What do Carl Sagan, Richard Feynman, and Natalie Portman have in common?
They all have the same Erdős-Bacon number: six.
Natalie Portman collaborated (as Natalie Hershlag) with Abigail A. Baird, who wrote mathematical papers in a further collaborative path which leads to Joseph Gillis. Gillis, having co-written a paper with Paul Erdős himself, has an Erdős number of one. This gives Portman an Erdös number of five. Bacon and Portman both appear a movie (which one? See the details in this Wikipedia article: http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Bacon_number), which gives Portman a Bacon number of one.
The Erdős-Bacon number is simply the sum of these two numbers — hence Natalie Portman’s six: five plus one.
Feynman’s and Sagan’s sixes are more balanced. Richard Feynman’s is the most so, since his Erdős and Bacon numbers are both three.
I haven’t been able to determine who first thought of an Erdős-Bacon number, but . . . wow. It came from the blogosphere (Where else?) — Wikipedia reveals that much.
Some blogger might be obsessive enough, someday, to exhaustively determine exactly how many people even have such numbers. However, that person will not be me.