**Erd****ös number**

Paul Erdös was a prolific and important mathematician. He also had hundreds of collaborators from around the world who coauthored papers with him.

Years ago, Casper Goffman explained an idea, called the Erdös number, that describes the “collaborative distance” between Erdös and someone else, where that distance is defined by the smallest number of steps based on coauthored papers. Erdös himself has an Erdös number of 0, while the 511 mathematicians who wrote papers with Erdös have an Erdös number of 1. One of these people is Persi Diaconis, a professional magician and Stanford mathematician specializing in probability theory.

Over 9,000 people have Erdös numbers of 2, meaning they wrote a paper with one or more of Erdös’s coauthors but never wrote a paper with Erdös himself. Two of these people are Berkeley professors Bernd Sturmfels, in the field of algebraic geometry, and Lior Pachter, a computational biologist. (Sturmfels coauthored three papers with Diaconis, and he wrote other papers with two more people with Erdös numbers of 1. Pachter wrote several papers with mathematician Daniel Kleitman, an Erdös coauthor.)

In 2007, I coauthored a paper with Pachter and Sturmfels in which we analyzed epistatic interactions to describe the geometric structure of a fitness landscape:

So that paper gives me an Erdös number of 3.

**Bacon number**

A group of students later came up with the idea of a Bacon number, a Hollywood version of the Erdös number that equals the smallest number of film links separating any other actor from Kevin Bacon. (Bacon had been previously described as the “center of the Hollywood universe” after a 1994 interview in which he said he worked with everybody in Hollywood or someone who’s worked with them, according to Wikipedia.)

So Kevin Bacon has a Bacon number of 0, while actors who have appeared in a film with him have Bacon numbers of 1. An actor who appeared in a film with any actors who appeared with Bacon, but not in a film with Bacon himself, have a Bacon number of 2.

Morgan Freeman has a Bacon number of 1 based on a 2013 documentary film called “Eastwood Directs: The Untold Story.” (You missed that one? Me, too.) Well, a couple of weeks ago, I appeared in an episode of the show “Through the Wormhole with Morgan Freeman.”

**Erd****ös-Bacon number**

Now there’s a really special number called the Erdös-Bacon number, which is the sum of a person’s Erdös and Bacon numbers. Not many people have an Erdös number, and not many have a Bacon number. And very few people have an Erdös-Bacon number because you have to have written a math or science paper *and* appeared in a film, and of course with known connections to Erdös and Bacon along both paths.

Cornell mathematics professor Steven Strogatz has an Erdös-Bacon number of just 4, having appeared in a TV documentary film with Kevin Bacon called “Connected: The Power of Six Degrees.” Of course, that film is about the very sort of mathematical links we’re talking about here!

So someone just suggested to me that I now have an Erdös-Bacon number of 5. If so, that would put me ahead of such luminaries as Carl Sagan and Richard Feynman! Awesome!!

**The fine print**

As I was looking into this exciting possibility, I discovered a website called “The Oracle of Bacon.” It seems to be the semi-official arbiter of Bacon numbers, and it says: “We do not consider links through television shows, made-for-tv movies, writers, producers, directors, etc.”

That documentary about Cliff Eastwood, with both Morgan Freeman and Kevin Bacon in it, apparently doesn’t qualify. So Morgan Freeman’s Bacon number rises to 2 (via many different paths through his many major films).

Even worse, though, my Bacon number evaporates entirely, since my link to Kevin Bacon goes through my appearance on a television show with Morgan Freeman.

So there you have it. I have an *officially non-kosher* Erdös-Bacon number of 5.

I guess I can live with that.

**But if Kevin Bacon, Morgan Freeman, or any of their Hollywood friends invites me to appear in a real film, I’ll probably accept!**

~~~

Note: It looks like Steven Strogatz’s Erdös-Bacon number of 4 is also compromised because his Bacon number is through a TV movie. You need to use non-default settings for it to show up on The Oracle of Bacon website. But maybe it’s *less non-kosher*, since it was a TV movie, not just a TV show.

The relevant xkcd for Erdös: https://xkcd.com/599/

Thanks, that’s funny! And maybe not too far from the truth. Years ago I heard about an author offering up a low Erdös number for the right collaboration.

Cas Goffman came up with Erdos numbers in an article for the MAA.

Thank you for this information. From the MAA note, it seems the Erdös number had already been discussed by mathematicians for some time. In any case, I’ve revised my post to cite Goffman, and I’ve provided a link to his MAA note.