Author here. I agree with your point but the map is still useful for seeing the directional trend. I took this projection because it is the usual way of plotting the world on a 2d map.

> the map is still useful for seeing the directional trend.

Isn't that also true of the original map, though?

It's not at all clear to me that your visualization is an improvement on the original. The center has moved from Scandinavia to Spain, and I can see why Scandinavia wasn't a great center, but I don't see why Spain is better. Meanwhile, your visualization depends on the projection used, which seems highly nonintuitive.

(If you go from the USA to China by the shortest distance, you go near the north pole. Calling the north pole the average of the two places may seem strange, but calling any other place the average is even stranger.)

Agreed to a point. The "middle of the map" theory only applies if you assume economic activity is relatively evenly spaced (which it mostly is). Unfortunately this representation won't tell us much about where economic activity really is.

There are better ways to represent the information presented. A 3D map would put economic activity somewhere in the middle of the earth, but you would eliminate the "starting center" bias.

3d would be pretty hard to see. But there's plenty of empty spots on the earth that are in the middle of all economic centers. Ideally bordering every economic center ... since economic activity (and land mass, which is likely why) is concentrated in the northern hemisphere, why not center the map around the north pole ? No economic activity, roughly equidistant of the 3 big centers. Sure it might not be perfect, as South Africa will effectively be counted with Europe and Australia with Japan, South America with the US (well, with California effectively), but it ought to be a bit better than this.

If that is still less than optimal, maybe try the south pole ?

Seems to me it might correct the bias seen here.

I'd try to resolve this by displaying the center of gravity in 3 dimensions. Then I could project each point to the surface if I wanted.

This was the Economist's original method.

From the article:

"There was one thing which bothered me, and I hope it bothers you too, the points from the 20th century are all positioned in or above Scandinavia which seems unlikely to be the center of anything in the world. You can find the reason for that in the caption on the McKinsey webpage. Their report looks at the Earth as a sphere and finds the economic center of gravity which falls somewhere inside the sphere. To plot it on the map, they take a radius through the center of gravity and intersect it with the surface."

That's fair, but looking at the earth as anything but a sphere is unlikely to produce more useful results. One possibility is that a center-of-gravity of wealth just isn't all that useful a measure of economic history: A major historical shift could end up being represented by a dot budging a few hundred miles in the middle of nowhere.

That's the method from the original article. It distorts the ratio between the economies in the North vs. South hemispheres.

Agree, COM in Mercator projection is even more wrong than the Economist method. If one wants to have it on sphere the only correct way to do this is by using the great circle distance. Obviously it still leaves a question what does this center of economic activity actually shows (;