give and take: math and linguistics

this is a response to the excellent post "Why Linguists Should Study Math" over at The Lousy Linguist, which i found via fellow Cornellian @nmashton on twitter. i was going to just write a comment there, but i realized that it would probably become rather long.

first of all, let me say that i am in absolute agreement with the sentiments put forth by Chris in his post. in fact, i'm going to be auditing the brand new, never-before-offered Statistics for Linguists course this semester. but i think that one major point needs to be added.

simply: there is a grave asymmetry in linguists learning math versus mathematicians (or statisticians, or computer scientists, etc.) learning linguistics.

here's the scenario. you're a grad student in linguistics. this means that you went to high school once, and probably were rather good at most of your subjects, or you wouldn't be a student anymore. in high school, they made you learn math. if you were really good at it, you made it through single-variable calculus; if not, probably trig. even if you didn't like it and haven't touched math since, you should have a decent sense of How Math Works, in case you need to pick it up again.

but the converse just isn't true. i've audited the NLP course at Cornell, which is taught by an excellent professor in the CS department who has a very solid grounding in theoretical linguistics. but that almost doesn't matter given the fact that there are zero prerequisites for the course. that's right, no LING101, no nothing. the demographics of the ~80-person lecture break down roughly as 70 CS undergrads, 9 linguistics undergrads, and 1 lonely linguistics grad student.

so what's the big problem? they'll learn as they go, right? learning by doing is the best way, no? wrong. as has been shown time after time on Language Log and elsewhere for this and other fields (law, education, etc.), these would-be NLPers have a complex against linguistics. i think they recognize that they're uninformed on the finer points of linguistic theory, but because "hell, i speak a language!" they don't think they need any more expertise to solve complex linguistic problems. throw more code at it, throw more servers at it, we can brute force our way through. i've watched them re-invent the wheel, and it's a square wheel with an off-center axis. and they're not looking to refine its design, or ask those crazy round-wheeler linguists what they've got cooking in their lab. instead they're trying to make titanium and carbon-fiber square wheels, thinking that will improve things. the mantra is to strive for good enough rather than (i concede, unattainable) perfection.

i think that linguists are more and more cognizant of the need for mathematical training. and for those who just aren't math types, they're willing to go find fellow linguists who are, or even statisticians and computer scientists outside their departments to collaborate with. but nobody comes knocking on the linguistics department door. it's open, guys, and seriously, you could stand to visit. we won't bite.