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definition of Wikipedia

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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^{[1]}^{[2]} and Benjamin Rosenbaum,^{[3]} among others,^{[4]} 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.^{[5]}

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 actress Natalie Portman, whose authorship of a psychology paper during her Harvard degree in psychology earned her an Erdős–Bacon number of 6 (see table below).

## Contents |

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).

Bruce Reznick, a professor at University of Illinois at
Urbana-Champaign has an Erdős number of 1 and a Bacon number (by virtue
of being an extra in *Pretty Maids All in a Row* with Roddy McDowall) of 2, and thus has an Erdős–Bacon number of 3.^{[6]}

For a time, the person with the lowest known Erdős–Bacon number was Dave Bayer, mathematical consultant to *A Beautiful Mind* who was on screen in a minor role 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 University technical report, later published in a 2004 compilation.^{[7]}
As such, Bayer's Erdős–Bacon number is 4. Diaconis himself has an
Erdős–Bacon number of 5, and Bacon number of 4. He was in the
documentary The Math Life^{[8]} with Freeman Dyson, who was in A Glorious Accident^{[9]} with Oliver Sacks. Sacks has a Bacon number of 2.^{[10]}

Robin E. Harte, former professor of mathematics at University College, Cork, Ireland,^{[11]} has an acting role in Tony Bill's *Oliver Twist* (1997). Elijah Wood, who appeared with Bacon in *Beyond All Boundaries*
(2009), plays the Artful Dodger in the film, giving Professor Harte a
Bacon number of 2. Professor Harte has co-authored with Mostafa Mbekhta,
who has co-authored with Endre Makai Jr, who has co-authored with Paul
Erdős, so has an Erdős number of 3. Harte's Erdős–Bacon number is 5.

Astronomer Carl Sagan has an Erdős number of no more than 4^{[12]} via Steven J. Ostro and a Bacon number of 3,^{[13]}^{[14]} for a total of 7. Physicist Richard Feynman has an Erdős number of 3^{[15]} and a Bacon number of 3, having appeared in the film Anti-Clock alongside Tony Tang.^{[16]} Physicist H. David Politzer has an Erdős number of 4 ^{[15]} and a Bacon number of 2. ^{[17]}

Karl Schaffer is a dancer/choreographer who appeared as a "Killer Klown" in the 1988 film *Killer Klowns from Outer Space*,^{[18]} and is also a mathematician at De Anza College, with a Bacon number of 2^{[19]} and an Erdős number of 3,^{[20]} for a sum of 5.

Computer science Professor Marco Pedicini at University of Rome has
an Erdős–Bacon number of 5; he has an Erdős number of 2 (through
Professor Vilmos Komornik) and a Bacon Number of 3 (appearing in the
Italian movie directed by Fausto Brizzi, Notte prima degli esami, Oggi with actress Alessandra Costanzo^{[21]} who played in The Order (2003 film) and this gives her Bacon number of two).

Mathematician and Economics Nobel laureate John Nash, better known in popular culture as the subject of the unauthorized biography *A Beautiful Mind* and the Academy Award-winning film adaptation has an Erdős number of 4^{[22]} and a Bacon number of 2,^{[23]} resulting in an Bacon-Erdős number of 6.

Electrical engineer Robert J. Marks II appeared in Ben Stein's movie Expelled: No Intelligence Allowed. Stein appeared with Bacon in Planes, Trains and Automobiles giving Marks a Bacon number of two. Marks has published with Donald C. Wunch II ^{[24]} who published with Frank Harary^{[25]}
who has coauthored with Erdős. Marks therefore has an Erdős number of
three and Erdős–Bacon number of five. Intelligent design proponent William A. Dembski also appeared in Expelled. He has published with Marks ^{[26]} and therefore has a Erdős–Bacon number of six.

Former NCAA gymnastics champion Kiralee Hayashi^{[27]} 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,^{[28]} and having a Bacon number of 2,^{[29]} giving her an Erdős–Bacon number of 5.^{[30]}

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.^{[31]}

US actress Natalie Portman has an Erdős–Bacon number of 6. She collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird,^{[32]} who has a collaboration path^{[33]}^{[34]}^{[35]} leading to Joseph Gillis, who has an Erdős number of 1.^{[36]} Bacon and Portman both appear in *New York, I Love You*, giving Portman a Bacon number of 1 and an Erdős number of 5.

Mayim Bialik has an Erdős–Bacon number of at most 7, having worked on a book chapter^{[37]} and having a 5 point Erdős path ^{[38]}^{[39]} connecting to Shing-Tung Yau. Her Bacon number is 2.^{[40]}

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",^{[41]} after he suggested on BBC Radio 4 that such a study could be done.^{[42]} Another author of that paper, Geraint Rees, has an Erdős number of 5,^{[43]}^{[44]}^{[45]} which gives Firth an Erdős number of 6. Firth appeared with Kevin Bacon in *Where the Truth Lies*, so his Bacon number is 1.

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,^{[46]} ^{[47]}^{[48]}^{[49]} 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 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),^{[50]} and he also appeared in *Summer Catch* with Susan Gardner, who was in *In The Cut* with Bacon.

For people listed in the Internet Movie Database who are connected to Kevin Bacon, the average Bacon number is 2.957.^{[51]} 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.^{[52]} There currently exists no exhaustive list of people with defined Erdős–Bacon numbers, but a select group is listed below.

Name | Erdős number | Bacon number | Erdős–Bacon number |
---|---|---|---|

David Albert | 4^{[46]}^{[47]}^{[48]}^{[49]} |
3^{(b)(i)} |
7^{(b)} |

Dror Bar-Natan | 2^{[53]} |
4^{(b)} |
6 |

Dave Bayer | 2^{(c)} |
2^{(d)(i)} |
4^{(c,d)} |

Patrick Billingsley | 4^{[54]}^{[55]}^{[56]}^{[57]} |
2^{[58]} |
6 |

Mayim Bialik | 5 | 2 | 7 |

Lenore Blum | 4 | 3^{(b)(i)} |
7^{(b)} |

David Dalrymple | 3^{[59]}^{[60]}^{[61]} |
2^{(b)(e)}^{[62]} |
5^{(b)(e)} |

Martin Davis | 3 | 3^{(b)(i)} |
6^{(b)} |

William A. Dembski | 4^{[citation needed]} |
2^{(b)(i)} |
6 |

Jan Denef | 3 | 3^{(b)(i)} |
6^{(b)} |

Persi Diaconis | 1^{(c)} |
4^{(b,e)(i)} |
5^{(b,c,e)} |

Solomon Feferman | 3 | 3^{(b)(i)} |
6^{(b)} |

Richard Feynman | 3^{[15]} |
3^{[16]} |
6 |

Colin Firth | 6^{(i)} |
1^{(i)} |
7 |

John Hagelin | 5 | 3^{(b)(i)} |
8^{(b)} |

Henry Houh | 5^{[63]}^{[64]}^{[65]}^{[66]}^{[67]} |
2^{[68]}^{[69]} |
7 |

Robert J. Marks II | 3 | 2^{(b)(i)} |
5^{[70]} |

Yuri Matiyasevich | 2 | 3^{(b)(i)} |
5^{(b)} |

William McCallum | 4^{[71]}^{[72]}^{[73]}^{[74]} |
3^{[75]}^{[76]}^{[77]} |
7 |

Danica McKellar | 4^{[46]}^{[78]}^{[79]}^{[80]} |
2 | 6 |

Nicholas Metropolis | 2 ^{[81]} |
2 ^{[82]} |
4 |

P.Z. Myers | 4^{[citation needed]} |
2 | 6 |

John Nash | 4 | 2 | 6 |

Bjorn Poonen | 2 | 3^{(b)(i)} |
5^{(b)} |

Natalie Portman (Hershlag) | 5^{[32]}^{[33]}^{[34]}^{[35]}^{[36]} |
1^{(i)} |
6 |

Hilary Putnam | 3 | 3^{(b)(i)} |
6^{(b)} |

Carl Sagan | 4^{[15]} |
3^{(b)}^{[13]}^{[14]} |
7 |

Dana Scott | 2 | 3^{(b)(i)} |
5^{(b)} |

Jared Van Snellenberg | 4^{[83]} |
2 | 6 |

Brian Wandell | 3^{[15]}^{[84]} |
2^{[85]}^{[86]} |
5 |

Kevin Warwick | 4^{[87]} |
2^{(e)}^{[88]} |
6^{(e)} |

Wendelin Werner | 3^{[89]}^{[90]}^{[91]} |
3^{[92]} |
6 |

Fred Alan Wolf | 5 | 3^{(b)(i)} |
8^{(b)} |

Notes:

^{(b)}Includes role as self^{(c)}Includes technical report posthumously published in a book (otherwise Erdős number 3, Erdős–Bacon number 5)^{(d)}Includes role as extra^{(e)}Includes documentary credit^{(g)}Includes nonacademic paper^{(h)}Includes archival footage^{(i)}See discussion above.

**^**Simon Singh (September 2005). "A Further Five Numbers, Programme 3: 6 degrees of separation". BBC. Also available at [1]. http://www.bbc.co.uk/radio4/science/further5.shtml. Retrieved 2006-12-01.**^**Simon Singh (May 2002). "And the Winner Tonight Is". London:*The Daily Telegraph*. http://www.telegraph.co.uk/connected/main.jhtml?xml=/connected/2002/04/30/ecfsci30.xml. Retrieved 2006-12-01.**^**Benjamin Rosenbaum (September 2004). "Bacon-Erdős numbers". http://www.benjaminrosenbaum.com/blog/archives/2004_09.html#000082. Retrieved 2006-12-01.**^**Cory Doctorow (September 2004). "Erdős-Bacon numbers".*Boing Boing*. http://www.boingboing.net/2004/09/14/erdosbacon_numbers.html. Retrieved 2006-12-01.**^**"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 [...]"**^**"Items of Interest Related to Erdös Numbers".*The Erdös Number Project*. Oakland University. http://www.oakland.edu/enp/related/. Retrieved December 29, 2011.**^**Persi Diaconis and Paul Erdős. On the distribution of the greatest common divisor. Technical report 252. Stanford University. Dept. of Statistics. October 10, 1977. Also issued as Department of Statistics technical report no. 12 under ARO Grant DAAG29-77-G-0031. Republished; see [2].**^**"The Math Life". cs.dartmouth.edu. http://www.cs.dartmouth.edu/~rockmore/mathlife.html. Retrieved December 29, 2011.**^**A Glorious Accident**^**Oliver Sacks's Kevin Bacon connection^{[dead link]}**^**Robin E. Harte**^**"The Erdős Number Project, Paths to Erdős". http://www.oakland.edu/enp/erdpaths.html. Retrieved 2009-10-27.^{[dead link]}- ^
^{a}^{b}"The Oracle of Bacon at Virginia". http://oracleofbacon.org/cgi-bin/oracle/movielinks?firstname=Bacon%2C+Kevin&game=1&secondname=Orson+Welles. Retrieved 2007-05-20.^{[dead link]} - ^
^{a}^{b}"IMDb:*Who's Out There?*". http://www.imdb.com/title/tt0073898/fullcredits. Retrieved 2007-05-20. - ^
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^{a}^{b}"The Oracle of Bacon at Virginia". http://oracleofbacon.org/cgi-bin/oracle/movielinks?firstname=Bacon%2C+Kevin&game=1&secondname=Richard+Feynman. Retrieved 2006-12-05.^{[dead link]} **^**"The Oracle of Bacon at Virginia". http://oracleofbacon.org/cgi-bin/movielinks?game=0&a=Kevin%20Bacon&b=David+Politzer+(I)&use_using=1&u0=on&start_year=1850&end_year=2050&dir=0&use_genres=1&g0=on&g4=on&g8=on&g16=on&g20=on&g1=on&g5=on&g9=on&g13=on&g17=on&g21=on&g25=on&g2=on&g6=on&g10=on&g14=on&g22=on&g26=on&g3=on&g11=on&g15=on&g23=on&g27=on. Retrieved 2009-06-23.**^**"Full cast and crew for Killer Klowns from Outer Space". Internet Movie Database. http://www.imdb.com/title/tt0095444/fullcredits#cast. Retrieved 2007-05-21. Schaffer's name is misspelled in the credits as "Karl Shaeffer".**^**Schaffer was in*Killer Klowns from Outer Space*(1988) with Danny Kovacs. Danny Kovacs was in*Murder in the First*(1995) with Kevin Bacon. "Full cast and crew for Murder in the First". Internet Movie Database. http://www.imdb.com/title/tt0113870/fullcredits#cast. Retrieved 2007-05-23.**^**In 2001, Schaffer wrote a joint paper with Sin-Min Lee, who has an Erdős number of 2."Erdos2, Version 2007". The Erdos Number Project. 2007-02-28. Archived from the original on 2007-04-28. http://web.archive.org/web/20070428165034/http://www.oakland.edu/enp/Erdos2. Retrieved 2007-05-23.**^**"actress Alessandra Costanzo". http://www.imdb.com/name/nm0182437.**^**"Paths to Erdos". http://www.oakland.edu/enp/erdpaths/. Retrieved Feb 26, 2010.**^**"The Oracle of Bacon". http://oracleofbacon.org/cgi-bin/movielinks?game=0&a=Kevin%20Bacon&b=John+Nash+%28V%29&use_using=1&u0=on&u1=on&use_genres=1&g0=on&g4=on&g8=on&g16=on&g20=on&g1=on&g5=on&g9=on&g13=on&g17=on&g21=on&g25=on&g2=on&g6=on&g10=on&g14=on&g22=on&g26=on&g3=on&g7=on&g11=on&g15=on&g23=on&g27=on. Retrieved Feb 26, 2010.**^**D.C. Wunsch II, T.P. Caudell, C.D. Capps, R.J. Marks II and R. A. Falk, "An optoelectronic implementation of the adaptive resonance neural network", IEEE Transactions on Neural Networks, vol.4, no.4, pp.673-684 (1993).**^**Harary, Frank; Lim, Meng-Hiot; Agarwal, Amit; Wunsch, Donald C. Algorithms for derivation of structurally stable Hamiltonian signed graphs. Int. J. Comput. Math. 81 (2004), no. 11, 1349--1356.**^**[3] William A. Dembski and Robert J. Marks II "Conservation of Information in Search: Measuring the Cost of Success" IEEE Transactions on Systems, Man and Cybernetics A, Systems & Humans, vol.5, #5, September 2009, pp.1051-1061**^**"Kiralee Hayashi's website". http://www.kiraleeh.com/.**^**"Paul Thompson's Erdos Number Page". http://www.loni.ucla.edu/~thompson/ERDOS/erdo.htm.**^**" Kiralee Hayashi at the Oracle of Bacon**^**"Erdos Number Page". loni.ucla.edu. http://www.loni.ucla.edu/~thompson/ERDOS/erdo.htm. Retrieved December 29, 2011.**^**"There's not much separating her from Bacon, Erdos", USA Today, August 14, 2007- ^
^{a}^{b}Baird AA, Kagan J, Gaudette T, Walz KA, Hershlag N, Boas DA (Aug 2002). "Frontal lobe activation during object permanence: data from near-infrared spectroscopy".*Neuroimage***16**(4): 1120–5. doi:10.1006/nimg.2002.1170. PMID 12202098. http://linkinghub.elsevier.com/retrieve/pii/S1053811902911705. - ^
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Marks II has an Erdos-Bacon number of five." Retrieved 2010-05-05.**^**MR931215**^**MR1185584**^**MR1802720**^**MR1018367**^**The Drover's Wife (TV 1968) - IMDb**^**The First Kangaroos (1988) - IMDb**^**Balto (1995) - IMDb**^**L Chayes, D McKellar, B Winn, "Percolation and Gibbs states multiplicity for ferromagnetic Ashkin–Teller models on Z 2," J. Phys. A: Math. Gen, 1998.**^**JT Chayes, L Chayes, R Kotecký, "The analysis of the Widom-Rowlinson model by stochastic geometric methods," Communications in Mathematical Physics, 1995.**^**R Kotecký, D Preiss, "Cluster expansion for abstract polymer models," Communications in Mathematical Physics, 1986.**^**http://www.fas.org/sgp/othergov/doe/lanl/pubs/00326872.pdf / Publications of Stanislaw Ulam**^**http://www.imdb.com/title/tt0104466/ Husbands and Wives (1992)**^**"Jared Van Snellenberg - Trivia". jaredvs.com. http://www.jaredvs.com/trivia. Retrieved December 29, 2011.**^**Yellott JI, Wandell BA (1976). "Color properties of the contrast flash effect: monoptic vs dichoptic comparisons".*Vision Res.***16**(11): 1275–80. doi:10.1016/0042-6989(76)90053-5. PMID 1006999. http://linkinghub.elsevier.com/retrieve/pii/0042-6989(76)90053-5.**^**"Full cast and crew for Fat Man And Little Boy". Internet Movie Database. http://www.imdb.com/title/tt0097336/fullcredits#cast. Retrieved 2007-06-19.**^**"Full cast and crew for Novocaine". Internet Movie Database. http://www.imdb.com/title/tt0234354/fullcredits#cast. Retrieved 2007-06-19.**^**Tsypkin, Ya. Z, Parks, P, Vishnyakov, A and Warwick, K:"Stability of Solutions of Linear Difference Equations with Periodic Coefficients",*International Journal of Control*, 64(5), pp959-966, 1996**^**"The Oracle of Bacon". The Oracle of Bacon. http://oracleofbacon.org/cgi-bin/movielinks. Retrieved 2009-09-26.**^**Shi, Zhan; Werner, Wendelin. Asymptotics for occupation times of half-lines by stable processes and perturbed reflecting Brownian motion. Stochastics Stochastics Rep. 55 (1995), no. 1-2, 71–85.**^**Csáki, Endre; Shi, Zhan. Large favourite sites of simple random walk and the Wiener process. Electron. J. Probab. 3 (1998), no. 14, 31.**^**Csáki, E.; Erdös, P.; Révész, P. On the length of the longest excursion. Z. Wahrsch. Verw. Gebiete 68 (1985), no. 3, 365–382.**^**[9] Wendelin Werner at the Oracle of Bacon

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