A common trope in recreational mathematics is the grazing goat problem (see this lovely write-up in Quanta). Briefly, there’s a goat tethered to a rope, and the problem is to determine the area it would be able to graze given the length of the rope and various other variables like the shape of the field and the presence of a fence or shed.
Towards the end of my recent piece for Annual Reviews I argue that linguistics has something of an inverse grazing goat problem.
I think it is fair to say we have made a solid start in linguistics exploring everything there is to explore — within the perimeters of our field, and tethered to our particular rope. That rope is the written-language, text-focused legacy of the field. We’ve done our bit grazing where we can. Some of us even went for the hard-to-reach places, pulling that rope as taut as can be and getting to the borders of what can be reduced to writing. The inverse grazing goat problem asks: what if we free the goat?
Mathematicians are of course wise enough to focus on the area that can be grazed. That’s a tractable question given enough information about the length of rope, the shape of blocking objects, the perimeter of the field, and so on. The inverse problem poses a different kind of question: what have we missed? How can we try and escape prejudices and unexamined assumptions about our field of study? Harder to answer, for sure, but therefore all the more worth asking.
Dingemanse, Mark. 2024. ‘Interjections at the Heart of Language’. Annual Review of Linguistics 10: 257–77. https://doi.org/10.1146/annurev-linguistics-031422-124743.