Thinking·OS

Graph explorer

Explore the knowledge graph

Set is part of Vector space. Activate to inspect this relation.Function depends on Set. Activate to inspect this relation.Subset is part of Set. Activate to inspect this relation.Cardinality measures Set. Activate to inspect this relation.Set operation applies to Set. Activate to inspect this relation.Topological space applies to Set. Activate to inspect this relation.Set theory applies to Set. Activate to inspect this relation.Group theory applies to Set. Activate to inspect this relation.Element is part of Set. Activate to inspect this relation.Subset is a Set. Activate to inspect this relation.Union applies to Set. Activate to inspect this relation.Intersection applies to Set. Activate to inspect this relation.Cartesian Product is derived from Set. Activate to inspect this relation.Relation is a Cartesian Product. Activate to inspect this relation.Function is a Relation. Activate to inspect this relation.Cartesian ProductSetRelationVector spaceSubsetCardinalitySet operationTopological spaceSet theoryGroup theoryElementUnionIntersectionFunction
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 concepts15 relationships7 disciplines4 relation families

Cartesian Product

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At a glance

The Cartesian product of two sets is the set of all ordered pairs with one element from each set.

Disciplines
Set Theory
Role in the graph
Cross-disciplinary bridge — reaches Discrete Mathematics, Mathematics
Relationships
2 · 2 relation families

Insights from this view

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

  • This view connects 7 disciplines: Algebra, Discrete Mathematics, Linear Algebra, Logic, Mathematics, Set Theory, Topology.
  • Cardinality is a bridge concept — viewed here through Mathematics, Set Theory.
  • The connections here span 4 relation families.

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.