McDonalds: more than 10 served

Megabus.com adds Philadelphia-D.C. line, from the Daily Pennsylvanian.

We learn from a Megabus spokesperson that their vehicles use "less than a pint of fuel per passenger mile".

For those of you who don't have the misfortune of knowing this, there are eight pints in a gallon. So these busses get better than eight passenger-miles to the gallon!

Since most cars in the US get at least 20 miles or more to the gallon, this is really nothing to be proud of.

(I'm guessing that busses are actually more fuel-efficient than cars, at least if they run sufficiently full.)

A variant of the traveling salesman problem

Josh Robbins attempts to see a baseball game in all thirty major league baseball parks in 26 days.

Yes, you read that right.

And Major League Baseball doesn't make that easy. As you can guess, he has to see two games in one day four times -- but in markets with two teams (New York, Chicago, San Francisco/Oakland, Los Angeles) they try to schedule the two teams to be on the home at opposite times. That makes sense, because that way if you think "I want to see a baseball game today" you've got a good chance.

In fact, his four doubleheaders are Dodgers-Padres (which apparently was a bit of a tight squeeze, since the Dodgers went into extra innings), Yankees-Mets (that one should be easy; every few years the Mets and the Yankees play a game at one park in the afternoon and at the other park the same night; they're doing it today); Phillies-Nationals (which will be tight even if the games go the ordinary length; they start six hours apart, average game length is three hours or so, and the cities are two and a half hours apart with no traffic -- oh, and he's doing it on a Thursday); Cubs-Brewers.

My point is that 25 days might be possible -- but probably not. Most baseball games are scheduled for around 1 PM or around 7 PM, and games last three hours, to see two in one day requires the sites to be no more than three hours apart. The pairs that are doable in one day are probably:

Mets-Yankees, Mets-Phillies, Yankees-Phillies
Phillies-Orioles, Phillies-Nationals, Orioles-Nationals
Dodgers-Padres, Padres-Angels, Angels-Dodgers
White Sox-Cubs, White Sox-Brewers, Cubs-Brewers
Giants-A's

but of course one can do only one from each row, so it's only possible to double up on five days. Basically, this is the problem of looking for the largest matching in the graph that I defined above, where the edges are teams within about three hours' driving distance of each other.

(Oddly enough, each two-team market (and yes, I know, Baltimore and Washington may or may not be the same market) seems to have another team a couple hours away. In two cases that team is the Phillies. As you may know, this blog likes the Phillies.)

So 25 is theoretically possible, if the Scheduling Gods worked in one's favor -- but I'd be scared to even look at the schedules to try and figure it out. And what happens if there's a rainout?

As a problem in actually scheduling things, the other tricky part is that Denver really isn't near any other team. And Robbins' schedule had him at a 7:05 game in San Diego, followed by a 1:05 game in Denver the next day -- but Denver's a time zone to the east of San Diego, so that's seventeen hours between starts. Fourteen hours driving time. For 1,078 miles.

For some other variants of the traveling salesman problem which involve the road network, see Barry Stiefel's 50 states in a week's vacation (driving, with flights to Alaska and Hawaii) and 21 states in one day. The last one cheats a bit -- it's a 26-hour day, since he started in the Eastern time zone during daylight savings time (GMT-4), and did the trip on a day when we went back to standard time (GMT-5) and then crossed into the Central time zone (GMT-6). The difference here is that you only have to enter each state instead of reaching a point.

Oh, and I feel obliged to point out that I find the meme of going on a long road trip this summer because "this is the last summer it'll ever be possible" kind of stupid. (Not that anybody here brought it up.)

Edited (Saturday morning): Google Maps says Cleveland to Detroit can be driven in 2:46. I didn't realize they were that close together. They'd be even closer if someone built a bridge across Lake Erie.
(Saturday afternoon): Cleveland to Pittsburgh in 2:18. I'll admit the reason I forgot this one is that mentally I think of Pittsburgh as being in the same state as me and Cleveland as not being in it, so they must be far apart. This is despite the fact that I live about five miles from New Jersey.
Anyway, you could shave off yet another day by combining the Indians with either the Pirates or the Tigers.

A mathematician goes to the post office

There's a pretty standard theorem that one proves at the beginning of, say, a differential geometry course -- that any (n-1)-dimensional manifold embedded in n-dimensional Euclidean space is locally the graph of some function. (To any geometers are reading this, I apologize if I haven't stated this correctly.)

This morning I had to go to the post office to pick up a piece of certified mail. I live on one side of a large set of railroad tracks; the post office is about a mile away on the other side of the tracks. I generally don't go past the tracks, because very little that interests me is there, and I hadn't looked at a map before setting out. It's important to know where the tracks are when walking around in that neighborhood, because there are a lot of streets that exist on both sides of the tracks but are interrupted by them. The street on which the post office is, Florence Avenue (links goes to Google satellite imagery) may be such a street; it exists on both sides of the tracks, and doesn't cross over the tracks. It might cross under; Google Maps won't tell me, and I'm not curious enough to head out there again and look. So the scheme of "follow the street with the same name" doesn't always work.

I knew the tracks run basically from northwest to southeast. (For those who know where I live, or who are looking at the map I linked to: all directions are "nominal", i. e. by "west" I mean "the direction in which the street numbers get higher".) At one point on the way back I crossed a bridge and I was wondering "could that have been the tracks I just walked over?" Then I thought "hmm... I'm further north than I was when I crossed the tracks heading to the post office, so the tracks must be further west here."

Why must they? Because the tracks are basically a one-dimensional manifold embedded in two-dimensional Euclidean space. So locally there's a function mapping east-west streets to north-south streets that gives the position of the tracks. Everyone knows this intuitively. If you asked someone who knows that neighborhood well "Where does [insert street here] cross the tracks?" you'd get an answer, even if they're totally ignorant of geometry.

Should you wait for the bus?

Take the lazy way (from Agence France-Presse, via the (Toronto) Globe and Mail,): it is better to wait for the bus than to walk along the route of the bus and get on the bus when it catches up to you. This is intuitively obvious: whether you start walking or not, you end up arriving at your destination on the same bus (and therefore at the same time), and if you walk you risk that the bus will pass you between stops. The result is due to Justin Chen, Scott Kominers, and Robert Sinnott.

This was actually in the arXiv a couple weeks ago (0801.02979v2), but I didn't see it. Surprisingly enough, a newspaper article about mathematics in the mainstream news actually linked to the original research it was referring to! (This is surprisingly rare, and not just for articles about mathematics, but for just about anything.)

On a personal note, I walk to school and back each day even though there is public transit paralleling my usual route. This is contrary to the solution explained in the paper, but there are things that the paper doesn't include. First, by walking (a mile and a half each way) I get exercise, so I don't have to go to a gym. Second, I get frustrated if I wait for the trolley and it doesn't come. Third, I get a lot of my best thinking done while walking; the trolley is noisy enough and bumpy enough that I can't think well on it. Fourth, I'm cheap. Fifth, bus schedules around herre works of fiction anyway, and solving this problem correctly would require a more sophisticated probabilistic model, which I'm not going to go to the trouble of doing.

And the comments on this on fark.com are actually rather interesting.

ways of drawing the Interstate Highway System

Earlier this year, Chris Yates made available online a simplified map of the Interstate highway system, where the interstates are for the most part straight lines. This made its way around the Internet for a while, and it was frequently pointed out that it was wrong -- certain interstates just aren't on it. (The ones I noticed were I-83 (which runs between Harrisburg and Baltimore) and I-88 (Albany to Binghamton); a lot of other people pointed out that it also omits the entire state of Wisconsin.)

It occurred to me that it would be nice to see this map done correctly, and I'm trying to do it myself; unfortunately I don't have a really big piece of paper! It's probably possible to represent all the two-digit Interstates on a single piece of paper, though. But this map from Hedberg Maps looks like what I was thinking of -- it basically assumes that as many of the two-digit Interstates as possible actually form a grid and then fills in the rest, including the three-digit Interstates, accordingly. Too bad it's $40. They explain how the map works here; basically, the map's author, Nat Case, attempted to respect the topology of the system and align the main roads of the system with the grid, so the distance between, say, I-70 and I-80 is the same as the distance between I-80 and I-90. (Case claims inspiration from Yates' map, but seems to be a lot less visible on the Internet, probably because you can't view it online.)

A lot of people compare these to "subway maps", but there's one big difference. On a map of a subway system, the various subway lines are generally denoted by different colors; this makes it obvious when one has to transfer from one line to another. (See, for example, the standard Washington Metro map; there's a recolored version of the map to indicate the different service patterns they run on July 4th.) And this makes sense, because a change of trains has a substantial cost -- you've got to get off the train, often walk up or down some steps, and wait for another train to come. Roads don't work like that -- the cost to go from one highway to another is minimal.

I'd also like to see a similar map of, say, Philadelphia; the street signs indicate that each intersection is a certain distance west or east of one axis (Front Street or Germantown Avenue, depending on location) and north or south of another (Market Street), but the grid breaks down the further you get from the historic city. I actually live along a "seam" in this grid; as you walk down my street the numbers immediately go from the 500s to the 900s. How is the map distorted if you try to place locations not where they are, but where the addressing system implies they are?

edited: Nat Case talks about the map at mapHead; you can see a larger version of the map here. (1080 by 1080, which is large enough to get a very good idea what's going on. It's particularly interesting how some of the shapes of states get distorted here -- Florida is now much longer east-west than north-south, for example, and Arizona and New Mexico end up having roughly the shape of Chile, and Illinois is huge.

Personally, I think it's a little crowded in the northeast, which is something you might not necessarily expect from the description.

And now I don't have to make this map myself to see what it looks like, which is a relief because I'm not particularly good at this sort of thing.

Life expectancy, walking, and that giant city a hundred miles north of me.

Why New Yorkers Last Longer, from New York magazine. (Thanks to Jess Haralson.)

The article mentions how life expectancy is calculated, and says:

The math works like this. Imagine that one man dies of AIDS at age 25. Since he was statistically supposed to live to 78.6 years, he’s died about 50 years too early, so he shaves 50 years off the city’s overall pool of life. If one Wall Street guy collapses of a heart attack at age 65, he shaves only ten years off. You’d have to have five Wall Streeters die at that age to equal the impact of one AIDS victim. By the same logic, one infant’s dying during childbirth—77.8 years too early—is equal to ten people’s succumbing to lung cancer at age 70. It is a very weird form of horse trading. The more you’re able to prevent young people—folks in their twenties and thirties—from dying, the more rapidly you boost a city’s overall life expectancy.

Although I'm not sure if the math works out exactly like that -- I've mentioned this before -- it certainly seems reasonable that it does. And a lot of the time, the "value" of a certain public health policy is computed in terms of number of years of potential life lost, not in terms of number of potential lives lost. This makes sense; younger people's lives are more valuable simply because what we're really valuing is the remainder of the life. And countries in sub-Saharan Africa that have been hit hardest by HIV do, in general, show the lowest life expectancies.

The article also makes the claim that New Yorkers live longer because they walk more. This seems reasonable to me. (And New Yorkers walk faster than the average person, too.) I don't live in New York -- I live in Philadelphia, which has a deep-seated inferiority complex in relation to New York. But we walk fast here, too -- I know this because people who move here from other places often say that we walk fast here, but rarely say that we walk slow. Walking fast is my own personal extreme sport, because I happen to walk faster than the average person (I have long legs) and so I actually end up weaving between people in order to go at my preferred speed. Am I healthier than average? I'm not sure.

Sometimes I wonder what my weaving through crowds would look like if time were made into a third spatial dimension -- or what a crowd of people in general would look like. People manage to not crash into each other. And when I'm walking, I will walk somewhere where someone else was a moment ago, where someone will be in a moment -- but we don't collide. Our world lines don't (indeed, can't) intersect. (World lines are usually thought of as positions in four-dimensional spacetime, but I'm assuming that my position is in two dimensions, thus a three-dimensional spacetime.) You'd see ordinary pedestrians' world-lines moving along in clumps. I go faster, so my world-line would be less steep (assuming time is the vertical dimensions). Clumps of tourists go slower and are probably more tightly clumped than ordinary people. (Don't believe me? Go down to Independence Hall. My theory is that tourists are afraid of being infiltrated by the natives.) Is it possible to identify tourists just by looking at their world-lines? And does a tourist alone be identified, or only a large clump of them? I would argue that the lone tourist doesn't exist, although it's difficult to articulate why -- perhaps because the lone tourist probably makes more of an effort to fit in with the crowd around them. All I know is that when I've been traveling alone in strange cities, people have actually come up to me and asked for directions. Somehow I manage to look like I belong.

the traffic.com "Jam Factor"

Traffic.com has something they refer to as the "Jam Factor" to tell you how much traffic there is on various major roads in your area. It's an apparently arbitrary number from 0 to 10.

Now, if I see that the jam factor is 3.1 right now, what does that mean? How long is it going to take me to get where I'm going?

They claim:

The Traffic.com Jam Factor is like a "Richter scale" for traffic. It's an overall measure of the traffic conditions on a roadway, or on a section of a roadway. Because the Jam Factor calculation uses real-time speed and travel time measurements from our sensors and those of our partners, as well as our detailed accident, construction and congestion information, it's a comprehensive measure of the state of traffic on any roadway.

The Jam Factor is measured on a scale of 0-10, with 10 being the worst traffic conditions. It is designed to give you a quick, at-a-glance picture of conditions on the roadways or personal MyTraffic Drives you care about, whether you're on our web site, looking at an emailed Traffic Report, or listening to a Traffic Report call to your phone. If you see (or hear) a high Jam Factor, you can then delve into the detailed information in the Traffic Report or on the Traffic.com site to find out more.

If you click on the name of any segment of road, it'll tell you how long it takes to get by that piece of road without traffic, and how long it'll take Right Now -- that seems like more meaningful data to me.

If I had to sum up traffic conditions in a single number, it would be the ratio of the two numbers in the previous paragraph. I'd like to know that it'll take me 50% longer to get where I'm going than it would if the roads were clear. It wouldn't surprise me to learn that the "jam factor" is just this number disguised somehow.

I prefer what, say, Google Maps does, just overlaying colors (red/yellow/green) on the road; a number, especially one with two significant digits (the Jam Factor is reported to the nearest tenth), implies some sort of precision. I'd rather have no number than a number which has extra decimal places tacked onto it to seem "scientific". (Would I be less annoyed by this if the Jam Factor was reported on a 0-100 scale, to the nearest unit? Who knows?)

Also, if they have sensors of some sort -- why am I limited to knowing how long it'll take to get from a preset point A to a preset point B? Why can't I input the exit I actually get on and off at and have it tell me how long I should expect to spend on the highway? This is a simple matter; they have the speed that the road is moving at at any given moment, so just integrate the reciprocal of speed over the length of road in question. (I realize that it's not quite this trivial, because just because a segment of road is moving at 30 mph right now doesn't mean it'll be moving at that same speed when I get there. My method is sort of like how life expectancies are calculated, which doesn't actually tell YOU how long you're going to live. But forecasting how traffic on any given day will evolve, or how medical care will evolve, is a lot harder than just observing it.)

The Richter scale itself is logarithmic, as many of you probably know -- a difference of one unit on the Richter scale corresponds to a factor of ten in the amplitude of the seismic waves (not a factor of ten in the energy released, as is widely reported; although this isn't my field, it looks like the corresponding increase in energy released is a factor of 10^3/2, or about 32). Other logarithmic scales that you see fairly frequently are decibels (for measuring sound) and Google PageRank (on the 0 to 10 scale); a decibel corresponds to an increase in volume of 10^0.1, and I've read various things but one unit of PageRank seems to correspond to a factor of about five. (No one outside of Google knows for sure.) All of these situations have one thing in common -- most earthquakes, sounds, and web pages are relatively small, and some are much more prominent, so there's a good reason to spread out the small end of the scale and compress the large end. But in the case of the Jam Factor, this isn't necessary; if it takes me an hour on average to drive somewhere, on a really lucky day it might take forty minutes, and on a really unlucky day it might take three hours, but it's never going to take even as much as a hundred hours.

(Incidentally, as you may h ave guessed by now, my preferred mode of transportation is walking. A large part of this is that even though it's slow, I always know exactly how long it's going to take me. There is essentially no situation that slows down or speeds up my walking speed. And even if there were, it never takes me twice as long to walk somewhere as it ordinarily would, whereas driving times that are twice the average are routine. Unfortunately, it's not totally clear whether I save fossil fuel by walking, because I have to eat more food in order to walk.)

Walkscore.com -- how walkable is your neighborhood?

WalkScore.com will tell you how walkable a neighborhood is. Put in an address you're considering living at, and it'll tell you which grocery stores, restaurants, coffee shops, bars, movie theaters, schools, parks, libraries, bookstores, "fitness", drugs stores, hardware stores, and clothing and music stores are within walking distance. (They don't seem to have a firm cutoff for "walking distance"; I suspect something counts more towards walking distance if it's closer.) It uses this information to generate a score out of 100 telling how walkable the neighborhood is; it seems to correlate pretty well with my subjective impressions of places I've lived or am otherwise familiar with, although most places I'm familiar with are towards either end of their scale and I'd like some more data from the middle.

(Incidentally, it is possible to get a score of 100, though I'd doubted it for a while; Rittenhouse Square in Philadelphia is an example.)

The biggest problem is that they use "as the crow flies" distances; this was noticeable for one place I've lived which happened to be near a river (the Charles) but midway between two of the bridges across it (the Harvard and Longfellow). In most cases this doesn't seem that serious, because of a fact about development patterns -- the places with "inefficient" street patterns (where as-the-crow-flies distances tend to be the worst understimates) are places with low population density anyway.

There's an interesting picture illustrating the efficiency of grids of streets, showing all the places within a one-mile walk (via streets) from a point in downtown Seattle and similarly from a point in the Seattle suburb of Bellevue. The area (in the plane) filled in in the case of the grid is much larger. It makes me wonder -- how much gasoline could we save by designing in such a way that there weren't so many damn cul-de-sacs?

I recently came across Michael Bluejay's claim that walking is less efficient than driving, in terms of fuel consumption, if you eat like a typical American (i. e. lots of meat). This is because walkers need more food than drivers. It looks like a vegetarian walking is more fuel-efficient than a typical car, and that cyclists, whether meat-eating or vegetarian, are more fuel-efficient than the typical car.

However, as Bluejay points out, this is only true on the level of the individual person who has to make a trip to a certain place. On the level of a whole society, if we develop our communities in such a way that they're friendly to walking, people will travel less miles -- because our communities will be more compact, so one can get to the same number of different places with less travel. In fact, car-unfriendly communities are necessarily more compact, simply because less space is taken up by roads and parking lots! I suspect there's a "critical density" of some sort below which a vicious cycle starts: enough people have cars that businesses feel they need to offer free parking, which lowers the population density, which means even more people get cars, which means more free parking, and so on.

geographical random walks

Let's say you have a map of the streets in an area. Could you guess, from looking at that map, which intersections the locals consider "most important"?

You could probably make a decent first guess by assuming that the importance of an intersection goes up with the number of roads at the intersection.

Why? Imagine you are randomly walking around a town. Each time you get to an intersection you choose uniformly at random from each of the possible ways you could go. (For the sake of simplicity, I'll assume that this includes going back the way you came.) It's a well-known result that this sort of random walk on a graph leads to a certain stationary distribution; that is, if a bunch of people walk around randomly you'll get to a point where the number of people at any given intersection is roughly constant. And that result is that number of people at any intersection is proportional to the number of roads coming into it. (I'll count the two directions of a road coming into the same intersection as two distinct roads.)

This has implications if, say, you want to start a business. If you're located in the middle of a block, there are two roads coming in. If you're at a "T"-shaped intersection, there are three. A normal grid intersection, four. An intersection like 48th and Baltimore or 23rd and South, five -- both of these have two streets that go through and a third that starts there. (Most of the intersections on Philadelphia's Baltimore Avenue are five-pointed, because the street grid has a sort of discontinuity there; this may explain why it's sort of the main street of its part of the city.) An intersection like Broad and McKean, which has three streets going through it, six. You want to be where there are more roads, so that more people will walk by. In Washington they have intersections like Dupont Circle where five roads go through, for a total of ten "arms". (The counting gets a bit tricky, because some of the roads don't actually go "through".) In Paris there's an intersection with eleven arms, fittingly called L'Etoile. (Much more than that seems impractical.)

Of course, this neglects a huge number of facts. Not all roads are equal. For example, I'm ascribing Baltimore Avenue's primacy in its part of Philadelphia to the fact that it's got five-pointed intersections; but probably more important is that, historically, it was the road that went to Baltimore. (Hence the name.) Also, a trolley runs down Baltimore Avenue and has for over one hundred years; but why is it there, and not somewhere else? Because people already were living or working on or near that street. And they were doing that because other people were. Once a slight imbalance is created -- say by the random-walk model I alluded to above -- people are naturally going to gravitate, even if it's very slightly, towards the place where people already are. The roads that lead towards the important nodes will become important in their own right. And street networks aren't static -- they can change. (River networks can't, though -- and a lot of cities are located where two rivers come together to form a third, the most famous U. S. example probably being Pittsburgh.) But the initial imbalance has to come from somewhere, and this is as good a place as any, especially in places where the roads mostly form a grid and hence their arrangement is determined well in advance of their actually being built.

Incidentally, this is my theory on why Boston and Philadelphia -- two cities which are of similar size and population density, at least if you consider them as the center of their respective metropolitan areas, and the two cities I am most familiar with -- differ in their transit system. Boston is able to have subways because for the most part it's obvious where the subway stops should be. Radical Cartography has a map of Boston as a series of squares; the original transit system was basically built around people getting from one square to the next. Philadelphia would have trouble supporting a subway system more extensive than its current two lines, because it's hard to point to a place that a huge number of people go which isn't served by the existing system; the population is more diffuse, because for the most part Philadelphia's streets form a grid and no node is any different from any other. If I wanted to I could draw, say, six or eight subway lines that I'd like to exist in Philadelphia -- but none of them seem essential to me, at least at the price that it costs to build a subway. (Some Philadelphians will point out that there's a long-standing plan to put a subway down Roosevelt Boulevard; to them, I will say that I have very rarely had any reason to be in Northeast Philly, so I forget about the Boulevard. I'm sorry.) Manhattan has subways -- even though it's for the most part a grid -- because it's so dense. (But I think I heard somewhere that Times Square is the busiest subway stop -- and it's under Broadway, which cuts through the grid diagonally.)

SEPTA fare hike "11 percent"?

Funding heads off SEPTA fare hike.

The public transit provider in Philadelphia, SEPTA, recently raised its fares; the article is saying that they won't have to raise fares again in September. In the media the fare increase was widely reported as an "11 percent" increase. And it basically was. People who hold a weekly pass for the buses and subways saw the price raised from $18.75 to $20.75; monthly pass holders, from $70 to $78. A one-day pass was raised from $5.50 to $6. (A rule was made that a one-day pass was actually only good for eight trips, though.) SEPTA also runs commuter trains from the suburbs. A typical fare increase there (zone 3, off-peak) was from $3.75 to $4.25; a weekly pass for such a commuter train went up from $34.50 to $39, a monthly from $126.50 to $142.50.

So far, all the fare increases I've mentioned were between 9% and 13%. So far, so good.

But how much of a fare increase will I, personally, see? Zero.

Why is this? SEPTA decided to eliminate the transfer. Currently, there are three ways one can pay for a single trip on SEPTA: pay a $2 "cash fare", use a token which costs $1.30 (but tokens are only available in quantities of more than one, and it can be astonishingly difficult to find someplace which sells tokens!), or use a transfer, which costs 60 cents but can only be used for the second or third vehicle in a trip that requires more than one vehicle.

The cash fare and the token will remain at $2 and $1.30, respectively. The transfer will be eliminated. Because of where I happen to live and where I happen to go on a regular basis, and the way SEPTA's routes are structured, I never need to transfer. (Also, I never figured out how to buy a transfer.)

SEPTA says only 6.8 percent of riders use transfers. This makes sense; under the old fare structure, if you needed to use a transfer for a round-trip five days a week, that came to $19 a week; compare $18.75 for a pass. These figures are quite similar, and I'm assuming that our hypothetical person never goes anywhere but to work. The people who get screwed are the people who ride less then daily but need a transfer when they do so; they'll have to pay $2.60 (twice $1.30) for their trip instead of $1.90, a 37% fare increase. And these are probably the people who can least afford it.

I would have preferred to see, say, the $2 cash fare raised to $2.20, the token raised to $1.45, and the transfer continuing to exist (at 65 or 70 cents). (I haven't done the math to know if this would actually bring SEPTA the same amount of money as what they're doing; I'm just applying the 11% figure across the board.)

The article says a hearing is being held to restore the transfer. I think that's the right thing. It's not the rider's fault that SEPTA doesn't have a single route that goes from where they are to where they want to be; designing a transit system such that everyone has a one-seat ride would be essentially impossible. A good transit system works because of these network effects -- two routes are more than twice as valuable as one, a hundred routes are more than twice as valuable as fifty. But only if you make it possible to use the system as a system.

swarm theory

National Geographic on Swarm Theory -- the field variously known as "complex systems", "emergent behavior", etc. In some sense certain complex systems are greater than the sum of their parts -- an ant colony seems to have some sort of "intelligence", even though a single ant doesn't. Each individual person betting on a horse race has their biases, but in parimutuel betting the final odds (which depend on how many people bet on each horse) very nearly reflect what actually happens. Juries are smarter than each of their individual members -- although only when the jurors act independently. (This makes me wonder: are people better or worse at following complex arguments than they were a couple hundred years ago?)

Public transportation systems, especially in the U.S., are notoriously inefficient; I suspect a large part of this is because they run on the same routes they've historically run on. I have to wonder if this sort of thing could be applied to redesign of public transit; the article mentions other logistical applications. Southwest Airlines, for example, has used this for scheduling. And American Air Liquide, which delivers gases made at a large number of plants to a large number of customers, has redone a lot of their delivery this way.

Unfortunately, though, Air Liquide has found that some of their drivers have to do unintuitive things -- they're no longer delivering from the plant nearest the customer to the customer. I have a feeling this wouldn't work well with people; you can't tell someone "well, it's going to take you an extra half-hour to get to work today, but that saves fifty other people one minute!" even though it does reduce total transit time.

I suspect there might be applications to, say, the dispatching of cabs, or the placing of shared cars (disclaimer: I am not a member of Philly Car Share but lots of people I know are). Or to a hypothetical company like the one Scott Adams suggested which would get people rides by having them text-message their destination to some central server and then hook them up with someone who's willing to give them a ride. Although the appropriate metaphor in this situation is actually more like traditional, decentralized hitchhiking. Hey, maybe that's the solution to the energy crisis!