An individual's Erdős–Bacon–Sabbath number (sometimes referred to as an EBS number) is the sum of three numbers, one's Erdős number, one's Bacon number, and one's Sabbath number. An Erdős number is the "collaborative distance" between an individual and mathematician Paul Erdős through co-authorship, a Bacon number is the "collaborative distance" between an individual and actor Kevin Bacon through acting roles, and a Sabbath number is the "collaborative distance" between an individual and any member of the band Black Sabbath through musical performances or recordings.
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The lower one's EBS number, the closer their connectedness to these three icons of science, film, and music, reflecting a small world phenomenon in academia and entertainment while contrarily revealing an exclusive list of accomplished individuals with the lowest EBS numbers. To have a defined Erdős–Bacon-Sabbath number, it is a necessary condition for an individual to be a published author, appeared in a film or television program, and contributed to a musical album or live performance, although it may still be impossible to reach Erdős through one's academic co-authors, Bacon through one's acting appearances, or Black Sabbath through one's musical endeavors.
Criteria
These collaborations with Erdős, Bacon, and members of Black Sabbath, or those connected through a series of collaborations, should be reasonably verifiable resulting in an academic, dramatic, or musical work in which both collaborators made legitimate contributions. During the summer of 2012, a website known as the EBS Project was created by Ross Churchley of Simon Fraser University in conjunction with the game's creator Sean O’Connor of Timeblimp.com, outlining the necessary criteria to obtain a finite Erdős-Bacon-Sabbath number.
The EBS Project determined that a valid Erdős number is based on co-authored academic papers, books, patents, or thesis papers. Erdős himself has an Erdős number of 0, each of his collaborators has an Erdős number of 1, anyone who collaborated with one of his co-authors (but not directly with Erdős) has an Erdős number of 2, and so on.
A valid Bacon number is assessed through co-starring roles in mutual films, television programs, and documentaries verifiable by the Internet Movie Database. Kevin Bacon has a Bacon number of 0, anyone who has appeared in a movie or television program with the actor has a Bacon number of 1, individuals who have appeared with one of Bacon's co-stars (but not directly with Bacon) have a Bacon number of 2, and so on.
A valid Sabbath number is based on live and recorded music through performance, production, composition, or samples. Members of Black Sabbath have a Sabbath number of 0, anyone who has performed or recorded with one of those members has a Sabbath number of 1, and so on.
Six degrees variations
In 1929, Hungarian author Frigyes Karinthy proposed the idea of six degrees of separation in his book Láncszemek, introducing the concept that all living humans are connected through no more than five acquaintances (or six degrees). The idea was adopted by mathematicians in 1969 when colleagues of Paul Erdős devised the concept of an Erdős number, publicly revealed that September by his cohort Casper Goffman in an article written for the American Mathematical Monthly. Erdős, a well-known Hungarian mathematician, published 1,475 academic papers before his death in 1996, arguably the most prolific mathematician in history. Including posthumous publications, the list of papers co-authored by Erdős has grown to at least 1,525, likely making him the only mathematician to exceed the prolificacy of Leonhard Euler. In an effort to digitally assess an abundance of potential Erdős numbers, Jerrold Grossman and Patrick Ion of Oakland University founded the Erdős Number Project in 1995. Additionally, the American Mathematical Society maintains a collaboration calculator on their website, however both directories remain limited to mathematical publications. As of 2017, there are only 512 humans with an Erdős number of 1 (having co-authored an academic work with Erdős) and just over 11,000 authors with an Erdős number of 2.
Six Degrees of Kevin Bacon, a Hollywood variation of the Erdős number, was developed in January of 1994 by three classmates at Albright College, Craig Fass, Brian Turtle, and Mike Ginelli. Originally known as the Kevin Bacon Game, it achieved national attention shortly after its inception when the three made an appearance on The Jon Stewart Show. During the winter of 1996, two computer science doctoral candidates at the University of Virginia, Brett Tjaden and Glenn Wasson, created a website titled The Oracle of Bacon at Virginia to calculate the Bacon number of any participant in a motion picture.
On May 16, 2010, a musical derivative of Six Degrees of Kevin Bacon emerged during Music Hack Day when Paul Lamere designed a computer program called Six Degrees of Black Sabbath, calculating the web of connections between various musicians and bands. The Grammy-winning rock band founded in 1968 has featured 35 members over the years who either recorded with the group in studio or performed with them live. Lamere's program is still featured on The Echo Nest website.
Fusion of six degrees games
Seemingly the earliest evidence of joining two or more games of the six degrees genre appeared on May 1, 2002, in an article written by Simon Singh for The Daily Telegraph. That spring a new craze swept Hollywood as celebrities and scholars alike were assessing the sum of their Erdős and Bacon numbers, although the game's originator remains unknown. Ultimately, Sean O’Connor introduced the idea of an Erdős-Bacon-Sabbath number, a fusion of all three games that garnered attention during the summer of 2012. O'Connor identified notable entertainers who possessed a finite and verifiable connection to Paul Erdős, Kevin Bacon, and Black Sabbath, listing only 14 humans with a number of 10 or less. That summer, musician Brian May was compelled to comment publicly, via Twitter, on the revelation that his EBS number was one of the lowest in the world.