"The Line: Why Saudi Arabia's ambitious city of the future is not optimal

In October 2022, construction work began on the mega-project "The Line", a 170-kilometre-long planned city in the Saudi Arabian desert. Nine million people are to be accommodated within a mere 34 square kilometres - an area comparable to Hockenheim, which is home to only 21,000 inhabitants. This is to be achieved through unique urban planning: "The Line" is to consist of two long rows of 500-metre-high skyscrapers facing each other at a distance of 200 metres and enclosing the desert city like a wall. In addition, urban life there is to be as sustainable as possible: Cars have no place in the futuristic city, and the entire energy supply is to be emission-free.

In a paper published at "Nature Partner Journal Urban Sustainability" in June 2023, mathematician Rafael Prieto-Curiel and physicist Dániel Kondor from the Complexity Science Hub Vienna argue that "The Line" is not particularly sustainable from a mathematical point of view. "A line is the least efficient form for a city," Prieto-Curiel says in a press release. "There is already a reason why mankind has built 50 000 cities, all of which are kind of round."

The main problem with the chosen geometric shape is the huge distances involved: If you randomly pick two people out of the planned city, they are on average 57 kilometres apart, as Prieto-Curiel and Kondor calculate. By comparison, in the South African metropolis of Johannesburg (which is home to a similar number of inhabitants in the metropolitan region as "The Line" is supposed to be in the future, but covers 3357 square kilometres), two people are on average a mere 33 kilometres apart.

In "The Line", the mobility problem is to be solved by a high-speed train. However, this would need around 86 stations so that everyone has a stop within walking distance. The many stops increase the length of the journey - moreover, a train cannot reach the desired high speeds in this way. Due to the many stops, a person would travel on average more than 60 minutes to their destination, Prieto-Curiel and Kondor calculate.

The advantage of two-dimensional cities

. A much more efficient solution is obvious, the two researchers say: "The Circle". If the skyscrapers planned in "The Line" were arranged within a circular area, the problems with sprawling distances would have been solved. A circle with the same area as "The Line" (34 square kilometres) has a diameter of only 6.6 kilometres. Two people picked at random would then have an average distance of 2.9 kilometres to each other. A high-speed train would not be necessary at all, since theoretically everything is within walking distance. A few additional bus lines as well as bicycles would suffice. The round city form would be less sensational, but still "most desirable, as it reduces commuting distances and energy requirements for transport", Prieto-Curiel and Kondor write. . The main reason for the advantage is that a circular area is two-dimensional from a mathematical point of view, while a line is one-dimensional. In one dimension, the number of reachable places scales linearly with the distance one is willing to walk - whereas in two dimensions, the number increases with the square of the distance. In addition, one-dimensional structures are much more vulnerable than those in higher dimensions. For example, if a fire breaks out somewhere within "The Line", thousands of people are directly cut off from a large part of the city. At least the project is getting people to discuss urban forms, says Prieto-Curiel, "and that is immensely important because cities are growing, especially in Africa."

Spectrum of Science

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