Erdős–Bacon number

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. However, the idea had appeared in print before, notably in 1998, when it was mentioned in response to Daniel Kleitman appearing in Good Will Hunting.[5]

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.[6]

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 and theoretical physicist Stephen Hawking.[7] 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

Scientists

Erdős himself has an Erdős-Bacon number of three. His Erdős number is zero by definition. His Bacon number is three since he appears in N Is a Number: A Portrait of Paul Erdős (1993) with Gene Patterson who was in Box of Moon Light (1996) with Sam Rockwell who was in Frost/Nixon (2008) with Kevin Bacon.

Daniel Kleitman, a mathematician at MIT, was an advisor for the movie Good Will Hunting and appeared briefly as an uncredited extra. Minnie Driver, who appeared in that movie, also appeared in Sleepers with Kevin Bacon; as such, Kleitman's Bacon number is 2. He also coauthored a paper with Erdős. This gives him an Erdős–Bacon number of 3.[5]

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.[8] 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[9] with Freeman Dyson, who was in A Glorious Accident[10] with Oliver Sacks. Sacks has a Bacon number of 2.[11]

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.[12]

Mike Hirschhorn, a pure mathematician at UNSW in Australia, also counts an Erdős–Bacon number of 4. He is heard giving a mathematics lecture in the background at the beginning of the 2001 movie The Bank, which stars Anthony LaPaglia, who was in the movie He Said, She Said with Bacon.[13] This gives Hirschhorn a Bacon number of 2. Hirschhorn was well acquainted with Erdős. He met Erdős in Rehovot in 1966, Sydney in 1969 and on several later occasions, including 1975, when Erdős entertained what he termed the Hirschhorn "epsilons" Jeremy and Andrew. They both now have Erdős number 3. Mike Hirschhorn’s Erdős number was nearly 1: Erdős was responsible for the crucial idea in Hirschhorn’s 1981 paper Infinitely many identities of Kolberg type but declined credit. However Hirschhorn has an Erdős number of 2 through both J.H. Loxton and Mathukumalli V. Subbarao.[14] His total Erdős–Bacon is therefore 2+2 = 4.

Robin E. Harte, former professor of mathematics at University College, Cork, Ireland,[15] 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[16] via Steven J. Ostro and a Bacon number of 3,[17][18] for a total of 7. Physicist Richard Feynman has an Erdős number of 3[19] and a Bacon number of 3, having appeared in the film Anti-Clock alongside Tony Tang.[20] Physicist H. David Politzer has an Erdős number of 4 [19] and a Bacon number of 2. [21] Theoretical physicist Stephen Hawking has an Erdős number of 4[19] 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. The mathematician Alex Schuster, a professor at San Francisco State University, has an Erdős number of 3. He also appeared in a single episode of the late 1980s Canadian television program ENG as an ice cream salesman. The show starred Victor Garber, who has a Bacon number of 2. Schuster thus has a Bacon number of 3 and an Erdős–Bacon number of 6.

Astrophysicist and cosmologist Ravi Sheth at the University of Pennsylvania also has an Erdős–Bacon number of at most 6. His Erdős number of 3 comes through a paper with Max Tegmark,[22] who wrote a paper with his father, Harold S. Shapiro,[23] who wrote a paper with Erdős.[24] He acquired a Bacon number of 3 by starring in the title role of the 1984 British TV film Kim, which also starred Peter O'Toole, who has a Bacon number of 2.[25] Karl Schaffer is a dancer/choreographer who appeared as a "Killer Klown" in the 1988 film Killer Klowns from Outer Space,[26] and is also a mathematician at De Anza College, with a Bacon number of 2[27] and an Erdős number of 3,[28] for a sum of 5.

Mathematics professor Laura DeMarco at UIC has an Erdős number of 3 (through Rumely and Pomerance) [29] and appeared briefly in Proof with Gwyneth Paltrow[30] which gives her a Bacon number of 3 (through Kelly Preston)[31] and hence an Erdős–Bacon number of 6. The documentary Julia Robinson and Hilbert's Tenth Problem,[32] with actress Danica McKellar as narrator, gave a Bacon number of 3 to several mathematicians appearing in the film as themselves, including Lenore Blum (4+3=7), Martin Davis (3+3=6), Jan Denef (3+3=6), Kirsten Eisenträger (2+3=5), Solomon Feferman (3+3=6), Steven Givant (2+3=5), Yuri Matiyasevich (2+3=5), Bjorn Poonen (2+3=5), Hilary Putnam (3+3=6), Dana Scott (2+3=5), and Alexandra Shlapentokh (2+3=5).[33]

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[34] and a Bacon number of 2,[35] 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 [36] who published with Frank Harary[37] 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 [38] and therefore has a Erdős–Bacon number of six.

Materials Scientist Tim Foecke has a Bacon Number of 2 (Martin Sheen having been the narrator of the Discovery Channel documentary Foecke participated in entitled "Titanic-Anatomy of a Disaster", and co-starred in the movie "JFK" with Kevin Bacon), and an Erdos Number of 4 (via Robb Thomson to Peter Bergmann To Ernst Straus to Paul Erdos), giving him an Erdős–Bacon number of 6.

Linguist and language commentator Geoff Nunberg has a Bacon Number of 3 by several routes. His website[39] cites the line through his appearance in the documentary F*ck[40] with Pat Boone, who was in The Cross and the Switchblade (1970) with Erik Estrada, who was in We Married Margo (2000) with Kevin Bacon. (An alternate calculation through Dennis Miller via The Joy of Lex[41] (2008) is also possible.) He has an Erdős Number of 4, as a co-author with Jan Pedersen,[42] who co-authored with John Tukey,[43] who is listed in the Erdős number Project,[44] with a number 2 two ways, having co-authored with Arthur Harold Stone and with Ralph Philip Boas, Jr., both of whom co-authored with Paul Erdős. This gives him an Erdős–Bacon number of 7.

Actors

Former NCAA gymnastics champion Kiralee Hayashi[45] 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,[46] and having a Bacon number of 2,[47] giving her an Erdős–Bacon number of 5.[48]

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.[49]

US actress Natalie Portman has an Erdős–Bacon number of 6. She collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird,[50] who has a collaboration path[51][52][53] leading to Joseph Gillis, who has an Erdős number of 1.[54] 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[55] and having a 5 point Erdős path [56][57] connecting to Shing-Tung Yau. Her Bacon number is 2.[58]

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",[59] after he suggested on BBC Radio 4 that such a study could be done.[60] Another author of that paper, Geraint Rees, has an Erdős number of 5,[61][62][63] 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,[64] [65][66][67] 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.

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),[68] and he also appeared in Summer Catch with Susan Gardner, who was in In The Cut with Bacon. Charles Seife, an author and journalist, co-authored a paper with Frank Moss (Erdős number 3) and appeared in a Discovery Channel special with Brian Greene (Bacon number 2) for an Erdős–Bacon number of 7.

Table

For people listed in the Internet Movie Database who are connected to Kevin Bacon, the average Bacon number is 2.957.[69] 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.[70] 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
Albert, DavidDavid Albert 4[64][65][66][67] 3(b)(k) 7(b)
Bayer, DaveDave Bayer 2(c) 2(d)(k) 4(c,d)
Billingsley, PatrickPatrick Billingsley 4[71][72][73][74] 2[75] 6
Bialik, MayimMayim Bialik 5 2 7
Blum, LenoreLenore Blum 4 3(b)(k) 7(b)
Davis, MartinMartin Davis 3 3(b)(k) 6(b)
Dembski, William A.William A. Dembski 4 2(b)(k) 6
Denef, JanJan Denef 3 3(b)(k) 6(b)
Diaconis, PersiPersi Diaconis 1(c) 4(b,e)(k) 5(b,c,e)
Durham, ThomasThomas Durham 6[76] 2(k) 8(k)
Erdős, PaulPaul Erdős 0 3 3
Feferman, SolomonSolomon Feferman 3 3(b)(k) 6(b)
Feynman, RichardRichard Feynman 3[19] 3[20] 6
Firth, ColinColin Firth 6(k) 1(k) 7
Joyce, AustinAustin Joyce 4 2 6
Foecke, TimTim Foecke 4 2(e) 6(e)
Hagelin, JohnJohn Hagelin 5 3(b)(k) 8(b)
Hawking, StephenStephen Hawking 4[19] 3(f) 7(f)
Hidalgo, CesarCesar Hidalgo 5[77][78][79][80][81] 1 [82](j) 6
Hirschhorn, MikeMike Hirschhorn 2[14] 2(d)(k) 4(d)
Houh, HenryHenry Houh 5[83][84][85][86][87] 2 7
Kleitman, DanielDaniel Kleitman 1 2(d)(k) 3(d)
Lotan, GiladGilad Lotan 5 3 8
Lehrer, TomTom Lehrer 4 2 6
Marks II, Robert J.Robert J. Marks II 3 2(b)(k) 5[88]
Matiyasevich, YuriYuri Matiyasevich 2 3(b)(k) 5(b)
McCallum, WilliamWilliam McCallum 4[89][90][91][92] 3[93][94][95] 7
McKellar, DanicaDanica McKellar 4[64][96][97][98] 2 6
Nash, JohnJohn Nash 4 2 6
Pell, BarneyBarney Pell 3[99][100][101] 2 5
Poonen, BjornBjorn Poonen 2 3(b)(k) 5(b)
Portman, NatalieNatalie Portman (Hershlag) 5[50][51][52][53][54] 1(k) 6
Putnam, HilaryHilary Putnam 3 3(b)(k) 6(b)
Sagan, CarlCarl Sagan 4[19] 3(b)[17][18] 7
Scott, DanaDana Scott 2 3(b)(k) 5(b)
Seife, CharlesCharles Seife 4 [102][103][104][105] 3(b)[106] 7
Van Snellenberg, JaredJared Van Snellenberg 4[107] 2 6
Wandell, BrianBrian Wandell 3[19][108] 2[109][110] 5
Warwick, KevinKevin Warwick 4[111] 2(e)[112] 6(e)
Werner, WendelinWendelin Werner 3[113][114][115] 3[116] 6
Wolf, Fred AlanFred Alan Wolf 5 3(b)(k) 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
(f) Includes television roles as self in The Simpsons, Futurama, and Star Trek: The Next Generation
(g) Includes nonacademic paper
(h) Includes archival footage
(i) Includes Academy Awards ceremony
(j) Includes role as production assistant
(k) See discussion above.

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