Culture on My Mind – Degrees of Separation

Culture on My Mind
March 6, 2020


This week’s “can’t let it go” is the confluence of mathematics and pop culture.

While working on the January 3rd edition of The Thing About Today, I came across Danica McKellar’s Erdős and Erdős–Bacon Numbers, and my curiosity was piqued by what these meant.

The Erdős Number is named for Hungarian mathematician Paul Erdős, one of the most prolific mathematical minds of the 20th century. The Erdős Number describes the collaborative distance between Erdős and another person as measured by the authorship of mathematical papers. By definition, Paul Erdős has an Erdős number of zero, a direct collaborator has an Erdős number of one, and anybody else’s Erdős number is defined as k + 1 where k is the lowest Erdős number of any coauthor.

Based on her collaborative work on research papers, Danica McKellar’s Erdős Number is four.

A more familiar separation number is related to the Six Degrees of Kevin Bacon parlor game, which is based on the larger “six degrees of separation” concept which posits that any two people on Earth are six or fewer acquaintances apart. The goal is to find the shortest path between any actor and the prolific Kevin Bacon. For example, Ian McKellan starred in X-Men: Days of Future Past with Michael Fassbender and James McAvoy, who were in X-Men: First Class with Kevin Bacon. Thus, James McAvoy and Michael Fassbender have Bacon Numbers of one and Ian McKellen is a Bacon Number two.

Back to our Danica McKellar example, she has a Bacon Number of two: She was in 21 and a Wake-up with Andre Royo who was in Super with Kevin Bacon.

Smashing those two separation numbers together, we end up with a rare measure of collaborative distance called the Erdős-Bacon Number. It is the sum of a person’s Erdős Number and Bacon Number, and is a rarity since the subject needs to have appeared in a film and co-authored an academic paper.

The lowest Erdős-Bacon Numbers among scientists belong to mathematicians Daniel Kleitman and Bruce Reznick at three. Physicist Richard Feynman, one of my favorites, has an Erdős-Bacon Number of six due to his sum of three and three. Stephen Hawking and Carl Sagan are also at six.

Among actors, Albert M. Chan has an Erdős-Bacon Number of four, Misha Collins and Danica McKellar both have a six, and Natalie Portman, Colin Firth, Mayim Bialik, and Kristen Stewart have sevens.

There are other variations and separation numbers, as well as several academic studies on the depth of social connections. One extension on the numbers presented here is the Erdős-Bacon-Sabbath Number (adding in the collaborative distance to the band Black Sabbath, of which Stephen Hawking has an eight and Natalie Portman has an 11). Another is the 1961 small-world empirical study by Michael Gurevich, which is analogous to the 2003 Columbia University Small World Project.

There is a ton of information at the “six degrees of separation” Wikipedia page, though I do caution that you may fall down a rabbit hole just like I did.


Culture on My Mind is inspired by the weekly Can’t Let It Go segment on the NPR Politics Podcast where each host brings one thing to the table that they just can’t stop thinking about.

For more creativity with a critical eye, visit Creative Criticality.


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