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World's Subways Share Common Mathematical Structure

samzenpus posted more than 2 years ago | from the common-design dept.

Math 159

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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My experience on worlds subways (4, Funny)

Mr. Hamburger (2641281) | more than 2 years ago | (#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!

Re:My experience on worlds subways (0)

luke923 (778953) | more than 2 years ago | (#40025509)

Come on! This should be modded up. This is the hardest I've laughed while reading /. in a long time.

Re:My experience on worlds subways (3, Funny)

simoncpu was here (1601629) | more than 2 years ago | (#40025539)

This joke is not meme-compliant as per Slashdot policy. The sandwich needs to run on Linux.

Re:My experience on worlds subways (5, Funny)

TeknoHog (164938) | more than 2 years ago | (#40025979)

This joke is not meme-compliant as per Slashdot policy. The sandwich needs to run on Linux.

Maybe it's an ice cream sandwich.

Re:My experience on worlds subways (0)

Anonymous Coward | more than 2 years ago | (#40026883)

Also, where is the car analogy?

Subway Runs BSD (2)

Kamiza Ikioi (893310) | more than 2 years ago | (#40027063)

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.

Re:My experience on worlds subways (1)

bmo (77928) | more than 2 years ago | (#40025537)

>modded into the basement

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

5 dollar footlongs forever.

--
BMO

Re:My experience on worlds subways (2, Funny)

JWSmythe (446288) | more than 2 years ago | (#40025677)

    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 your tasty meal.

    The tasty meal part isn't necessarily proven. That would depend on what you had put on it.

    I could really use a meatball sub with extra sauce. Damn you, Subway, why don't you have a location near me open 24 hours? I'd even be willing to take a subway to the Subway, so I could enjoy my Subway sub, except there is no subway close to me to take to the Subway.

Yo Dawg.. (3, Funny)

kickedfortrolling (952486) | more than 2 years ago | (#40026429)

..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..

Re:My experience on worlds subways (0)

mirix (1649853) | more than 2 years ago | (#40025679)

Why don't we have that here?? Aah, spicy pepperoni, cheese and marinara sauce. Do want.

There are two kinds of pepperoni in North America. One is a semi-dry delicious salami, mildly spicy generally. This is delicious.

The other is the kind that shitty pizza joints and most places that make ersatz-pizza (like pizza subs) use. It's like bologna with a bit of spice. Salami just shouldn't be wet... Disgusting.
Typical bullshit people will eat here - I'd rather pay a few cents more for actual meat. I guess it's like everything else here, bigger, cheaper, shittier. 4000sqft mansions made out of paper and sticks, American "cheese", hotdogs, Budweiser, etc.

Side note, I learned pepperoni is an americanism when I went to Italy when I was a kid. My dad and I had argued over whether to order salami or peperoni pizza, and I opted for the latter - which turned out to be sweet peppers. I had a stomach ache the whole next day. (oddly, peppers no longer do this to me.. hmm).

Re:My experience on worlds subways (1, Offtopic)

u38cg (607297) | more than 2 years ago | (#40025729)

My gf kept telling me to try something new. So I tried her sister.

Re:My experience on worlds subways (3, Funny)

Hognoxious (631665) | more than 2 years ago | (#40025947)

You motherfucker!

Re:My experience on worlds subways (1)

Anonymous Coward | more than 2 years ago | (#40026325)

Calm down odorous swine: he said "her sister", not "her mother".

Honestly though, u38cg's gf's mom is totally hot, and does that thing with her tongue.

Re:My experience on worlds subways (0)

Anonymous Coward | more than 2 years ago | (#40026695)

Her sister was his mother, isn't that clear?

Re:My experience on worlds subways (0)

Anonymous Coward | more than 2 years ago | (#40026803)

So, u38cg was originally an auntiefucker?

Re:My experience on worlds subways (1)

mrclisdue (1321513) | more than 2 years ago | (#40025859)

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,

Re:My experience on worlds subways (1)

turing_m (1030530) | more than 2 years ago | (#40025895)

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. Something between 8 and 10 inches would be perfect.

Every other fast food joint has a range of different sized options suited to my specific caloric needs but not Subway. What gives? Is it part of their marketing strategy to encourage every cheap bastard to get the 12 inch option? Have they considered dividing a foot long sub into 3 segments (4, 8, 12) but realized that lots of women would order 4 inches instead of 6?

Re:My experience on worlds subways (1)

zippthorne (748122) | more than 2 years ago | (#40026295)

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

Re:My experience on worlds subways (1)

RaceProUK (1137575) | more than 2 years ago | (#40026319)

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.

Re:My experience on worlds subways (1)

Skater (41976) | more than 2 years ago | (#40026443)

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 tempted to get a 12" sub and I'd probably eat the whole thing, instead of stopping at 8" and tossing 4". Now what I do is eat the 6" sub with ~300 calories, then have a little chocolate/peanut butter snack for another 90 calories or so, and I'm still 210 calories ahead of where I was calorie-wise after eating just a 12" sub. The apple the previous poster mentioned is even better if you aren't going to crave sweets after the apple anyway.

Re:My experience on worlds subways (0)

Anonymous Coward | more than 2 years ago | (#40026975)

It's probably not what she said, but anyways: 6 inch should be just enough for her, unless she's a size queen. 12 would probably kill.

Re:My experience on worlds subways (1)

Pope (17780) | more than 2 years ago | (#40027095)

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

Re:My experience on worlds subways (1)

Truedat (2545458) | more than 2 years ago | (#40026015)

light mayo is the ultimate sauce

I was with you until you mentioned that abomonation.

Re:My experience on worlds subways (1)

Siridar (85255) | more than 2 years ago | (#40026121)

I'm gonna level with you.

I was expecting another "cleanmyPC" spam.

Did you know we have pizza subs in Australia, too?

Re:My experience on worlds subways (0)

Anonymous Coward | more than 2 years ago | (#40026147)

Subway is actually some of the worst fast food you can possibly eat.

Neat but expected (3, Insightful)

bonch (38532) | more than 2 years ago | (#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.

Re:Neat but expected (2)

Dupple (1016592) | more than 2 years ago | (#40025511)

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

Re:Neat but expected (4, Insightful)

marcello_dl (667940) | more than 2 years ago | (#40025757)

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 (2)

Hognoxious (631665) | more than 2 years ago | (#40025801)

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:Neat but expected (0)

Anonymous Coward | more than 2 years ago | (#40025879)

Or yet another example of somebody demonstrating that just because they don't grok something (and probably haven't even bothered reading more than 3% of somebody's work) that the fault must lie in the work and not in themselves.

Physics, not humans : slime (4, Interesting)

chrb (1083577) | more than 2 years ago | (#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."

Re:Neat but expected (5, Funny)

tgv (254536) | more than 2 years ago | (#40025515)

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...

Re:Neat but expected (0)

Anonymous Coward | more than 2 years ago | (#40025535)

Yep.

Methinks maybe they accidentally rediscovered an application of the central limit theorem.

Re:Neat but expected (0)

Anonymous Coward | more than 2 years ago | (#40025803)

True dat. In other news, a different transportation research team has discovered that all wheels share similar mathematical properties.

Re:Neat but expected (1)

mike260 (224212) | more than 2 years ago | (#40025815)

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

Re:Neat but expected (0)

Anonymous Coward | more than 2 years ago | (#40026769)

Maybe if Picasso designed the routes it would be different.

But they were done by engineers, and engineers are logical, and logic applied to the same process leads to the same results.
-A series of trains that never intersect (ie no transfers) is a pain in the ass to use
-A series of trains that DOESN'T match the rough layout of the city its in is just stupid

Let's look at interstates/freeways around major cities.....we should be shocked that they generally form a crosshatch across the city, connect to each other, and frequently have a major route that forms a ring around the city too?

Re:Neat but expected (1)

StripedCow (776465) | more than 2 years ago | (#40027035)

They're just lucky nobody patented stuff like that.

Two words (1)

Anonymous Coward | more than 2 years ago | (#40025521)

Constructal Theory.

Obvoiusly, Intelligent Design at work here . . . (4, Insightful)

PolygamousRanchKid (1290638) | more than 2 years ago | (#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:Obvoiusly, Intelligent Design at work here . . (2, Funny)

Anonymous Coward | more than 2 years ago | (#40025561)

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.

Re:Obvoiusly, Intelligent Design at work here . . (1)

Weatherlawyer (2596357) | more than 2 years ago | (#40025585)

Lives both sides of a large river near the sea and has a couple of million servants minimum.

Is his name Neptune?

It would explain the tattoos and the estuarine smell -even most of the dirt.

Re:Obvoiusly, Intelligent Design at work here . . (1)

Anonymous Coward | more than 2 years ago | (#40025655)

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?

Re:Obvoiusly, Intelligent Design at work here . . (2)

Myu (823582) | more than 2 years ago | (#40025735)

"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.

Re:Obvoiusly, Intelligent Design at work here . . (1)

jedrek (79264) | more than 2 years ago | (#40026049)

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

Re:Obvoiusly, Intelligent Design at work here . . (1)

RaceProUK (1137575) | more than 2 years ago | (#40026331)

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 :)

the existence of dominant, universal mechanisms? (4, Insightful)

G3ckoG33k (647276) | more than 2 years ago | (#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]

Didn't RTFA (2)

billcopc (196330) | more than 2 years ago | (#40025551)

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 (3, Informative)

Xest (935314) | more than 2 years ago | (#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!

Re:Didn't RTFA (1)

MikeBabcock (65886) | more than 2 years ago | (#40027009)

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

Methinks you don't understand math.

Anyone know which subways they compared? (1)

MartinSchou (1360093) | more than 2 years ago | (#40025569)

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.

Re:Anyone know which subways they compared? (1)

DarwinSurvivor (1752106) | more than 2 years ago | (#40025707)

Well it sure as hell doesn't describe Vancouver's skytrain even the slightest! (not counting bus routes)

Re:Anyone know which subways they compared? (4, Interesting)

AHuxley (892839) | more than 2 years ago | (#40025719)

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

Slime Mold Grows Network Just Like Tokyo Subway (4, Interesting)

Anonymous Coward | more than 2 years ago | (#40025571)

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

Stockholm is an outlier? (3, Interesting)

IonSwitz (609514) | more than 2 years ago | (#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. :)

Re:Stockholm is an outlier? (1)

oskarfasth (187750) | more than 2 years ago | (#40025661)

The article says:

The “core” typically sits beneath the city’s center, and its stations usually form a ring shape.

Note that it doesn't say "loop" anywhere. So I gather they don't mean a central loop line like the moscow subway system. If you think of it more like a geographical grouping of the core stations in a ring shape, I'd say (squinting my eyes a bit) there's an embryo of it in Stockholm city between Slussen, Fridhemsplan and Östermalmstorg with T-centralen in the middle. Here's the map, btw... [sl.se]

Re:Stockholm is an outlier? (1)

MartinSchou (1360093) | more than 2 years ago | (#40025897)

That's not really a loop, unless you want to accept the outlying stations in the loop as VÃstra Skogen, Ã...keshov, Ã-stermalmstorg, Liljeholmen and SkÃrmabrink.

Re:Stockholm is an outlier? (2)

Sique (173459) | more than 2 years ago | (#40025667)

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.

Re:Stockholm is an outlier? (2)

Bogtha (906264) | more than 2 years ago | (#40025737)

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

Re:Stockholm is an outlier? (0)

Anonymous Coward | more than 2 years ago | (#40025773)

Well, their sample size of over 13 subway systems is sure to eliminate any significant overfitting of the data. Why they're even able to make draw the same conclusions on conditional subsets like systems sharing location, start date, and rate of growth. :-)

Re:Stockholm is an outlier? (0)

Anonymous Coward | more than 2 years ago | (#40026231)

It's just proof the Swede's are falling behind. Probably due to the same inbreeding that produced all the sexy long-legged blondes.

So, FOX headline tomorrow: (2, Funny)

mathfeel (937008) | more than 2 years ago | (#40025583)

"Public transportation project found to spontaneous converge toward a centrally organized communist entity spontaneously, Liberal academia found."

Kicking in an open door (2)

dutchwhizzman (817898) | more than 2 years ago | (#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?

Chaos Theory (1)

Spinalcold (955025) | more than 2 years ago | (#40025615)

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."

Re:Chaos Theory (4, Interesting)

Hognoxious (631665) | more than 2 years ago | (#40025739)

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.

Re:Chaos Theory (1)

khallow (566160) | more than 2 years ago | (#40026223)

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.

The dude at the desk is part of the system.

Re:Chaos Theory (1)

jeremyp (130771) | more than 2 years ago | (#40026413)

But the fact that the system contains a human who designs it makes the fact that it is self organising not interesting. Self organisation amongst humans has been observed frequently in the last few millennia and should not be surprising.

Re:Chaos Theory (1)

khallow (566160) | more than 2 years ago | (#40026427)

But the fact that the system contains a human who designs it makes the fact that it is self organising not interesting.

No it doesn't. That dude is limited in what he can do both by funding, physical limitations, and assigned mission. He can't add a Taj Mahal to one of the stations, for example.

Self organisation amongst humans has been observed frequently in the last few millennia and should not be surprising.

Ok, tell us how that history of self organization is going to manifest in subways?

Re:Chaos Theory (1)

Spinalcold (955025) | more than 2 years ago | (#40026919)

Intent is the important aspect here. If the person had no intent to plan by a set of rules is he part of the system, if he was using a set of rules to make the plans then he is a control mechanism.

Re:Chaos Theory (1)

flaco629 (1671226) | more than 2 years ago | (#40026465)

And how often is it the same dude drawing maps for different cities?

Re:Chaos Theory (0)

Anonymous Coward | more than 2 years ago | (#40026207)

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."

No it isn't. The major idea of chaos theory is dynamic systems whose attractors have fractal dimension. Nothing to do with complex systems.

Moscow Metro (5, Funny)

mirix (1649853) | more than 2 years ago | (#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...)

Re:Moscow Metro (0)

Anonymous Coward | more than 2 years ago | (#40025867)

I always heard that story was in the Moscow to St. Petersburg railway line, where he traced a straight line between to the two cities on the map on the wall to show where it should go, and in doing so, traced around his thumb. So up until the '90s the train went on a funny dog's leg diversion for many km over flat land. ... the story went with the same scenario of none of the rail builders were willing to defy the line he drew.

Re:Moscow Metro (4, Insightful)

nadaou (535365) | more than 2 years ago | (#40025891)

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 [wikipedia.org]

Re:Moscow Metro (4, Interesting)

Sique (173459) | more than 2 years ago | (#40026505)

While this is a myth, another anecdote probably is no myth. The russian word for trainstation is vokzal. The word is not of russian origin, but english. When the first railroad was built in Russia, the 12 mile track between St. Peterburg and Tsarskoye Selo and further to Pavlovsk Palace, there were extensive pleasure gardens around Pavlovsk Palace, which were called vokzal (Vauxhall translated to russian letters) in the russian language - and got their name from the Vauxhall Pleasure Gardens in London. Thus the terminus at Pavlovsk Palace was called vokzal, giving raise to the generic russian word for terminus.

Re:Moscow Metro (1)

KiloByte (825081) | more than 2 years ago | (#40026107)

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...

Brilliant Conclusion... (1)

JWSmythe (446288) | more than 2 years ago | (#40025635)

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 are frequently underground, that's an awful lot of expensive tunneling.

The 'core' typically sits beneath the city's center, and its stations usually form a ring shape.

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.

Second, the branches tend to be about twice as long as the width of the core. The wider the core, the longer the branches.

So the bigger the city, the larger the suburban sprawl.. As there are vertical limits, that's the other choice.

Last, an average of 20 percent of the stations in the core link two or more subway lines, allowing people to make transfers.

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%

'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.'"

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

Re:Brilliant Conclusion... (1)

Myu (823582) | more than 2 years ago | (#40025751)

'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.'"

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.

Again, "The Existence of Dominant, Universal Mechanisms Governing" is just the way philosophically naive academics say "There are relevant matters of fact concerning". What's with this rush to accuse people of practicing theology?

I'm starting to worry about the apparent inability of people to tell the difference between positing factivity and being religious. Either it's an expressive problem on the part of researchers or a lack of interpretive charity on the part of readers, but either way, it doesn't bode well for public science.

Re:Brilliant Conclusion... (1)

ArsenneLupin (766289) | more than 2 years ago | (#40026571)

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.

Except for Melbourne Australia..... (4, Insightful)

Dr Black Adder (1764714) | more than 2 years ago | (#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?

Re:Except for Melbourne Australia..... (2)

AHuxley (892839) | more than 2 years ago | (#40025725)

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.

Re:Except for Melbourne Australia..... (2)

Malc (1751) | more than 2 years ago | (#40026595)

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?

Re:Except for Melbourne Australia..... (0)

Anonymous Coward | more than 2 years ago | (#40026635)

Wow! Not knowing anything about Melbourne and just looking at that map I'd almost speculate that system was built to fail. Generally your branch lines just let you get from the suburbs into the city, but there is a lot of interconnectedness in the city so you don't need to make more than one transfer to get anywhere in the city from anywhere in the city or suburbs. In this map the 'core' only works if the city itself is no more than 5 blocks square, enough for a town of about 50 to 100 thousand people. But a city that size wouldn't have a subway and from the number of stops I assume Melbourne has at least 500 thousand people in which case this design is colosal failure.

Re:Except for Melbourne Australia..... (1)

Anonymous Coward | more than 2 years ago | (#40026725)

We have over 4 million people in Melbourne. The subway is an epic fail...

I have a theory (4, Funny)

greggman (102198) | more than 2 years ago | (#40025811)

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 (1, Insightful)

Chrisq (894406) | more than 2 years ago | (#40025821)

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

Re:I use the Glasgow Subway you insensitive clod (0)

Anonymous Coward | more than 2 years ago | (#40026117)

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

Glaswegians are outside the normal rules of nature.

Re:I use the Glasgow Subway you insensitive clod (0)

Anonymous Coward | more than 2 years ago | (#40026361)

s/outside/above

Re:I use the Glasgow Subway you insensitive clod (1)

egladil (1640419) | more than 2 years ago | (#40026549)

So the Glasgow subway is missing the branches, and the Stockholm subway is missing the ring? Then we'll just have to colocate them. Problem solved! :)

Re:I use the Glasgow Subway you insensitive clod (1)

chrb (1083577) | more than 2 years ago | (#40027011)

Systembolaget [wikipedia.org] in Glasgow? Now that would be an interesting experiment...

Korea, not so much (1)

crossmr (957846) | more than 2 years ago | (#40025845)

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.

Re:Korea, not so much (-1)

Anonymous Coward | more than 2 years ago | (#40026153)

Which line do you see more dog ramen shops on?

I thought this was pretty obvious... (-1)

Anonymous Coward | more than 2 years ago | (#40026211)

When you go to a Subway, they have something called a "menu," and when you order something on it, you get something that shares a mathematical structure with other menu items at other Subways around the world.

I mean, really, why is this even on slashdot? News for nerds, more like news for terds.

Mathematics of subway system (1)

rossdee (243626) | more than 2 years ago | (#40026243)

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

dominant, universal mechanism (1)

Arancaytar (966377) | more than 2 years ago | (#40026261)

"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.

File this under "Duh!" (1)

divisionbyzero (300681) | more than 2 years ago | (#40026451)

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.

Haphazard NYC? (1)

Malc (1751) | more than 2 years ago | (#40026621)

What makes NYC's subway network particularly haphazard?

Topology (2)

moeinvt (851793) | more than 2 years ago | (#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.

No way! (1)

nedlohs (1335013) | more than 2 years ago | (#40026795)

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?

Should Be Common (1)

MacGyver2210 (1053110) | more than 2 years ago | (#40027285)

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.

New buzzword (1)

EvilBudMan (588716) | more than 2 years ago | (#40027357)

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

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