Finding the World's Economic Center of Gravity(nbviewer.ipython.org)
nbviewer.ipython.org
Finding the World's Economic Center of Gravity
http://nbviewer.ipython.org/github/djv/world_economic_center/blob/master/map.ipynb
7 comments
This is interesting because I was thinking about a somewhat related sort of statistical measure (trying to determine average times over repeated measurements of a wall clock) and happened upon this: https://en.wikipedia.org/wiki/Mean_of_circular_quantities
I think this particular trend could benefit from some insights therein, they would help avoid the issue of hovering around the center of the 2d coordinate plane. If you use 3d coordinates on the sphere, your center of gravity will appear on the unit sphere and the radius can be used to determine how strongly it favors that particular area.
As an example of where this could add confusion, if you have a huge economy in the US and a huge economy in China, you basically are canceling out the values with the current axes, if you shifted them, it may change the plots dramatically with the purely 2d representation.
I think this particular trend could benefit from some insights therein, they would help avoid the issue of hovering around the center of the 2d coordinate plane. If you use 3d coordinates on the sphere, your center of gravity will appear on the unit sphere and the radius can be used to determine how strongly it favors that particular area.
As an example of where this could add confusion, if you have a huge economy in the US and a huge economy in China, you basically are canceling out the values with the current axes, if you shifted them, it may change the plots dramatically with the purely 2d representation.
This is essentially what The Economist did. It results in the 'center of mass' being in the northern hemisphere, somewhere near Greenland, because the two biggest economies are both in the hemisphere but at opposite longitudes.
Interesting, do you have any ideas how to apply this to finding the average of multiple points on a sphere?
Maybe project the x/y coordinates onto a unit sphere, then find the center of mass in spherical coordinates, then convert those spherical coordinates to the relevant 2d coordinate system you're using, discarding the radius (but keeping it for the information it provides).
See also: https://en.wikipedia.org/wiki/Directional_statistics
See also: https://en.wikipedia.org/wiki/Directional_statistics
That's exactly how it's done, for what it worth (though you use 3D cartesian coordinates instead of spherical coordinates).
Treat each point on the sphere as a 3D unit vector, weight as appropriate, and the center of mass is the sum of all of the vectors.
Treat each point on the sphere as a 3D unit vector, weight as appropriate, and the center of mass is the sum of all of the vectors.
One way would be to search for points on the sphere which have the closest (weighted) average distance to all the points. Or some similar metric like that.
So instead of finding a point in the middle of the Earth, it would find a point that is geographically closest to the US and China.
So instead of finding a point in the middle of the Earth, it would find a point that is geographically closest to the US and China.
This is equivalent to what The Economist did. Average of the cartesian points, extend along the radius to the surface.
A lot of discussion about the "right" way to calculate a result, without discussing why.
My guess is something along the lines of an assumption that income is roughly equal to spending so you want "the" place on earth thats ideally suited to building your food processing plant or refrigerated warehouse to minimize total air shipping costs assuming everything will ship by air.
I'm not really sure what meaning this "center" has beyond that unless strange assumptions are made, like income is perfectly proportional to capital market size, or income is perfectly proportional to military power or something.
There is very fast alternative discrete rather than continuous method to calculate "a center" that scales very poorly as resolution increases (which doesn't matter because the input data is junk wrt sig figs and truth) which is just to make a giant mesh network of clusters of a discrete billion bucks at a certain lat/lon or whatever, then add an imaginary center that can move that optimizes itself to a minimum distance from all other existing points. You'll get into huge arguments about high enough res and metastability and rounding errors and local maxima/minima but you can ignore all that, given that as an engineering estimate the input data is junk, you just figure the total distance for each points at all whole degree intersections (88 W 43 N aka Chicago-ish, next 89 W 43 N, then 90 W 43 N ... ) so you figure 360*180 (actually more like 178 than 180, and a +2 for polar reasons) and then sort the 64000 or so results and pick the lowest.
Using the discrete method, if you figure there's 64K (16 bits) degree intersections on the globe and maybe 1024 (10 bits) or so clusters of a billion bucks, that is maybe 26 bits worth of distance calcs and additions, figure 3 bits per decimal digit for "less than 10 digits of operation" and we have multicore processors that run about that many ops per second (if you have the memory and IO bandwidth LOL, which you won't), that followed by a very modest sort, so this is quite tractable and has a resolution probably higher than the sig figs in the input data you're feeding it. No, it doesn't scale well to a higher resolution, and thats OK because the input data doesn't warrant it.
The whole topic smells of a really bad dotcom "brain twister" interview question for a CRUD app designer or CSS jockey. Back when that was how it was decided who was a good or bad one based on solving riddles and stuff.
My guess is something along the lines of an assumption that income is roughly equal to spending so you want "the" place on earth thats ideally suited to building your food processing plant or refrigerated warehouse to minimize total air shipping costs assuming everything will ship by air.
I'm not really sure what meaning this "center" has beyond that unless strange assumptions are made, like income is perfectly proportional to capital market size, or income is perfectly proportional to military power or something.
There is very fast alternative discrete rather than continuous method to calculate "a center" that scales very poorly as resolution increases (which doesn't matter because the input data is junk wrt sig figs and truth) which is just to make a giant mesh network of clusters of a discrete billion bucks at a certain lat/lon or whatever, then add an imaginary center that can move that optimizes itself to a minimum distance from all other existing points. You'll get into huge arguments about high enough res and metastability and rounding errors and local maxima/minima but you can ignore all that, given that as an engineering estimate the input data is junk, you just figure the total distance for each points at all whole degree intersections (88 W 43 N aka Chicago-ish, next 89 W 43 N, then 90 W 43 N ... ) so you figure 360*180 (actually more like 178 than 180, and a +2 for polar reasons) and then sort the 64000 or so results and pick the lowest.
Using the discrete method, if you figure there's 64K (16 bits) degree intersections on the globe and maybe 1024 (10 bits) or so clusters of a billion bucks, that is maybe 26 bits worth of distance calcs and additions, figure 3 bits per decimal digit for "less than 10 digits of operation" and we have multicore processors that run about that many ops per second (if you have the memory and IO bandwidth LOL, which you won't), that followed by a very modest sort, so this is quite tractable and has a resolution probably higher than the sig figs in the input data you're feeding it. No, it doesn't scale well to a higher resolution, and thats OK because the input data doesn't warrant it.
The whole topic smells of a really bad dotcom "brain twister" interview question for a CRUD app designer or CSS jockey. Back when that was how it was decided who was a good or bad one based on solving riddles and stuff.
I guess this is somehow related, world population by latitude and longitude, which you can use to of course derive center.
http://blog.andersen.im/2013/05/interactive-map-of-world-pop...
http://blog.andersen.im/2013/05/interactive-map-of-world-pop...
It seems surprising that by the outbreak of WW1, the economic centre of gravity was hovering to the west of Greece. In other words, all of the European imperial powers scrambling over Africa and the New World still produced less combined output than Asia, Oceania, the Middle East and eastern parts of Europe and Africa.
Yeah I found that curious too
[deleted]
The problem with this chart is that it's heavily biasing the "center of economic activity" towards the center of the Map. The reason it's constantly above Europe is that Europe is pictured between Asia and America.
If you center the Map over America you'll see the center of economic activity being America. If you center it over Asia, it'll be Asia.
Therefore this map does not contain much more information than "Greenwich lies in the middle".
If you center the Map over America you'll see the center of economic activity being America. If you center it over Asia, it'll be Asia.
Therefore this map does not contain much more information than "Greenwich lies in the middle".
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.)
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.
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.
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."
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.
[deleted]
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 (;
- Center of all landmass
- Center of all arable land
- Center of population
- Center of population weighted by income
Especially if viewed over time, this would give a better sense of the meaning of this data.