The study of social networks is greatly influenced by the 'small world' hypothesis - that everyone on the planet is connected to each other via a finite number of friends. The term 'six degrees of separation' has since entered into popular discourse, suggesting that on average we are connected to any other person by a chain of six acquaintances.
When I was growing up, I remember we used to play a game called Six Degrees of Kevin Bacon in which we would try to link any actor or director to the actor Kevin Bacon in a chain of less than six names. Out of this game came the assignment of a Bacon number to every actor: Kev himself had a Bacon number of 0, if you worked on a film with him you got a Bacon number of 1, if you worked with someone who worked with Kevin you got two and so on. (It is actually mathematically proven that actors would on average get lower Connery numbers or Caine numbers, but 'Six degrees of Kevin Bacon' just has a nice ring to it)
Around the same time, there was a similar game in action surrounding the famous Hungarian mathematician Paul Erdös. Erdös had a way of life which kind of reminds me of the roving Irish musicians of yesteryear; he would travel from campus to campus, show up on a colleague's doorstep, work on a few papers and then move on to the next place; his personal possessions could all fit in a suitcase. In this way he coauthored 1500 papers with 409 people, and became one of the most prolific mathematicians ever. An Erdös number of one is given to anyone who collaborated with him, and the chain continues just like the Kevin Bacon game - many a mathematics faculty coffee morning has been spend joining together the links!
Now for the ultimate test of polyability and social connectedness: have you starred in a film with Kevin Bacon AND coauthored a paper with Paul Erdös? Introducing - the Erdös-Bacon number, got by adding your Erdös and Bacon numbers together! Erdös and Bacon both actually have undefined Erdös-Bacon numbers, since they stayed in their own fields. The lowest known Erdös-Bacon number is 3 for MIT mathematician Daniel Kleitman who coauthored a paper with Erdös and appeared as an extra in Good Will Hunting which gave him a Bacon number of 2. Popular string theory author Brian Greene has an Erdös-Bacon number of 5. Richard Feynman has 6, and Stephen Hawking has 7.
Among professional actors and actresses, the lowest is 6 for Danica McKellar (who played Winnie Cooper in The Wonder Years) and has an Erdös number of 4 for a paper she coauthored whilst still an undergrad at UCLA. Possibly the only other full-time actor to have a defined Erdös-Bacon number is Natalie Portman, who has 9.
Apparently, I have an Erdős number of 5, so all I need is a starring role alongside Kevin Bacon to boost me into that elite league :)