Somewhere in the dark recesses of mathematics lies a number that is simultaneously utterly self-indulgent and completely inconsequential. It is a number that sets one apart as a member of an elite club. Mathematicians, remember, are a weird bunch. Capable of spending months, even years, in isolation working at a frantic pace, they seem the unlikeliest to have a lighter side. But they do. Proof of this is the Erdös-Bacon number.
Recall the meme about actor Kevin Bacon (based on Stanley Milgram’s ‘Small World’ experiments of the 60s)? The Bacon number of any actor is defined as the number of links in a chain between him and Kevin Bacon, the links being relevant co-stars in feature films.
As much as Hollywood would love to take credit for it, the idea is simply a modification of the Erdös number. Paul Erdös was a Hungarian mathematician who co-authored over 1,500 mathematical papers, a world record; such productivity begged for the invention of the Erdös number. Whereas the Bacon number counts co-stars as links, the Erdös number counts co-authors of scientific papers. Having a finite Erdös number is common even for non-mathematicians.
As described in the fabulous biography, The Man who Loved Only Numbers, Paul Erdös was eccentric, to put it mildly. He famously collaborated on papers with anyone willing to give him a place to sleep. His motto ‘Another Roof, Another Proof’ attests to this fact. As a result, people with an Erdös number of 1 (people who have collaborated directly with Erdös) can be found scattered in various fields of academia—like statistics, chemistry and even biology.
Add these two numbers, and you get the Erdös-Bacon number. This is where it gets interesting. It is estimated that 90 per cent of current mathematicians have an Erdös number of eight or less. The average Bacon number of a Hollywood actor is between two and three. However, the overlap of the two fields is relatively small, so finding people with finite and small Erdös-Bacon numbers is a bit of a challenge. Interestingly, both Erdös and Bacon have infinite E-B numbers (though collaborations on documentaries instead of feature films would assign Erdös a Bacon number of four).
Columbia University physicist and popular science writer Brian Greene has a famously low E-B number of five. Greene wrote a paper with Shing-Tung Yau, who wrote a paper with Ronald Graham, who wrote a paper with Erdös, giving Greene an Erdös number of three. His route to Bacon is shorter—he appeared in the film Frequency (2000) with John Di Benedetto, who was in Sleepers (1996) with Kevin Bacon. There is a slight temporal ambiguity in calculating Bacon numbers, since future collaborations may lower an existing Bacon number. Daniel Kleitman, a Harvard physicist, has held the record for the lowest E-B number since 1997. Kleitman appeared as an extra in Good Will Hunting, a film on which he was also a maths consultant. This gives him a Bacon number of two (Minnie Driver, who was in that film, was also in Sleepers with Kevin Bacon).
Then there are Hollywood actors who have collaborated on scientific papers (an unsurprisingly small bunch). The recent Oscar winner Natalie Portman has a low Erdös-Bacon number of seven. As a psychology undergraduate at Harvard, her published papers give her an Erdös number of five to go with her Bacon number of two (she was in New York, I Love You with Eli Wallach, who was in Mystic River with Bacon).
There is no exhaustive list of people with finite Erdös-Bacon numbers. Lists have been compiled using a couple of online generators, one for the Bacon number (oracleofbacon.org), the other for the Erdös number (http://www.oakland.edu/enp/compute/). The Erdös Number Project website, with appropriate gravitas, suggests that ‘once you find your Erdös number, you can use it in various ways, such as your licence plate number’.
By most accounts, Professor Kleitman has the lowest E-B number currently, and it is unlikely to be lowered. The one person who has a sporting chance of doing it is Bacon himself, who, with a Bacon number of zero, is in too good a position not to give academia a try.
He could certainly use a finite licence plate number...