# Talk:Center of population

There are quite some mathematical (and otherwise) commentary about calculating the Center of population at http://blag.xkcd.com/2008/05/01/center-of-population/#comments that would be great to incorporate here! For one thing, there appears to be several useful definitions that give different center points. —Preceding unsigned comment added by 193.77.156.40 (talk) 15:48, 5 September 2008 (UTC)

Strongly disagree! There are centers of population around the world that are not US-centric. -- Brhaspati\talk/contribs 14:25, 12 May 2008 (UTC)

## Center of world population

I am removing the following statement "The centre of world population is in the extreme north of the Indian subcontinent.", because there is no culture-neutral way to determine the borders of the map. 2D maps only work for a territory that does not curve back on itself; we could consider most countries, even continents without taking the curvature of the Earth into account, but we can not examine the Earth as a whole. If we use the map currently seen in Western Europe and the Americas, the Atlantic is in the middle, and the population centre could be in India; older maps in North America put the Americas in the centre, splitting Eurasia, meaning there would be a different centre of population, as all 2.5 billion people living in Asia would be on the extreme left of the map, but all 500 mio. people in Europe would be on the extreme right. The map currently used in much of Asia, however, I believe places Japan/the Pacific in the middle, meaning there would be a third set of borders, and a third population centre. samwaltz (talk) 20:42, 13 April 2008 (UTC)

I'm reinstating the "Center of world population" section, as it is a very natural question to ask on this topic. There is indeed a culturally neutral way to determine it, which was described in the reference that was listed in the earlier version of the section before it was deleted. Essentially, the question to ask is "What is the point on the surface of the Earth whose average distance to all the people on Earth is the smallest?", or, more loosely, "What place on Earth is closest to everybody on average?". Keep in mind that the answer deals only with the globe, and not with a two-dimensional projection of the Earth's surface. As a result, the answer is independent of which projection is used or where it is centered. There are however a few caveats: one may get slightly different answers depending on both the data and the method. The granularity of the data is important: using country-wide totals will give different answers from region-wide or city-wide totals. The distance metric used is also important: using a geodesic distance along the surface will give different answers from a Euclidean distance in a straight line (tunneling through the Earth as needed). The reference listed before used a granularity of 1000 km, and measured distances along the surface of the Earth. If anyone has different results using different data/metrics, please add them to the article. -- Brhaspati\talk/contribs 14:17, 12 May 2008 (UTC)

## Removed statement

I've removed this statement from the article: Centroids can be 3D, but for statistical purposes only 2D calculations are published by statistical offices. for not quoting a reference on who specifies such rules, and on whether such rules are universally followed or not. Please quote appropriate references when reinstating. -- Brhaspati\talk/contribs 14:23, 12 May 2008 (UTC)

That wasn't really a controversial statement. Technically, the center of population using a 3D centroid would be *in* the earth and not *on* it. It was just saying that surface distances are used. DavidRF (talk) 04:04, 21 July 2008 (UTC)

## Credit to Daniel Dennett?

What's up with this? He "first used" the term in a paper in 1991, yet the US Census has been reporting such a thing since 1790? Doesn't make sense. We should remove this, no? DavidRF (talk) 04:08, 21 July 2008 (UTC)

• I have no idea why someone (an anonymous user) added that claim to the article. Just an Internet search alone is sufficient to show that the term was in use in the 19th century. Most likely the claim was added by some confused person with no connection to Dennett. I have removed it. --Metropolitan90 (talk) 13:41, 22 July 2008 (UTC)
Mea Culpa. This was my edit and it was apparently inaccurate. Dennett certainly talks as if he is 'inventing' the concept. And in my defense, you could interpret the statement as being about Dennett's first usage of the term rather than the terms first usage. In which case I am guilty of irrelevance, but not inaccuracy. 137.222.230.13 (talk) 17:04, 29 July 2008 (UTC)

## No references?

There was an {{unreferenced}} template on this page from August 2008, but the page now contains footnotes. I've removed the template, but am not sure if the article still lacks sufficient references. Perhaps a {{morefootnotes}} template would be in order? Robert Skyhawk (Talk) 05:55, 28 November 2008 (UTC) This article has had references... there was one for Canada, I have added 2 for Great Britain. Reinstating the refs rather than (silly?) templates would be a great idea. Victuallers (talk) 16:13, 28 November 2008 (UTC)

## Farthest point

The text below the map says "Its antipodal point is correspondingly the farthest point from everyone on earth". It's not hard to prove this, but it would be nice to have a reference for it. 89.53.112.139 (talk) 07:50, 16 March 2009 (UTC)

I believe Uruguay ends up being the costliest country to travel too, in term of time and money. Their borders are 90 pc antipodic to all of Japan, and the Canton Province. Not only is Uruguay small, but it is less stretched out, even if you compare it to Paraguay.--83.108.30.141 (talk) 23:55, 20 July 2010 (UTC)

## Center of population versus centroid

"For the particular case of flat maps, the center of population could also be defined as a center of mass (centroid) of the population of the area of interest." Well, you could define it that way, but then it would be a different point. The centroid does not minimize the average distance, but the average squared distance of all the inhabitants. Same difference as that between mean and median in one dimension. --Jmk (talk) 11:04, 21 September 2009 (UTC)

The same confusion appears in the country-specific examples. Among the 10 countries mentioned, three had no citation, and two I could not verify (UK cites an article I could not access, Japan cites a webpage in Japanese). Of the five that I was able to check, only Finland's point is indeed claimed to be the geometric median ("Weber's point"). Sweden's was the intersection of median latitude and median longitude (which is different). Australia, Germany and USA had centroids (which is again different). — Seems that these different "population centerpoints" are constantly confused with each other. Perhaps this article should be supplemented with a paragraph that explains their difference. --Jmk (talk) 12:32, 29 September 2009 (UTC)
I found a very nice paper [1] (Mark P. Kumler & Michael F. Goodchild: The population center of Canada - Just north of Toronto?!?) that clearly explains the three different definitions (and notes that they were confused already in the 1920s). --Jmk (talk) 09:23, 30 September 2009 (UTC)
Concerning Japan, I ran the (Japanese) source through Google Translate, and found several hints that this is also the centroid: (1) the machine translation contains the term "center of gravity"; (2) it talks about "maintaining equilibrium"; and (3) the formula given is clearly the centroid formula. --Jmk (talk) 11:36, 7 October 2009 (UTC)
According to the Japanese page it's getting closer and closer to Kyoto. - Cy21 (talk) 14:08, 1 March 2010 (UTC)

Concerning the main image, I agree that the image is misleading. I'll try and make one when I get the time. Cy21 (talk) 14:08, 1 March 2010 (UTC)

## purpose of this

I clicked the link to try and find out what the purpose of a "center of population" is, but its not explained. — Preceding unsigned comment added by 70.156.220.219 (talk) 02:42, 1 June 2011 (UTC)

It's so you you know where the center of population is...Smarkflea (talk) 03:25, 1 June 2011 (UTC)

## Remove Claim Re US Census Bureau Methodology

It is claimed without citation that "one could define the centroid directly on a flat map projection; this is, for example, the definition that the US Census Bureau uses." However, the Census Bureau states "To avoid unduly complex factors in the computations, the mathematical formulae used were those that would be precise for a true sphere." [1] I have removed the claim that the US Census Bureau uses this method and re-worded accordingly.

It was not really without citation; the citation is in the article Mean center of United States population, where you can find:
the point at which an imaginary, flat, weightless, and rigid map of the United States would balance perfectly if weights of identical value were placed on it so that each weight represented the location of one person on the date of the census. [2]
That citation is still valid. We have now two conflicting claims, apparently both sourced from the Census bureau. --Jmk (talk) 13:01, 27 August 2011 (UTC)
After closer reading of [3], it still appears that the formulae are for a flat map projection. Latitudes are treated as if they were Y coordinates (on a flat map), and longitudes as if they were X coordinates (albeit corrected for the convergence of meridians towards the poles). This is really a projection to a 2-dimensional (= flat) map. It is certainly different from computing the averages in 3D. When they say "true sphere" they simply mean that the projection is done as if from a true sphere, without regard to the ellipsoid shape of the Earth. So, the article's claim "on a flat projection" was indeed correct, and honoured user Albickers's objection was based on misunderstanding of the document cited. --Jmk (talk) 13:15, 27 August 2011 (UTC)
It does seem that I was mistaken. I've reverted the change, thanks to Jmk for clarifying.Albickers (talk) 21:18, 8 September 2011 (UTC)

## Geonames for more accuracy?

Surely someone has used geonames to come up with a more accurate center-of-world-population than the CIA factbook methodology? Barry.carter (talk) 06:30, 30 April 2013 (UTC)

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1. ^ Centers of Population Computation (PDF) http://www.census.gov/geo/www/centers_pop.pdf. Retrieved 25 August 2011. Missing or empty `|title=` (help)