Thinking·OS

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Boundary condition constrains Partial differential equation. Activate to inspect this relation.Boundary condition constrains Ordinary differential equation. Activate to inspect this relation.Boundary Value Problem applies to Partial differential equation. Activate to inspect this relation.Continuity depends on Limit. Activate to inspect this relation.Continuity depends on Limit. Activate to inspect this relation.Continuous function depends on Limit. Activate to inspect this relation.Derivative depends on Continuity. Activate to inspect this relation.Derivative depends on Limit. Activate to inspect this relation.Derivative requires Continuity. Activate to inspect this relation.Derivative depends on Limit. Activate to inspect this relation.Differential equation depends on Rate of change. Activate to inspect this relation.Differential equation is a Equation. Activate to inspect this relation.Dynamical System depends on Differential equation. Activate to inspect this relation.Dynamical System models Ordinary differential equation. Activate to inspect this relation.Fourier Series enables Partial differential equation. Activate to inspect this relation.Fundamental theorem of calculus explains Derivative. Activate to inspect this relation.Infinity applies to Limit. Activate to inspect this relation.Initial Value Problem applies to Ordinary differential equation. Activate to inspect this relation.Integral is analogous to Rate of change. Activate to inspect this relation.Limit enables Integral. Activate to inspect this relation.Limit enables Rate of change. Activate to inspect this relation.Linear Differential Equation is a Ordinary differential equation. Activate to inspect this relation.Mean value theorem depends on Derivative. Activate to inspect this relation.Ordinary differential equation is analogous to Partial differential equation. Activate to inspect this relation.Ordinary differential equation depends on Derivative. Activate to inspect this relation.Ordinary differential equation is a Differential equation. Activate to inspect this relation.Partial differential equation is analogous to Ordinary differential equation. Activate to inspect this relation.Partial differential equation depends on Derivative. Activate to inspect this relation.Partial differential equation is a Differential equation. Activate to inspect this relation.Rate of change depends on Limit. Activate to inspect this relation.Sequence and series applies to Limit. Activate to inspect this relation.Uniform continuity is a Continuity. Activate to inspect this relation.DerivativeContinuityOrdinary differential equationPartial differential equationLimitLimitFundamental theorem of calculusMean value theoremUniform continuityDifferential equationBoundary conditionDynamical SystemInitial Value ProblemLinear Differential EquationBoundary Value ProblemFourier SeriesRate of changeIntegralContinuous functionSequence and seriesInfinityEquation
Relationship types

172 concepts viewed through this lens. Bridge concepts connect this view to Acoustics, Actuarial Science, Agriculture, Algorithms….

Legend
  • Focused concept
  • Connected concept
  • Bridge concept (just outside the lens)
  • 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
22 concepts32 relationships8 disciplines6 relation families

At a glance

The derivative measures a function's instantaneous rate of change — the slope of the tangent to its graph.

Disciplines
Mathematical Analysis · Mathematics
Role in the graph
Cross-disciplinary bridge — reaches Calculus, Differential Equations
Relationships
7 · 2 relation families

What am I looking at?

In this lens (172)

Bridge concepts (186)

Just outside the lens — they connect it to other context.

  • Rate of change5
    Calculus, Economics, Physics · connects to Differential equation, Integral, Limit…
  • Enumerative counting4
    Combinatorics · connects to Combination, Generating function, Permutation…
  • Graph data structure4
    Computer Science, Data Structures · connects to Connectivity, Edge, Shortest path…
  • Machine learning3
    Artificial Intelligence, Computer Science, Machine Learning, Statistics · connects to Algorithm, Pattern, Probability
  • Optimization3
    Business, Economics, Engineering, Mathematical Modelling, Optimization, Systems Engineering · connects to Inequality, Linear programming, Mathematical model

Insights from this view

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

  • This view connects 8 disciplines: Algebra, Calculus, Differential Equations, Economics, Mathematical Analysis, Mathematical Modelling, Mathematics, Physics.
  • Derivative is a bridge concept — viewed here through Mathematical Analysis, Mathematics.
  • The connections here span 6 relation families.
  • Stocks and flows explains 2 concepts in this view (Calculus, Economics, Mathematics, Physics).

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.