# Erdős–Bacon number

A person's Erdős–Bacon number is the sum of one's Erdős number—which measures the "collaborative distance" in authoring academic 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.[1][2] The lower the number, the closer a person is to Erdős and Bacon, which reflects a small world phenomenon in academia and entertainment.[3]

In general, to have a defined Erdős–Bacon number, it is a necessary (but not a sufficient) condition for one to have both appeared in a film and co-authored an academic paper. It is not sufficient because it may still be impossible to reach Erdős through one's academic coauthors or Bacon through one's film co-appearances.

## Scientists

Astronomer Carl Sagan has an Erdős number of no more than 4[4] via Steven J. Ostro and a Bacon number of 2,[5] for a total of 6. Physicist Richard Feynman has an Erdős number of 3[6] and a Bacon number of 3, having appeared in the film Anti-Clock alongside Tony Tang.[7]

Geneticist Jonathan Pritchard appeared in the 1998 movie Without Limits[8] which gives him a Bacon Number of 2.[9] Pritchard has an Erdős Number of 4[10][11][12][13] thus giving him an Erdős–Bacon Number of 6.

Theoretical physicist Stephen Hawking has an Erdős–Bacon number of 6: His Bacon number of 2 (via his appearance alongside John Cleese in Monty Python Live (Mostly) who acted alongside Kevin Bacon in The Big Picture) is lower than his Erdős number of 4.[14]

## Actors

Canadian actor Albert M. Chan has an Erdős–Bacon number of 4. He co-authored a peer-reviewed paper on OFDM, giving him an Erdős number of 3.[15][16][17] Chan was cast alongside Kevin Bacon in Patriots Day, giving him a Bacon number of 1.[18]

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 she has a Bacon number of 2, both of them having worked with Margaret Easley.[2]

Israeli-American actress Natalie Portman has an Erdős–Bacon number of 7. She collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird,[19] who has a collaboration path[20][21][22] leading to Joseph Gillis, who has an Erdős number of 1.[23] Portman appeared in A Powerful Noise Live (2009) with Sarah Michelle Gellar, who appeared in The Air I Breathe (2007) with Bacon, giving Portman a Bacon number of 2 and an Erdős number of 5.

British actor Colin Firth has an Erdős–Bacon number of 7.[24] Firth is formally credited as co-author of a neuroscience paper, "Political Orientations Are Correlated with Brain Structure in Young Adults",[25] after he suggested on BBC Radio 4 that such a study could be done.[26] Another author of that paper, Geraint Rees, has an Erdős number of 5,[27][28][29] which gives Firth an Erdős number of 6. Firth appeared with Kevin Bacon in Where the Truth Lies, so his Bacon number is 1.[24]

## Others

Hank Aaron, a baseball player, is jokingly said to have an Erdős–Bacon number of 3, as he appeared in Summer Catch with Susan Gardner, who was in In The Cut with Kevin Bacon, and he and Erdős both autographed the same baseball.[30] The baseball originated due to a shared connection with mathematician Carl Pomerance.[31] In 1974, Pomerance watched the baseball game on TV during which Aaron famously surpassed Babe Ruth's 714 home-run record, establishing a new record of 715. Pomerance noticed that the prime factors of 714 and 715 each sum to the same number, 29, and published a related paper with two of his students,[32] calling such consecutive integers Ruth–Aaron pairs. In late 1974, Paul Erdős learned of the paper and wrote a letter to Pomerance,[33] a first correspondence between the two which led to 21 joint publications.[34] 21 years later, at the 1995 commencement, Emory University simultaneously granted Hank Aaron and Paul Erdős honorary degrees.[35] Carl Pomerance, a faculty member at the University of Georgia, attended the nearby event and asked both men to sign the baseball.[36]

## Table

Name Erdős number Bacon number Erdős–Bacon number
Behe, Michael J.Michael J. Behe 4[37] 3[38](b)(c) 7
Bialik, MayimMayim Bialik 5[39] 2[39] 7
Billingsley, PatrickPatrick Billingsley 4[40][41][42][43] 2[44] 6
Chan, Albert M.Albert M. Chan 3[15][16][17] 1[18] 4
Dalrymple, DavidDavid Dalrymple 3[45][46][47] 2(b)(c)[48] 5(b)(c)
Dembski, William A.William A. Dembski 4[49][50][51][52] 2(b)[53] 6
Hare, DonovanDonovan Hare 2[54][55] 2[56][57] 4
Houh, HenryHenry Houh 5[58][59][60][61][62] 2[63][64] 7
Knight, RobertRobert Knight 4[65][66][67][68] 2(c)[69][70] 6(c)
Marks II, Robert J.Robert J. Marks II 3[49][50][51] 2(b)[71] 5
McKellar, DanicaDanica McKellar 4[72][73][74][75] 2(d) 6
Metropolis, NicholasNicholas Metropolis 2[76] 2[77] 4
Portman, NatalieNatalie Portman (Hershlag) 5[19][20][21][22][23] 2(d) 7
Pritchard, JonathanJonathan Pritchard 4[10][13][78][79] 2[8][9] 6
Sagan, CarlCarl Sagan 4[6] 2(b)[5] 6
Yannai Gonczarowski 3[80] 3[80] 6
Stern, TomerTomer Stern 4[81][82][83][84] 3[85][86][87] 7
Strogatz, StevenSteven Strogatz 3[88][89][90] 1(b)(c)[91] 4(b)(c)
Chomsky, NoamNoam Chomsky 4[92][93][94][95] 3(b)(c)[91] 7(b)(c)
Chazelle, BernardBernard Chazelle 2[96][97] 3[98] 5
Gyöngy, IstvánIstván Gyöngy 3[99][100][101] 3[102] 6
Vidas, TimothyTimothy Vidas 4 [103][104][105][106] 3(b)(c)[107][108][109] 7

Notes:

(a) See discussion (Others) above.
(b) Includes role as self
(c) Includes documentary credit
(d) See discussion (Actors) above.

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