New from Panini Press!

Linguists! You’ve spent years dissecting syntax trees, contemplating the very origin of language itself, and arguing about the Sapir-Whorf hypothesis or the Voynich manuscript with clueless neckbeards online—safe in the knowledge that you’d never again have to do anything more mathematically complicated than figure out the tip on your dinner bill—and if you have tenure, you don’t even have to do that... just throw down an extra tenner and call it a day. However, the real world often has other plans, so, for your own good, this book is here to drag you, kicking and screaming, through a series of math problems designed just for linguists—because if you can analyze ergativity, surely you can handle a little light algebra.

From phoneme frequency statistics to the terrifying realities of funding cuts (percentages and subtraction—oh my!), each helps you to confront and accept the unavoidable truth: math is everywhere.

Nonetheless, should a mathematician happen to flip through the book out of curiosity, they’ll be confused by the polysemy of x—variable! phoneme! syntactic category!—and horrified by the occasional irreducible squishiness of the social sciences.

Stimulate your imagination with a few sample problems:

12. If it takes one PhD student 6 months of fieldwork and 2 years of writing to produce a 400-page reference grammar of a language, how long would it take a team of 4 tenured professors to produce a 50-page reference grammar of the same language? (For the sake of this exercise, you may assume that the language is not Austronesian and does not have grammaticalized evidentials.)

29. A certain linguistics department has five members: a sociophonologist, a syntactician, an Oto-Manguean reconstruction specialist, a discourse-functionalist, and a Lecturer who teaches five sections of Introduction to Language for Education majors. For each member of this faculty, there is a unique pairing of exactly two colleagues who do not particularly enjoy conversation with that person’s significant other. Prove that the set of significant others contains only staff of the University’s parking enforcement office.

73. A computational linguist discovers a bug in the search engine she works on. Fixing it would increase the count of true positives and decrease the count of false negatives by the same amount, improving recall by 1.176% and precision by 1.818% on a regression test set. If the current F₁ score of the search engine on the regression test set is 86.49%, what would the new F₁ score be after the bug fix? Extra credit: Will the computational linguist get a larger raise by using her knowledge of NLP (the good kind) to fix bugs like this, or by using her knowledge of NLP (the bad kind) to schmooze her boss?

82. After her book was accepted by a publisher, a linguist determined to proofread carefully to remove all typos. In the first read-through, she found 25 typos in 17 hours. The second read-through went faster, but in 14 hours she found only 16 typos. How many hours will she need to spend to feel confident that no typos remain?

104. The chair of the linguistics department is having his budget cut for the next academic year by 18.4%. Based on data from many previous budget cuts across many departments, the tenured nerds from the statistics department have modelled the formula for the proportion of adjunct faculty that will quit if you decrease their pay by a given proportion to be:

1

1 + e n – kx

where n and k vary by department. For example, in the engineering department, where adjunct faculty retain a modicum of self respect, n is 7 and k is 142. In the linguistics department, n is 8 and k is 10. If adjunct faculty salaries make up 32.7% of the department budget, can the chair make the necessary cuts? Can he redirect an additional 8% of the current budget from adjunct salaries to cost-of-living increases for tenured faculty? If so, by what proportion will the workload of the individual remaining adjunct faculty increase next academic year, assuming their total collective workload reliably increases by 17% year-over-year?

Solutions to odd-numbered word problems are provided in the back of the book. Solutions to even-numbered problems can be found on the internet. Correct solutions to even-numbered problems are available in the accompanying teacher’s guide.

For those linguists with more mathematical maturity—yeah, that’s a real thing—the book includes a collection of more complex project outlines. These projects are also appropriate to assign to advanced and/or annoying students in a mathematical linguistics or linguistical mathematics course. A sample project outline:

Project 17. In perhaps the most striking scene in The Thing, the geologist Vance Norris, who has been infected, is decapitated after his chest cavity opens up into a feeding chamber, whereupon his head turns into an arachnoidal Thing.

(i) Using Praat and the standard assumptions, determine the cardinal vowel formants and calculate the transfer function for the schwa in Norris’s voice pre-infection from his speech earlier in the movie.

(ii) Next, calculate the transfer function for the portions of the vocal tracts in the arachnoidal Thing and the rest of Norris (henceforth, “remnant Thing”). Use the stills provided (a–d) to estimate the length of each, and modify the simplification of the head as a homogeneous sphere by modelling it as an appropriate ellipsoid, given that Charles Halloran was 5′11″, using stills (e–f). Similarly, model the outlet on the trunk as a piston ending at a standard baffle (justify whether the baffle can be treated as infinite in extent or must be modeled as elliptical).

(iii) Assume that the remnant Thing can narrow the remnant vocal tract by contracting circularly at only one point at any position along the tract. Modelling the tract with the standard three-tube model without corrections for the lips, coupled with the chest as a Helmholtz resonator with and without an opening in the chest front, calculate the transfer function for the remnant Thing’s speech, assuming it needs to communicate with the canine Things over their full auditory spectrum up to 60 kHz (note that you cannot simply assume that transverse vibrations in the vocal tract can be ignored), and modelling the connection between the chest cavity and the vocal tract as an acoustic source consisting of a taut ring vibrating under air flow.

(iv) Using the results thus far obtained, simulate the remnant Thing singing “Lose Your Head” by London Grammar with the vocal tract singing high parts and the chest cavity low parts. Note any portions where the coupling between the chest cavity and the vocal tract causes non-human vocal phenomena.

With a clear understanding of and empathy for your deep, abiding disdain for poorly constructed word problems, being asked how many languages you speak, and prescriptive grammarians, Roberts’ Word Problems For Linguists from Panini Press will challenge your brain and maybe—just maybe—convince you that math isn’t that hard.