We’ve all looked out at the night sky and wondered at how much the stars look like strings of cities. But there’s more than a passing resemblance — according to a team of astrophysicists who compared the two, there’s a much deeper connection at work. We aren’t just made of stars, we act like them too.
A new study from two scientists at the Harvard-Smithsonian Center for Astrophysics posits that way we group and grow across the Earth is remarkably similar to the way that galaxies grew in space during the early days of our universe. According to them, we can learn a lot about the mysteries playing out on the Earth’s surface by looking at what we know about the deep reaches of space.
Zipf’s Law: A Recap
First, a little background. If you’ve spent any time hanging around with urban planners, you’re probably familiar Zipf’s law, a mathematical formula that accurately predicts the size of large cities. If you’re not familiar with it, you should check out this excellent explainer on io9 by Annalee Newitz. The law was named for a linguist who noticed that in any given language, a small number of words are used more frequently than a large number of rarely used words. More specifically, the most-used word is always used twice as much as the second-most-used word, and three times as much as the third. And so on.
Oddly enough, Zipf’s law can also predict how a country’s large cities will grow. Basically, the city with the highest population in a country will be twice as large as the next most populous city, and three times as large as the third most populous city, and so on. Despite some caveats (that Newitz brings up), it’s a remarkably consistent and accurate law. But the most interesting thing about Zipf is that no one really knows why it works so well. It just does.
Little Rock, Arkansas. Picture: NASA
An Answer From the Universe
So no one truly understands what makes Zipf so accurate. And who would have guessed that two astrophysicists would be the ones to cast more light on the mystery?
On January 5, Abraham (aka Avi) Loeb — Chair of the Department of Astronomy at Harvard — and Henry Lin published a paper called A Unifying Theory for Scaling Laws of Human Populations. In it, the duo recount how they borrowed a mathematical formula from cosmology that explains how galaxies form in the universe and applied it to how human cities form on Earth, and found that the two are remarkably similar.
Normally, the pair explain, scientists studying urban growth think of city size as the “fundamental entity”, while the population is the thing that forms based on the city’s size. But Loeb and Lin reversed that logic, thinking of population as the fundamental that drives the formation of cities. That opened up a lot of similarities to a topic they’re well-versed in — namely, how galaxies emerged out of matter. Here’s how MIT Technology Review explains the idea:
That is exactly how cosmologists think about the way galaxies evolved. They first consider the matter density of the early universe. Next, they look at the mathematical structure of any variations in this density. And finally they use this mathematics to examine how this density can change over time as more matter is added or taken away from specific regions.
But instead of galaxies and matter density, the team applied this model to cities and population density. And after checking their work against actual census data, they found it was remarkably consistent:
The situation is therefore conceptually and mathematically analogous to the formation of galaxies in the universe, where non-linear gravitational collapse occurs when the matter density exceed some critical value. Our conceptual advance here is also a practical one, since we can apply the mathematical tools developed in cosmology to the problem at hand.
Eventually the same model could be used to predict all sorts of non-linear structures, beyond space and cities, like epidemics: “Just as the development of models for non-linear structure formation in the universe led to a wealth of theoretical and observational work in cosmology,” they explain, “future work here could include the calculation of new observables such as the bias factor for the spread of epidemics.”
Looking at Earth to Explore Space?
If the names Loeb and Lin sound familiar, it’s because this isn’t the first time we’ve written about the team over the past year. The pair, along with a colleague named Gonzalo Gonzalez Abad, also published a paper suggesting that NASA’s future James Webb Space Telescope could be used to search for chlorofluorocarbons in the atmosphere of an inhabited exoplanet. In short, the team argued that looking for a planet’s pollution might be more efficient than looking for the planet itself.
AP Photo/Alexandre Meneghini.
So this isn’t the first time that this team of astrophysicists have linked ideas about space and cities, and it probably won’t be the last. It seems the phenomena of Earth — the clouds of pollution, the waxing and waning of mega-cities — could provide remarkable insight into studying the universe beyond it, and vice versa.
What else about universe could help us understand natural phenomena here on Earth? It’s an awesome, unexpected thought — that the patterns strewn across deep space look so much like the ones we’re unwittingly acting out here at home.
Picture: The Koreas by Night, via NASA