Thinking·OS

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Algorithm models Turing machine. Activate to inspect this relation.Approximation algorithm applies to NP-completeness. Activate to inspect this relation.Church-Turing Thesis depends on Turing machine. Activate to inspect this relation.Complexity Class NP depends on Nondeterminism. Activate to inspect this relation.Complexity Class NP is part of PSPACE. Activate to inspect this relation.Class P depends on Time Complexity. Activate to inspect this relation.Class P is part of Complexity Class NP. Activate to inspect this relation.Class P is part of Computational complexity theory. Activate to inspect this relation.Computability depends on Turing machine. Activate to inspect this relation.Finite automaton is analogous to Turing machine. Activate to inspect this relation.NP-completeness depends on Reduction (complexity). Activate to inspect this relation.NP-completeness is part of Complexity Class NP. Activate to inspect this relation.NP-completeness is part of Computational Complexity. Activate to inspect this relation.NP-completeness requires Polynomial-Time Reduction. Activate to inspect this relation.NP-completeness is part of Computational complexity theory. Activate to inspect this relation.One-way function depends on P versus NP. Activate to inspect this relation.P versus NP applies to Complexity Class NP. Activate to inspect this relation.P versus NP applies to Class P. Activate to inspect this relation.P versus NP is analogous to Riemann hypothesis. Activate to inspect this relation.P versus NP applies to Algorithm. Activate to inspect this relation.PCP theorem applies to NP-completeness. Activate to inspect this relation.Polynomial-Time Reduction is a Reduction (complexity). Activate to inspect this relation.Reduction (complexity) applies to NP-completeness. Activate to inspect this relation.Space Complexity explains PSPACE. Activate to inspect this relation.Space Complexity measures Turing machine. Activate to inspect this relation.Space Complexity requires Big O notation. Activate to inspect this relation.Time Complexity measures Turing machine. Activate to inspect this relation.Time Complexity requires Big O notation. Activate to inspect this relation.Turing machine is a Finite automaton. Activate to inspect this relation.Turing machine models Computability. Activate to inspect this relation.Turing machine models Algorithm. Activate to inspect this relation.P versus NPComplexity Class NPClass PRiemann hypothesisAlgorithmOne-way functionNondeterminismPSPACENP-completenessTime ComplexityComputational complexity theoryTuring machineSpace ComplexityReduction (complexity)Computational ComplexityPolynomial-Time ReductionApproximation algorithmPCP theoremBig O notationFinite automatonComputabilityChurch-Turing Thesis
Relationship types

14 concepts viewed through this lens. Bridge concepts connect this view to Algorithms, Computer Science, Cryptography, Discrete Mathematics….

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 concepts31 relationships10 disciplines5 relation families

P versus NP

Open concept →

At a glance

The central open question of whether every problem whose answer is easy to check is also easy to solve.

Disciplines
Computer Science · Mathematics · Computational Complexity
Role in the graph
Cross-disciplinary bridge — reaches Algorithms, Cryptography, Discrete Mathematics, Logic, Number Theory, Software Engineering, Theory of Computation
Relationships
5 · 3 relation families

What am I looking at?

In this lens (14)

Bridge concepts (15)

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

  • Computability3
    Computer Science, Theory of Computation · connects to Decidability, Halting problem, Turing machine
  • Algorithm2
    Algorithms, Computer Science, Discrete Mathematics, Logic, Mathematics, Software Engineering, Theory of Computation · connects to P versus NP, Turing machine
  • Computability theory2
    Computer Science, Logic · connects to Decidability, Turing machine
  • Computational complexity theory2
    Algorithms, Computer Science · connects to Class P, NP-completeness
  • Analysis of algorithms1
    Algorithms, Computer Science · connects to Big O notation

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: Algorithms, Computational Complexity, Computer Science, Cryptography, Discrete Mathematics, Logic, Mathematics, Number Theory, Software Engineering, Theory of Computation.
  • P versus NP is a bridge concept — viewed here through Computational Complexity, Computer Science, Mathematics.
  • The connections here span 5 relation families.
  • Information explains 2 concepts in this view (Algorithms, Computational Complexity, Computer Science, Discrete Mathematics, Logic, Mathematics, Software Engineering, Theory of Computation).

Relationships as a list

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

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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.