Who are Erdős, Bacon, and Sabbath?

Paul Erdős was an eccentric Hungarian mathematician known for publishing more papers with more collaborators than any other modern mathematician. He spent most of his life as a vagabond, traveling between scientific conferences and the homes of colleagues all over the world. He would typically show up at a colleague's doorstep and announce "my brain is open", staying long enough to collaborate on a few papers before moving on a few days later.

Kevin Bacon is an American actor whose notable films include Footloose, Apollo 13, and Mystic River. He has appeared in over 70 movies and TV shows, which led him in 1994 to comment that he had worked with everybody in Hollywood or someone who's worked with them. This idea also occurred to three Albright College students, who presented the Six Degrees of Kevin Bacon game to the world.

Black Sabbath are an English rock band, formed in 1969 by guitarist Tony Iommi, bassist Geezer Butler, singer Ozzy Osbourne, and drummer Bill Ward. The band were early pioneers of the heavy metal genre and have been widely cited as influences on later rock bands. The lineup of Black Sabbath has changed so much over the years that Wikipedia has an entire page listing its members.

What is an Erdős-Bacon-Sabbath number?

The Erdős number measures the “degrees of separation” between a given researcher and Paul Erdős. Each of Erdős' 511 coauthors has an Erdős number of one. Anyone who has collaborated with a coauthor of Erdős has an Erdős number of two.1 In general, your Erdős number counts the coauthored academic publications it takes to connect you with Erdős.

The Bacon number applies the same idea to Hollywood: it counts acting roles instead of publications to connect a given actor with Kevin Bacon.

The Sabbath number similarly counts musical collaborations. Every person who is listed on Wikipedia as a current or former member of Black Sabbath has a Sabbath number of zero. Anyone who has recorded a song with any of them has a Sabbath number of one, and so forth.

A few talented people have well-defined Erdős, Bacon, and Sabbath numbers. These people have an Erdős-Bacon-Sabbath number — which is just the sum of the three components — and are entitled to a place on this site!

What counts as a collaboration?

The bare minimum requirements are:

However, what exactly should count is the subject of endless debate. We don't like playing gatekeeper, so we take an inclusive approach to determining the existence of an EBS number. Collaborations listed on this site include:

Our goal at the EBS Project is to celebrate creative academics and academic creatives, so we also feature on this site a few people who have research and creative accomplishments that don't quite fall under the Erdős-Bacon-Sabbath umbrella.

How do I find if I have an Erdős-Bacon-Sabbath number?

The most useful tool for computing Erdős numbers is MathSciNet's collaboration distance calculator. Unfortunately, it only indexes journals related to mathematics, so linking Erdős to researchers in other fields often requires manual search.

The Bacon number is almost always found by consulting the Oracle of Bacon, which finds a path through credited roles on IMDB. We find ourselves having to modify paths only rarely to exclude things we think are a bit of a stretch.

Sabbath numbers are typically hardest to find except for well-known musicians. The Six Degrees of Sabbath calculator makes things easier, although the path returned by its weighted algorithm can often be improved on.

How can I contribute to the EBS Project?

The Erdős-Bacon-Sabbath Project is an open-source endeavour that lives on GitHub. We welcome everything from modest suggestions to wild conjectures to fully fleshed-out contributions!