The Categorical Imperative — Dr. Katya Steiner on Purrs, Papers, and Polaris
# The Categorical Imperative — or: why your cat’s purr and a peer review are cousins
If you like the idea of science as a single dramatic eureka, I have a bridge to sell you — it’s built from grant reports, shared repositories, and the occasional passive‑aggressive comment under a preprint. The more accurate model is a distributed system: noisy, resilient, and full of talented people who take the weird job of policing certainty very, very seriously.
Let’s nerd out together — because the messy sociology of science maps surprisingly well onto a few tidy corners of mathematics and logic. I’ll be cheerful about it when I can, blunt when I must, and mildly bitchy where warranted.
## Functors, Forums, and Friendly Scientists
Category theory is the math of relationships: objects, arrows, and rules about how arrows compose. Replace “objects” with communities (a subreddit, a lab, a journal) and “arrows” with the translations between them (policies, standards, citation practices) and you’ve got a high‑level language for how scientific culture propagates.
A functor is a structure‑preserving map. Think of effective science communicators as living functors: they translate dense research (the source category) into plain language posts and verified answers (the target category) without collapsing the crucial structure. Good translation preserves relationships — not just facts, but how evidence links to claim. That’s why communities reward folks who declare their field, cite sources, and play by shared norms.
But functors aren’t magic: they can be lossy. Overly simplified outreach risks becoming a left‑adjoint that forgets context. The art is to preserve enough structure so that a casual reader could, with a nudge, reconstruct the original argument.
## Topology of Research Infrastructure: connectivity matters
Topology is about continuity and connectedness. A research ecosystem with many well‑connected nodes (diverse labs, open databases, trained technicians) is more robust to shocks. Cut a funding stream here or a data archive there, and you can create holes — like a torus suddenly turning into Swiss cheese.
This isn’t metaphysics. It’s engineering: contingency plans, shared repositories, and public advocacy are topological repairs. Citizens who care about science policy are acting like homotopies — continuous deformations that keep the space intact. Vote, call your representative, support libraries: it’s the math‑adjacent activism that keeps the scientific shape from tearing.
## Probability, Bayesianism, and the Frequentist Fight Club
Statistics is the language of uncertainty. But too many conversations confuse a p‑value with the probability that a hypothesis is true. Enter Bayesian thinking: assign prior credences, update with data. It’s cleaner in principle, but priors are subjective, and that scares people.
Both sides have virtues. Frequentist tools give repeatable decision rules; Bayesian methods encode prior knowledge elegantly. In community science, the practical takeaway is humility — show your priors, quantify uncertainty, and don’t pretend a single significance threshold solves epistemic complexity. The internet’s comment threads are Bayesian filters: claims that survive scrutiny get higher posterior probability.
## Logic: formal proofs vs constructive practice
Classical logic is the math of yes/no truth. Intuitionistic logic insists on construction: to claim existence you must supply a witness. That distinction maps neatly onto two scientific temperaments.
The formalist loves an elegant proof, a tidy theorem — the kind you can write up and submit. The constructivist wants usable artifacts: a dataset that reproduces, an algorithm people can run. Peer review often sits between these logics. Journals historically leaned toward theorems; modern reproducibility demands constructive deliverables. Both are necessary. Insisting only on formal beauty risks producing brittle science; insisting only on pragmatic deliverables risks losing explanatory depth.
## Naming Things and Model Theory
Taxonomy is model building. Model theory studies structures that satisfy a language of axioms. When a taxonomist proposes a new species, they’re proposing a model that fits observed traits and genetic data. The International Code of Nomenclature is the syntax that keeps models communicable.
There’s a social layer too: naming is a durable act of record. Name too flippantly (yes, don’t christen a beetle after your ex), and you embed personal drama into the scientific record. Model theory reminds us: models are powerful because they’re reproducible, falsifiable, and interoperable. Respect the rules and your classification will travel.
## Computability, Reproducibility, and the Human Factor
Computability theory asks what can be algorithmically decided. Reproducibility asks whether independent teams can run your procedures and reach the same conclusions. They’re cousins. But human factors — undocumented data cleaning, ad‑hoc lab hacks, unshared code — are like undecidable problems: messy, sometimes impossible to perfectly resolve.
That’s why community norms matter. Open code, containerized environments, and plain language protocols are ways of building decidability into empirical practice. If you treat reproducibility as an engineering problem rather than a moral failing, you get solutions; if you treat it as shaming, you get defensive silence.
## A Two‑Sided Verdict
Formalisms (proofs, codes, models) give clarity and portability. Social practices (forums, moderation, advocacy) provide resilience and context. Leaning too hard on either side breaks the system: pure formalism forgets people; pure sociality forgets rigor. The healthy system is hybrid — rigorous where it matters, humane where it must be.
And yes, your cat’s purr is a neat example of that hybrid: a physiological oscillator with social consequences. Biology gives us the mechanism; anthropology gives us the meaning. Both are true and both incomplete on their own.
## Parting Thought (and a question to keep you up at night)
If category theory describes translations between communities, topology describes the overall health of the research landscape, and logic gives us the rules for truth claims, then what are we missing? Maybe the missing piece is ethics as an operad — the composition law for good scientific actions.
So I’ll leave you with this: if you could design one mathematical metaphor that policy‑makers would actually understand (and maybe act on), what would it be — and how would it change the way we fund, name, and defend science?
