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Math Transportation Science

World's Subways Share Common Mathematical Structure 159

Posted by samzenpus
from the common-design dept.
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.'"
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World's Subways Share Common Mathematical Structure

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  • by Mr. Hamburger (2641281) on Thursday May 17, 2012 @02:02AM (#40025481)
    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 [subway.com]? 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!
    • by bmo (77928)

      >modded into the basement

      Don't feel bad, some people have no sense of humor, OP.

      5 dollar footlongs forever.

      --
      BMO

    • Re: (Score:3, Funny)

      by JWSmythe (446288)

      But did you notice the mathematical trend between the subways you visited? In every one, there was a number of bread containers for said subway. Within that container, there was a number of items which could be placed within it. And finally, and the clearest proof intelligent design is behind subway is that, at the end of the subway assembly, a numeric value was placed upon it, to which you were required to tender local currency or suitable plastic representation, to take possession of y

      • ..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..
        • by JWSmythe (446288)

              We've probably made several English majors cry, and have increased sales of Subway subs a trivial amount. I'm still hungry for a sub. :)

    • Re: (Score:2, Offtopic)

      by u38cg (607297)
      My gf kept telling me to try something new. So I tried her sister.
    • Oh, c'mon, this is an obvious google-troll/ms-astroturfer. First post, perfect grammer, same timestamp. Just substitute M$ (heh) for subway, and google for girlfriend, and you have your proof.

      Oh yeah, hi bonch.

      cheers,

    • by turing_m (1030530)

      I know I'm setting myself up for a flood of "that's what she said" jokes, but perhaps the only reason this hasn't been raised before is because of that very reason. So here goes.

      What I could never understand about Subway is the distinct lack of options between the 6 inch and 12 inch. The 6 inch is not quite enough food, and furthermore it is much more expensive per gram than the 12. The 12 inch is much better value, and though it certainly can be eaten in one sitting I feel like a lard bucket for doing so.

      • How does the 6" sub fare if you have it with, say, an apple?

      • Cost.

        If Subway did offer an 8-inch sub, then they'd be left with loads of 4-inch stubs that no-one wants, which would increase waste.

        The alternative, making 8- and 12-inch sub rolls, would mean a potential increase in required oven/rack space, which would mean an expensive renovation in most branches.

        • by Skater (41976)

          Quizno's gets around this by making loooonnnnnnngggg rolls, then cutting them off at the appropriate length for the customer. Along with the ends.

          I see the GP's point. I used to eat 12" subs every time, but now I've switched to 6" subs to save calories (no, I'm not Jared, but I will happily say I've lost 25 lbs and am now down to ~160 lbs, which is basically the right weight for my height, from 185 or so, by being more careful with portions). If I found that 6" just wasn't enough, then I'd still be tem

          • by tehcyder (746570)

            If I found that 6" just wasn't enough, then I'd still be tempted to get a 12" sub and I'd probably eat the whole thing, instead of stopping at 8" and tossing 4"

            As a UK reader this is just pure comedy gold. . Fnarrr fnarrr.

      • by Pope (17780)

        That's why D'Angelo's rocks so hard: 3 sizes of subs, plus properly cooked hot subs. Hot damn, I miss Boston! :)

      • by tehcyder (746570)

        realized that lots of women would order 4 inches instead of 6

        That's definitely not what she said...

      • by xevioso (598654)

        I eat at Subway all the time. I always choose the 6inch and if I am especially hungry I will add some chips in. That will put you literally halfway between the 6inch and 12inch as far as calories go, as the average bag of chips is somewhere close to 200 calories at Subway.

    • by Wraithlyn (133796)

      Turkey and ham, lettuce tomato green pepper & onion, and MUSTARD. Awesome cold sub. And low calorie too.

  • Neat but expected (Score:3, Insightful)

    by bonch (38532) * on Thursday May 17, 2012 @02:02AM (#40025485)

    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.

    • by Dupple (1016592)

      Humans build systems to suit humans. The commonality is humans. The same need is fulfilled by the same mechanism

      • by marcello_dl (667940) on Thursday May 17, 2012 @03:45AM (#40025757) Homepage Journal

        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.

        • I'm not a formal student of philosophy, but I've read a few intro books, listened to TTC lectures and the like. My two cents worth is that Plato mostly talked a load of assfeathers but got more credence than he deserved because he was a good entertainer. An early example of a personality cult and/or the halo effect?

          • Re: (Score:3, Insightful)

            by AlecC (512609)

            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."

          • by tehcyder (746570)

            I'm not a formal student of philosophy, but I've read a few intro books, listened to TTC lectures and the like. My two cents worth is that Plato mostly talked a load of assfeathers but got more credence than he deserved because he was a good entertainer. An early example of a personality cult and/or the halo effect?

            Thanks for that.

            I'll be sure to check out the rest of your no doubt illuminating series on the history of philosophy.

            • *Sigh*. I openly admitted to the fact that my opinions are in no way authoritative[1] (if anything can be in a subject that largely consists of making shit up), and yet all the smug little pissants feel the need to pile in with their pathetic and unfunny snide remarks.

              So how about you tell me why he wasn't talking shite? Or tell me why Aristotle, who certainly disagreed with him on many matters, was talking shite? They can't both be right, after all.

              Hey, you could set that as an exercise for your student

      • by chrb (1083577) on Thursday May 17, 2012 @05:36AM (#40026089)

        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. [bbc.co.uk]

        Slime Design Mimics Tokyo's Rail System: Efficient Methods of a Slime Mold Could Inform Human Engineers [sciencedaily.com] "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."

      • by tehcyder (746570)

        Humans build systems to suit humans. The commonality is humans. The same need is fulfilled by the same mechanism

        Agreed, it's a bit like saying that most houses round the world share certain common characteristics like doors between about six and seven feet tall, and ceilings roughly eight feet high.

    • by tgv (254536) on Thursday May 17, 2012 @02:14AM (#40025515) Journal

      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...

      • Exactly. It's obvious that e.g. distances between stations can't be too short or too long.

        Actually they can be both. They should be closer together near your departure point or destination. All the other ones between are fucking worthless and should be closed.

      • by Fnord666 (889225)

        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...

        Slow down there cowboy! First you need to secure a grant...

      • I agree, and the calculation would be the trade off of walking distance, or bike distance that would make people choose to pay for a ride vs their own trip. For areas where people can and will go longer distances on foot of bike, the central core would be further out and stations further apart because people would not choose them.

        The one part of the article that seemed like a wrong conclusion was the implied assumptions that these systems were built and evolved in isolation. What I suspect is the case is th

    • by mike260 (224212)

      Second. The article makes it sound like the guy discovered the Mandelbrot set hiding in the tube map.

    • They're just lucky nobody patented stuff like that.

  • by PolygamousRanchKid (1290638) on Thursday May 17, 2012 @02:24AM (#40025533)

    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.

    • Re: (Score:2, Funny)

      by Anonymous Coward
      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.
    • by Myu (823582)
      "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.
    • by jedrek (79264)

      The Warsaw subway is only one line, but it's clean, doesn't stink and is pretty clean of graffiti.

      • 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 :)

        • by ai4px (1244212)
          Hardly... you can't move around in the station at all because of all the Poles in the friggin way.
  • by G3ckoG33k (647276) on Thursday May 17, 2012 @02:27AM (#40025545)

    "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 [wikipedia.org]

  • by billcopc (196330) <vrillco@yahoo.com> on Thursday May 17, 2012 @02:28AM (#40025551) Homepage

    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.

    • Re:Didn't RTFA (Score:4, Informative)

      by Xest (935314) on Thursday May 17, 2012 @06:45AM (#40026363)

      "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!

    • Most math is made up of a collection of trivial observations.

      Methinks you don't understand math.

  • 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.

  • by Anonymous Coward on Thursday May 17, 2012 @02:33AM (#40025571)

    http://www.wired.com/wiredscience/2010/01/slime-mold-grows-network-just-like-tokyo-rail-system/ .. old news?

  • by IonSwitz (609514) on Thursday May 17, 2012 @02:35AM (#40025581)
    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. :)
    • by Sique (173459)

      So the smallest of al metro systems of the world, the Dorfbahn [wikipedia.org] (village metro) of Serfaus, obviously doesn't need to follow the rule. But in fact, it does. It has a core, the stations Seilbahn and Raika, it has a single leg, consisting of Kirche and Parkplatz. About 25% of the stations, the Seilbahn one is connected to other lines, the ropeway and the busses.

    • by Bogtha (906264)

      It's okay, when they add the 101st station, the whole thing will spontaneously evolve to match the structure they describe.

    • The simple explanation for this is that geography dominates. Stockholm is built on an archipelago, so that it's not easily amenable to developing a ring line. Nevertheless the Stockholm system does have a ring line (the Tvärbanan) which serves - as all ring lines do - to interconnect outlying regions and offload some of the congestion in the core lines, but note that this ring can only exist because of a favorable landscape. In general the Stockholm system is dominated by branching radial lines, con
  • by mathfeel (937008) on Thursday May 17, 2012 @02:35AM (#40025583)
    "Public transportation project found to spontaneous converge toward a centrally organized communist entity spontaneously, Liberal academia found."
  • by dutchwhizzman (817898) on Thursday May 17, 2012 @02:38AM (#40025591)
    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?
  • by mirix (1649853) on Thursday May 17, 2012 @02:54AM (#40025631)

    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...)

    • by KiloByte (825081)

      Not the first time something like this happened. The tsars used to draw foreign engineers, usually from Germany, to modernize the country, and when the engineers asked "should the railroad gauge be like ours, or bigger?", the tsar answered with a common Russian expletive, "for a dick bigger?". And so it stuck...

  • Subway satisfies a particular need. They move people throughout a city, and usually extend to the suburban areas. The points from the summary...

    subway networks can be divided into a core and branches, like a spider with many legs.

    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 a

    • but their list could include other items like ... subways are underground.

      Not always true. Many have elevated sections [wikipedia.org].

      subways have stations.

      Agreed. Hard to imagine an exception to this without making the system useless...

      subways have purpose built trains

      Not necessarily true. The planned Luxembourg "City Tunnel" (project Schummer) [www.rer.lu] would run with regular trains (one of its main selling points by the way. Regular trains would just enter the subway system at city boundaries, so people don't need to get off the train and on a subway)

      subways have ticket, coin, or other payment systems.

      Not necessarily true either. The Serfaus Dorfbahn, smallest subway in the world [funimag.com] is free of charge.

      • by JWSmythe (446288)

        but their list could include other items like ... subways are underground.

        Not always true. Many have elevated sections

        You know, I actually intended to say something to that effect. Most of the subways I've ridden on are mixed above/below ground, even on single routes.

        Not necessarily true either. The Serfaus Dorfbahn, smallest subway in the world is free of charge.

        Another exception, in actual use, is the subway system under Atlanta International Airport. It services a metropolitan need, it does have an e

  • by Dr Black Adder (1764714) on Thursday May 17, 2012 @03:06AM (#40025671)
    In Melbourne http://ptv.vic.gov.au/maps-stations-stops/metropolitan-maps/metropolitan-train-network-map/ [vic.gov.au] 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?
    • by AHuxley (892839)
      In Australia you where meant to buy a car or 2 or 3 and drive to work or use rail/bus (with cars for weekend/shopping).
      The main aspect driving classic Australian urban design was import costs and keeping the local car industry employing 1000's.
    • by Malc (1751)

      I think you missed the point about it being subway networks. Most of the map you linked to is suburban rail. How much is actually subway?

  • by greggman (102198) on Thursday May 17, 2012 @04:09AM (#40025811) Homepage

    All brontosauruses are thin at one end, much much thicker in the middle and then thin again at the far end.

    • by cellocgw (617879)

      All brontosauruses are thin at one end, much much thicker in the middle and then thin again at the far end.
      Hey! I'm an apatosaurus, you insensitive clod!

  • I use the Glasgow Subway you insensitive clod [wikipedia.org]. 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.

  • 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.

  • 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?

  • by moeinvt (851793) on Thursday May 17, 2012 @07:33AM (#40026643)

    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 havin

  • 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.

  • Pipe theory. Maybe the same it true with water mains, sewer systems, electrical grids, and even the internet?

  • People saw a subway that worked, and they copied it.
  • It's intelligent design ...

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