SoylentNews is people
SoylentNews
Where is the geographic center of a state, country or a continent?
It's a question fraught with uncertainty. Do you include water in your calculation? What about islands? What happens when the shoreline shifts?
The U.S. Geological Survey alluded to these complexities in a 1964 report on the centers of states, which opened by stating, "There is no generally accepted definition of geographic center, and no completely satisfactory method for determining it." More recently, various representatives of the agency have given quotes to newspapers saying much the same, hedging.
But to University at Buffalo geologist Peter Rogerson, PhD, the challenge of finding a middle doesn't mean you shouldn't try.
"There are all these people out there saying, 'There's no real good way to do this,'" says Rogerson, a SUNY Distinguished Professor of geography in UB's College of Arts and Sciences. He respectfully disagrees: "As a geographer, my feeling is that if we want to come up with a good way of defining a center, we can and we should."
In a 2015 paper in The Professional Geographer, an academic journal, Rogerson describes a new method for pinpointing the heart of a spatial entity. The approach improves on past techniques, he says, by taking the curvature of the Earth into account appropriately and by identifying geographic centers using a definition that's mathematically sound.
In late 2016, he employed his method to find the heart of North America. The result was serendipitous: According to his calculations, the center of the continent is in a place called Center, a town of 570 people in North Dakota.
(Score: 3, Insightful) by FatPhil on Saturday January 07 2017, @10:50AM
Of course, using his projection, all areas will be completely fucked up. He could of course apply a weighting function. Alas the website supposedly hosting the paper is borked. so I can't check. As things are stretched linearly, rather than summing d^2, you'd want to sum |d| instead. This has the nice property (assuming that the country's convex, which it isn't) of meaning that you could just sum d^2 of the *perimeter* (with a non-convex shape you can fix that by subtracting the d^2 of the points in the perimiter winding in the wrong direction).
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 2) by Immerman on Saturday January 07 2017, @03:36PM
How is there not a uniquely defined center of mass? Any specific distribution of mass will have a center - just find the mass-weighted average of the positions of every atom in it (or sufficiently convenient infinitesimal volumes.) It doesn't even matter where you measure from, the final result will factor in the bias and always be positioned at the same point within the object. When not in freefall it's relatively easy to find physcally by just hanging the mass from various points and finding where the vertical lines through those points would intersect. In freefall it's considerably more difficult, but the COM will still be in the exact same point.
Also, unless I'm very much mistaken, swimming in space works exactly the same way as swimming in water - you push the fluid one way, and the reactive force pushes you in the opposite direction - simple conservation of momentum. The only difference being that the fluid is air instead of water. If the mechanism was anything else, then reactionless "swimming ships" would be a thing. If you're in freefall *and* a vacuum then you can wave your limbs about however you like and your center of mass won't move an inch. Doing so would violate conservation of momentum.
As for measuring the centroid of a region on a sphere - well there you may well run up against your precise definitions. But as a simple physical solution, start with a spherical shell of uniform infinitesimal thickness, and cut away all the parts that *don't* cover your region of interest. Then find the center of mass of the resulting 3D shape, and draw a line through that point and the sphere's center. Where it intersects the surface would be the center of the shape, at least by several definitions. At the very least it would be the only point directly above the center of mass. And without having done the math, I strongly suspect that it would be colocated with the average position of al infinitesimal areas within the region as measured in spherical coordinates.
Of course if you try to work from a 2D map everything will be ugly, as you'll essentially have to reverse the horribly distorted mapping before you can even begin to do any sort of meaningnful calculations.
(Score: 2) by FatPhil on Tuesday January 10 2017, @12:08PM
You clearly know a different space from the one that I think we're floating in.
However, my point is that apparently "the concept of center-of-mass is ill-defined in non-Euclidean space" -- http://www.science20.com/hammock_physicist/swimming_through_empty_space , and that the surface of a sphere such as the earth is non-Euclidean.
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 2) by Immerman on Tuesday January 10 2017, @07:22PM
I've seen people swimming in the space station (in space). Never seen them swimming in vacuum - and as I pointed out, doing so would violate conservation of momentum.
...ah, read your linked article and see that the "swimmer" is a theoretical construct, not a human swimmer. In fact, it sounds like even if it might actually work, achieving translation with no net change in momentum, the "swimmer" would likely need to operate on a similar scale to the space curvature that it's exploiting. So, not something that's likely to be useful for anything.
It is true that as a mathematical abstraction, the surface of a sphere is indeed non-Euclidian space. However, in our universe that surface is itself inherently embedded in 3D space that's at least flat enough that the non-Euclidian reality can be ignored for most purposes. Basically, most challenges largely disappear if you stop trying to oversimplify the problem.