Erdős-Bacon Computation

When I was living in the Lower East Side in the '70s, a couple of scenes from Godfather II were filmed in my neighborhood and I signed up as an extra. This earned me a check for $35, of which there may be some record somewhere, and I can provide witnesses, but otherwise I have no hard proof of my role in the film.

In my first scene, I was one of many Italian immigrants dancing in the street. (I don't recall what we were supposed to be celebrating.) As my wife will be happy to tell you, though I can manage a passable two-step, I'm not much on free-style dancing. But until I met her, the only real complaint I ever received came from Coppola himself, who stopped the scene, shouting from a third-story window, ''You with the blue cap—get out of the street.'' (Makeup had given me a really bad haircut and a wool cap to conceal it.)

Then there was the funeral procession. Hoping to accentuate my screen presence, I positioned myself in the midst of a group of little people who were walking behind the casket. Once again, I was asked to leave the scene.

Thanks to the later work of my co-stars Robert De Niro and Bruno Kirby, both of whom appeared on my behalf in Sleepers (1996), my Bacon number is 2.

With regard to Erdős, it's painful to think about missed opportunities. At the height of my film career in New York, I was also writing a dissertation in number theory at the Courant Institute. My advisor was Harold N. Shapiro, who knew Erdős well and had coauthored several papers with him. Shapiro once acknowledged my contribution to a paper of his in an addendum to the paper, but didn't see fit to list me as a coauthor, so I don't suppose that gets me anything.

One morning, while I was teaching at the University of Texas, I received a phone call out of the blue from Erdős himself. We met for lunch and spent the afternoon together, discussing a problem I was working on. There was some subsequent correspondence, in which he gave me an idea for finishing my proof, but, alas, I never published with him either. I still have an idea of writing up that proof and naming Erdős as a posthumous coauthor, which would help my cause dramatically.

The fact is that I rarely coauthor anything. I find it hard enough to write a satisfactory paper on my own without having to worry about someone else's preferences about how it should be written. But as an exception to this policy, I once offered to put Matt Kaufmann's name on a paper (reporting work on which we had indeed collaborated) in return for his promise (a) not to offer any suggestions for revision and (b) to present it on my behalf at a conference. And as luck would have it, Kaufmann's Erdős number is 2 (by way of either Michael Makkai or Saharon Shelah—take your pick). This makes mine 3. Do the math.