The World’s Tightest Cluster of People

By Danny Quah - 26 April 2016

In 2013 Ken Myers guessed and verified that his Valeriepieris circle – a circular region on a 2-dimensional map, centred in the South China Sea and about 4,000 km in radius – contained more than half the world’s population. More people lived inside that one-sixth of the world’s land area than outside.

Kenneth Myers’s Valeriepieris Circle

(Ken’s map appeared, uncredited, in every major aggregator site I know, and in countless news stories; it must have been viewed by scores of millions of people. Caitlin Dewey did the math explicitly; the depiction was no. 24 on the Washington Post’s 40 Maps That Explain the World, and no. 12 on Twisted Sifter’s 40 Maps That Will Help You Make Sense of the World. Robbie Gonzalez described on io9 the map’s significance.)

That representation, however, left open the question, Where is the smallest circle one can draw on our planet that contains at least half the world’s people?

I worked out (in my book-in-progress Ordering the World) an algorithm to answer that question. I addressed this question on a 3-dimensional planet, for those readers who worried about the distortion induced by the 2-dimensional projection in Ken Myers’s picture.

With the help of Ken Teoh, a remarkable SEAC summer intern (a Wharton School student at the time) this month I showed that Ken Myers’s guess turned out to be remarkably close to the 2015 optimum. Of course, populations in different parts of our planet shift over time but in 2015, using population data with 100 km resolution on Earth’s surface, the smallest circle on our planet containing a majority of the world turns out to be that circle centred near Mong Khet, in Myanmar, with great-circle distance 3,300km. That’s the conclusion. Details and code will be made available presently. But to see the result a little more clearly, here’s a 3-d interactive animation of where, if the world were a democracy, it would make decisions of global significance. (I’ve been told this animation doesn’t work on all hardware/browser configurations. I’m working to fix the problem but have not yet succeeded in doing so; apologies. If it does work for you, however, what you do is follow the link to a new webpage; click your mouse on the globe image, hold and drag to rotate; use the mouse wheel/middle button to zoom.)

PS This circle I’ve drawn differs from that Ken Myers produced. There are three important conceptual differences:

Ken’s picture stated that, there, included in his circle was more than half the world’s population. In my circle here, I ask instead, Where is the smallest circle on Earth that includes within it fraction x of the world’s population (where in my picture, for illustration, x is half – what I present here can be re-done for any x between 0 and 1). In other words, I solve a variational problem, optimizing over a parameter space that is the surface of our planet. Ken had the brilliant insight to just set down his circle. He eyeballed a map of the world and then added up the populations of countries.
Ken used entire nations – India, China, Japan, and so on – to total up his population count. I instead draw on geographical data produced by agencies that surveyed and estimated population densities down to resolutions of 100km. It is possible to go even finer in geographical space, but even at the resolution I used, the computation time on ordinary LSE computers to find the tightest cluster already took days. In my calculation, parts of countries might be excluded; in Ken’s entire countries are either in or out.
I cast a net of circles formed by radial distance on the surface of our 3-dimensional planet. Ken, bravely, drew a circle covering a geographical expanse depicted on a 2-dimensional map. A circle on a 2-dimensional projection is, of course, not a circle in 3 dimensions, and vice versa.