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The places we visit most frequently are the ones closest to us.

The mathematical relationship between distance and our displacements explained by an article on Nature

How can we explain how often people travel to visit certain places? Based on our daily experience and intuition, we could say that distance is a key element and that we tend to visit more often those places that are close to us in space. It may seem a foregone conclusion, but now there is mathematical law to prove it, supported by a mass of data collected from four million smartphones around the world and published on Nature. The paper title is “The universal visitation law for human mobility” and it’s signed, among others, by Paolo Santi, Research Director of the IIT-CNR and researcher at the Senseable City Lab of the Massachussets Institute of Technology. 

“What we have found is that there is a very clear inverse relationship between how far you go and how frequently you go there,” says Paolo Santi. “You only seldom go to faraway places, and usually you tend to visit places close to you more often. It tells us how we organize our lives.”

The study is based on global data sets and it has shown that people tend to travel more frequently to places they can reach by covering shorter distances. Thanks to the analysis of a huge amount of anonymized telephone data, collected in the metropolitan areas of Abidjan (Ivory Coast), Boston (USA), Braga, Lisbon and Porto, (Portugal), Dakar (Senegal) and Singapore, the researchers have managed to define this inverse relationship very accurately compared to what has been done up to now in the urban studies literature.

Cellphone data are perfect for this type of study because they allow you to identify the area where a person resides and to track his or her most frequent movements for a significant amount of time, with maximum accuracy of the results. Santi and the team of researchers involved in the study charted over 8 billion geographic data, generated by over 4 million people, following their movements for a few months.

The “inverse law” of visitation that links the distance and frequency of a visit was found in every area analyzed, allowing researchers to discover a precise mathematical relationship between these two variables. The cases in which a deviation from this “inverse law” was observed concerned specific places, such as tourist attractions or ports, which can attract people even from greater distances.

The article confirms the so-called “Theory of Central Places”, formulated almost a hundred years ago by the German geographer Walter Christaller. A theory that became very influential over the years, so much so that it is often used, for example, to choose the location of shopping malls and other activities within a city. But Christaller’s theory had never been proven with empirical data until today.

The methodology of this study can be successfully used in urban and regional planning, for example to predict how the mobility of a city can be influenced by the positioning of new areas of interest.

“It’s a push toward understanding how we design good urban infrastructure,” Santi says. “Another implication is using more data in the process of planning. I’m not saying this information should replace all other factors that influence planning, but definitely I think a process informed by what people do is important – and this finding shows you can use big data for this purpose. I think this paper is good news for people working in urban planning.”

The study involved a network of researchers from all over the world: in addition to Paolo Santi, the paper is signed by Markus Schlapfer, researcher at the Urban Complexity Project of the ETH Future Cities Lab in Singapore, Lei Dong, researcher at Peking University of Beijing, Kevin O’Keeffe and Mohammad Vazifeh, postdoc of the Senseable City Lab at MIT, Michael Szell, associate professor in Data Science at the IT University of Copenhagen, Hadrien Salat of the Future Cities Laboratory, Singapore-ETH Center, Samuel Anklesaria, researcher of the Senseable City Lab of MIT, and Geoffrey West, former president of the Santa Fe Institute.

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