Erdős–Bacon number
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An individual's Erdős–Bacon number is the sum of his Erdős number—which measures the "collaborative distance" in authoring mathematical papers between that individual and Hungarian mathematician Paul Erdős—and Bacon number—which represents the number of links, through roles in films, by which the individual is separated from actor Kevin Bacon. These numbers, the primary measures of the small world phenomenon in academia and entertainment, respectively, are generally allowed to be more flexible for Erdős–Bacon number calculation, as few published academics have also been professional actors. For example, roles as self, as a cameo, or as an extra are often included. However, in general, to have a finite Erdős–Bacon number, it is necessary (but not sufficient) for one to have both appeared in a film and co-authored an academic paper.
Daniel Kleitman, a mathematician at MIT, was an advisor for the movie Good Will Hunting and appeared briefly as an uncredited extra. Minnie Driver appeared in that movie, and she also appeared in Sleepers with Kevin Bacon. So Kleitman's Bacon number is 2. On the other hand, he coauthored a paper with Erdős. This gives him an Erdős–Bacon number of 3. This would probably be the infimum of the set of all existing Erdős–Bacon numbers. The only ways a lower number could be achieved would be:
- for an individual who had co-authored an academic paper with Paul Erdős to appear in a movie with Kevin Bacon, which would give that person an Erdős–Bacon number of 2,
- for Bacon to co-author an academic paper with someone with an Erdős number of 1, which would give Bacon himself an Erdős–Bacon number of 2, or
- for anyone who appeared in the documentary N is a number along with Erdős to appear in a film with Bacon, which would posthumously give Erdős an Erdős–Bacon number of 2.
[edit] Persons with defined Erdős–Bacon numbers
For a time, the sole person with the lowest known Erdős–Bacon number was popular string theorist Brian Greene. He appeared in Frequency with John Di Benedetto, who was in Sleepers with Kevin Bacon, for a Bacon number of 2. He also wrote a paper with Shing-Tung Yau, who wrote a paper with Ronald Graham, who wrote a paper with Paul Erdős, for an Erdős number of 3 and a combined Erdős–Bacon number of 5.
Brian Greene was later topped by Dave Bayer, mathematical consultant to A Beautiful Mind who received a minor role on screen in the movie. Rance Howard was also in A Beautiful Mind and in Apollo 13 with Kevin Bacon to give Bayer a Bacon number of 2. Bayer wrote a paper with Persi Diaconis, who has an Erdős number of 1 due to a jointly authored 1977 Stanford technical report, later published in a 2004 compilation[1]. So Bayer's Erdős–Bacon number is 4.
Popular astronomer Carl Sagan has an Erdős number of 3 [2] and a Bacon number of 3 [3], for a total of 6. Popular physicist Richard Feynman also has an Erdős number of 3 [4] and a Bacon number of 3 [5], tying Sagan. Popular theoretical physicist Stephen Hawking has an Erdős number of 4 [6] and, if one can include any of his television guest roles as himself in The Simpsons, Futurama, and Star Trek: The Next Generation, a Bacon number of 3.
In the acting world, 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. This gives her the lowest known Erdős–Bacon number for a professional actor/actress. Her paper was a collaboration with Lincoln Chayes, who collaborated with Roman Kotecký, who collaborated with David Preiss, who has an Erdős number of 1, giving her an Erdős number of 4. Her total is 6 because she and Bacon have both worked with Margaret Easley.
Natalie Portman has an Erdős–Bacon number of at most 9. She collaborated with David A. Boas [7] (using her birth name, Natalie Hershlag), who collaborated with Dana H. Brooks [8], who collaborated with Elias S. Manolakos [9], who collaborated with Hussain Al-Asaad [10], who collaborated on multiple papers with John P. Hayes [11], who collaborated with Frank Harary, who has an Erdős number of 1. Bacon and Portman have both worked with Matt Dillon, giving Portman a Bacon number of 2 and an Erdős number of at most 7.
The movie What the Bleep Do We Know!?, which featured both persons published in the sciences and an actress with Bacon number 2 (Academy Award winner Marlee Matlin), gave Erdős–Bacon numbers to David Albert (Erdős 4, Erdős–Bacon 7), Fred Alan Wolf (Erdős 5, Erdős–Bacon 8), and Natural Law Party Presidential Candidate John Hagelin (Erdős 5 through frequent collaborator Dimitri Nanopoulos, Erdős–Bacon 8), all appearing as themselves.
Hank Aaron, a baseball player, is sometimes also considered to have an Erdõs–Bacon number of 3, as he and Erdős both autographed a 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.
Erdős himself seems to have an undefined Erdős–Bacon number as well. While Erdős' Erdős number is clearly 0, his Bacon number is likely undefined; it was previously believed to be lower due to a conflation of similarly named persons. Similarly, Bacon's Erdős number is likely undefined. Relaxing the definition of Bacon number to include crew, however, yields an Erdős–Bacon number of 3 for Erdős. He appeared in the documentary N is a number: A Portrait of Paul Erdős, with original music by Mark Adler, who also provided music for The Rat Pack, which co-starred Joe Mantegna, who appeared with Bacon in Queens Logic.
[edit] Table of persons with defined Erdős–Bacon numbers
| real name | Erdős number | Bacon number | Erdős–Bacon number |
|---|---|---|---|
| Hank Aaron | 1(1) | 2(2) | 3(1,2) |
| David Albert | 4 | 3(2) | 7(2) |
| Dave Bayer | 2(3) | 2(4) | 4(3,4) |
| Paul Erdős | 0 | 3(5) | 3(5) |
| Richard Feynman | 3 | 3 | 6 |
| Brian Greene | 3 | 2(2) | 5(2) |
| John Hagelin | 5 | 3(2) | 8(2) |
| Stephen Hawking | 4 | 3(8) | 7(8) |
| Natalie Hershlag (Portman) | 7 | 2 | 9 |
| Daniel Kleitman | 1 | 2(4) | 3(4) |
| Danica McKellar | 4 | 2 | 6 |
| Geoffrey Nunberg | 5 | 3(2) | 8(2) |
| Steven Pemberton[citation needed] | 3(6) | 3(9) | 6(6,9) |
| Bertrand Russell | 3(6) | 3(2,7) | 6(6,2,7) |
| Carl Sagan | 3 | 3 | 6 |
| John Platt | 3 | 3(10) | 6(10) |
| Fred Alan Wolf | 5 | 3(2) | 8(2) |
Notes:
- (1) Strictly facetious and fatuous: both signed a baseball
- (2) Includes role as self
- (3) Includes technical report posthumously published in a book (otherwise Erdős number 3, Erdős–Bacon number 5)
- (4) Includes role as extra
- (5) Includes documentary and film score credits
- (6) Includes nonacademic paper
- (7) Includes archival footage
- (8) Includes television roles as self in The Simpsons, Futurama, and Star Trek: The Next Generation
- (9) Includes voice-over and television work
- (10) Includes Academy Awards ceremony
