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A person's Erdős–Bacon number is the sum of one's Erdős number—which measures the "collaborative distance" in authoring mathematical papers between that person and Hungarian mathematician Paul Erdős—and one's Bacon number—which represents the number of links, through roles in films, by which the individual is separated from American actor Kevin Bacon. The lower the number, the closer a person is to Erdős and Bacon, and this reflects a small world phenomenon in academia and entertainment.

The idea of Erdős–Bacon numbers has been written about by Simon Singh in the British media and Benjamin Rosenbaum, among others, in the blogosphere. Roles as self, as a cameo appearance, or as an extra are often included for the Bacon component. The Erdős criterion technically refers to collaboration on mathematical papers, but it is often relaxed to include general research articles for the Erdős–Bacon number.

In general, to have a defined Erdős–Bacon number, it is necessary (but not sufficient) for one to have both appeared in a film and co-authored an academic paper.

Notable scientists with defined Erdős–Bacon numbers include popular astronomer Carl Sagan. One of the best-known actors with a number is Natalie Portman, whose authorship of a psychology paper while at Harvard University earned her an Erdős–Bacon number of 7 (see table below).

Scientists

It is sometimes reported that Erdős himself has an Erdős–Bacon number of three. His Erdős number is zero by definition. His Bacon number is erroneously thought to be three since he appears in N Is a Number: A Portrait of Paul Erdős (1993) with a Gene Patterson, and a Gene Patterson was in Box of Moon Light (1996) with Sam Rockwell who was in Frost/Nixon (2008) with Kevin Bacon. However, this is incorrect, as the Gene Patterson in N Is a Number: A Portrait of Paul Erdős is not the same person as the one in Box of Moon Light (1996).

Astronomer Carl Sagan has an Erdős number of no more than 4 via Steven J. Ostro and a Bacon number of 2, for a total of 6. Physicist Richard Feynman has an Erdős number of 3 and a Bacon number of 3, having appeared in the film Anti-Clock alongside Tony Tang.

Electrical and computer engineering professor Robert J. Marks II has an Erdős–Bacon number of five. His colleague, intelligent design advocate William A. Dembski consequently has an Erdős–Bacon number of six and biochemist Michael Behe has an Erdős–Bacon number of seven

Actors

Former NCAA gymnastics champion Kiralee Hayashi may be the professional actress with the lowest Erdős number (3), having co-written a peer-reviewed mathematics paper on Riemannian manifolds with Fields medalist Shing-Tung Yau, and having a Bacon number of 2, giving her an Erdős–Bacon number of 5.

Danica McKellar, most famous for her role as Winnie Cooper in The Wonder Years, has an Erdős–Bacon number of 6, having coauthored a mathematics paper published while an undergraduate at UCLA. Her paper gives her an Erdős number of 4, and a Bacon number of 2, both of them having worked with Margaret Easley.

US actress Natalie Portman has an Erdős–Bacon number of 7. She collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird, who has a collaboration path leading to Joseph Gillis, who has an Erdős number of 1. Portman appeared in A Powerful Noise Live (2009) with Sarah Michelle Gellar, who appeared in The Air I Breathe (2007) with Bacon, giving Portman a Bacon number of 2 and an Erdős number of 5.

British actor Colin Firth has an Erdős–Bacon number of 7. Firth is formally credited as co-author of a neuroscience paper, "Political Orientations Are Correlated with Brain Structure in Young Adults", after he suggested on BBC Radio 4 that such a study could be done. Another author of that paper, Geraint Rees, has an Erdős number of 5, which gives Firth an Erdős number of 6. Firth appeared with Kevin Bacon in Where the Truth Lies, so his Bacon number is 1.

Others

Hank Aaron, a baseball player, is sometimes also considered to have an Erdős–Bacon number of 3, as he and Erdős both autographed the same baseball (for which he is jokingly referred to as having Erdős number of 1), and he also appeared in Summer Catch with Susan Gardner, who was in In The Cut with Bacon.

Table

For people listed in the Internet Movie Database who are connected to Kevin Bacon, the average Bacon number is 2.957. For mathematicians listed in the American Mathematical Society's MR Collaboration Distance search engine who are connected to Erdős, the average Erdős number is 4.65. There currently exists no exhaustive list of people with defined Erdős–Bacon numbers, but a select group is listed below.

Notes:

See discussion above.

Includes role as self

Includes role as extra

Includes documentary credit

References

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5. "There's not much separating her from Bacon, Erdos", USA Today, August 14, 2007: "As a UCLA undergraduate, McKellar co-wrote a theorem proving a magnetic field property So McKellar's "Erdos-Bacon" number is 6. Some academics who have had film cameos have lower Erdos-Bacon numbers "
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