Computability
The theory of which problems can in principle be solved by any algorithm and which are provably undecidable.
At a glance
Key signals
0% cross fields · reaches 1 more
- Computer Science
- Theory of Computation
- Explanation
- Examples
- Misconception
- Sourced relations
- Attribution
Dependencies
What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.
Foundations · builds on
Computabilitydepends onTuring machineEstablished
Defined by the Turing machine.
Mechanism: A problem is computable if a Turing machine can solve it — the definition of mechanical computation.
Enables · leads to
Computational Complexitydepends onComputabilityEstablished
Open Computational Complexity →
Computational Complexity depends on Computability.
System context
Decidabilityis part ofComputabilityEstablished
Decidability is a part of Computability.
Halting problemis part ofComputabilityEstablished
The first undecidable problem.
Mechanism: The halting problem is the canonical proof that some questions are beyond any algorithm.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Currently dark in the atlas: no key date stored · 6 of 6 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).
structural · Structural graph analysis — not a claim of importance, causation or history.
Structural neighbourhood: 5 → 14 → 45 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
All 5 of its relationships stay within its own discipline — a field-specific concept in the current atlas.
structural · Structural graph analysis — not a claim of importance, causation or history.
cross-field
5 within-field, 0 cross-field
Strengths & constraints
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
- No dated history stored — the atlas records no key date for this concept. atlas representation
Conditions
- Its dependency reading rests on 1 foundation relation. structural
- Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural
Dependency radial
What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.
What builds on this
1 concept build on this directly, 1 in total, across 1 discipline.
Structural downstream reach along dependency edges — not a claim of historical necessity.
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to Turing machine, Turing machine, Halting problem and Decidability.
Through this lens it connects to Turing machine, Turing machine, Halting problem and Decidability.
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
- Connects 5 other ideas across 2 disciplines.
- Most of its connections are of the “Kind & structure” kind.
Derived from the graph’s real structure — observations, not a score.