## My Chalabi Number

Just a few days ago, I wrote about my discovery that I’m connected mathematically to the Iraqi politician Ahmed Chalabi, ending with the thought that I might even have attended conferences with him. My pal Sándor Kovács has kindly pointed out to me in an email that one can quantify just how close Chalabi and I are.

The relevant measure of distance is one that has been used by mathematicians for decades in measuring their level of connectedness to the late, prolific Hungarian mathematician Paul Erdős. Erdős has an Erdős number of 0. If you wrote a joint paper with Erdős, your Erdős number is 1. If you didn’t, but you wrote a joint paper with someone who wrote a paper with Erdős, your Erdős number is 2. And so on. A widely known movie industry counterpart to this involves measuring how closely connected a movie actor is to Kevin Bacon by calculating the actor’s Bacon number. It is 1 if the actor appeared in a movie with Bacon, 2 if the actor didn’t appear with Bacon but appeared with someone who appeared in some other movie with Bacon, and so on. (See Six Degrees of Kevin Bacon for more on Kevin Bacon, here for a discussion of Erdős number, and here for a discussion of six degrees of separation. You’ll find more links at these sites.)

With this notion of measure in hand, what is my Chalabi number? In other words, what is the length of the shortest path from me to Ahmed Chalabi? **Five**. MathSciNet has a handy tool that lets you type in the names of two authors, and it then finds a shortest path from one to the other. (Shortest in terms of the data in its database. Shorter paths may exist via links, or papers, it doesn’t know about.) The path from me to Chalabi that MathSciNet provides is: Irving-Small-Goldie-Chatters-Khuri-Chalabi, with each successive pair having written a paper together.

Lance Small is my old friend and co-author at UCSD. Alfred Goldie was one of the giants of ring theory, a fascinating man whose obituary in The Independent from three years ago is worth reading. Chatters is another English ring-theorist, whose book *Rings with Chain Conditions*, written with C.R. Hajarnavis, I used to use all the time. As we get farther down the path, my connection weakens. I was familiar with Soumaya Khuri’s work, but I don’t recall whether I met her or not. And of course that brings us to Chalabi himself, whose connection to me is still more remote. Did I meet him? The best bet, if I did, is that he would have been in Antwerp with me in August 1978 at a large ring theory conference. This is about the time he would have been working on the paper with Khuri, his paper that represents his largest foray into ring theory. (One thing about that conference. We spent lots of time in the lobby of the modern Antwerp hotel where the conference organizers put us, a hotel located on the edge of a ring highway, halfway between the university campus and the wonderful central city, but near neither. One of our pastimes was to play with the prototype of a funny device created by the brother of one of the mathematicians, a cube, parts of which one could rotate in different directions until one managed to line up the colors, one color per side. Little did we know that two years later it would be an international sensation.)

What’s my Erdős number? It’s 4. There are lots of length 4 paths from me to Erdős.

How does Hank Aaron manage to have Erdős number 1? You see, he and Erdős jointly autographed a baseball when they received honorary degrees from Emory University.