In addition to walking speed, studies have found evidence that invention, job diversity, social interactions, restaurant diversity and crime also increase in bigger cities, and also follow the 12 per cent rule. There is some variability from city to city, but the average increase is 12 per cent per doubling of the population. These studies show that, in general, cities foster greater social interaction (both positive and negative), diversity, culture and generation of ideas. These principles are summarised by the 12 per cent rule (and a few others) and seem to apply across cultures and over time, as far back as 1150 BCE.