Paul Erdős is flanked by Kevin Bacon and the members of Black Sabbath.

Who else has an Erdős-Bacon-Sabbath number?

A little while ago, I did some sleuthing to find out the Erdős number of Brian May, astrophysicist and guitarist from Queen. My travels led me to Timeblimp, who threw together three measures of professional collaboration to make a rather fun parlour game. Assuming that the people in your parlour are three kinds of nerds and enjoy long and complicated internet scavenger hunts. Which I am and I do.

The game is to find a well-known person who has published academically, released a song, and been involved in a movie or TV show. Then, you play three versions of Six Degrees of Kevin Bacon: find a series of movies to connect them to prolific actor Kevin Bacon, a series of coauthored papers to connect them to the eccentric mathematician Paul Erdős, and a series of musical collaborations to get to Black Sabbath. Add up all the links and you get the Erdős-Bacon-Sabbath number.

Brian Cox has an Erdős-Bacon-Sabbath number

If anyone has an Erdős-Bacon-Sabbath number, Brian Cox is exactly the sort of person you might expect to have one. The keyboardist, particle physicist, and BBC science presenter is no more than 7+3+3 degrees of separation from the centers of the EBS graph.

Sean from Timeblimp first suggested the possibility of Brian Cox having a well-defined Erdős-Bacon-Sabbath number, but to my knowledge nobody had worked out his Erdős number until now. I managed to find a path of length seven.

Erdős number Researcher Citation
7 Brian Cox Hard colour singlet exchange at the Tevatron
6 Leif Lönnblad Small-x dipole evolution beyond the large Nc limit
5 Gösta Gustafson The action-angle variables for the massless relativistic string in 1+1 dimensions
4 Bo Söderberg Scaling laws for mode locking in circle maps
3 Boris Shraiman Scaling theory for noisy period-doubling transitions to chaos
2 C Eugene Wayne The Euler-Bernoulli beam equation with boundary energy dissipation
1 Steven George Krantz Intersection graphs for families of balls in ℝn
Paul Erdős

The above connections use only papers with three coauthors or fewer. Cox has worked in gigantic collaborations like ATLAS, so it’s quite possible that there might be a shorter path.

Brian Cox — not to be confused with the other Brian Cox — is three degrees of separation from Kevin Bacon through his many TV appearances, including cameos on Doctor Who.

Bacon number Actor Credit
3 Brian Cox Doctor Who “The Power of Three”
2 Matt Smith Charlie Says
1 Sosie Bacon Story of a Girl
Kevin Bacon

Brian Cox had a successful music career before finishing his PhD and also has a Sabbath number of three.

Sabbath number Musician Band/Album
3 Brian Cox Dare
2 Darren Wharton Thin Lizzy
1 Tommy Aldridge Speak of the Devil
 Ozzy Osbourne Black Sabbath


After I published this post, someone brought it to the attention to none other than Brian Cox himself!

A screenshot of a tweet by Brian Cox, reading "It has just been pointed out to me that I have an Erdős-Bacon-Sabbath number!!"

The resulting hullabaloo led to the discovery of many other Erdős-Bacon-Sabbath numbers. Eventually, I retired from EBS research after realizing its flaws as a game and as a social construct.