{"id": "card_cs_computability", "kind": "reference", "title": "Computability and complexity — Turing to P vs NP", "body": "A Turing machine defines what is computable; the universal machine runs any program (the engine, the laptop, the brain's computation). Some problems are undecidable (the halting problem); among the decidable, how fast is the open P vs NP question. Rests on P vs NP and the mind.", "source": {"label": "Narrow Highway — computer science", "url": "", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "computer_science", "bands": ["computer science", "pillar", "computability", "one map"], "subject": "Computability and complexity — Turing to P vs NP", "connections": [{"to_card_id": "card_floor_computer_science", "relationship": "part_of", "evidence": "a pillar of computer science (Computability and complexity)"}, {"to_card_id": "card_floor_p_vs_np", "relationship": "connects_at", "evidence": "computability and complexity - the halting problem and P vs NP"}, {"to_card_id": "card_floor_the_mind", "relationship": "connects_at", "evidence": "the brain computes - neural networks borrow its shape"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.computer.science", "facets": {"subject": ["computability", "computer science", "one map", "pillar"]}, "presentation": {"glyph": "•", "kind_label": "computer science", "by": "Narrow Highway — computer science", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_computer_science", "title": "Computer science — bits, logic, and what can be computed", "relationship": "part of", "why": "a pillar of computer science (Computability and complexity)", "href": "/card/card_floor_computer_science", "resolved": true}, {"id": "card_floor_p_vs_np", "title": "The P versus NP chain - from the machine and the circuit to the three barriers", "relationship": "connects at", "why": "computability and complexity - the halting problem and P vs NP", "href": "/card/card_floor_p_vs_np", "resolved": true}, {"id": "card_floor_the_mind", "title": "The mind — matter aware of itself", "relationship": "connects at", "why": "the brain computes - neural networks borrow its shape", "href": "/card/card_floor_the_mind", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_cs_computability", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_cs_computability"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}