So let me set consciousness aside. Here’s a different kind of “China Brain” question more up my alley: Are the people of China actually organized in a brain-like fashion? This is not a thought experiment, but a genuine question. A silly question, you might say. But countries do tend to be cohesive complex systems that function via the movement of people, goods and information. In fact, cities are more cohesively organized than countries, and the same question can be asked of them: Are cities organized like brains?
Although most cities don’t at first glance look much like brains, there are some initial similarities.
First, unless you buy a thousand acres of land and have your own city built to order, cities get their shapes via (political and economic) selection forces over many decades. Like brains, cities evolve: ones that are not well organized wilt (people move away over time) or modify themselves to become more efficient.
Second, cities interconnect themselves with highways, and are under selection pressure to connect themselves efficiently. Highways break out of the two dimensional street grid, and “pull” the city’s edges closer to one another. Brains, too, have highways: white matter axons. The pyramidal neurons in the cortex send their axons out of the gray matter to faraway parts of the cortex.
I long ago stopped my subscription to the Flat Earth Society newsletter, but I still have reason to believe that cities are flat, and this is a third similarity between cities and brains. Even if you live in San Francisco, your city lies on the surface of the Earth, rather than, say, being built in a three-dimensional array below ground, or like the Borg cube. Our cortex is also flat, and if you’re lucky enough to be used in an experiment, researchers will flatten your gray matter onto the nearest cold metal table.
Having noticed these prima facie city / brain similarities, and having long had an interest in understanding why brains are shaped as they are, I thought I would take a closer look. I asked, Given what we know about how brains change when they get larger, do we find that cities change in similar ways as they get larger? So graduate student Marc Destefano and I took data from U.S. cities varying in population from about 10 thousand to about 10 million, and determined how city organization changed as city size increased. Our paper just appeared in the journal Complexity.
We found that cities and brains are quantitatively very similar in how they change their organization as a function of size. For example, the number of highways increases more slowly than does the surface area of a city, something already known to be the case for our brain’s highways (i.e., our white-matter-projecting neurons); in particular, in each case the number increases at about the 3/4 power of surface area. And the total number of highway exits in a city increases faster than the land area of the city, also the case for the total number of synapses in the brain; in fact, in each case the number increases at about the 9/8 power of surface area. Our paper discusses a number of other similarities – and discusses differences – e.g., for the diameter of highways, their propagation velocity (i.e., cross-city travel time), and the number of compartments (akin to cortical areas).
One notable problem with the analogy is people. What does population mean for the cortex? We’re not sure, but we found that the population of cities increases very fast as a function of land area, namely nearly as the 3/2 power of land area. That means population density in cities tends to increase as the 1/2 power, or as the square root, of land area. Bigger cities seem to demand that people really get up close and personal. That’s too bad for your and my kids, because cities are growing ever larger, and I don’t want anyone getting up close and personal to my wee girl.
Why do larger cities demand greater population density? Well, our measurements show that the total surface area of highways in a city also increases approximately as the 3/2 power of land area. Perhaps an efficiently running city highway system requires that each person in the city gets an invariant swathe of highway, so that no matter the size of the city, the total number of people per unit area of highway is a constant. Our data suggest that this is, indeed, roughly a constant across cities, although whether this is itself one of the evolutionary drivers of city highway organization is unclear.
Given our findings that city highway systems tend to obey certain quantitative scaling laws, and presuming that they obey these scaling laws because they have been selected over time for greater efficiency, then one way to diagnose the health of a city highway system is to see whether a city’s data point is where it should be for its land area. For example, if one plots total number of highway exits versus land area for many cities, and one sees a city that does not fall on the line (e.g., maybe it has too many exits), then one would know how to purposely get a city into line, rather than waiting for selective forces to work over the decades to come.
Cities are a lot smarter than we have thought. And that, I contend, is true about most complex systems that are under selection pressure for considerable periods of time. If we can understand the organization of cities, then we might have a leg up in understanding the brain. And cities make it easy, because relative to the size of these city-brains, we are nano-particles traveling through them like the characters from Fantastic Voyage.
Mark Changizi is Professor of Cognitive Science at RPI, and the author of The Vision Revolution (Benbella, 2009) and The Brain from 25,000 Feet (Kluwer, 2003).
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