Cities are a meta-innovation: an innovation that creates more innovations. It takes some smart thinking to build a thriving, cultured metropolis where a zillion people can live on top of each other and not go insane, but once you do that, the city gives back by turning all those people into geniuses.

Really — studies show that having a large number of people gathered together helps create genius innovators. As Smithsonian writes:

Research published [in June] by scientists from M.I.T. concluded that productivity and innovation in urban areas grow at roughly the same rate as population, largely because the greater density of people living in a city increases the opportunities for personal interactions and exposure to different ideas.

The Atlantic Cities got geeky about this:

“If you look at the interaction patterns of cities,” [study author Wei] Pan says, “You will see that they grow super-linearly with population with the same growth rate as productivity, as innovation, as crime, as HIV, as STDs.”

All of those facets of urban life have appeared until now to share a somewhat mysterious mathematical relationship. But this research suggests that this particular super-linear growth rate is directly tied to how dense cities enable us to connect to each other. As cities grow, our connections to each other grow by an exponential factor. And those connections are the root of productivity.

But there’s a catch. You need public transportation for all this to work. Good public transportation. Smithsonian, again:

[Pan's] model doesn’t hold up, however, for some huge African and Asian cities that have even denser populations than cities in the West. But Pan has an explanation for that. Generally, those cities have terrible transportation systems. If people can’t get around, can’t have those serendipitous interactions, a city’s density has less impact.

Basically, what they’re saying is that boosterism for cities and public transportation is what’s going to save not just the planet, but the human race. We promise not to say “we told you so.” OK, we promise not to say it too often.