# Forest Fires

August 16, 2010Link: Forest Fires

This is a cute java applet that illustrates a mathematical phenomenon known as percolation, which has a lot of applications in the real world. If you can actually measure the chance that a fire will jump from one tree to the next (a chance the applet gives you the option to set), it ends up having very meaningful outcomes for the entire forest. For example, try setting the probability of the fire spreading to 0.25, light a fire, and then regrow the forest and try again at 0.35. Not too big a difference, right? Now compare 0.45 to 0.55. You end up with a radically different picture. What’s the story?

Percolation is a subfield of probabilistic graph theory, a field my girlfriend once studied. I was eternally envious of how she could explain the uses of her field to people.

**People (to me):** What do you do with K3 surfaces in the real world?

**Me:** Uh… there may be some kind of thing with string theory, though that doesn’t really relate to my problem directly…

People (cutting me off, to my girlfriend): What can you do with probabilistic graph theory?

**Her:** It’s good a modeling things like the spread of a disease. Say you know the chance of a disease spreading between two people who come in contact. You can study a group of people using probabilistic graph theory and predict whether you’ll end up with an epidemic or a tiny flare up.

**People:** That sounds really interesting. And useful!

**Me:** (jealous sulking) …

So there you have it! Probability and statistics are hugely applicable in today’s data driven world. In the implementation, though, I tend to find them a little less pretty. So that’s the cost: beauty for use. That’s what prevents me from being an applied mathematician, I suppose.