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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.'"
The first subway I tried was in Berlin, Germany and it was somewhat daunting experience for someone who hadn't got used to the system. Previously I've only used systems where you pick what you want and get it.
But now there was tons of choices and moving around to get the whole trip finished. The lady over the counter would ask me tons of questions - like do I want white italian, parmesan & oregano, wheat or sesame bread. Southwest sauce, sweet onion, barbecue sauce or light mayo. Cheddar cheese, onions, lettuce, pickles, green peppers, jalapenos, with a choice of meat. Like pepperoni, salami, tuna, chicken, roast beef, meatballs, steak and cheese... ham or spicy italian... do I want extras like double cheese or bacon? Did someone say double bacon? Footlong or 6-inch...
The system greatly confused me. But being a warrior of food, I survived. I got my delicious subway. And you know what? Ever since I've loved subways. It is absolutely delicious. Chipotle southwest with ranch or light mayo is the ultimate sauce. What I cannot, however, understand is why would anyone put MUSTARD on a subway?
Oh dear god, American subway has PIZZA SUB? Why don't we have that here?? Aah, spicy pepperoni, cheese and marinara sauce. Do want.
Interesting story regarding pizzas, sandwiches and subways by the way. My old girlfriend used to LOVE tuna subways, while I only ate ham & cheese. She always laughed about it and told me to try something new. Too bad I didn't. But a few years later, I hit the wall. I could not eat anymore ham on pizzas or subways. It just started to taste like shit. I don't know why. But then I discovered the magical taste of tuna subways and pizzas along with salami and pepperoni and bacon. So for all of you who only eat one kind of ingredient all the time - do try something new. You only have one life to enjoy!
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.
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.
Schroedinger's Brexit: The UK is both in and out of the EU at the same time!
"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
http://www.wired.com/wiredscience/2010/01/slime-mold-grows-network-just-like-tokyo-rail-system/ .. old news?
The article says that "all subway systems with more than 100 stations match this". According to Wikipedia, the Stockholm subway system has 101 stations, out of which 100 are active, and the Stockholm subway system does not have this core loop that they talk about. I hope they don't extend to more than 100 active stations, it would invalidate all this important research. :)
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
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?
His team analyzed the geometry of all of the subway networks in the world that possess more than 100 stationsâ"including Barcelona, Beijing, Berlin, Chicago, London, Madrid, Mexico, Moscow, New York City, Osaka, Paris, Seoul, Shanghai, and Tokyo i.e. no Vienna
Domestic spying is now "Benign Information Gathering"
Except it's not self-organisation. The stations don't dynamically shift around and lay new tracks according to their perception of traffic flow and population density; a dude sits down at a desk and draws it on a map.
Article is a barrowload of sensationalist monkey spunk.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
All brontosauruses are thin at one end, much much thicker in the middle and then thin again at the far end.
Humans build systems to suit humans. The commonality is humans.
The commanity is physics and math; research on slime has shown that, when faced with the same constraints as the rail network, it will grow into almost exactly the same network structure.
Slime Design Mimics Tokyo's Rail System: Efficient Methods of a Slime Mold Could Inform Human Engineers "The model captures the basic dynamics of network adaptability through interaction of local rules, and produces networks with properties comparable to or better than those of real-world infrastructure networks... The work of Tero and colleagues provides a fascinating and convincing example that biologically inspired pure mathematical models can lead to completely new, highly efficient algorithms able to provide technical systems with essential features of living systems, for applications in such areas as computer science."
"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!
..I heard you like Subway, so why not put a Subway on the subway so you can eat your Subway while you ride the subway? Incidently, reading this post, the word Subway has lost all meaning to me..
--AlexC
Just because I dont agree with climate change doesnt make me a troll