Originally Published: Friday, 18 May 2001 Author: Kristina Pfaff-Harris
Published to: opinion_articles/opinion Page: 1/1 - [Printable]

Kristina in Space: Six Degrees of Paul Erdös

The indomitable right and left-brained Kristina Pfaff-Harris takes us on another Friday exploration in Geek land. This week follow Kristina into the mystical world of mathematics and numbers, discover how their arcane secrets can reveal mysterious relationships in the world of mathematicians, movie stars and other pop culture personalities!

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May I make a confession? I sometimes have a very short attention span. Not that I can't stay up coding on something that I don't quite understand for fourteen or more hours straight, but once I've figured out how the code needs to work, I tend to lose interest. I mean, if I've figured out the problem, it just seems so boring and unnecessary to actually write the code itself. Unfortunately, this sometimes happens before I've actually written the code in question, and when it does, I somehow find thousands of ways to waste my time rather than go and work on the project. This time, it was Paul Erdös' and, more specifically, Jerry Grossman's fault: I suddenly felt a need to find out if I had an Erdös number.

You see, I was wandering around the Web, searching for something important to take my time away from what I should have been doing, and remembered that a few years ago I had co-authored a paper with my father (a mathematics professor) on developing an Online Web-Based Math Course. This was before the days when Flash and even Java were widely supported, so there were several obstacles we had to overcome in the presentation. We presented this paper at the International Conference on Technology in Collegiate Mathematics, so by the most bizarre of coincidences, I, a Linguistics major with little to no background in mathematics, had a paper in a mathematical publication. It was possible that I could have an Erdös number! Oh the glee, the sheer glee! There are few things geekier than knowing (or having) your own Erdös number.

For those of you who aren't in Mathematics or Computer Science, or other such field, or who are and haven't heard of an "Erdös Number," I'll summarize. Paul Erdös was an extremely prolific mathematician who lived between 1913 and 1996. During his lifetime, he published more than 1,500 papers with over 500 co-authors. At some point which I've been unable to determine, people began to speak of one's "Erdös Number" as a function of the links between these co-authors, and their co-authors, and so forth.

It works like this: Paul Erdös himself has an Erdös number of 0. Anyone who co-authored a paper with Erdös has an Erdös number of 1. Anyone who co-authored a paper with a co-author of Erdös has an Erdös number of 2, and so on. The Erdös Number Project homepage has much more data about this, so I won't cover it all here.

I was ready -- but how to find out who had co-authored papers with whom? All I knew of was Dad, and all I knew of his other papers were from the notes on his homepage at the universitythat say simply: he "has published two research papers that you wouldn't even want to know the titles of." Not very helpful. I called Dad. Dad wasn't home. Drat! I must look further. Back to the Erdös page: maybe they will have some helpful information.

I scoured through the pages looking for helpful hints and found links to databases like Zentralblatt MATH 1931 - ... and The American Mathematical Society's MR Lookup and the Association for Computing Machinery's Computer Science Bibliography. A quick search for "Pfaff, D" brought me Dad's publications. (He's right -- I didn't want to know the names of them, but at least they're not quite as pornographic-sounding as one of my former professor's "Wildly Ramified V-Rings.") Since the Erdös Number page has a list of everyone with an Erdös Number of 2 or less, I ran to look up Dad's co-authors: no luck.

Okay, so back and forth and back and forth between the databases I went. You see, if you don't subscribe to Zentralblatt or AMS' databases, you can only get three results on a search. Dad's co-authors had many papers, but I couldn't get past the first three! It was maddening. Each time I found a new name, I'd rush back to the Erdös list to see if I could find it therein, but I never did. Finally, I somehow managed to track down an Erdös number of five for Dad, which would be six for me, but I wasn't satisfied. I must have a lower Erdös number than that! It obsessed me.

Suddenly, it occurred to me that I still had an account on my University's server! Maybe they had a subscription to MathSciNet and I could get there through the faculty server. SSH and Lynx were my only hope now: I sshed into my account, Lynxed into the AMS lookup -- and I was in! There they were, arrayed before my eyes: all 37 papers by Dad's most prolific co-author and all of his co-authors in turn. I quickly ran ':set ignorecase' in vi, so I could search for Erdös numbers without worrying about capitalization: sure enough, Dad was a four! Making me a five! At last, I had an Erdös number that counts.

Technical Reports

I surfed back over to the Erdös project page to browse some more and bask in the glory of this achievement, when I suddenly hit a brick wall: "not normally included," the page said "are ... technical reports..." Hmmm. I was suddenly worried: could our paper be considered a "technical report?" After all of this, was it possible that I didn't have an Erdös number at all? It couldn't be: the page also states that a criterion is "some mathematical collaboration...resulting in a published work." There was collaboration, there was mathematics, there was a published work: Surely that'd be okay! Besides, some argue that because Hank Aaron (the famous baseball player) once autographed a baseball which was also autographed by Erdös, that they had a joint publication. Surely my paper was in at least the same league (no pun intended) as an autographed baseball!

There was nothing to do but ask the expert. So I emailed Jerry Grossman who runs the Erdös Number Project, and tried not to beg:

From: Kristina Pfaff-Harris
To: Jerry Grossman
Subject: Do I have an Erdos number?

Well, this is probably an enormous stretch, but my father and I co-authored a paper we presented at the International Conference on Technology in Collegiate Mathematics years ago, on issues we encountered in create a web-based mathematics course. It was published in the "proceedings" of that conference. Does this count as far as Erdos numbers are considered? Dad's would be 5 by virtue of actual "real" mathematical publications (Erdos->Graham->Lawler->Arnold->Morse->Pfaff); and if this counts, then I guess mine would be 6.

I would really like to have an Erdos number. It wasn't really clear from the website whether a presented paper such as this would count, so if I could get your opinion, that'd be great.

I resisted the urge to close with, "Please, please, PLEASE, pretty please!" Dignity, always maintain dignity. Never let them see you sweat, especially when it's something this important. I awaited Dr. Grossman's response.

Six Degrees of Kevin Bacon

In the meantime, I decided to console myself by calculating where I fell in the Six Degrees of Kevin Bacon. This is similar in concept to the Erdös Number, except that one's Bacon Number is based on mutual films. It was once theorized that anyone with a finite Bacon number would have a number of six or less, but this has been proven to be false in the last several years, and there are now people discovered with ten degrees of Kevin Bacon. (If there are no links between you and Kevin Bacon, for example, if you've never done a film, your Bacon number is said to be infinite.)

Since I occasionally work as an extra, and since I actually appeared on screen briefly in "Jane Austen's Mafia," (for those 23 of you who saw the film, I was one of the blackjack players in the casino who gets electrocuted), I figured I had a Bacon number as well. Off to the Oracle of Bacon search site. Since my name wouldn't be in their database (no screen credit for even electrocuted extras), I had to look up my "co-stars." I hit pay dirt on my first search for Olympia Dukakis: her Bacon number was one making mine two. Hah! Let those mathematicians and computer scientists try to top that one!

I went on to discover that my Laurel and Hardy number is three (through the late Lloyd Bridges in "Mafia") and that my Natalie Portman number is two (through Christina Applegate, also in "Mafia"). I felt somehow redeemed even though I might (or might not) have an actual Erdös number.

Thinking back, I have no idea why having an Erdös number had become so overwhelmingly important; nevertheless it had. I even began scheming about how I could reduce my Erdös number. Could I bribe an Erdös two or even an Erdös one to put me in as a co-author? With twenty-three cents in my checking account, it didn't seem likely. Could I go back to school where one of these lower-numbered folks teach, and somehow get my name on a paper with one? Maybe I could get Jerry Grossman to sign a baseball for me!

Ah, well, another day wasted. I suppose I had really better get back to my project. Wait ... what's that: The Mathematics Geneology Project? And no similar project for Linguistics? MySQL database, here I come, and another Friday well spent!


I did hear back from Dr. Grossman on my inquiry. He replied: "Why not? It sounds like a research publication to me, so give yourself an Erdos number." Oh Joy! He went on to point out the path to a five for me, since when I wrote to him, I only had a six. It's rare that one finds such a generous soul in academia!

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