Four.

Well. . . .

Geoffrey K. Pullum’s remarks on ErdÅ‘s numbers tickled my whimsy (or is that my vanity?). Why? Well, let’s set up the situation by quoting from the aforelinked post:

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).

Pullum is enthused at the prospect of having an Erdős number of 4. How does he manage it?

Back in the 1980s when he worked at Bell Laboratories, Mark [Liberman] 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 ErdÅ‘s (P. ErdÅ‘s, 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.

Because Liberman and Pullum published a collection of their Language Log posts — Far from the Madding Gerund (2006) — Pullum can claim a tenuous 4. As it happens, on three separate occasions, Mark Liberman quoted my e-mails in his Language Log posts. Even though none of these have appeared in book form and even though they scarcely qualify as academic writing, I’m going to grab my 4 and run with it!

My cameo appearances on Language Log have been as follows:

1. Mark Liberman, “The fujimotic chigger of scholarship” (14 February 2006).
2. Benjamin Zimmer, “No snowclone left behind” (25 February 2006).
3. Mark Liberman, “Bogosity” (29 August 2006).
4. Mark Liberman, “Envy, navy, whatever” (27 October 2006).

(More recently, Pullum has written that via András Kornai, he can claim an ErdÅ‘s number of 3, established by peer-reviewed, two-author papers all the way. I guess that’s sort of like being able to claim the throne of France under the Salic Law.)