
Finding the World's Economic Center of Gravity - jsm386
http://nbviewer.ipython.org/github/djv/world_economic_center/blob/master/map.ipynb
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xvedejas
I wonder how the center of economic activity would compare to other measures.
For instance:

\- 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.

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codezero
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](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.

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djvv
Interesting, do you have any ideas how to apply this to finding the average of
multiple points on a sphere?

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codezero
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](https://en.wikipedia.org/wiki/Directional_statistics)

~~~
jofer
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.

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VLM
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.

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Sami_Lehtinen
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-population-
by-point-latitude-and-longitude/)

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magikroundabout
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.

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pitt1980
Yeah I found that curious too

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waps
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".

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analog31
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.

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archgoon
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."

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analog31
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.

