World's Subways Share Common Mathematical Structure 159
Hugh Pickens writes "No two subway systems have the same design. New York City's haphazard rail system differs markedly from the highly organized Moscow Metro, or the tangled spaghetti of Tokyo's subway network. Now BBC reports that a study analyzing 14 subway networks around the world has discovered that the distribution of stations within each of the subway networks, as well as common proportions of the numbers of lines, stations, and total distances seem to converge over time to a similar structure regardless of where the networks were, when they were begun, or how quickly they reached their current layout. 'Although these (networks) might appear to be planned in some centralized manner, it is our contention here that subway systems like many other features of city systems evolve and self-organize themselves as the product of a stream of rational but usually uncoordinated decisions taking place through time,' write the study authors. The researchers uncovered three simple features that make subway system topologies similar all around the world. First, subway networks can be divided into a core and branches, like a spider with many legs. The 'core' typically sits beneath the city's center, and its stations usually form a ring shape. Second, the branches tend to be about twice as long as the width of the core. The wider the core, the longer the branches. Last, an average of 20 percent of the stations in the core link two or more subway lines, allowing people to make transfers. 'The apparent convergence towards a unique network shape in the temporal limit suggests the existence of dominant, universal mechanisms governing the evolution of these structures.'"
Re:Didn't RTFA (Score:4, Informative)
"Didn't RTFA"
"How is it "math" if it's a trivial observation ?"
Sometimes you don't need to rtfa to get an idea of the topic at hand, sometimes you don't need to read it to be able to ask valid questions. This is not one of those times, your question is well answered in tfa.
It's mathematical because they found a number of mathematical properties, I can't remember what these are as I read this yesterday on the way home, and I've slept since then, but they were things such as the number of stations being a consistent factor relative to other properties such as line length and that sort of thing. They even tell you what those factors are. There was something like 14 mathematical properties that could be used to count, and/or predict certain properties about a subway network regardless of it's age etc.
Though I suppose you could claim that these ratios and so forth were discovered via trivial observation if you want to be pedantic, and well, great, but in that case just about all math stems from trivial observation based on some arbitrary definition of trivial giving the paradox that if you're implying, as you are from your comment, that something discovered via trivial observation isn't ever math, then no math is necessarily math depending on what you class as trivial.
It doesn't really matter what you deem trivial, at the end of the day it's still math, just as how I might rip a piece of paper in two and observe trivially that I now have two pieces of paper - it still means that ripping said piece of paper in two results in two pieces has a grounding in math trivial or not.
Well, sorry for being pedantic anyway, I'm in one of those moods!