Scholars with even a passing interest in mathematics usually know what an Erdös number is; it is the number of degrees of separation between a scholar and Paul Erdös, calculated by stepping through collaborative publications. Paul Erdös was a sort of enigmatic freelance mathematician who was very good at proving things, and very prolific with the aid of something like 500 different collaborators. It has become something of a sport in modern times for mathematical scholars to compute their Erdös number, since basically everyone who has published a mathematics article with a collaborator ends up having an Erdös number. I've read that most real mathematicians have an Erdös number of 8 or less.

A more interesting thing is when scholars in neighboring fields, such as mathematical linguistics, end up with Erdös numbers due to cross-fertilization. It turns out that one of my professors, Ed Keenan, appears to have an Erdös number of 4, which is really very low for a scholar outside mathematics. It's so unusual, it bears a stated proof. One chain of collaborative work connecting Keenan with Erdös is the following:

Keenan, E. and Westerståhl, Dag (2011) “Generalized quantifiers in linguistics and logic,” in J. van Benthem and A. ter Meulen (eds.), Handbook of Logic and Language. Second Edition, Amsterdam: Elsevier.

Hella, Lauri; Väänänen, Jouko; Westerståhl, Dag (1997) "Definability of polyadic lifts of generalized quantifiers." J. Logic Lang. Inform. 6:305–335.

Magidor, Menachem; Väänänen, Jouko (2011) "On Löwenheim-Skolem-Tarski numbers for extensions of first order logic." J. Math. Log. 11:87–113.

Erdős, P.; Magidor, M. (1976) "A note on regular methods of summability and the Banach-Saks property." Proc. Amer. Math. Soc. 59:232–234.

And the wonderful conclusion to all this is the theorem that my own Erdös number is 5, thanks to a paper I published with Ed Keenan in a rather obscure special volume of Linguistische Berichte in 2002. Does this increase my mathematical credibility? Not really. But it's nice to know I am somehow closer to the inner circle than I thought. A special bonus will soon come from my upcoming collaboration with Nick Chater, who also has an Erdös number of 4. So then I'll have earned my number 5 in two different ways.

## Thursday, March 29, 2012

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