Before justifying my EBS number, I should explain a little more about the background.  The project, as its website says, studies the connections between science, performing arts and music. It is based on the idea underlying the game The Six Degrees of Kevin Bacon, which is based on the premise that you can link any actor to Kevin Bacon in no more than 6 links. So for example, actor A appeared in a movie with actor B who appeared in a movie with actor C who appeared in a movie with Kevin Bacon. So actor A's Bacon number is 3. 

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 movies: 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.

What counts as a collaboration?

• for Erdos - coauthored academic papers, popular science or nonfiction books, patents, and academic advising relationships which result in a project or thesis;
• for Bacon - movie and TV appearances, documentaries, and other acting and directing roles;
• for Sabbath - song performances (recorded and live), samples, production, composition, and lyrics.

My Erdős-Bacon-Sabbath number: 15

I have an Erdös number of no more than 7: I was co-author of a paper which was supervised by Johanna Jarvis, who co-authored (under her maiden name) with Barry Smalley, who co-authored with Andrew Norton, who co-authored with Lars Bildsten, who co-authored with George Djorgovski, who co-authored with Jogesh Babu, who co-authored with Paul Erdös.

I have a Bacon number of no more than 5: I briefly appeared in a video taken by John Mason, who appeared in TV programmes with Patrick Moore, who appeared on The Sky at Night with Buzz Aldrin, who appeared in Transformers: Dark of the Moon with Jim Meskimen, who appeared in Apollo 13 with Kevin Bacon

I have a Sabbath number of no more than 3: I performed with Richard Thompson, who toured with Kenny Aronoff, who recorded with Tony Ionni, who was of course a founder member of Black Sabbath.

References

Synthesis of the Beryllium 3131Å spectral region, Ashwell, Jeffries & Smalley, Memorie della Società Astronomica Italiana Supplement, 2005, 8, 206

The WASP Project and the SuperWASP Cameras, Pollacco, D. L.; Skillen, I.; Collier Cameron, A.; Christian, D. J.; Hellier, C.; Irwin, J.; Lister, T. A.; Street, R. A.; West, R. G.; Anderson, D.; Clarkson, W. I.; Deeg, H.; Enoch, B; Evans, A.; Fitzsimmons, A.; Haswell, C.A.; Hodgkin, S.; Horne, K.; Kane, S. R.; Keenan, F. P.; Maxted, P. F. L.; Norton, A. J.; Osborne, J.; Parley, N. R.; Ryans, R. S. I.; Smalley, B.; Wheatley, P. J. and Wilson, D. M., Publications of the Astronomical Society of the Pacific, 118(848) (pp. 1407-1418)

Multiwavelength observations of the Be-star/X-ray binary EX02030+375 during outburst, Norton, A. J.; Coe, M. J.; Everall, C.; Roche, P.; Bildsten, L.; Chakrabarty, D.; Prince, T. A.; Stollberg, M. T.; Wilson, R. B., International Astronomical Union. Symposium no. 162; Kluwer Academic Publishers; Dordrecht, p.206

The Palomar Transient Factory: System Overview, Performance, and First Results, Law, Nicholas M.; Kulkarni, Shrinivas R.; Dekany, Richard G.; Ofek, Eran O.; Quimby, Robert M.; Nugent, Peter E.; Surace, Jason; Grillmair, Carl C.; Bloom, Joshua S.; Kasliwal, Mansi M.; Bildsten, Lars; Brown, Tim; Cenko, S. Bradley; Ciardi, David; Croner, Ernest; Djorgovski, S. George; van Eyken, Julian; Filippenko, Alexei V.; Fox, Derek B.; Gal-Yam, Avishay; Hale, David; Hamam, Nouhad; Helou, George; Henning, John; Howell, D. Andrew; Jacobsen, Janet; Laher, Russ; Mattingly, Sean; McKenna, Dan; Pickles, Andrew; Poznanski, Dovi; Rahmer, Gustavo; Rau, Arne; Rosing, Wayne; Shara, Michael; Smith, Roger; Starr, Dan; Sullivan, Mark; Velur, Viswa; Walters, Richard; Zolkower, Jeff, Publications of the Astronomical Society of the Pacific, Volume 121, issue 886, pp.1395-1408

Some Statistical and Computational Challenges, and Opportunities in Astronomy, Babu, G. Jogesh; Djorgovski, S. George. Some Statistical and Computational Challenges, and Opportunities in Astronomy. Statist. Sci. 19 (2004), no. 2, 322--332

A Note on the Distributive Function of Additive Arithmetical Functions in Short Intervals, Gutti Jogesh Babu, Paul Erdon, Canad. Math. Bull. Vol. 32 (4), 1989

I briefly appeared (on the deck of the Norwegian ship MS Trollfjord during a trip in November 2013 to see the Northern Lights) in a video taken by Dr John Mason, an astronomer who was a friend of Patrick Moore.

John Mason is a professional astronomer who was a friend of, and regularly appeared on The Sky at Night with, Patrick Moore.

Buzz Aldrin, the Apollo 11 astronaut who became the second man to walk on the Moon after Neil Armstrong, often appeared as a guest on The Sky at Night.

Jim Meskimen's part was uncredited in the movie, but he appears in the cast list on IMDb.

Both appear in the cast list on IMDb

I used to run a folk music club, with some friends, at The Old House at Home in Harborne, Birmingham. We booked Richard Thompson to do a show (on 15th April 1981 - I still have a recording of it). At that time I was in a duo with my friend Pauline, and we were one of two support acts. I did not actually perform a song with Richard, but he did tune my guitar for me. I reckon that counts!

Kenny Aronoff played drums with Richard Thompson on a tour in 1989, after regular drummer Dave Mattacks had broken his arm

Kenny Aronoff played drums on Tony Iommi's solo album, Fused.

At the time of writing (October 2015), Sabbath are planning (another) farewell tour.