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 individual 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 an individual is to Erdős and Bacon.

These numbers, which reflect 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 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 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. This idea has been popularized by Simon Singh in the British mediacite web
url = http://www.bbc.co.uk/radio4/science/further5.shtml
author = Simon Singh
title = A Further Five Numbers, Programme 3: 6 degrees of separation
accessdate = 2006-12-01
month = September
year = 2005
publisher = BBC. Also available at [http://www.simonsingh.net/Erdos-Bacon_Numbers.html] ] cite web
url = http://www.telegraph.co.uk/connected/main.jhtml?xml=/connected/2002/04/30/ecfsci30.xml
author = Simon Singh
title = And the Winner Tonight Is
accessdate = 2006-12-01
month = May
year = 2002
publisher = "The Daily Telegraph"] and Benjamin Rosenbaum,cite web
url = http://www.benjaminrosenbaum.com/blog/archives/2004_09.html#000082
author = Benjamin Rosenbaum
title = Bacon-Erdős numbers
accessdate = 2006-12-01
month = September
year = 2004] among others,cite web
url = http://www.boingboing.net/2004/09/14/erdosbacon_numbers.html
author = Cory Doctorow
title = Erdős-Bacon numbers
accessdate = 2006-12-01
month = September
year = 2004
publisher = "Boing Boing"] in the blogosphere. However, the idea had appeared in print before, notably on the Erdős-number project in 1998, when it was mentioned in response to Daniel Kleitman appearing in "Good Will Hunting". [ [http://www.oakland.edu/enp Erdos Number Project Home Page ] ]

Notable scientists with Erdős–Bacon numbers include popular string theorist Brian Greene, who had an Erdős–Bacon number of 5, Astronomer Carl Sagan and theoretical physicist Stephen Hawking; one of the best-known actors with a number is Israeli-US actress Natalie Portman of "Star Wars" prequel trilogy fame, whose authorship of psychology papers during her Harvard degree in psychology earned her an Erdős–Bacon number of 7.

Methodology

Erdős himself may have an Erdős–Bacon number of 3, 4, or 6. Erdős' Erdős number is clearly 0, and his Bacon number is currently 4 according to data from the Internet Movie Database. [cite web
url = http://oracleofbacon.org/cgi-bin/oracle/movielinks?game=0&firstname=Kevin+Bacon&secondname=Paul+Erdos&start_year=1850&end_year=2007&dir=0&using=1&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
title = The Oracle of Bacon at Virginia
accessdate = 2008-04-02] However one of the links is disputed on the Erdős Number Project website. [cite web
url = http://www.oakland.edu/enp/related.html
title = Items of Interest Related to Erdös Numbers
accessdate = 2008-04-04] Without this link, his Bacon number rises to 6. [According to IMDB, Paul Erdős was in "N is a Number" with Anne Davenport, who was in "Amartolo Trio" with Charles Stewart, who was in "Schalken the Painter" with Jeremy Clyde, who was in "The Musketeer" with Tim Roth, who was in "Don't Come Knocking" with Tim Matheson, who was in "Animal House" with Kevin Bacon.] 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. [Guinness (identified by name by the narrator) and Erdős appear together at the beginning of the film, receiving honorary doctorates at the University of Cambridge in 1991.cite web
url = http://janus.lib.cam.ac.uk/db/node.xsp?id=EAD%2FGBR%2F0265%2FO.VIII%2017%2F21
title = Janus: Records relating to the administrative and academic officers of the University
accessdate = 2008-06-26 Guinness has a Bacon number of 2; he was in "Kafka" (1991) with Theresa Russell, who was in "Wild Things" (1998) with Kevin Bacon.cite web
url = http://oracleofbacon.org/cgi-bin/oracle/movielinks?game=1&secondname=alec+guinness
title = The Oracle of Bacon at Virginia
accessdate = 2008-06-26]

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. On the other hand, he coauthored a paper with Erdős. This gives him an Erdős–Bacon number of 3.

The only way 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;
* for Bacon to co-author an academic paper with someone with an Erdős number of 1, which would give Bacon an Erdős–Bacon number of 2;
* 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;
* for Kevin Bacon to appear in a film that also uses stock footage of Erdős, giving Erdős an Erdős-Bacon number of 1;
* for a heretofore unknown joint academic paper by Bacon and Erdős to be published, giving Bacon an Erdős-Bacon number of 1.

cientists

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.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 [http://www.imstat.org/publications/books/lnms45.pdf] .] 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 [ [http://www.cs.dartmouth.edu/~rockmore/mathlife.html The Math Life] ] with Freeman Dyson, who was in A Glorious Accident [ [http://www.imdb.com/title/tt0107018/ A Glorious Accident] ] with Oliver Sacks. Sacks has a Kevin Bacon number of 2. [ [http://oracleofbacon.org/cgi-bin/oracle/movielinks?firstname=Bacon%2C+Kevin&game=1&secondname=oliver+sacks Oliver Sacks's Kevin Bacon connection] ]

Astronomer Carl Sagan has an Erdős number of 6cite web
url = http://www.oakland.edu/enp/erdpaths.html
title = The Erdős Number Project, Paths to Erdős
accessdate = 2006-12-01] and a Bacon number of 3,cite web
url = http://oracleofbacon.org/cgi-bin/oracle/movielinks?firstname=Bacon%2C+Kevin&game=1&secondname=Orson+Welles
title = The Oracle of Bacon at Virginia
accessdate = 2007-05-20] cite web
url = http://www.imdb.com/title/tt0073898/fullcredits
title = IMDb: "Who's Out There?"
accessdate = 2007-05-20] for a total of 9. Physicist Richard Feynman has an Erdős number of 3 and a Bacon number of 3.cite web
url = http://oracleofbacon.org/cgi-bin/oracle/movielinks?firstname=Bacon%2C+Kevin&game=1&secondname=Richard+Feynman
title = The Oracle of Bacon at Virginia
accessdate = 2006-12-05] Theoretical physicist Stephen Hawking has an Erdős number of 4 and, if one can include any of his television guest roles as himself in "The Simpsons", "Futurama", and "", 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 [cite journal| journal=Physical Review D| doi=10.1103/PhysRevD.74.123507| title=Cosmological constraints from the SDSS luminous red galaxies| first=M.| last= Tegmark| coauthors=et al. | url= http://adsabs.harvard.edu/abs/2006PhRvD..74l3507T | accessdate=2008-06-13| year=2006| volume=74| pages=123507] , who wrote a paper with his father, Harold S. Shapiro [cite journal| journal=Physical Review D| doi=10.1103/PhysRevE.50.2538| title=Decoherence produces coherent states: An explicit proof for harmonic chains| first=M.| last= Tegmark| coauthors=Shapiro | url= http://adsabs.harvard.edu/abs/1994PhRvE..50.2538T| accessdate=2008-06-13| year=1994| volume=50 | pages=2538] , who wrote a paper with Erdős [cite journal | journal = Michigan Math. J. | first = P. | last = Erdős | coauthors = Shapiro, H. S.; Shields, A. L. | title=Large and small subspaces of Hilbert space. | year=1965| volume=12 |pages=169 | doi=10.1307/mmj/1028999306] . 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. [cite web
url = http://oracleofbacon.org/cgi-bin/oracle/movielinks?firstname=Bacon,%20Kevin&game=1&secondname=O'Toole,+Peter+(I)
title = UVA Computer Science: The Oracle of Bacon at Virginia
publisher = UVA Computer Science | accessdate = 2008-06-13] Karl Schaffer is a dancer/choreographer who appeared as a "Killer Klown" in the 1988 film "Killer Klowns from Outer Space", [cite web
url = http://www.imdb.com/title/tt0095444/fullcredits#cast
title = Full cast and crew for Killer Klowns from Outer Space
publisher = Internet Movie Database
accessdate = 2007-05-21 Schaffer's name is misspelled in the credits as "Karl Shaeffer".] and is also a mathematician at De Anza College, with a Bacon number of 2 [Schaffer was in "Killer Klowns from Outer Space" (1988) with Danny Kovacs. Danny Kovacs was in "Murder in the First" (1995) with Kevin Bacon. cite web
url = http://www.imdb.com/title/tt0113870/fullcredits#cast
title = Full cast and crew for Murder in the First
publisher = Internet Movie Database
accessdate = 2007-05-23] and an Erdős number of 3, [In 2001, Schaffer wrote a joint paper with Sin-Min Lee, who has an Erdős number of 2.cite web
url = http://www.oakland.edu/enp/Erdos2
title = Erdos2, Version 2007
publisher = The Erdos Number Project
date = 2007-02-28
accessdate = 2007-05-23] for a sum of 5.

Mathematics professor Laura DeMarco at UIC has an Erdős number of 3 (through Rumely and Pomerance)cite web
url = http://www.ams.org/mathscinet/freeTools.html
title = MR: Collaboration Distance
publisher = American Mathematical Society
accessdate = 2008-06-06] and appeared briefly in "Proof" with Gwyneth Paltrowcite web
url = "http://www.terra.es/cine/laverdadoculta/notas.pdf"
title = Proof" (La verdad oculta [Proof] )
accessdate = 2008-06-06] which gives her a Bacon number of 3 (through Kelly Preston)cite web
url = http://oracleofbacon.org/cgi-bin/oracle/movielinks?firstname=Bacon%2C+Kevin&game=1&secondname=Gwyneth+Paltrow
title = The Oracle of Bacon at Virginia
accessdate = 2006-06-06] and hence an Erdős-Bacon number of 6. The documentary "Julia Robinson and Hilbert's Tenth Problem",cite web
url = http://www.zalafilms.com/films/jrparticipants.html
title = Zala Films: Julia Robinson and Hilbert's Tenth Problem
publisher = Zala Films
accessdate = 2008-02-12] 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).cite web
url = http://www.ams.org/mathscinet/freeTools.html
title = MR: Collaboration Distance
publisher = American Mathematical Society
accessdate = 2008-02-12]

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,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.] cite web
url = http://www.oakland.edu/enp/Erdos1
title = The Erdős Number Project, Erdos1
accessdate = 2006-12-20] and a Bacon number of 2, both of them having worked with Margaret Easley. Former NCAA gymnastics champion Kiralee Hayashicite web|url=http://www.kiraleeh.com/|title=Kiralee Hayashi's website] 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,cite web|url=http://www.loni.ucla.edu/~thompson/ERDOS/erdo.htm|title=Paul Thompson's Erdos Number Page] and having a Bacon number of 2, [http://oracleofbacon.org/cgi-bin/oracle/movielinks?firstname=Bacon%2C+Kevin&game=1&secondname=Kiralee+Hayashi" Kiralee Hayashi at the Oracle of Bacon] ] giving her an Erdős-Bacon number of 5. [http://www.loni.ucla.edu/~thompson/ERDOS/erdo.htm Erdos Number Page ] ] She narrowly beats McKellar as the actress with the lowest Erdős–Bacon number.

Israeli-US actress Natalie Portman has an Erdős–Bacon number of at most 7. She collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird,Abigail A. Baird, Jerome Kagan, Thomas Gaudette, Kathryn A. Walz, Natalie Hershlag and David A. Boas. Frontal Lobe Activation during Object Permanence: Data from Near-Infrared Spectroscopy. NeuroImage. Volume 16, Issue 4, August 2002, Pages 1120-1126. [http://dx.doi.org/10.1006/nimg.2002.1170] ] who has a collaboration pathBaird AA, Colvin MK, Vanhorn JD, Inati S, Gazzaniga MS. Functional connectivity: integrating behavioral, diffusion tensor imaging, and functional magnetic resonance imaging data sets.J Cogn Neurosci. 2005 Apr;17(4):687-93. [http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=ShowDetailView&TermToSearch=15829087&ordinalpos=5&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVDocSum] ] Victor, J.D., Maiese, K., Shapley, R., Sidtis, J., and Gazzaniga, M.S. (1989) Acquired central dyschromatopsia: analysis of a case with preservation of color discrimination. Clinical Vision Sciences 4, 183-196. [http://www-users.med.cornell.edu/~jdvicto/vimash89.html] ] Azor, R., Gillis, J., and Victor, J.D. (1982) Combinatorial applications of Hermite polynomials. SIAM Journal on Mathematical Analysis 13, 879-890. [http://www-users.med.cornell.edu/~jdvicto/erdos.html] ] leading to Joseph Gillis, who has an Erdős number of 1.P. Erdos and J. Gillis, "Note on the transfinite diameter," J. Lond. Math. Soc. 12 185 (1937).] Bacon and Portman have both worked with Matt Dillon, giving Portman a Bacon number of 2 and an Erdős number of at most 5. Mayim Bialik also has an Erdős–Bacon number of at most 7, having worked on a book chapter [ [http://books.google.com/books?id=fROW4vqDGvEC&printsec=toc&dq=zaidel+bialik book chapter] ] and having a 5 point Erdős path [ [http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=ShowDetailView&TermToSearch=16837835&ordinalpos=1&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVDocSum] Luders E, Narr KL, Zaidel E, Thompson PM, Toga AW. Gender effects on callosal thickness in scaled and unscaled space. Neuroreport. 2006 Jul 31;17(11):1103-6.] [ [http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=ShowDetailView&TermToSearch=16686016&ordinalpos=3&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVDocSum] Wang Y, Gu X, Hayashi KM, Chan TF, Thompson PM, Yau ST. Brain surface parameterization using Riemann surface structure. Med Image Comput Comput Assist Interv Int Conf Med Image Comput Comput Assist Interv. 2005;8(Pt 2):657-65. ] connecting to Shing-Tung Yau. Her Bacon number is 2. [ [http://oracleofbacon.org/cgi-bin/oracle/movielinks?firstname=Bacon%2C+Kevin&game=1&secondname=mayim+bialik] Mayim Bialik at the Oracle of Bacon]

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,Y Aharonov, DZ Albert, L Vaidman, "How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100," Physical Review Letters, 1988.] Y Aharonov, PG Bergmann, JL Lebowitz, "Time symmetry in the quantum process of measurement," Phys. Rev, 1964. ] B Hoffmann, V Bargmann, PG Bergmann, EG Straus, "Working with Einstein" in "Some strangeness in the proportion : a centennial symposium to celebrate the achievements of Albert Einstein", 1980.] 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),cite web
url = http://www.oakland.edu/enp/related.html
title = The Erdős Number Project, Items of Interest Related to Erdös Numbers,
accessdate = 2006-12-20] 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 that are connected to Kevin Bacon, the average Bacon number is 2.957. [ [http://oracleofbacon.org/cgi-bin/oracle/center-cgi?who=Kevin+Bacon UVA Computer Science: The Oracle of Bacon at Virginia ] ] For mathematicians listed in the American Mathematical Society's [http://www.ams.org/mathscinet/collaborationDistance.html MR Collaboration Distance search engine] that are connected to Erdős, the average Erdős number is 4.65. [ [http://www.oakland.edu/enp/trivia.html Erdős number facts ] ] There currently exists no exhaustive list of people with defined Erdős–Bacon numbers, but a select group is listed below.

Notes:

:^(a) Both signed the same baseball:^(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 "":^(g) Includes nonacademic paper:^(h) Includes archival footage :⁽ⁱ⁾ Includes Academy Awards ceremony

References