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A study of Baron von Haussmann's Paris.

Cities are often studied as a kind of organism, a complex entity capable of evolving, and ruled by self-organization. Which raises an awkward question for urban planners: Where do they fit in? If cities evolve in size and shape according to their own unwritten rules, does "central planning" really change anything?

Several French academics recently analyzed one of the most obvious case studies for this elusive question: Paris in the time before and after infamous master-planner Georges-Eugène Haussmann rolled through town razing roads, plotting new ones, and trying to rationalize the city's windy medieval street grid (hat tip to the BBC for noticing the study). The paper in Scientific Reports digitized historic maps of the city from 1789, 1826, 1836, 1888, 1999, and 2010.

The analysis borrowed as much from complex networks theory as from the more traditional eyeball method of assessing old-timey maps. Street networks generally follow some pretty common patterns over time, as new intersections and roads are created both pushing the network outward and densifying it at its core (as we've previously written, OpenStreetMap contributors actually follow these very same processes, too).

In studying those six maps of Paris, these mathematical physicists and historians, led by Marc Barthelemy, were trying to count and measure these links and nodes, and the best ways to travel between them. They focused on Haussmann's modifications and the street network contained within what was Paris in 1789, or what constitutes the central city today. On the below left-hand map from the paper, the 1789 network of Paris in blue is plotted atop a map of the city today. The teal lines at right show the roads created during the Haussmann period of the second half of the 19th century:

The number of nodes and the length of roads appeared to increase between 1836 and 1888 in predictable proportion with the city's growing population, suggesting not much influence by Haussmann's hand. "Our results for central Paris reveal that most indicators follow a smooth evolution," the authors write, and one that mimics cities studied elsewhere.

But the roads Haussamnn planned did have a dramatic impact on how people spatially navigated through the city, likely alleviating congestion. The researchers gauged this looking at something called "betweenness centrality," which we will let them explain: It "essentially measures the number of times a link is used in the shortest paths connecting any pair of nodes in the network, and is thus a measure of the contribution of a link in the organisation of flows in the network."

Certain roads, in other words, become more important in connecting people to points across town. And while Haussmann's new roads and avenues made up only 6 percent of the total length of the area's network today, that 6 percent appears to have fundamentally shifted the spatial organization of the city. Here, those most central nodes that enabled people to travel the shortest paths through town are plotted across time:

"Self-organization versus top-down planning in the evolution of a city" by M. Barthelemy et. al in Scientific Reports.

Post-Haussmann, from 1888 onward, the spatial pattern has remained pretty stable. Barthelemy and colleagues offer little guidance as to how we should use these results to look back on Haussmann's legacy:

It is unclear at this stage if Haussmann modifications were optimal and more importantly, if they were at a certain point inevitable and would have happened anyway (due to the high level of congestion for example). More work, with more data on a larger spatial scale are probably needed to study these important questions.

Top image: Map of Paris from 1853, which shows the city with some of Haussmann's newly planned streets: Paniconography by Firmin Gillot (b 1820, d 1872). Engraving by F. Delamare/courtesy of Wikimedia Commons.

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