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Reusable cognitive primitives

Probability

A way to reason about uncertainty by assigning each possible outcome a share of the whole, between impossible (0) and certain (1).

Origins & development

The mathematical theory of probability grew out of the 1654 correspondence between Pascal and Fermat on games of chance.

Sources: MacTutor History of Mathematics Archive, Encyclopaedia Britannica

Where it appears

Dependencies & synergies

Derived from the graph’s real structure — 22 concepts across 27 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.

  • Kind & structure31 edges
  • Teaching link27 edges
  • Cause & effect19 edges
  • Dependency18 edges
  • Explains & models6 edges
  • Analogy & transfer5 edges
  • Time order3 edges
Furthest-reaching carriers

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

  • Machine learningreachesAlgorithmsBiochemistryBiologyBiotechnologyBusinessCognitive ScienceData ScienceDesignDiscrete MathematicsEconomicsEducationEducational ScienceEngineeringEvolutionary BiologyHuman-Computer InteractionLogicMathematical ModellingMathematicsNeuroinformaticsNeuroscienceOptimizationProbabilitySoftware EngineeringSystems BiologySystems EngineeringSystems ScienceTheory of Computation
  • ProbabilityreachesActuarial ScienceArtificial IntelligenceBiostatisticsComplexity ScienceComputer ScienceData ScienceDecision TheoryDiscrete MathematicsEconomicsEpistemologyEthicsFinanceInformation TheoryMachine LearningMedicinePhysical ChemistryPhysicsPublic PolicyQuantum PhysicsStatistical PhysicsThermodynamics
  • RiskreachesActuarial ScienceBusinessData ScienceEntrepreneurshipEnvironmental ScienceEpidemiologyEpistemologyMachine LearningMathematicsNetwork SciencePhotographyProbabilityPublic HealthToxicology
  • CorrelationreachesBiostatisticsEconometricsEconomicsEpidemiologyEthicsFinanceHistoryMathematicsMedicineMetaphysicsPhilosophy of SciencePsychologyPublic Policy
  • PredictionreachesBiologyCognitive ScienceComputer ScienceData ScienceEducational ScienceEpistemologyHistory of ScienceLogicMachine LearningMathematical ModellingPhysicsSystems Science
  • GeneralizationreachesArtificial IntelligenceComputer ScienceData ScienceEducationEducational ScienceLinguisticsLiteratureMathematicsPhilosophyPhilosophy of Science

Foundation of the pattern

Carrying concepts that others in the same pattern build on (they depend on or follow from these).

  1. Probability 5 other concepts build on it
  2. Probability distribution 2 other concepts build on it

Examples across disciplines

Statistics

A weather forecast of 30% rain means: on days that look like this, it rains about three times in ten.

Physics

We cannot say where one gas particle is, but probability describes the behaviour of trillions together.

Medicine

A screening test's result shifts the probability that a patient has a condition; it rarely proves it outright.

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 27 disciplines over 22 carrier concepts — a broadly transferable pattern.

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

  • 7 of its 22 carrier concepts are themselves cross-disciplinary connectors.

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

Coverage matrix

How these concepts distribute across domains and concept families — real counts, not a score.

SystemsInformationMatterChangePatternsEnergyLifeScaleStructureDecisionNetworksWavesCausalityComputationEarthSpaceOptimizationNumberProbabilitySecurityThresholdsConstraintsNatural sciencesFormal sciencesEngineeringMedicine & healthSocial sciencesHumanitiesProfessionalArtsInterdisciplinary3111341332

Knowledge timeline

Real, sourced key dates of these concepts.

5 events
18801900192019401866 · Mendelian inheritance1896 · Radioactive decay1900 · Quantum mechanics1944 · Game theory1950 · Game theory

The statistical fingerprint

How the 22 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.

  • Established22 · 100%
Common misconception

That past independent results (like coin flips) change what is 'due' to happen next.

Journeys where it shows up

Try a transfer challenge

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

Correlation
The intuition

Instead of 'will it happen?', ask 'how often would it happen if this repeated many times?'

The reach of this pattern
  • Recurs across 27 disciplines.
  • 65 concepts exercise this thinking pattern.
  • It is practised in 1 learning journey.

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

How to recognise it

Instead of 'will it happen?', ask: across many repetitions what share would turn out this way — and how much of what I see could be chance?

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