Aug 5, 2007

Deriving Importance From Maps

The God Plays Dice blog that I've been reading recently had an interesting entry on trying to derive the importance of intersections from a map of a city. The core observation is that a good first approximation of importance of an intersection is the number of roads leading into and out of it.

Manhattan has some qualities that make this interesting to ponder. Primarily, the city was allowed to evolve naturally until 1811, when the Commissioner's Plan set forth the layout from 14th Street to the north side of Harlem, and the most important locations in Manhattan (depending on your point of view) are split between the Financial District, which is unplanned, and Midtown, which is planned.

In the planned section, the given approximation works out well. The plan included one major irregularity: Broadway, which cuts across diagonally from about 77th Street to 10th Street. As a result, the grid section includes 6 intersections that have 6 roads leading into and out of them instead of four:

All of these are major intersections, and certainly rank highly among the most important intersections in the City.

Below 14th Street, though, the theory breaks down heavily. The West Village in particular has streets going all different directions and includes many intersections of 6 roads, some of as many as 8. However, none of those intersections are particularly important to the city as a whole (though some have local importance). Partly this is because Greenwich Village is built on land that is unsuitable for large buildings and partly it is because of the history of the area (which was once a literal village for people who didn't want to live in the bustling metropolis that was lower Manhattan).

Perhaps the core of the matter, though, is that the importance of an intersection is proportionate to the importance of the streets that intersect there. Intersections with more streets thus stand a better chance of being important simply because there are more streets that might contribute some importance. In that manner, we could find important intersections by trying to find the important streets. Ideas for what features one might look for to determine that could include unusual streets (such as Broadway), streets which are further apart from similar streets (such as the Avenues), streets that carry two-way traffic (as these tend to be larger than one-way streets), and streets on the edges of major parks.

Isabel also includes a side note about subways and why she feels that Boston has a thorough subway system while Philadelphia doesn't. She compares Manhattan to Philadelphia in that the system is a grid, so there aren't "obvious" places to put subway stops, but that isn't actually true for Manhattan. The Commissioner's Plan designated fifteen Streets (14th, 23rd, 34th, 42nd, etc) to be wider than normal, and many carry two-way traffic nowadays (which is very unusual in Manhattan, even the Avenues are largely one-way). Because they're regularly placed and main thoroughfares, these became the obvious places for subway stops when the system came along. That's why there are 4 separate stops on 125th Street, but no stops on any of 117th-124th or 126th-134th.