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.

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.)

You're paying for the bottle, not the water

A couple weeks ago I came across a suspicious-sounding claim that New York City tap water costs 24 cents a gallon; the correct figure is 0.24 cents per gallon.

The New York Times gets it right today; in an article about how people drink more bottled water and less of just about everything else, they claim that

THOSE eight daily glasses of water you’re supposed to drink for good health? They will cost you $0.00135 — about 49 cents a year — if you take it from a New York City tap.

As I said before, NYC water rates recently went up to 0.27 cents per gallon; assuming that "eight glasses" means "eight [measuring] cups", or half a gallon, this is correct. They then go on to point out that buying bottled water at the same rate would cost about $1,400 yearly. If you work it out, that's $4 a day, which values a 16-ounce bottle of bottled water at $1; that seems about right if you buy them individually, not in cases.

But with bottled water, you're really paying for the bottle, not the water.

On a related note, the Philadelphia Water Department is now giving out free bottles of tap water for events. The thinking is not financial, but environmental; they figure that if people are aware that tap water tastes good, then they won't use as much bottled water in the future. Bottled water is bad for the environment, because it's packaged in plastic containers and is often transported very long distances. Yesterday I saw someone buying FIJI water at the store on my corner. This comes from -- you guessed it -- Fiji, which is eight thousand miles away.

Personally, I buy bottled water for the convenience when I'm away from home but would never consider buying bottled water for my home. I've also been known to refill empty bottles with tap water, although there are rumors that that's unsafe.