Paul Romer asks whether Detroit is Denser than Denver. It's a set up because Romer is calling attention to the widespread silliness of referring to city-wide overall densities. Readers of this blog have heard it many times. Romer mentions that we have to look at local maps and consider small area peculiarities.
Researchers at the Santa Fe Institute are doing interesting cross-sectional work on cities. They report finding scalability over a large international set of cities. But we know that definitions and boundaries vary considerably from place to place. There are local economies (labor markets) everywhere, to be sure. Do the definitions of spatial units used in the SFI sample match these?
Zipf-rule rank-size distributions apparently describe all sorts of artifacts. SFI researchers often cite the example of gas stations. But we can bet that the density of these artifacts does not scale.
What matters most is the networking opportunities -- in Detroit or Denver or any place. We prosper when we can exchange goods and ideas at acceptable costs. We apparently do this in all sorts of densities and settings.