Erdős–Bacon number

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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, or as an extra are often included. However, 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.

Erdős himself seems to have an undefined Erdős–Bacon number. While Erdős' Erdős number is clearly 0, his Bacon number is likely undefined; it was previously believed to be finite due to a conflation of similarly named persons. Similarly, Bacon's Erdős number is likely undefined. Relaxing the definition of Bacon number to include crew, however, yields an Erdős–Bacon number of 3 for Erdős. He appeared in the documentary N Is a Number: A Portrait of Paul Erdős, with original music by Mark Adler, who also provided music for The Rat Pack, which co-starred Joe Mantegna, who appeared with Bacon in Queens Logic.

Contents

[edit] 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. This would probably be the minimum over all existing Erdős–Bacon numbers. 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, which would give that person an Erdős–Bacon number of 2,
  • for Bacon to co-author an academic paper with someone with an Erdős number of 1, which would give Bacon himself an Erdős–Bacon number of 2, or
  • 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.

[edit] Persons with defined Erdős–Bacon numbers

[edit] Scientists

For a time, the sole 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.

Brian Greene was later topped 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.[5] As such, Bayer's Erdős–Bacon number is 4.

Astronomer Carl Sagan has an Erdős number of 6[6] and a Bacon number of 3,[7] for a total of 9. Physicist Richard Feynman has an Erdős number of 3[6] and a Bacon number of 3.[8] Theoretical physicist Stephen Hawking has an Erdős number of 4[6] 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.

[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. This gives her the lowest known Erdős–Bacon number for a professional actor/actress. Her paper gives her an Erdős number of 4,[9][10][11][12] and she and Bacon have both worked with Margaret Easley.

Natalie Portman has an Erdős–Bacon number of at most 9. She collaborated with David A. Boas[13] (using her birth name, Natalie Hershlag), who has a collaboration path[14][15][16][17][18] leading to Frank Harary, who has an Erdős number of 1.[12] Bacon and Portman have both worked with Matt Dillon, giving Portman a Bacon number of 2 and an Erdős number of at most 7.

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,[19][20][21][12] 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),[22] and he also appeared in Summer Catch with Susan Gardner, who was in In The Cut with Bacon.

[edit] Table of persons with defined Erdős–Bacon numbers

real name Erdős number Bacon number Erdős–Bacon number
Hank Aaron 1(a) 2(b) 3(a,b)
David Albert 4[19][20][21][12] 3(b) 7(b)
Dave Bayer 2(c) 2(d) 4(c,d)
Paul Erdős 0 3(e) 3(e)
Richard Feynman 3[6] 3[8] 6
Brian Greene 3 2(b) 5(b)
John Hagelin 5 3(b) 8(b)
Stephen Hawking 4[6] 3(f) 7(f)
Natalie Hershlag (Portman) 7[13][14][15][16][17][18][12] 2 9
Daniel Kleitman 1 2(d) 3(d)
Danica McKellar 4[9][10][11][12] 2 6
Geoffrey Nunberg 5[23] 3(b)[23] 8(b)
John Platt 3 3(i) 6(i)
Bertrand Russell 3(g)[6] 3(b,h) 6(g,b,h)
Carl Sagan 6[6] 3[7] 9
Fred Alan Wolf 5 3(b) 8(b)

Notes:

(a) Strictly facetious and fatuous: both signed a 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

[edit] References

  1. ^ Simon Singh (September 2005). A Further Five Numbers, Programme 3: 6 degrees of separation. BBC. Also available at [1]. Retrieved on 2006-12-01.
  2. ^ Simon Singh (May 2002). And the Winner Tonight Is. The Daily Telegraph. Retrieved on 2006-12-01.
  3. ^ Benjamin Rosenbaum (September 2004). Bacon-Erdös numbers. Retrieved on 2006-12-01.
  4. ^ Cory Doctorow (September 2004). Erdös-Bacon numbers. Boing Boing. Retrieved on 2006-12-01.
  5. ^ Persi Diaconis and Paul Erdos. 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].
  6. ^ a b c d e f g The Erdős Number Project, Paths to Erdős. Retrieved on 2006-12-01.
  7. ^ a b The Oracle of Bacon at Virginia. Retrieved on 2006-12-05.
  8. ^ a b The Oracle of Bacon at Virginia. Retrieved on 2006-12-05.
  9. ^ 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.
  10. ^ a b JT Chayes, L Chayes, R Kotecký, "The analysis of the Widom-Rowlinson model by stochastic geometric methods," Communications in Mathematical Physics, 1995.
  11. ^ a b R Kotecký, D Preiss, "Cluster expansion for abstract polymer models," Communications in Mathematical Physics, 1986.
  12. ^ a b c d e f The Erdős Number Project, Erdos1. Retrieved on 2006-12-20.
  13. ^ 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]
  14. ^ a b Brooks, D.H. Yiheng Zhang Franceschini, M.A. Boas, D.A. Reduction of physiological interference in optical functional neuroimaging using eigenvector-based spatial filtering. Biomedical Imaging: Macro to Nano, 2004, IEEE International Symposium on. Pages 672-675 Vol. 1. 15-18 April 2004. [4]
  15. ^ a b Manolakos, E.S. Stellakis, H.M. Brooks, D.H. Parallel processing for biomedical signal processing. Computer. Volume: 24, Issue: 3, Pages 33-43. Mar 1991. [5]
  16. ^ a b Al-Asaad, H. Manolakos, E.S. A two-phase reconfiguration strategy for extracting linear arraysout of two-dimensional architectures. Defect and Fault Tolerance in VLSI Systems, 1993, The IEEE International Workshop on. Pages 56-63. 27-29 Oct 1993. [6]
  17. ^ a b Hussain Al-Asaad, John P. Hayes: ESIM: A Multimodel Design Error and Fault Simulator for Logic Circuits. VTS 2000: 221-230. (Other collaborations listed here)
  18. ^ a b Frank Harary, John P. Hayes: Node fault tolerance in graphs. Networks 27(1): 19-23 (1996).
  19. ^ 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.
  20. ^ a b Y Aharonov, PG Bergmann, JL Lebowitz, "Time symmetry in the quantum process of measurement," Phys. Rev, 1964.
  21. ^ 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.
  22. ^ The Erdős Number Project, Items of Interest Related to Erdös Numbers,. Retrieved on 2006-12-20.
  23. ^ a b Geoffrey Nunberg. Publications. Retrieved on 2006-12-07.
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