Bacon number

The Bacon Number or Kevin Bacon Number (KBZ) is the length of the shortest chain of actors who play together in a film, to Kevin Bacon . It provides an illustration of the of Stanley Milgram discovered small-world phenomenon ( small world phenomenon is). Based on the theory of six degrees of separation is also called the Six Degrees of Kevin Bacon .

calculation

Kevin Bacon himself has the Bacon number 0. Every actor who starred in a film with him has the Bacon number 1. An actor who has made a film with one of these actors, but not with Kevin Bacon, has this Bacon number 2 etc.

Example: Elvis Presley was seen with Edward Asner in the film Change of habit (1969). Edward Asner starred with Kevin Bacon in the 1991 film JFK . Elvis Presley didn't star in any movie with Kevin Bacon, so he has the Bacon number 2.

The idea of finding the shortest chain of actors for Kevin Bacon probably goes back to Craig Fass, Brian Turtle and Mike Ginelli, and was popularized by their appearance on Jon Stewart's The Jon Stewart Show in January 1994 and their 1996 book.

Mathematical definition and implications

Let S be the set of all film actors and the symmetrical relation , defined by: if and only if there is a film in which both and played. Then forms an undirected graph G. An actor's Bacon number is now defined as the distance from s to Kevin Bacon in G. ${\ displaystyle R \ subseteq S \ times S}$ ${\ displaystyle (s_ {1}, s_ {2}) \ in R}$ ${\ displaystyle s_ {1}}$ ${\ displaystyle s_ {2}}$ ${\ displaystyle (S, R)}$ ${\ displaystyle s \ in S}$

Since the quantities S and R increase over time (new elements are added, but an existing element will never disappear), an actor's Bacon number can decrease even further over time (but never increase) . This is even possible after the death of the relevant actor (or Kevin Bacons).

The relation R is already symmetrical and reflexive (if one only looks at actors who have already played in a film). In order to be an equivalence relation , only transitivity is missing. If one considers the transitive hull of R, then this is an equivalence relation. Exactly those actors who are in an equivalence class with Kevin Bacon have a finite Bacon number.

Others

According to The Oracle of Bacon at Virginia, the largest KBZ is 8. In the Hall of Fame of the Oracle of Bacon there is a report from December 2000, according to which a certain Ashley King responded to an actor with an KBZ of 11, one with a 10 and several with a 9 came across.

The Bacon number gives an indication of the small world phenomenon ("I know someone who knows someone, who knows someone again ..."), which leads from any person to any other via very few intermediate stops. With over 800,000 actors, the average KBZ in August 2005 was less than 3.

The Erdős number is a corresponding quantity in mathematics, which represents a publication relationship to Paul Erdős . In physics, the Pauli number is known, which represents the connection with Wolfgang Pauli .

literature

Craig Fass, Brian Turtle, Mike Ginelli: Six Degrees of Kevin Bacon . Plume, 1996, ISBN 0-452-27844-9 .

Web links

The Oracle of Bacon at Virginia

Individual evidence

↑ Craig Fass, Brian Turtle, Mike Ginelli: Six Degrees of Kevin Bacon . Plume, 1996, ISBN 0-452-27844-9 .

[1] Craig Fass, Brian Turtle, Mike Ginelli: Six Degrees of Kevin Bacon . Plume, 1996, ISBN 0-452-27844-9 .