Frequently Asked Questions

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. This is partly because Erdős-Bacon-Sabbath numbers actually involve two different games: one to determine the existence of a person’s EBS number, and another to find the optimal collaboration paths.

Our goal at the EBS project is to celebrate creative academics and academic creatives, so we take an inclusive approach to the existence game. Collaborations listed on this site include:

However, these may not be the best criteria with which to play the optimization game. Allowing music production credits, for example, opens the door for too many easy shortcuts that go against the spirit of the Sabbath game. Therefore, we consider only more “traditional” collaborations when comparing two EBS numbers:

All collaborations on this site are annotated and fully cited. We want you to check our work and decide for yourself whether our EBS calculations should count!

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. Microsoft’s Academic Search is a good place to start, but its paths need to be checked manually: in our experience, it tends to return many false positives due to researchers with similar names.

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.

Why haven’t you added new candidates lately?

The EBS project has proven that smart, creative, and successful people are far from rare. We have confirmed dozens of Erdős-Bacon-Sabbath numbers and have a list twice as long of multi-talented people worth celebrating on this site.2 With this goal accomplished,3 we have decided to put the project on hiatus to focus on other mildly interesting things.

If you discover a new Erdős-Bacon-Sabbath number, we encourage you to share it on Twitter with the hashtag #ErdosBaconSabbath.

Who made this?

Sean is the proprietor of Timeblimp and maintainer of this site. He is active on Twitter and independently invented the EBS number.

Ross Churchley is a graduate student in graph theory at Simon Fraser University. He created and formerly maintained this website. He has an Erdős number of three and a Sabbath number of eight.

The Erdős Bacon Sabbath Project is a joint effort between Sean, Ross, and the many contributors who help us out on Twitter.

  1. The number of people with an Erdős number of two is over 9000
  2. Just look at astronaut Chris Hadfield, psychologist/actress Pamela Stephenson, biophysicist/bard Sergey Nikitin, recreational mathematician Vi Hart, philosopher Cornel West, and actress/gymnast Kiralee Hayashi, among many others. 
  3. The one unfinished job we do have is addressing the lack of diversity in the EBS Holders list. It is not clear how much of this is due to (A) the social structure of academia, entertainment, and music; (B) unequal opportunities for interdisciplinary success; and (C) our own biases in deciding which famous people to investigate. If you have any suggestions to fill in our blind spots, please let us know at @ErdBacSab