The Categorical Imperative: Speak Up, But Not Like That (A Mathematician’s Field Guide to Asking Linguists)

# The Categorical Imperative: Speak Up, But Not Like That

If you’ve ever tried to ask a linguist a question and gotten a reply that felt like being handed an abstract proof instead of a cocktail napkin answer, congratulations: you’ve stepped into a universe where assumptions carry the moral weight of axioms. Welcome. Think of this as a short field guide by someone who reads both syntax trees and commutative diagrams for fun — and who believes you can be politely curious without being That Person.

Let’s start with the obvious: the weekly communal clinic for language questions is glorious and terrifying. It’s where curiosity goes to be instrumented. But if you treat it like a drive-thru (“Explain English history, please”) you’ll get a terse polite nudge and maybe a link to a textbook. Why? Because good answers require clean input. In math terms: bad data + ill-specified question = meaningless posterior.

Here are some mathematical metaphors to make that stick — and to show why the way you ask matters.

– Category theory: mind your morphisms

Category theory is obsessed with structure-preserving maps. When you ask a linguist “Why do Brits drop their Rs?” you’re implicitly asking for a morphism from phonetic observation to sociolinguistic explanation. Which functor do you want? A historical functor (diachronic change), a sociophonetic functor (prestige and indexicality), or an articulatory-phonetic functor (coarticulation and reduction)? Each preserves different structure and answers different questions. Don’t expect one map to commute for all diagrams.

– Probability and Bayesian inference: name your priors

When people toss ChatGPT output into a thread and ask “Is this right?” it’s like handing over a posterior without revealing the prior or the likelihood. Models have priors: training data, architecture, prompt context. Linguistic claims have priors, too — theoretical commitments, fieldwork contexts, speaker demographics. If you want a Bayesian-friendly answer, tell us your priors (where you heard it, who said it, what counts as evidence for you). Otherwise, we’ll produce a posterior that’s technically coherent and practically useless.

– Dynamical systems: accents are attractors, not bugs

Accents aren’t bugs to be patched; they’re attractors in a high-dimensional state space shaped by initial conditions (L1), inputs (exposure), control parameters (motivation), and coupling with social networks. Change the topology — immersion, corrective feedback, identity incentives — and you move the basin of attraction. But don’t expect gradient descent to exile your accent overnight. The landscape is rugged, with local minima and plateaus. That’s the mathy way of saying: yeah, accent work is messy and slow, and sometimes you’ll decide you like the local minimum.

– Model theory vs. descriptive statistics: Harris and Chomsky, redux

The Harris–Chomsky dust-up is a tale of method wars: distributional description versus rule-driven generative explanation. Flip that into math-speak and you get model theory (what structures satisfy which axioms?) and empirical statistics (what distributions arise from data?). Both are useful. If you want to engineer technology (speech recognizers, literacy interventions), you often need statistical, data-rich approaches. If you want deep explanatory power (what makes human language unique?), formal models illuminate possibilities. Think of them as different bases in the same vector space: change basis depending on the computation you need to perform.

– Proof theory and reproducibility: show your work

In mathematics, a proof without steps is useless. In linguistics, a claim without data, methods, and code is basically a fairy tale. The recent fights over research infrastructure are not academic drama for drama’s sake: losing the scaffolding means losing the ability to replicate, to test alternative hypotheses, to build on prior work. If you care about being taken seriously — or about building things that actually work — fund reproducibility, insist on open datasets (within ethical limits), and don’t fetishize novelty over verifiability.

– Type theory and interface: speech, reading, and compositionality

Speech to literacy is less a pipeline than a composition of functions: phonology -> phonological awareness -> decoding -> comprehension. Each step has an interface and a contract. Break the contract (mis-assessment, siloed intervention), and downstream outputs fail. That’s why integrated assessment matters: it’s like type-checking in a functional program. You can’t pass a phonological type into a comprehension function and expect it to compile.

So what’s etiquette in this categorical landscape?

– Be precise. Ambiguity is cute in poetry, lethal in troubleshooting. Tell us the speaker’s age, dialectal background, recording quality, and why you care. If you can include audio, do it. If not, say so.

– Respect scopes. Are you asking about perception, production, acquisition, historical change, or social meaning? Each scope invites different tools.

– Don’t outsource your curiosity to AI. Use it as an instrument, not an oracle. Ask the underlying question: what aspect of the phenomenon do you want explained or modeled?

– Remember that models carry assumptions. When someone offers a generative account, they’re writing axioms. When someone offers a corpus study, they’re sampling a distribution. Both are statements packed with implicit choices.

Let’s be frank: there’s a performative element to all this. People want crisp answers; social media rewards pithy takes. Math and logic punish sloppy premises. The result is occasional bitchy snarks in comment threads — deserved sometimes, overenthusiastic other times. Balance matters. If you want the rigor, accept the rigor’s conversational cost; if you want warmth, accept a bit less formal precision.

Practical takeaways (for the curious, the policy-minded, the amateur linguist):

– Attach the audio. Please. I will die on this hill.
– Say what you’ve already googled. It saves everyone time.
– Be explicit about goals: pedagogy, curiosity, design, or policy? The answer shape follows the goal.
– Support infrastructure: reproducible datasets are the pipes through which good science flows.

And yes, sometimes you’ll get a sharp reply. That’s the disciplinary immune system doing its job. But let’s keep it not-needlessly-mean. Precision and politeness are not mutually exclusive.

I’ll leave you with one last mathy thought: categories and imperatives both ask you to respect structure. In category theory you preserve commutation; in conversation, preserve context. When you speak up, do it with a map of the terrain — and for heaven’s sake, put the audio in the packet.

What’s one small change you could make the next time you ask a question (to a linguist, a mathematician, or anyone working with complex systems) that would transform the answer from “meh” to actually useful?