Scientists have good news: human society can potentially be analysed and predicted using simple maths. This introduces a completely new way of understanding social problems and predicting the future structure of society, which may be a boon to intellectuals, policy experts and investors alike.
Young children love cutting and folding paper to make symmetrical snowflakes, joining seemingly random dots to make pictures, and otherwise imposing order on their world. Adults are not very different: they seek a sense of structure too. Grownups who enjoyed maths or physics at high school or university may wish that the affairs of human society were governed by laws that corresponded with Pythagoras’ theorem – the C=2πR formula for calculating the circumference of a circle, and other handy equations. It would make analysis and prediction so much simpler.
A leading exponent of the idea that there are hidden but useful mathematical patterns in the world is Geoffrey West, physicist and former president of New Mexico’s Santa Fe Institute. The institute is dedicated to using a range of different disciplines to study the principles of complex systems, including biological and social systems.
Professor West points out that the amount of energy that different creatures require tends to increase by about 75% for any doubling in its size. He has devised a chart which shows that this rule applies to a veritable menagerie of living beings, including mice, hens, horses, elephants, cassowaries condors – and people.
This is striking enough, but Professor West has gone one step further, by working out similar simple mathematical patterns for cities. He finds that if one city is twice as large as another, it needs about 15% less infrastructure per thousand people – 15% fewer petrol stations, for example. However, a many other things increase by around 15% per person, including crime, creativity (as measured by patents) and income.
Professor West and his colleagues are not the first people to find unexpected mathematical patterns in society.
In 1948, the English physicist and meteorologist Lewis F. Richardson published the splendidly entitled “Variation of the Frequency of Fatal Quarrels with Magnitude”. Motivated by his desire as a Quaker to prevent violence by understanding its patterns, he looked at all wars between 1820 and 1945.
Richardson found that for each ten-fold increase in the severity of a war, as measured by the number of deaths, the frequency of war decreased by somewhat less than a factor of three. Roughly speaking, wars with about 10,000 deaths occurred about one-third as often as wars with a thousand deaths.
Two geologists at Cornell University, D.C. Roberts and Donald Turcotte found similar mathematical patterns for forest fires. They drew parallels between the two phenomena: after the initial ‘ignition’, both wars and forest fires have a tendency to peter out, but a small number manage to spread by finding the ‘fuel’ to keep going. For a forest fire, this fuel comes from trees. For a war, it might come from unstable countries bordering the original conflict.
“In all chaos there is a cosmos, in all disorder a secret order”, wrote Carl Jung, the renowned Swiss psychiatrist, in 1959. Discovering the secret order and simplicity of the world could well be a rewarding endeavour.