Slashdot Mirror
World's Subways Share Common Mathematical Structure
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.'"
Exactly. It's obvious that e.g. distances between stations can't be too short or too long. And obviously the structure is determined by the structure of the city, the distribution of its population and their destinations. And subway planners might also have taken a look at solutions in other cities. I think I'm going to do a study on mathematical properties of articles in the Journal of the Royal Society Interface. I will of course assume that such articles are self-organizing, and arrive at the surprising conclusion that they're all made up of words; I might even find that some words are much more frequent than others, despite there being so many opportunities in so many different pieces of text. I expect this conclusion to reach Slashdot in due time...
Moscow metro is like they describe, a centre core, and legs out in all directions. However, there is a larger ring, outside the 'natural core' that is caused by crossing lines.
The (presumably apocryphal) story goes that... The designers brought the plans for the Metro expansion to Stalin. He had set a coffee cup on it, and left a coffee ring around the centre. None of the engineers were willing to go against what could be perceived as Stalin's 'edit', so the coffee ring was built.
(It's always coloured brown, on maps of the metro. It's kind of cute...)
Sent from my PDP-11
This joke is not meme-compliant as per Slashdot policy. The sandwich needs to run on Linux.
Maybe it's an ice cream sandwich.
Escher was the first MC and Giger invented the HR department.