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Reusable cognitive primitives

Bayesian updating

A belief's strength should be revised by combining how likely it was beforehand (the prior) with how strongly new evidence bears on it.

Origins & development

Bayes stated the theorem (published posthumously in 1763); Laplace independently developed and generalised it into a systematic method of inference.

Sources: MacTutor History of Mathematics Archive, Encyclopaedia Britannica

Where it appears

Dependencies & synergies

Derived from the graph’s real structure — 3 concepts across 5 disciplines carry this pattern. Every figure is a count, not a score.

Reach across disciplines

How many concepts carrying this pattern are seen through each discipline.

Patterns that travel with it

Other thinking patterns that recur on the same concepts — the more shared concepts, the more often they co-occur.

The shape of its reasoning

What kinds of relationships the carrying concepts form — the relational signature of the pattern.

  • Explains & models2 edges
  • Teaching link2 edges
  • Dependency1 edges
  • Analogy & transfer1 edges
Furthest-reaching carriers

Concepts where this pattern does the most cross-disciplinary work — each reaches disciplines beyond its own.

Examples across disciplines

Medicine

Reading a positive test through the pre-test probability, not sensitivity alone.

Epidemiology

The same lab result implies different things at high versus low prevalence.

Machine Learning

A classifier's posterior combines a prior with the likelihood of the data.

Law

Weighing a new piece of evidence against the prior probability of the claim.

How this pattern travels

Interpreted from where the pattern recurs in the atlas — structural transfer and coverage, not a claim it is universally the "best" model.

  • Recurs across 5 disciplines over 3 carrier concepts — concentrated (67% of carriers in one field).

    structural · Structural recurrence in the atlas — a pattern is a reasoning lens, not a law.

  • 2 of its 3 carrier concepts are themselves cross-disciplinary connectors.

    structural · Structural recurrence in the atlas — a pattern is a reasoning lens, not a law.

  • Explicit "where it breaks" notes exist for 0 of 3 annotated assignments.

    curated · Curated boundary annotations — absence is a representation gap, not evidence the model has no limits.

  • Currently dark in the atlas: no assignment cites a source · no boundary annotations.

    atlas representation · Describes the current Thinking OS representation, not the model itself.

The statistical fingerprint

How the 3 concepts that exercise this pattern distribute — from the graph, not a ranking.

Disciplinary fingerprint

Carrier concepts under each illuminating lens.

How settled its carriers are

Epistemic status of the concepts that exercise this pattern.

  • Established3 · 100%

Technical detail

Formally, Bayes' theorem gives P(H|E) = P(E|H)·P(H) / P(E): the posterior probability of a hypothesis equals its prior times the likelihood of the evidence, normalised. In odds form, posterior odds = prior odds × likelihood ratio. The practical lesson is that a test result must be weighed against the base rate — in a low-prevalence setting even a highly specific test yields mostly false positives.

Common misconception

A positive test means the condition is present. Its meaning depends on the prior — in a low-prevalence setting most positives can be false.

Try a transfer challenge

You have seen this model in one place. Where else could it apply — and where would the analogy break?

Infectious dose
The intuition

A result doesn't speak alone — weigh it against how common the thing was to begin with. The same positive test means different things in a high- versus low-prevalence setting.

The reach of this pattern
  • Recurs across 5 disciplines.
  • 7 concepts exercise this thinking pattern.

Derived from the graph — a pattern is a reasoning lens, not a law.

How to recognise it

Before trusting this result, what was the prior chance — and how much does this evidence actually shift it, not just 'is it positive'?

Keep this question handy when you meet something new — it helps you notice the pattern, not just name it.