Erdős–Bacon number

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A person's Erdős–Bacon number is a concept which reflects the small world phenomenon in academia and entertainment. It 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.

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 string theorist Brian Greene, who has an Erdős–Bacon number of 5, astronomer Carl Sagan and theoretical physicist Stephen Hawking. The late Randy Pausch has an Erdős–Bacon number of 6 after being invited by J. J. Abrams to appear in the 2009 Star Trek film. 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.

Contents

[edit] Methodology

Erdős himself may have an Erdős–Bacon number of 3,[7] 4, or 6. Erdős' Erdős number is 0 by definition, and his Bacon number is currently 4 according to data from the Internet Movie Database.[8] However, one of the links is disputed on the Erdős Number Project website.[9] Without this link, his Bacon number rises to 6.[10] Also, Sir Alec Guinness appears in N is a Number with Erdős. Although Guinness' name is not in the credits, this gives Erdős a Bacon-Erdős number of 3.[11]

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]

[edit] Scientists

For a time, the person with the lowest known Erdős–Bacon number was 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. Greene was later outdone 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 University technical report, later published in a 2004 compilation.[12] 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[13] with Freeman Dyson, who was in A Glorious Accident[14] with Oliver Sacks. Sacks has a Kevin Bacon number of 2.[15].

Mathematician Ronald Graham has an Erdős number of 1. He co-authored numerous papers with Paul Erdős. Graham, however, also has a Bacon number of 2, appearing in a short biographical film about Erdős' life on N Is a Number: A Portrait of Paul Erdös (1993), with the co-star of Obi-wan.

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 movie The Bank (2001), which stars Anthony La Paglia: La Paglia was in the movie He Said, She Said(1991) with Bacon[16]. 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: Erdos 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 M.V. Subbarao[17]. His total Erdős–Bacon is therefore 2+2 = 4.

Astronomer Carl Sagan has an Erdős number of no more than 4[18] via Steven J. Ostro and a Bacon number of 3,[19][20] for a total of 7. Physicist Richard Feynman has an Erdős number of 3[21] and a Bacon number of 3.[22] Physicist H. David Politzer has an Erdős number of 4 [21] and a Bacon number of 2. [23] Theoretical physicist Stephen Hawking has an Erdős number of 4[21] 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[24], who wrote a paper with his father, Harold S. Shapiro[25], who wrote a paper with Erdős[26]. 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.[27] Karl Schaffer is a dancer/choreographer who appeared as a "Killer Klown" in the 1988 film Killer Klowns from Outer Space,[28] and is also a mathematician at De Anza College, with a Bacon number of 2[29] and an Erdős number of 3,[30] for a sum of 5.

Mathematics professor Laura DeMarco at UIC has an Erdős number of 3 (through Rumely and Pomerance) [31] and appeared briefly in Proof with Gwyneth Paltrow[32] which gives her a Bacon number of 3 (through Kelly Preston)[33] and hence an Erdős–Bacon number of 6. The documentary Julia Robinson and Hilbert's Tenth Problem,[34] 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).[35]

[edit] Actors

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. Her paper gives her an Erdős number of 4, and a Bacon number of 2, both of them having worked with Margaret Easley.[36] Former NCAA gymnastics champion Kiralee Hayashi[37] 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,[38] and having a Bacon number of 2,[39] giving her an Erdős–Bacon number of 5.[38]

US actress Natalie Portman has an Erdős–Bacon number of 6. She collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird,[40] who has a collaboration path[41][42][43] leading to Joseph Gillis, who has an Erdős number of 1.[44] 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 also has an Erdős–Bacon number of at most 7, having worked on a book chapter[45] and having a 5 point Erdős path [46][47] connecting to Shing-Tung Yau. Her Bacon number is 2.[48]

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,[49] [50][51][52] 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.

[edit] 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),[53] 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.

[edit] Table

For people listed in the Internet Movie Database that are connected to Kevin Bacon, the average Bacon number is 2.957.[54] For mathematicians listed in the American Mathematical Society's MR Collaboration Distance search engine that are connected to Erdős, the average Erdős number is 4.65.[55] 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[49][50][51][52] 3(b) 7(b)
Bayer, DaveDave Bayer 2(c) 2(d) 4(c,d)
Billingsley, PatrickPatrick Billingsley 4[56][57][58][59] 2[60] 6
Blum, LenoreLenore Blum 4 3(b) 7(b)
Davis, MartinMartin Davis 3 3(b) 6(b)
DeMarco, LauraLaura DeMarco 3 3(d) 6(d)
Denef, JanJan Denef 3 3(b) 6(b)
Diaconis, PersiPersi Diaconis 1(c) 4(b,e) 5(b,c,e)
Eisenträger, KirstenKirsten Eisenträger 2 3(b) 5(b)
Erdős, PaulPaul Erdős 0 4(e) 4(e)
Feferman, SolomonSolomon Feferman 3 3(b) 6(b)
Feynman, RichardRichard Feynman 3[21] 3[22] 6
Givant, StevenSteven Givant 2 3(b) 5(b)
Greene, BrianBrian Greene 3 2(b) 5(b)
Hagelin, JohnJohn Hagelin 5 3(b) 8(b)
Hawking, StephenStephen Hawking 4[21] 3(f) 7(f)
Van Snellenberg, JaredJared Van Snellenberg 4 2 6
Hayashi, KiraleeKiralee Hayashi[37] 3[38] 2[39] 5
Hidalgo, CesarCesar Hidalgo 5[61][62][63][64][65] 1 [66](j) 6
Hirschhorn, MikeMike Hirschhorn 2[67] 2(d) 4(d)
Kleitman, DanielDaniel Kleitman 1 2(d) 3(d)
Matiyasevich, YuriYuri Matiyasevich 2 3(b) 5(b)
McKellar, DanicaDanica McKellar 4[49][68][69][70] 2 6
Nunberg, GeoffreyGeoffrey Nunberg 4[71] 3(b)[71] 7(b)
Pausch, RandyRandy Pausch 4 2 6
Pell, BarneyBarney Pell 3 2 5
Platt, JohnJohn Platt 3 3(i) 6(i)
Poonen, BjornBjorn Poonen 2 3(b) 5(b)
Portman, NatalieNatalie Portman (Hershlag) 5[40][41][42][43][44] 1 6
Putnam, HilaryHilary Putnam 3 3(b) 6(b)
Russell, BertrandBertrand Russell 3(g)[21] 3(b,h) 6(g,b,h)
Sagan, CarlCarl Sagan 4[21] 3(b)[19][20] 7
Schaffer, KarlKarl Schaffer 3 2 5
Graham, RonaldRonald Graham 1 2 3
Scott, DanaDana Scott 2 3(b) 5(b)
Seife, CharlesCharles Seife 4 [72][73][74][75] 3(b)[76] 7
Sheth, RaviRavi Sheth 3 3 6
Shlapentokh, AlexandraAlexandra Shlapentokh 2 3(b) 5(b)
Wandell, BrianBrian Wandell 3[21][77] 2[78][79] 5
Warwick, KevinKevin Warwick 4 2(e) 6(e)
Werner, WendelinWendelin Werner 3[80][81][82] 3[83] 6
Wolf, Fred AlanFred Alan Wolf 5 3(b) 8(b)
King, K.N.K.N. King 4[84] 3(d) 7

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 and film score credits
(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

[edit] References

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