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.'"

Comments

Neat but expected

[bonch]

Neat, but is it surprising that transportation systems designed for the exact same purpose become mathematically similar over time? I'd be surprised if there wasn't emergent similarity in all urban transportation networks.

Re:Neat but expected

[marcello_dl]

Yep, the idea of abstract mechanisms *governing* the evolution of systems sounds inspired by Plato and quite unscientific. Science is about abstracting and formalizing those mechanisms, not giving them a godlike status according to unprovable assertions on reality. Leave that to philosophers, they gotta make a living too.

Re:Neat but expected

[AlecC]

I think Plato did have a lot of sense mixed with his nonsense. But the sense has become so much part of our common knowledge that we don't realise that it was, in his time, original. Of course, the nonsense has remained nonsense.

A bit like the woman leaving a performance of Hamlet, who said "I don't know why they think Shakespeare is so great - that was just a load of well known quotes tied together."

Obvoiusly, Intelligent Design at work here . . .

[PolygamousRanchKid]

Just read it out loud and clear:

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.

However, if this Intelligent Design Being is the inspiring influence of subways that I have ridden on, He is dirty, stinks of piss, swallows ticket money, but barfs up no ticket, and it tattooed from head to foot in graffiti.

the existence of dominant, universal mechanisms?

[G3ckoG33k]

"the existence of dominant, universal mechanisms governing the evolution of these structures"

Hallelujah, praise the lord?

Intelligent design?

Or just plain antpaths?

My vote goes to antpaths: http://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms

Except for Melbourne Australia.....

[Dr Black Adder]

In Melbourne http://ptv.vic.gov.au/maps-stations-stops/metropolitan-maps/metropolitan-train-network-map/ have a core ring about 2km wide, consisting of 5 stations, 4 (80%) of which link two or more lines, and our 'spider legs' are 30km + much more than 2x the core width. Maybe this is why our system is a constant failure?

I use the Glasgow Subway you insensitive clod

[Chrisq]

I use the Glasgow Subway you insensitive clod. Now I feel that I am outside the normal rules of nature!

Re:Moscow Metro

[nadaou]

It wasn't Stalin, it was (supposedly) Czar Nicholas and the Verebinsky bypass.

http://en.wikipedia.org/wiki/Moscow_%E2%80%93_Saint_Petersburg_Railway#Myths