The Categorical Imperative: How We Know What We Know — From Reddit Mods to Roaring Cats and Lost Stars
# The Categorical Imperative: How We Know What We Know — From Reddit Mods to Roaring Cats and Lost Stars
We like neat answers: a label on a jar, a citation at the end of a post, a username with a tiny colored badge that says “trust me, I have a PhD.” But the world doesn’t hand us certainty on a silver platter. It builds it — with dusty observatories, holotypes in museum drawers, and volunteer moderators squinting at your comment history. Let’s take a jaunt through the scaffolding of knowledge and do it with the picky love of someone who delights in logic, category diagrams, and the occasional cat anecdote.
## Peer review by social proof (and graph theory)
Reddit’s AskScience panel is a gorgeous little model of distributed certification. Think of the subreddit as a graph: nodes are users, edges are interactions. The panelists are high-degree nodes with verified flair. Their credibility isn’t a single bit of data; it’s a pattern — a subgraph of consistent, referenced, teachable answers. In network language, reputation is an emergent centrality measure.
From a mathematical standpoint, this is social proof acting like a noisy oracle. Probabilistically, each authoritative answer shifts your subjective posterior probability about a claim. Bayesian updating explains why a stream of consistent, well-referenced replies makes belief coalesce faster than a single flashy claim. But beware: highly connected networks can amplify biases, not truth. Complexity theory reminds us that the cost of verifying every claim scales badly — which is why heuristics (flair, prior publications, linked answers) are used instead of exhaustive verification.
## Naming beetles and homotopy-type feelings
Taxonomy’s insistence on holotypes and priority reads like a category theorist’s dream: objects (specimens) and morphisms (comparisons, measurements) arranged into a structured system with strict identities. The holotype is a chosen object that anchors an isomorphism class — the referent that future morphisms map to. Homotopy type theory offers a playful metaphor: identity is not just equality but a path, and that path must be recordable and inspectable.
The ICZN/ICN codes are not mystical; they’re constraint systems that make the category of species manageable. Without those coherence laws, names would be leaky; with them, we can compose descriptions, cite specimens, and reason about biological objects with mathematical rigor. The downside? The codes are social constructs maintained by humans; they inherit fallibility and institutional fragility.
## Naked-eye astronomy and constructive logic
The ancients tracked stars with repetition, not magic. They used constructive methods: demonstrate by doing. A gnomon’s shadow gives a proof witness that anyone with a stick at noon can replicate. That’s constructive logic in practice — a proof that yields a construction the next observer can carry out.
Model theory delights here. A star catalogue is a model of the sky. Different cultures built different models with the same observable data: Babylonian tables, Greek catalogs, Indian siddhantas. Each model had axioms (assumptions about motion) and derived predictions (eclipses, conjunctions). The success of a model is judged by its predictive power and by whether its structure allows useful morphisms to other models — translations, if you like.
## Cats purring: signal processing, game theory, and ethics (sort of)
Your lap cat purring is biology meeting negotiation. Physically, purring is a periodic signal created by laryngeal contractions. Signal processing gives us immediate tools: analyze frequency content, look for the solicitation purr’s frequency modulation, measure power spectral density. Information theory asks: how much information is in this purr about the cat’s intent? Not infinity.
Game theory shows why the “sales tactic” works: humans have been conditioned to respond to certain auditory cues (infant-like frequencies, urgency modulations). A cat that optimizes for food acquisition will develop behaviors that maximize payoff; the solicitation purr is such a strategy. Ethically, this is amusing, not sinister — your cat is not plotting global domination; it’s using a local utility function.
## Logic: classical, modal, and the moral calculus of trust
Different forms of logic map onto different epistemic practices. Classical logic treats statements as true or false relative to a model. Modal logic lets us talk about necessity and possibility — handy when distinguishing “this species must be distinct” from “this specimen might be novel.” Intuitionistic/constructive logic is that old-school experimentalist’s credo: to assert existence, show a specimen.
Proof theory and type theory: in mathematics, a theorem without a construction can be unsatisfying; in science, a statistical claim without data is suspect. The rise of preregistration, open data, and reproducible pipelines is a social move towards constructive proofs: show your work, or don’t claim the prize.
## Failure modes and robustness: information theory to the rescue
Why do records survive centuries? Redundancy and error-correcting practices. Babylonian tablets, multiple catalogues, museum duplicates — these are low-tech repetition codes. Information theory teaches that to preserve a message you need redundancy and a channel resistant to noise (institutional memory, funding, legal protections).
When institutions are underfunded or politicized, the channel capacity drops. Entropy rises. Data get lost, type specimens vanish, and what remains are fragments — high-entropy, low-trust signals.
## Two sides of the coin: skepticism and trust
Skeptics insist on verification: prove it, show data, produce the specimen. Trust-ers point out that no one can double-check everything; we rely on delegated authorities, reputational heuristics, and institutional protocols. Both sides are mathematically defensible: skepticism minimizes Type I errors (false positives); delegation reduces verification costs and the expected time to action.
The trick is balancing. Use Bayesian priors informed by community structures and update aggressively with reproducible evidence. Design institutions with redundancy, cheap verifiability where possible, and incentives aligned toward maintenance rather than short-term headlines.
## Parting thought (and a small, guilty confession)
I love that a volunteer moderator’s colored flair, a brittle clay tablet, a drawer labeled “holotype,” and a cat’s plotted spectrogram can all be folded into the same conceptual suitcase. Knowledge is a network of proofs, models, witnesses, and incentives — a living category whose morphisms we must preserve.
So here’s a teasing question to leave on the table (and to annoy both the skeptic and the trusting parts of your brain): if you could design one mathematical rule that every knowledge institution must obey to survive political storms and budget cuts, what would it be — and how would you prove it works?
(And yes, my cat will be cross-examined for not citing sources.)
