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Can maths make better cities?

Groundbreaking new research out of the US has found that despite their unique differences, all cities obey the same simple mathematical parameters.

Physics Professor Luís M. A. Bettencourt from the Santa Fe Institute in the US, who is famous for his interdisciplinary research, has dipped into physics, economics, sociology, biology and several other sciences to show that all cities follow a similar mathematical pattern or model, and operate like a “social reactor” that is part star and part network.

The paper, “The Origins of Scaling in Cities”, is published in the journalScience and is making headlines because it has the potential to help us better understand and plan our cities in an very urbanised world.

Defining the indefinable

Professor Bettencourt says that while cities are becoming increasingly important to humans, our ability to understand and manage them scientifically has been limited.

In our attempt to define and label them, cities have been compared to organisms, ant colonies or river networks, but these analogies don’t reflect how cities really function.

Bettencourt says it has been difficult to take a scientific approach to cities because of the many interdependent “social, economic, infrastructural and spatial complex systems that exist in similar but changing forms over a huge range of scales”.

His mathematical approach shows that cities are actually like nothing in nature – they’re something altogether new.

Bettencourt and his colleagues crunched data on all sorts of things found in cities – from the length of road networks, to the average income of inhabitants, number of social interactions, land use, socioeconomic data, infrastructure and even the number of patents per capita.

They found that these things scaled with the size of the city, so as the population of a city grew, so did these characteristics. And the results were consistent globally and throughout time.

These mathematical formulas or “quantitative theory of cities” describe how a city’s properties vary in relation to their population sizes, allowing Bettencourt a framework for understanding how cities function and grow that predicts very closely dozens of statistical relationships observed in thousands of real cities around the world.

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