Sally has been musing on how many linguists have low Erdős numbers. There are somewhat more than one might think, because there is a certain amount of crossover in fields like mathematical linguistics, computational linguistics, logic, and so on. Mark Liberman is actually a 3 because of a piece of work he did on a mathematical topic, and thus I am under one construal a (tenuous) 4 like Sally, and the fairly large number of people in my circle of immediate collaborators therefore have Erdős numbers no higher than 5. The details follow.
By convention, Paul Erdős is regarded as having the Erdős number 0. All of his many collaborators on publications have 1 as their Erdős number, and that is irreducible, since they can never become Erdős. Their collaborators have an Erdős number of 2, and that is irreducible: they can never co-author with Erdős, because he is now dead, so 2 is the lowest they will ever have. Persons with the Erdős number 3, however, could in principle lower their number: they have 3 in virtue of having collaborated with someone whose number is 2, but if in the future they co-write a paper with someone whose number is 1, they can acquire the number 2. That is why my friend Phokion Kolaitis likes to point out that he has the lowest Erdős number that is capable of being further reduced (he is a 3).
Now, I am not aware of any linguist with a lower Erdős number than 3, and Mark does have that distinction. Back in the 1980s when he worked at Bell Laboratories, Mark once co-authored a paper with the mathematician J. B. Kruskal (J. B. Kruskal and M. Y. Liberman, 1983: "The symmetric time-warping problem: From continuous to discrete", in D. Sanko and J.B. Kruskal (eds.), Time Warps, String Edits and Macromolecules, Addison-Wesley). Kruskal had previously published a paper with A. J. Hoffman (A. J. Hoffman and J. B. Kruskal, 1956: "Integral boundary points of convex polyhedra", Annals of Mathematics Study 38:223-241); and long after that Hoffman became a co-author of a paper with Erdős (P. Erdős, S. Fajtlowicz and A. J. Hoffman, 1980: "Maximum degree in graphs of diameter 2", Networks 10:87-96). So Hoffman is a 1, which makes Kruskal a 2, and thus Liberman is a 3.
A consequence of this is that because Mark and I published a joint collection of some of our early Language Log posts entitled Far From the Madding Gerund, I am now a 4 like Sally, and the fairly large number of people in my circle of immediate collaborators therefore have an Erdős number no higher than 5. Also like Sally, I would regard my 4 as only a rather tenuous 4, because I don't really equate my name on a collection of blog posts that Mark and I wrote almost entirely separately as comparable to a real collaboration on a piece of scientific research. I am actually a 5 via a different route that involves collaboration on scholarly papers all the way up. The chain goes via Paul Postal, David E. Johnson, Larry Moss, and Jon Barwise to an Erdős collaborator.
But hey, I have my whole future ahead of me (which is where I like to keep it). My Erdős number could one day reduce. So, almost certainly, could yours, if you have one. Get collaborating. Collaboration is good for you. It teaches cooperation, tolerance, a critical attitude, and patience. (Dear God, I pray you will grant me a larger share of your precious blessing of patience with my fellow human beings. And if it's all right, I'd like it right now.)
Update: Jordan Boyd-Graber of Princeton claims to be an aspiring computational linguist (and that counts as a linguist under the usual big-tent view we maintain here), and he reports an Erdős number of 2, in virtue of a publication ("Participatory design: Participatory design with proxies: developing a desktop-PDA system to support people with aphasia", by Jordan L. Boyd-Graber, Sonya S. Nikolova, Karyn A. Moffatt, Kenrick C. Kin, Joshua Y. Lee, Lester W. Mackey, Marilyn M. Tremaine, and Maria M. Klawe, April 2006, Proceedings of the SIGCHI conference on Human Factors in computing systems (CHI '06), ACM Press) with Maria Klawe, whose Erdős number is 1 in virtue of a 1978 publication with Erdős and Frank Harary. Jordan has co-authored with computational linguists Christiane Fellbaum and Alexander Geyken, so their Erdős numbers are not greater than 3.Posted by Geoffrey K. Pullum at April 8, 2007 07:40 PM