Population Distribution
So i hope i can be permitted a brief excursion into geography and demography here. Today i came across this site, which describes a methodology for determining the center of population for the US. On page 2 it details a process that culminates in what is mathematically known as a "centroid", and distinguishes this calculation from that of a "median". My question is, how does one determine a median for a two-dimensional data set? Is this even possible without preselecting two arbitrary axes with respect to which the calculation is to be performed (or, for an n-dimensional data set, n arbitrary hyperplanes)? i must say though i am impressed with the mathematical precision used by the Census Bureau to perform this analysis..
In other population data news, i found this site that includes a graph showing total population at each degree of latitude. For what it's worth, you can find some really interesting demography information by going a Google image search on latitude population. The site also contains a link to a map showing population bands for every "square" degree of the globe. This picture is the closest thing i've found yet to what i'm currently looking for: that ever-elusive population map of Alaska that pinpoints settlements in the bush the same way i saw done for a map of Namibia while i was there. There's just something amazing about a map of a sparsely-populated region that can show you vast stretches where the population density is not just less than 1 but rather is exactly 0..
While i'm at it, i should tie this in to economics and policy somewhat. Since i'm spending the summer in Anchorage, i've had an opportunity to reflect quite a bit on how population patterns in the far north effect the regional power structure. For instance, i think the closest city larger than Anchorage may be Vancouver, a distance of over two thousand kilometers. This situates Anchorage to be a major regional power, both economically and politically, despite its very small population in absolute terms; it also explains why Anchorage has so much infrastructure and clout for a city of a quarter million people. So it makes me wonder how many cities in the world can make the claim that they are the largest city within a two thousand kilometer radius? i also wonder whether Anchorage can claim to be the largest city this far north, and how many cities in the world can make that claim as well..
5 Comments:
"that ever-elusive population map of Alaska that pinpoints settlements in the bush the same way i saw done for a map of Namibia while i was there."
What about something like this?
http://www.darkskysociety.org/images/gallery/usatnight.jpg
As far as I remember, they have night maps and population maps at the National Geographic Museum.
i've always been a fan of those maps. For a long time i used http://antwrp.gsfc.nasa.gov/apod/ap001127.html as the wallpaper on my computer (before i installed a map of the U.S. federal court system). While they give a good sense of where electricity is being consumed, though, they don't accurately reflect population per se. After all, Africa is the second most populous continent even though vast stretches of it look uninhabited in this image..
i was talking to The Lindsay today, and we came up with some ideas for researching this topic. First, it would be interesting to determine the maximum number of points we could place on the globe such that none were within 2000 km (or 18 degrees) of each other (there will be hundreds though), and compare that to the actual number of cities that are the largest in a 2000 km radius..
We also determined that given a spreadsheet with data consisting of population rank, latitude, and longitude, we could set up a macro that would quickly calculate the minimum distance to a larger city. What would be really interesting though would be to set up a program (perhaps in Mathematica?) that would successively run through the largest cities in the world and shade in a spherical cap around them at a 2000 km surface radius so we could watch the surface get filled in..
An interesting corollary to both these ideas is that the 2000 km radius could be adjusted to see what the effects were of using a different threshold..
i found some websites that look good to use for data:
http://www.citypopulation.de/
http://www.infoplease.com/ipa/A0001769.html
And if i wanted to shell out some cash, it looks like these would have exactly what i need:
http://www.meridianworlddata.com/
http://www.maxmind.com/app/worldcities
Seeing as how this post has become the repository for sites i find on demographic and mapping data, i figured i would add this one:
http://www.princeton.edu/~rvdb/JAVA/election2004/
Also figured i'd toss in a link to a project i did last week:
http://mathleague.org/usanim.jpg
Here's a little description of this map: First i took a map of the lower 48 states and used 24 different colors to color the states. Then i took the least populous state (according to 2000 census data) and made it a part of the largest state bordering it. Thus after step 1 there were 47 states. i repeated this process until the entire lower 48 consisted of one state, namely Texas. i found it interesting that Minnesota and Pennsylvania held out for such a long time, but ultimately i felt this diagram didn't do what i wanted it to. i'm working on some other ideas..
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