Living in a complex world
Many things in life are more than the sum of their parts. Whether its the behaviour of crowds of people, flocking birds or shoaling fish, the unpredictable patterns of the weather or the complex structure of the Internet, it's often the interaction between things, rather than the things themselves, that generates complexity.
It's a challenge to science, whose traditional approach of taking things apart and looking at the individual bits doesn't work when faced with emergent complexity. But there are mathematical techniques to understand this phenomenon. The Living in a Complex World website, originally launched to accompany an exhibit at the Royal Society Summer Science exhibition, explores complexity in the real world and has some great factsheets looking at the maths used to understand it. It's well worth a look!