Comments on: Center of Population

By: Jon

Jon — Mon, 07 Jul 2008 19:20:17 +0000

I found the center of population on the surface of the earth to be at 30.89N,76.53E. I found this by calculating the weighted average distance a given point was from all the people on the earth until I found the smallest average distance. I did this at a resolution of 1 degree latitude and 1 degree longitude around the entire earth. Then I increased the resolution and decreased the search area to get the values I got. It turns out that the average person is 5032 km from this point. I also recorded the average distance for all 65,000ish points, so I could make a map showing the average distance everyone is from a given point, but I’m not sure how to make the map. I also found the center of population based on a center of mass calculation and found that, assuming everyone weighs the same, the center of mass is 637 km under 15.68N,75.60E.

By: caffeine effects on babies

caffeine effects on babies — Mon, 07 Jul 2008 17:07:19 +0000

caffeine effects on babies…

Sorry, don’t agree 100% with you on this!…

By: Jonathan Birge

Jonathan Birge — Fri, 27 Jun 2008 06:50:22 +0000

200 comments for an idea which is stupid for the following reason: with your definition, the point is not neccesarily unique on a periodic surface. For example, imagine a world uniformly distributed with people. All points fit your definition. Certainly, in our current world, a lot of points probably do to a decent approximation. It’s a dumb idea, certainly far dumber than 200 comments would warrant. Let’s move on, people.

By: Shantanu Bhadoria

Shantanu Bhadoria — Tue, 24 Jun 2008 14:09:06 +0000

I don’t think the center of mass is the correct stuff to use for the location of school problem.
Simple reason being that all the heavier kids would get more weight in the equation.
other reason being that I wasn’t particularly weighty as a kid.
of course that equation might help in reducing the sum of work done to get to school by the kids.

By: John

John — Sun, 22 Jun 2008 20:53:49 +0000

There’s a problem with just laying out the skin of a sphere and finding the center of mass on that flat plane. With a sphere (or any 3-D object for that matter), The center will adjust depending on how you unfold the object.

To find the center of mass, we still need to treat the earth as a 3-D object. I think we should just find the population of individual latitudes (up to whatever level of precision you prefer), and then longitudes. The spot with the most populated latitude AND longitude is the center of mass.

By: LovelessGent

LovelessGent — Sat, 21 Jun 2008 21:56:54 +0000

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By: Ishamoridin

Ishamoridin — Mon, 16 Jun 2008 06:53:22 +0000

Noticing that there is a copious number of comments already, I’ll just hope that I’m not repeating someone else here ^.^

if you calculated the sentre of mass of the earth as a sphere, then projected it on to the surface by moving it away from the core, would that not be the population desnsity?

If this is wild and preposterously untrue, I blame lack of sleep and/or caffeine ¬.¬

By: derf

derf — Wed, 11 Jun 2008 15:16:04 +0000

This is called a “Fréchet Mean”, and is a fairly standard part of Riemannian geometry. There’s a gradient descent algorithm for computing it, which is basically the method described by CJ above, where the solution from the previous iteration becomes the new “north pole” for the next. See, for example, Karcher’s classic article on the algorithm http://doi.wiley.com/10.1002/cpa.3160300502 or Kendall’s proofs on existence and uniqueness http://scholar.google.com/scholar?cluster=16807413806928015094
Probably the best general introduction to the concepts for computer scientists I know about is Tom Fletcher’s PhD thesis: http://midag.cs.unc.edu/pubs/phd-thesis/PTFletcher04.pdf
Read chapters 2 and 4.

By: Johan

Johan — Wed, 11 Jun 2008 10:46:24 +0000

I’ve been reading the site for a while and this thread a while ago and an idea suddenly just now came to me.
For the sake of the argument, assume the earth is a perfect sphere (or transmorgrify it into a sphere), and say it was a thin hollow and massless shell and the people point-masses positioned on that shell, and placed in a uniform gravitational field on a surface so that due to uneven balance from the point-masses it would reposition itself (rotate due to the frictionless nature), wouldn’t the contact-point between the sphere and the surface then be the center of mass of the population.. so to speak?
Well.. cheers.

By: derf

derf — Tue, 10 Jun 2008 17:25:16 +0000

This is called a “Fréchet Mean”, and is a fairly standard part of Riemannian geometry. There’s a standard gradient descent algorithm for computing it, which is basically the method described by CJ above, where the solution from the previous iteration becomes the new “north pole” for the next. See, for example, Karcher’s classic article on the algorithm http://doi.wiley.com/10.1002/cpa.3160300502 or Kendall’s proofs on existence and uniqueness http://scholar.google.com/scholar?cluster=16807413806928015094
Probably the best general introduction to the concepts for computer scientists I know about is Tom Fletcher’s PhD thesis: http://midag.cs.unc.edu/pubs/phd-thesis/PTFletcher04.pdf
Read chapters 2 and 4.