Thinking·OS

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Explore the knowledge graph

Flow is a Rate of change. Activate to inspect this relation.Velocity is a Rate of change. Activate to inspect this relation.Acceleration is a Rate of change. Activate to inspect this relation.Integral is a Mathematical expression. Activate to inspect this relation.Polynomial is a Mathematical expression. Activate to inspect this relation.Slope models Rate of change. Activate to inspect this relation.Limit enables Rate of change. Activate to inspect this relation.Limit enables Integral. Activate to inspect this relation.Continuous function depends on Limit. Activate to inspect this relation.Rate of change depends on Limit. Activate to inspect this relation.Integral is analogous to Rate of change. Activate to inspect this relation.Differential equation depends on Rate of change. Activate to inspect this relation.Tangent depends on Rate of change. Activate to inspect this relation.Derivative depends on Limit. Activate to inspect this relation.Continuity depends on Limit. Activate to inspect this relation.Derivative depends on Continuity. Activate to inspect this relation.Derivative requires Continuity. Activate to inspect this relation.IntegralMathematical expressionRate of changeLimitPolynomialFlowAccelerationVelocitySlopeDifferential equationTangentContinuous functionDerivativeContinuity
Relationship types
Legend
  • Focused concept
  • Connected concept
  • Arrow points from cause / source to effect / target
  • A line with no arrow is a two-way relationship
  • Node colour marks the concept’s primary discipline
14 concepts17 relationships10 disciplines5 relation families

At a glance

In mathematics, an integral is the continuous analog of a sum, and is used to calculate areas, volumes, and their generalizations.

Disciplines
Mathematics · Calculus
Role in the graph
Cross-disciplinary bridge — reaches Algebra, Economics, Physics
Relationships
3 · 3 relation families
Mental models
1

Insights from this view

Structural observations about the concepts shown here — descriptions of this graph, not claims about the world.

  • This view connects 10 disciplines: Algebra, Calculus, Economics, Geometry, Mathematical Analysis, Mathematical Modelling, Mathematics, Mechanics, Physics, Systems Science.
  • Integral is a bridge concept — viewed here through Calculus, Mathematics.
  • The connections here span 5 relation families.
  • Stocks and flows explains 3 concepts in this view (Calculus, Economics, Mathematics, Physics, Systems Science).

Relationships as a list

The focused concept’s relationships. Pick another concept in the graph above to update this list.

Explore through a different lens

A lens is a deterministic projection of the graph. Pick a discipline, thinking pattern or journey to reframe the whole view.

By discipline

ChemistryBiologyPhysicsMathematicsComputer ScienceGeologyMineralogyEconomics

By thinking pattern

Bayesian updatingCause and effectCompoundingConservationConstraintsDefense in depthDiffusion & spreadEmergenceEnergy transformationEntropy & irreversibilityEquilibriumFeedback loopIncentivesInformationLevels & hierarchyModularityNetworksOptimizationOscillationProbabilityRecursion & self-similarityScaleSignal vs noiseSource–pathway–receptorStocks and flowsSymmetry & invarianceThresholds & tipping pointsTrade-offsTriangulationVariation & selectionWaves

By journey

From a Leaf to the ClimateWhy Music Moves UsHow Machines LearnReasoning about a Leaf and the Climate

Concept collections

Concept collections are curated lenses onto the fabric — themed sets of ideas that recur across disciplines. They are not journeys; they are a way to read the graph.

About this view

What this is

Start from one concept and expand outward. The view never shows everything at once — click a node to refocus, filter by relationship type, or switch to an accessible list.

One fabric

3750 concepts and 5051 typed relations form one connected component — no isolated silo.

How to read it

Focus a concept, or apply a lens (discipline, mental model, journey) to see only the threads that matter.