Erdős–Bacon number

From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by Nernom (talk | contribs) at 09:25, 14 June 2008 (→Table of persons with defined Erdős–Bacon numbers: Added Ravi Sheth). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Jump to navigation Jump to search

An individual'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 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 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 media[1][2] and Benjamin Rosenbaum,[3] among others,[4] 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.[5]

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 the Internet Movie Database.[6] However one of the links is disputed on the Erdős Number Project website.[7] Without this link, his Bacon number rises to 6,[8] although it drops to 3 if the rules are relaxed to include film music composers.[9]

Minimum

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 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;
  • 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.

Persons with defined Erdős–Bacon numbers

Scientists

For a time, the 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.

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.[10] 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[11] with Freeman Dyson, who was in A Glorious Accident[12] with Oliver Sacks. Sacks has a Kevin Bacon number of 2.[13]

Astronomer Carl Sagan has an Erdős number of 6[14] and a Bacon number of 3,[15][16] for a total of 9. Physicist Richard Feynman has an Erdős number of 3[14] and a Bacon number of 3.[17] Theoretical physicist Stephen Hawking has an Erdős number of 4[14] 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, 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[18], who wrote a paper with his father, Harold S. Shapiro[19], who wrote a paper with Erdös[20]. 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.[21]

Karl Schaffer is a dancer/choreographer who appeared as a Killer Klown in the 1988 film Killer Klowns from Outer Space,[22] and is also a mathematician at De Anza College, with a Bacon number of 2[23] and an Erdős number of 3,[24] for a sum of 5.

Mathematics professor Laura DeMarco at UIC has an Erdős number of 3 (through Rumely and Pomerance) [25] and appeared briefly in Proof with Gwyneth Paltrow [26] which gives her a Bacon number of 3 (through Kelly Preston) [27] and hence an Erdős-Bacon number of 6.

The documentary Julia Robinson and Hilbert's Tenth Problem,[28] 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).[29]

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,[30][31][32][33] and a Bacon number of 2, both of them having worked with Margaret Easley. Former NCAA gymnastics champion Kiralee Hayashi[34] 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,[35] and having a Bacon number of 2,[36] giving her an Erdős-Bacon number of 5.[35] She narrowly beats McKellar as the actress with the lowest Erdős–Bacon number.

Natalie Portman has an Erdős–Bacon number of at most 7. She collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird,[37] who has a collaboration path[38][39][40] leading to Joseph Gillis, who has an Erdős number of 1.[41] 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[42] and having a 5 point Erdős path [43][44] connecting to Shing-Tung Yau. Her Bacon number is 2.[45]

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][33] 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),[49] 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).

Table of persons with defined Erdős–Bacon numbers

For people listed in the Internet Movie Database that are connected to Kevin Bacon, the average Bacon Number is 2.957.[50] For mathematicians listed in the American Mathematical Society's MR Collaboration Distance search engine that are connected to Erdos, the average Erdos Number is 4.65.[51] There currently exists no exhaustive list of people with defined Erdős–Bacon numbers, but a select group is listed below.

real name Erdős number Bacon number Erdős–Bacon number
Hank Aaron 1(a) 2(b) 3(a,b)
David Albert 4[46][47][48][33] 3(b) 7(b)
Dave Bayer 2(c) 2(d) 4(c,d)
Patrick Billingsley 4[52][53][54][55] 2[56] 6
Lenore Blum 4 3(b) 7(b)
Martin Davis 3 3(b) 6(b)
Laura DeMarco 3 3(d) 6(d)
Jan Denef 3 3(b) 6(b)
Persi Diaconis 1(c) 4(b,e) 5(b,c,e)
Kirsten Eisenträger 2 3(b) 5(b)
Paul Erdős 0 4(e) 4(e)
Solomon Feferman 3 3(b) 6(b)
Richard Feynman 3[14] 3[17] 6
Steven Givant 2 3(b) 5(b)
Brian Greene 3 2(b) 5(b)
John Hagelin 5 3(b) 8(b)
Stephen Hawking 4[14] 3(f) 7(f)
Kiralee Hayashi[34] 3[35] 2[36] 5
Daniel Kleitman 1 2(d) 3(d)
Yuri Matiyasevich 2 3(b) 5(b)
Danica McKellar 4[30][31][32][33] 2 6
Geoffrey Nunberg 4[57] 3(b)[57] 7(b)
Barney Pell 3 2 5
John Platt 3 3(i) 6(i)
Bjorn Poonen 2 3(b) 5(b)
Natalie Portman (Hershlag) 5[37][38][39][40][41] 2 7
Hilary Putnam 3 3(b) 6(b)
Bertrand Russell 3(g)[14] 3(b,h) 6(g,b,h)
Carl Sagan 6[14] 3(b)[15][16] 9
Karl Schaffer 3 2 5
Dana Scott 2 3(b) 5(b)
Charles Seife 4 [58] [59] [60] [61] 3(b)[62] 7
Ravi Sheth 3 3 6
Alexandra Shlapentokh 2 3(b) 5(b)
Brian Wandell 3[63][14] 2[64][65] 5
Wendelin Werner 3[66] [67] [68] 3[69] 6
Fred Alan Wolf 5 3(b) 8(b)

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 Star Trek: The Next Generation
(g) Includes nonacademic paper
(h) Includes archival footage
(i) Includes Academy Awards ceremony

References

  1. ^ Simon Singh (2005). "A Further Five Numbers, Programme 3: 6 degrees of separation". BBC. Also available at [1]. Retrieved 2006-12-01. {{cite web}}: External link in |publisher= (help); Unknown parameter |month= ignored (help)
  2. ^ Simon Singh (2002). "And the Winner Tonight Is". The Daily Telegraph. Retrieved 2006-12-01. {{cite web}}: Italic or bold markup not allowed in: |publisher= (help); Unknown parameter |month= ignored (help)
  3. ^ Benjamin Rosenbaum (2004). "Bacon-Erdős numbers". Retrieved 2006-12-01. {{cite web}}: Unknown parameter |month= ignored (help)
  4. ^ Cory Doctorow (2004). "Erdős-Bacon numbers". Boing Boing. Retrieved 2006-12-01. {{cite web}}: Italic or bold markup not allowed in: |publisher= (help); Unknown parameter |month= ignored (help)
  5. ^ Erdos Number Project Home Page
  6. ^ "The Oracle of Bacon at Virginia". Retrieved 2008-04-02.
  7. ^ "Items of Interest Related to Erdös Numbers". Retrieved 2008-04-04.
  8. ^ 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.
  9. ^ According to IMDB, Paul Erdős was in N is a Number, which had original music by Mark Adler, who provided music for The Rat Pack, which starred Joe Mantegna, who was in Queens Logic with Kevin Bacon.
  10. ^ 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].
  11. ^ The Math Life
  12. ^ A Glorious Accident
  13. ^ Oliver Sacks's Kevin Bacon connection
  14. ^ a b c d e f g h "The Erdős Number Project, Paths to Erdős". Retrieved 2006-12-01.
  15. ^ a b "The Oracle of Bacon at Virginia". Retrieved 2007-05-20.
  16. ^ a b "IMDb: Who's Out There?". Retrieved 2007-05-20.
  17. ^ a b "The Oracle of Bacon at Virginia". Retrieved 2006-12-05.
  18. ^ Tegmark, M. (2006). "Cosmological constraints from the SDSS luminous red galaxies". Physical Review D. 74. doi:10.1103/PhysRevD.74.123507. Retrieved 2008-06-13. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  19. ^ Tegmark, M. (1994). "Decoherence produces coherent states: An explicit proof for harmonic chains". Physical Review D. 50: 2538. doi:10.1103/PhysRevE.50.2538. Retrieved 2008-06-13. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  20. ^ Erdös, P. (1965). "Large and small subspaces of Hilbert space". Michigan Math. J. 12: 169. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  21. ^ "UVA Computer Science: The Oracle of Bacon at Virginia". UVA Computer Science. Retrieved 2008-06-13.
  22. ^ "Full cast and crew for Killer Klowns from Outer Space". Internet Movie Database. Retrieved 2007-05-21. Schaffer's name is misspelled in the credits as "Karl Shaeffer".
  23. ^ 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. Retrieved 2007-05-23.
  24. ^ 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. Retrieved 2007-05-23. {{cite web}}: Check date values in: |date= (help)
  25. ^ "MR: Collaboration Distance". American Mathematical Society. Retrieved 2008-06-06.
  26. ^ ["http://www.terra.es/cine/laverdadoculta/notas.pdf" "Proof" (La verdad oculta [Proof])"]. Retrieved 2008-06-06. {{cite web}}: Check |url= value (help)
  27. ^ "The Oracle of Bacon at Virginia". Retrieved 2006-06-06.
  28. ^ "Zala Films: Julia Robinson and Hilbert's Tenth Problem". Zala Films. Retrieved 2008-02-12.
  29. ^ "MR: Collaboration Distance". American Mathematical Society. Retrieved 2008-02-12.
  30. ^ a b 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.
  31. ^ a b JT Chayes, L Chayes, R Kotecký, "The analysis of the Widom-Rowlinson model by stochastic geometric methods," Communications in Mathematical Physics, 1995.
  32. ^ a b R Kotecký, D Preiss, "Cluster expansion for abstract polymer models," Communications in Mathematical Physics, 1986.
  33. ^ a b c d "The Erdős Number Project, Erdos1". Retrieved 2006-12-20.
  34. ^ a b "Kiralee Hayashi's website".
  35. ^ a b c "Paul Thompson's Erdos Number Page". Cite error: The named reference "Yau" was defined multiple times with different content (see the help page).
  36. ^ a b " Kiralee Hayashi at the Oracle of Bacon
  37. ^ a b 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. [3]
  38. ^ a b Baird 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. [4]
  39. ^ a b 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. [5]
  40. ^ a b Azor, R., Gillis, J., and Victor, J.D. (1982) Combinatorial applications of Hermite polynomials. SIAM Journal on Mathematical Analysis 13, 879-890. [6]
  41. ^ a b P. Erdos and J. Gillis, "Note on the transfinite diameter," J. Lond. Math. Soc. 12 185 (1937).
  42. ^ book chapter
  43. ^ [7] 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.
  44. ^ [8] 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.
  45. ^ [9] Mayim Bialik at the Oracle of Bacon
  46. ^ a b 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.
  47. ^ a b Y Aharonov, PG Bergmann, JL Lebowitz, "Time symmetry in the quantum process of measurement," Phys. Rev, 1964.
  48. ^ a b 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.
  49. ^ "The Erdős Number Project, Items of Interest Related to Erdös Numbers,". Retrieved 2006-12-20.
  50. ^ UVA Computer Science: The Oracle of Bacon at Virginia
  51. ^ Erdos number facts
  52. ^ Baum, Leonard E.; Billingsley, Patrick. Asymptotic distributions for the coupon collector's problem. Ann. Math. Statist. 36 1965 1835--1839
  53. ^ Baum, Leonard E.; Herzberg, Norman P.; Lomonaco, S. J., Jr.; Sweet, Melvin M. Fields of almost periodic sequences. J. Combinatorial Theory Ser. A 22 (1977), no. 2, 169--180.
  54. ^ Conway, J. H.; Lomonaco, S. J., Jr.; Sloane, N. J. A. A $[45,13]$ code with minimal distance $16$. Discrete Math. 83 (1990), no. 2-3, 213--217.
  55. ^ Conway, J. H.; Croft, H. T.; Erdös, P.; Guy, M. J. T. On the distribution of values of angles determined by coplanar points. J. London Math. Soc. (2) 19 (1979), no. 1, 137--143.
  56. ^ Pat Billingsley at the Oracle of Bacon
  57. ^ a b Geoffrey Nunberg. "Publications". Retrieved 2008-01-29.
  58. ^ Phys. Rev. Lett. 78 (1997): Enrico Simonotto, Massimo Riani, Charles Seife, Mark Roberts, Jennifer Twitty, and Frank Moss - Visual Perception of Stochastic
  59. ^ MR: Matches for: MR=1713088
  60. ^ MR: Matches for: MR=927222
  61. ^ MR: Matches for: MR=942062
  62. ^ "The Universe" Beyond the Big Bang (2007)
  63. ^ Cite error: The named reference WandellYellott was invoked but never defined (see the help page).
  64. ^ Cite error: The named reference WandellDern was invoked but never defined (see the help page).
  65. ^ Cite error: The named reference DernBacon was invoked but never defined (see the help page).
  66. ^ 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.
  67. ^ Csáki, Endre; Shi, Zhan. Large favourite sites of simple random walk and the Wiener process. Electron. J. Probab. 3 (1998), no. 14, 31.
  68. ^ Csáki, E.; Erdös, P.; Révész, P. On the length of the longest excursion. Z. Wahrsch. Verw. Gebiete 68 (1985), no. 3, 365--382.
  69. ^ [10] Wendelin Werner at the Oracle of Bacon
Retrieved from "https://en.wikipedia.org/w/index.php?title=Erdős–Bacon_number&oldid=219252862"