# Lots of diffusion, many Kims, few Deaths

I am teaching things called partial differential equations at the moment. One of the most important of these is the diffusion equation. As the name suggests, it describes diffusion. Diffusion is everywhere. For example, in your body, diffusion is how the oxygen gets from your blood into the cells where it is needed.

Diffusion is a random process, the molecules move at random. Very similar random processes, also modelled by the diffusion equation, appear all over the place. One example I like is surname extinction. Ever wondered why there so many Wangs in China, and Kims in Korea? After reading a scientific paper with 5 Korean authors, all called Kim, I did. One possible explanation is called the Galton-Watson process.

The maths is just the sort of thing I am teaching but I won’t go into that here. However, the basic idea is simple. Say you have a population of 100,000 people in a country when surnames first arise. Koreans invented formal surnames around 2,000 years ago. At this time let’s say there are 1,000 different surnames. So on average 100 people have the same name.

But then simply due to chance these 100 people perhaps have fewer children than average, or more girls. Like in the UK, children take their father’s name. Then the next generation has perhaps only 80 people with this name. If they have many boys the number might bounce back to 100 but if again by chance they have few boys the number could drop to 60, and so on, until the name becomes extinct.

Once extinct it is gone forever. Now the longer surnames are around, the more of them become extinct, simply by chance, and the fewer surnames there are left.

So in Korea where surnames have been around for 2,000 years, more than 1 in 5 people are called Kim, while in The Netherlands, where surnames are only 200 years old, there are tens of thousands of surnames. This includes odd ones like “De Dood”, which means “The Death”. In another 1,800 years that name will itself probably be dead.