← All mental models

Reusable cognitive primitives

Scale

How a system's size changes what matters about it. Quantities rarely scale in step: doubling a length can quadruple an area and multiply a volume eightfold.

Where it appears

Dependencies & synergies

Derived from the graph’s real structure — 47 concepts across 33 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 & structure90 edges
  • Dependency25 edges
  • Teaching link25 edges
  • Explains & models15 edges
  • Cause & effect10 edges
  • Analogy & transfer7 edges
  • Evidence2 edges
Furthest-reaching carriers

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

  • Quantum mechanicsreachesAtomic PhysicsChemistryComputational ChemistryComputer ScienceCondensed Matter PhysicsMathematicsProbabilityQuantum ComputingStatistics
  • RatioreachesAlgebraArchitectureAstronomyBiologyCell BiologyGeographyGeometryMusicPhysics
  • EarthreachesAtmospheric ScienceCartographyGeographyGeoinformaticsGeologyMeteorologyPhysics
  • DecibelreachesAlgebraAudiologyInformation TheoryMathematicsPhotographySignal ProcessingTelecommunications Engineering
  • HierarchyreachesCognitive ScienceDesignEducationEducational ScienceMachine LearningMathematicsProject Management
  • InfinityreachesBioinformaticsCalculusComputer ScienceData StructuresDiscrete MathematicsHistoryMolecular Biology

Foundation of the pattern

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

  1. Avogadro constant 1 other concept build on it
  2. Ratio 1 other concept build on it
  3. Speed of light in vacuum 1 other concept build on it

Examples across disciplines

Biology

Small cells absorb enough through their surface; too large, and their volume outpaces the surface feeding it.

Geography

A process that looks random in one town can be a clear trend across a whole continent.

Physics

Thinking in orders of magnitude tells you whether an effect matters before you calculate it exactly.

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 33 disciplines over 47 carrier concepts — a broadly transferable pattern.

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

  • 14 of its 47 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 3 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 origin recorded · no assignment cites a source.

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

Coverage matrix

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

SystemsInformationMatterChangePatternsEnergyLifeScaleStructureDecisionNetworksWavesCausalityComputationEarthSpaceOptimizationNumberProbabilitySecurityThresholdsConstraintsNatural sciencesFormal sciencesEngineeringMedicine & healthSocial sciencesHumanitiesProfessionalArtsInterdisciplinary42119111211131

Knowledge timeline

Real, sourced key dates of these concepts.

4 events
1900191019201930194019501900 · Quantum mechanics1912 · Gini coefficient1935 · Richter scale1958 · Integrated circuit

The statistical fingerprint

How the 47 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.

  • Established47 · 100%

Where the model breaks

This pattern is a reasoning lens, not a law. Here is where it stops helping:

  • Decibel (mechanism): A logarithmic ratio: you cannot add or average decibels linearly, and a dB value is meaningless without its reference level.
  • Richter scale (mechanism): Each unit is ~32× the energy; comparing magnitudes as if linear massively understates how much bigger a large quake is.
  • Sound pressure level (mechanism): Because it is logarithmic, doubling perceived loudness is roughly +10 dB, not ×2 — linear intuition about "twice as loud" fails.
Common misconception

That things simply get bigger uniformly; areas and volumes grow far faster than lengths.

Try a transfer challenge

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

Area
The intuition

Ask what changes when you make it ten times bigger or smaller — the rules often change with the size.

The reach of this pattern
  • Recurs across 33 disciplines.
  • 94 concepts exercise this thinking pattern.
  • 3 of them explicitly note where the model breaks down.

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

How to recognise it

If you made this ten times larger or smaller, which quantities would grow out of step — and would the governing rule itself change?

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