Science has created a mathematical model to judge whether a city is truly great

Sydney Opera House built from lego at Sydney Town Hall. Brendon Thorne/Getty Images

What makes a city great? The answer could be: Great cities connect people and failed cities isolate people.

And now scientists have developed a mathematical model which they say can determine the inter-connectedness of humans within a city and its ramifications on a society.

The researchers say their model provides a framework to work out the impact from a range of issues including the value of transport systems and threats from infectious diseases.

In an age of supercharged urbanisation, the scientists say the fundamental importance of physical, face-to-face social ties is still important.

Previous attempts attempts at estimating social ties in cities often relied on over-simplifications, the researchers say.

“Size is clearly not a sufficient measure of greatness, just like rank and title can be poor predictors of influence in social networks,” the researchers write.

“Of the many candidates, the simplest objective measure of success is, possibly, the extent to which a city fulfils its primary purpose of maximising the number of face-to-face, opportunity-spawning, interactions between its inhabitants.

“From the rise of the Medici in fifteenth century Florence to the prestige of an efficient transport system in a 21st century metropolis, this connectivity is synonymous with both the eminence of individuals and the success of whole cities.”

This latest model assess the impact of transport developments, population growth and other infrastructure and demographic changes on a city.

It also looks at gross domestic product, HIV infection rates, census data, transport information, plus the connectivity and geometry of a city.

The model operates under a set of principles.

One is a nod to the variety of city life, the heterogeneity. This looks at wealth, beauty and artistic skills. On the less attractive side, crime is also a factor added to the model.

The second principle is human endeavour, a variation on the theory of rational choice where individuals are said to act in their own best interests as they see them.

The third principle reflects the finite nature of resources. This looks at the maximum amount of time a person is willing to spend on a single commuting trip.

And the final principle is about opportunity for face-to-face interaction. This looks at mobility and social contact patterns in cities.

The model then works on a series of formula. Here’s the one for connectivity:

The total number of ties is represented by “T” and “Ti” is local connectivity. There is a full explanation of the formula in the paper, Great cities look small. The model by Professor Michael Stumpf of Imperial College London and colleagues is published in the Journal of the Royal Society Interface.

The researchers haven’t yet run the model over an Australian city.

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