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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.
Constructal Theory.
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
How is it "math" if it's a trivial observation ? Transit is generally organised in a network of hubs and spokes, with interconnects where necessary/convenient. The same semi-concentrated topology can be seen in large corporate networks where the core switches are much fatter than per-floor and per-office distribution switches.
This doesn't teach us anything about subway design. The average 12 year old gamer could draw an optimal shortest-route network in a matter of minutes. The challeges faced in urban planning are of a political nature, not technical. Can't dig here because of heritage blah blah, can't dig there because it's a wealthy neighbourhood, can't dig anything because the bus drivers' union is suing the city... We already have all the tech we could want, but what we're lacking is people smart enough to step aside and let progress happen.
-Billco, Fnarg.com
You know that bum that rides the L train all night long using a the NYT as a blanket? There's your Intelligent Design Being. Next time you see him, say thanks.
The articles only mention New York, London, Moscow and Tokyo.
I'm curious to see if the two large ones I know personally were included.
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. :)
"Public transportation project found to spontaneous converge toward a centrally organized communist entity spontaneously, Liberal academia found."
The only possible interpretation of any research whatever in the 'social sciences' is: some do, some don't
Is his name Neptune?
It would explain the tattoos and the estuarine smell -even most of the dirt.
What a big steaming pile of DUH. Even Ants are known to do their road layout by "instinct" and still come up with mathematically sound solutions for the most economic tracks. Why would subway layouts be any different? Because they are usually government projects and governments are mathematically proven to be extremely inefficient, compared to ants?
I was promised a flying car. Where is my flying car?
Self organization of complex systems is one of the major idea's of Chaos Theory. Nothing really new here except they're showing that yet one more system displays this tendency. So "dominant, universal mechanisms'" is just the author trying FAR to hard to avoid using the term Chaos Theory and make Jeff Goldbloom suddenly appear in everyone's head saying "Life uh, uh, uh finds a way."
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
Subway satisfies a particular need. They move people throughout a city, and usually extend to the suburban areas. The points from the summary...
The core of the city typically has the most people traveling to and through it. Even traveling from one side to another, the choices are to pass through a central location, or route around it. Routing around it would require an unnecessary and extensive path. Since subways are frequently underground, that's an awful lot of expensive tunneling.
Amazing, the center of the travel need would be a place to put the center of a transportation system. And the article cites exceptions, so the ring shape isn't a factor.
So the bigger the city, the larger the suburban sprawl.. As there are vertical limits, that's the other choice.
That's not a mathematical proof that they fall into the same formula. It's an average across the sample set. If they defined the range, and it happened to be 19% to 21%, I'd be impressed. The second page of the article cites Moscow at 50%, so I'm guessing the range is 1% to 50%
And the suggestion is intelligent design has guided subway design, but their list could include other items like ... subways are underground. subways have stations. subways have purpose built trains. subways have ticket, coin, or other payment systems.
They missed the other huge coincidence. Transportation started as paths, then trails, then roads, then highways. And subways resemble those same systems. Not precisely, because they aggregate many routes. They also evolve as demand dictates. It's not some magic mathematical formula, and this one obviously isn't if the ranges are 1% to 50% in one part, and "some do, some don't" in another. It's "shit, this route is always busy, we need to add trains", which becomes "we are saturated with trains on this route, we need another one". Well, proper planning watches trends, and hopefully has the construction complete on the addition before the need totally saturates the available resources.
Well shit. I'm really in the wrong business. I should start doing studies. Look at subway maps, write papers, and get published. And they get paid for it?
JWSmythe Study and Reporting Service
Sponsored by Captain Obvious
Serious? Seriousness is well above my pay grade.
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.
Wait a minute... are you saying that my old college roommate is the Intelligent Designer?
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?
"The Existence of Dominant, Universal Mechanisms Governing" is just the way philosophically naive academics say "There are relevant matters of fact concerning". I wouldn't read too much into the way this has been phrased.
Myu:
All brontosauruses are thin at one end, much much thicker in the middle and then thin again at the far end.
I use the Glasgow Subway you insensitive clod. Now I feel that I am outside the normal rules of nature!
The Seoul subway, not so much. The "core" is arguably the #2 line in Seoul.
At it's widest point it's around 10km.
one branch is 70km as the bird flies, another direction around 80km.
the amount of transfers is around 40-50%
the #2 isn't fully below the city center. some parts of it are. maybe the center of seoul metro, but not seoul proper.
it actually goes more around the edges of seoul proper at several points.
The Warsaw subway is only one line, but it's clean, doesn't stink and is pretty clean of graffiti.
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."
Has anybody read a short story called "A Subway named Moebius" - I forget the name of the author but it was included in several anthologies of classic SF
"Carry the most passengers as fast as possible for as little money as possible" sounds quite universal, and dominates in the long term over investments like the cost of new stations.
I'm sure all 8 passengers are pleased :P
Actually, I have no idea how busy the Warsaw subway is. I just couldn't resist the joke :)
No colour or religion ever stopped the bullet from a gun
..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
Gee, who would have thought that structure built by and for humans would have any similarities? I get the point that superficially they may appear different but it's not at all surprising they have something in common as they essential serve the same human need and humans are very similar.
What makes NYC's subway network particularly haphazard?
Wouldn't all subway systems share the same Euler number? Isn't a subway system just a connection of varying numbers of segments with varying numbers of nodes?
I suppose that there could be "faces" in the topology as well. Definitely if you look from a 3D standpoint. Do lines actually have physical 'intersections' in a 3D sense? I don't think that changes the Euler number however.
Subway systems that move people from outside to the city center and back again for work/etc and also within the city center tend to have a set of core stations in the city center and branches to those outer areas that people live.
The core tends to be a ring - something efficient for moving people from any station to any other station without producing a huge bottleneck.
The bigger the city the more sprawling the residential areas around it are and so a bigger core ring gives longer branches.
Rather than having trains that visit every station in the network the denser core stations often support transferring to other trains in order to get from one overlapping section to another.
Who would have thunk that might happen?
This joke is not meme-compliant as per Slashdot policy. The sandwich needs to run on Linux.
Subway runs BSD. Bacon, Salami, Dill Pickle.... it comes on OS 9 Grain Wheat, and is great toaster-ed with LoJack cheese.
I8-D
I'm not too surprised by this. It reminds me of how the vascular system evolved, how streets frequently have the same length proportions regardless of location, and how the Internet's base structure evolved/continues to evolve.
If you look into it, most of these things follow simple fractal equations.
If the only way you can accept an assertion is by faith, then you are conceding that it can't be taken on its own merits
Pipe theory. Maybe the same it true with water mains, sewer systems, electrical grids, and even the internet?
Form follows function, who woulda thought?
Comment removed based on user account deletion
Hardly... you can't move around in the station at all because of all the Poles in the friggin way.
... or two.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
I didn't know there were any left, I thought they were all in the UK causing pipes to leak.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
It's intelligent design ...
"I love my job, but I hate talking to people like you" (Freddie Mercury)
Have they considered that maybe there were engineers who were actually doing their jobs? Part of the job of designing complex systems is to first see how past such projects were designed and built. If you can, you also try to tap the ideas and resources of the engineers who designed the previous ones and get ideas on what to do - and what NOT to do. That's part of the reason for groups like IEEE and ASME.
Furthermore, good designers also develop a reputation in creating certain types of systems. Formula racing car mechanical engineers, Office building architects... even game design "engineers" (think Shigeru Miyamoto and Mario bros). These "rock star" designers can end up designing or leading projects all over the world for decades. Do you think they are going to completely approach the problem completely differently from their past successes - even once?
This "research" is like pointing out that a suprising number of video games have characters that jump and focus on defeating ever increasing large adversaries "regardless of where the (games) were, when they were begun, or how quickly they reached their current" version!
Lastly, what the heck kind of math produces statements like "an average of 20 percent of the stations" from a single sample set?
In my experience subways *pretty much* mirror the overlying infrastructure. They could have as easily studied the layout of streets, population densities, and zoning (industrial/commercial). You need one central location for maintenance. It really isn't rocket science.
Floating in the black seas of infinity without a paddle.
http://news.softpedia.com/newsImage/CT-Scans-Reveal-Ant-Colony-Architecture-Patterns-2.jpg/
The first statement is true for Chicago: the Loop encircles the core of the city.
The second statement is not true for Chicago: the branches are far longer than twice the width of the Loop.
The third statement doesn't hold true for Chicago: 100% of the lines have transfer points in the Loop. From any line, you can ultimately get to any other line somewhere in the Loop. I can't think of any exception.
I thought the pipes leaked already, and that's why all the Poles are there.