I am writing this after a day at a statistical physics conference in London, and before kick-off of the Portugal-Wales Euro 2016 semi-final. My team (Wales) are one match from their first ever final of a major championship, so I am partly writing this as a distraction from getting stressed. The pre-match build up heavily features Wales’ star Gareth Bale.
Dragon-King sounds like the title of a kids’ movie, but in fact it is the impressive sounding name a statistical physicist called Didier Sornette has given to a type of extreme (large) event, such as a stock market crash, a big earthquake, a massive meteorite strike, a once-in-a-century heatwave, etc. The idea is that if you want to model say stock market movements, then you may need one model for the run-of-the-mill market fluctuations but a different model for the once-in-fifty-years crash. This crash is your dragon-king, king because it is so big, dragon because it has a different, more mysterious origin, than the usual events.
It is an interesting idea, indeed sometimes if you have N events or objects, then N-1 of them are kind of similar, while 1 is qualitatively different. An example Sornette gave in his talk today is that of the distribution of city sizes in a country. In England for example, London is a obvious outlier in terms of size, it is much larger than any other English city, and so is a potential candidate for a dragon-king. Here there is an obvious difference between London and all other English cities: it is the capital.
Put like this, dragon-king looks like a dramatic name for a relatively trivial classification scheme. One where we classify unusually big things into: A) things that are mostly like regular-size things, but bigger, and B) into things that are in some way qualitatively different from the little guys. But trivial or not, this classification looks useful to me, and a name like that makes it easy to remember.
But it is perhaps as well to note that some events may have a different origin but maybe not be that big, perhaps they should be called dragon-princesses. While some anomalously large events may have the same origin as the little guys, they could be called peasant-kings.
For example, at low temperatures quantum particles called bosons can form what are called Bose-Einstein condensates, which behave as a single quantum object. You can have a billion atoms, of which, say, half a billion are in a single object, the condensate, while the other half a billion are either lone atoms, or pairs or threes – much much smaller. But the physics that governs the condensate is exactly the same is that which governs the single atoms. This is an example of a peasant-king.
But win or lose tonight, and whatever he does tonight, I think Gareth Bale is Wales’ dragon-king.
Chance & Necessity 