Thursday, May 14, 2020

in search of erdos-bacon

The good news: I may have an Erdos-Bacon number afterall.

The bad news: Confirming as much, and figuring out what it is may be a bit tricky.

To review, A Bacon number represents the number of steps separating an actor from Kevin Bacon. Kevin Bacon himself has a Bacon number of  zero. Any actor who appeared with him has a Bacon number of one. Actors who didn't appear with him, but appeared with an actor who has a Bacon number of one have a Bacon number of two. I have a Bacon number of three, courtesy of the movie, Being, in which I appeared as an extra. I wrote about that in a previous post. People who don't have a traceable connection to Kevin Bacon are said to either have an infinite Bacon number, or an undefined Bacon number -- or simply not to have a Bacon number. I've seen all three formulations, and I can't say which is correct.

Similarly, an Erdos number* represents the number of steps separating someone from the prolific (and prolifically collaborative) mathematician, Paul Erdos. Paul Erdos has an Erdos number of zero. his coauthors have an Erdos number of one. Etc. For what it's worth my uncle, Andrew Whinston, has an Erdos number of two. Since Paul Erdos passed away in 1996, it's probably difficult for anyone to get an Erdos number of one.

A person's Erdos-Bacon number is the sum of that person's Erdos and Bacon numbers. The lowest Erdos-Bacon number a person (other than Erdos and Bacon) can have is two**.

All of this brings me to my favorite subject -- me. As noted above, my Bacon number is three. But, until yesterday I thought I don't have an Erdos number. To be clear, I'm still not sure if I do, but there's a possibility which I will address below. I know a few people with Erdos numbers, but haven't had the chance to coauthor with any of them.

Last night I Googled myself. This wasn't just for the sake of ego -- though I'm not above Googling for ego. I was wondering -- suppose, hypothetically, I was looking for another job. What would a potential employer see if he or she decided to do a little research via Google. And I came across "Synthetic GIC Reserve Proposal" which I, as part of the Deposit Funds Subgroup of the American Academy of Actuaries' Annuity Reserve Working Group. I wasn't a major contributor to the paper, and -- truth be told -- I can't even remember what my contributions were. But I coauthored with 14 other actuaries. And that jogged my memory -- I also used to be a member of the Academy's Committee on Professional Responsibility. As such, I coauthored a 2003 whitepaper, "The Actuary's Relationship with Users of a Work Product." There were seven other coauthors, none of whom were also on the GIC proposal. So that means that I have 21 potential paths to an Erdos number. The problem is, I don't know who among those 21 also authored other papers and with whom. And I don't feel comfortable emailing them to ask. Well, I feel comfortable asking one of them, and I emailed him last night. We'll see what he says.

*If I am not mistaken, the concept of an Erdos came first. The Bacon number came along afterwards.
**proof left to reader.

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