africa. Another direct response is “The true true size of Africa” by the Economist (in the wonderful Graphic Detail section). They use a different projection than Krause, which favours equal areas between countries.

Visualisation of map distortion

A simple and effective way to visualise the distortion of all map projections is Tissot’s Indicatrix. This method overlays the world with circles of the same size. These circles are then easier to compare than the arbitrarily shaped countries. These interactive versions by Max Galka and by Mike Bostock demonstrate it. Another method is to draw a rectangular shape on a flat map and highlight the corresponding area on a globe, as in this tool by Mathigon. A third method is to use human faces as references. As early as 1921, the authors Charles H. Deetz and Oscar Sherman Adams compared four projections in “Elements of map projection with applications to map and chart construction” (page 51). Andy Woodruff created a D3.js version of this, which Jim Vallandingham used to create small multiples. And this reddit post a photograph of a face. Similar to Kai Krause’s poster discussed above, Neil Kaye’s static and animated scaling of countries to their more correct size is a good way to display the distortion.

Comparison of map projections

Besides the extensive Wikipedia article about map projections and the dedicated list of map projections, xkcd offers a humorous overview of the most popular projections called “What your favourite map projection says about you”.

The open source JavaScript library D3 (started by Mike Bostock) has not only shaped the discipline of data visualisation by making the creation of interactive graphs and charts accessible to a wide (programming) audience, but has also democratised map making on the web by releasing a dedicated d3-geo library that allows geographies to be displayed in an astonishing number of projections.

The variation in projections is perhaps most impressively demonstrated in the transitions between them, as shown in this notebook by Mike Bostock itself. How not only the projection but also the rotation, i.e. the centre point, is crucial for the final result is shown in this similar notebook called “Map Projection Transitions” by (also incredibly important for d3.js) Jason Davies. Another notebook by Mike Bostock allows you to compare two overlapping projections.

One very radical alternative projection is the Dymaxion map by Buckminster Fuller. Or the Goode homolosine projection, which is also featured in this xkcd comic. Ben Fry made a comment on Twitter on these type of projections.

Another projection is the equal-area type world map projection Authagraph inverted by Japanese architect Hajime Narukawa in 1999, which is apparently used in official Japanese school books. The Narukawa Lab created a folding paper version which allows you to physically play with the projection.

Problems when using maps in visualisations

The advantage to use a map to visualise quantities in geographies is obvious: By colouring, for example, geographies by their population numbers makes it easy to compare them. Instead of showing the numbers in a bar chart, you can directly see how, for example, countries more to the east have a higher population. It is a clear advantage to have the inherent geographical position, size and shape of an entity displayed. But what happens, when you color a map according to the political winner? This was widely discussed when a mostly red (= Republican) map of the USA was shared on Twitter with the threat “Try to impeach this.”. Karim Douïeb reacted with displaying circles scaled to the population instead of the actual county shape. An animated version can be seen on Nathan Yau’s website. More on this can be found in articles by The New York Times, Washington Post, Wired and National Geographic

Other

Tom MacWright complains how there seems to be not standard in which order to use latitude and longitude. Keith Ng used a meme to remember which describes the x- and which the y-axis.