Thinking·OS

Graph explorer

Explore the knowledge graph

Axiom of choice depends on Function. Activate to inspect this relation.Axiom of choice influences Cardinal Number. Activate to inspect this relation.Cardinal Number models Cardinality. Activate to inspect this relation.Cardinality measures Set. Activate to inspect this relation.Cartesian Product is derived from Set. Activate to inspect this relation.Category theory applies to Function. Activate to inspect this relation.Continuous function is a Function. Activate to inspect this relation.Dynamical systems applies to Function. Activate to inspect this relation.Element is part of Set. Activate to inspect this relation.Empty Set is a Subset. Activate to inspect this relation.Function is a Relation. Activate to inspect this relation.Function depends on Set. Activate to inspect this relation.Function depends on Variable. Activate to inspect this relation.Group theory applies to Set. Activate to inspect this relation.Intersection applies to Set. Activate to inspect this relation.Power Set depends on Subset. Activate to inspect this relation.Power Set influences Cardinality. Activate to inspect this relation.Relation is a Cartesian Product. Activate to inspect this relation.Set operation applies to Set. Activate to inspect this relation.Set is part of Vector space. Activate to inspect this relation.Set theory applies to Set. Activate to inspect this relation.Subset is a Set. Activate to inspect this relation.Subset is part of Set. Activate to inspect this relation.Topological space applies to Set. Activate to inspect this relation.Union applies to Set. Activate to inspect this relation.Cartesian ProductSetRelationVector spaceCardinalityElementGroup theoryIntersectionSet operationSet theorySubsetTopological spaceUnionFunctionCardinal NumberPower SetEmpty SetVariableAxiom of choiceCategory theoryContinuous functionDynamical systems
Relationship types

15 concepts viewed through this lens. Bridge concepts connect this view to Algebra, Calculus, Category Theory, Geometry….

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 concepts25 relationships8 disciplines5 relation families

Cartesian Product

Open concept →

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

What am I looking at?

In this lens (15)

Bridge concepts (14)

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

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, Discrete Mathematics, Linear Algebra, Logic, Mathematics, Set Theory, Topology.
  • Axiom of choice is a bridge concept — viewed here through Logic, Set Theory.
  • The connections here span 5 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.