I am quite proud of my Erdös number of 4. An Erdös number of 4 means via a trail of 4 papers I can reach the prolific Hungarian-born mathematician Paul Erdös. Erdös published papers with an astonishing 511 other mathematicians. The path of papers is here, but basically I have written a paper with a good friend Jon Doye (Erdös number of 3), who has written a paper with a guy called Richard Berry (Erdös number of 2), who wrote a paper with a P. Salaman, who published a paper with Paul Erdös himself and so has an Erdös number of 1.
Erdös numbers show how connected scientists and mathematicians are; how much we work together. It is also shows up a fundamental feature of networks, which is that for many networks you can get from almost anyone on the network to anyone else in just a handful of steps, 4 in my case.
This also shows up in Six Degrees of Kevin Bacon, which is the same idea as Erdös numbers, but with Kevin Bacon instead of Erdös, and appearing a film together replacing writing a paper together.
Now of course, if you write a scientific paper, and appear in a film as well, you can have both an Erdös number and a Bacon number. Better still, there is musical version called a Sabbath number, and so if you write scientific papers, appear in a film, and record music, you can have Erdös, Bacon and Sabbath numbers. Indeed you can add them together to get an Erdös-Bacon-Sabbath number.
Timeblimp reckons Richard Feynman has an Erdös-Bacon-Sabbath number of 10. One of his many achievements is an impressively low (particularly for a physicist) Bacon number of 3. He needs it to fend off competition from Natalie Portman.
Natalie Portman has an Erdös-Bacon-Sabbath number of 11, so Feynman only just beats her. Natalie Portman published a paper (she is listed as Natalie Hershlag, her real name) while doing psychology at Harvard, and has an Erdös number of 5. Only one more than me, although my colleague Paul Stevenson is two ahead of her.