We walked out onto Cramond Island on the outskirts of Edinburgh. It was a calm day and the views were fantastic. It reminded me of an important question in Physics: How long is the coastline of the UK? According to a recent edition of Physics World magazine, this started with a piece of research by a pacifist who wanted to show that there was a proportionality between the length of a country's borders and the likelihood of war. But the problem is one of what do you measure and when do you measure it? If you stop to measure round every stone the length goes up and up. And the distance changes as the tide changes. In fact, you get a distance that tends towards a huge number (not infinite as far as I know) but with an area that is finite. That is, if you stop to measure round every grain of sand. This research was one of the early works that led to fractal geometry that is itself key to Chaos Theory. A straight line has one dimension and a flat plane has two dimensions. In some sense the wiggly coastline has a dimension in between, some fraction of a dimension, hence fractal.
