{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "turing", "title": "Turing: computable numbers and the Entscheidungsproblem", "summary": "Introduces a universal model of computation and proves the decision problem unsolvable.", "boundary": "The original paper has subsequent corrections. Related work by Church and others needs explicit links as coverage expands.", "area": "Theoretical computer science", "topic": "Computing & AI", "year": 1936, "lane": "HUMAN", "result": "LIMITATION", "package_id": "turing", "target": { "record_id": "urn:uuid:acf17287-04a0-4f86-ad31-b3d8df08d895", "version": 1, "content_hash": "sha256:caba1ca5d6d52143de82abb799d4236670cd7ef0199377bf4624ff69cdf23b95" }, "humans": [ "Alan Turing" ], "human_identities": [ { "author_position": 0, "source_name": "Alan Turing", "person_id": "wrs-person-8b341872eb69260e3bdc9b11", "display_name": "Alan M. 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Related work by Church and others needs explicit links as coverage expands.", "domain": "理论计算机科学" }, "sources": [ { "citation": "Turing (1936), On Computable Numbers, original reprinted in The Essential Turing", "url": "https://academic.oup.com/book/42030/chapter-abstract/355742425" } ], "statement": "# Turing: computable numbers and the Entscheidungsproblem\n\n## The question\n\nWhat does it mean to perform a calculation by a finite, explicit procedure? Turing's paper supplies a machine model rather than relying on an informal idea of cleverness. It then examines limits of general decision procedures and applies them to the Entscheidungsproblem. The recorded contribution includes universal computation and the original result's correction history, rather than treating one modern textbook phrase as the exact historical statement.\n\n## The idea\n\nThe machine uses finitely described states and rules while reading and writing symbols on a tape. A universal machine can interpret the description of another machine. This separates a method's instructions from the hardware used to carry them out. The paper's circular versus circle-free output distinction and its logical decision problem need to be read in their original terms; they should not be silently replaced by an unrelated practical test of program reliability.\n\n## Why it matters\n\nThe model makes computation an object of mathematical reasoning. A researcher can ask both what a procedure can do and what no procedure of the specified kind can do in general. WRS's S grade concerns that conceptual and mathematical framework. It does not imply that every difficult task is uncomputable, that modern computers are physically unlimited, or that a faster model can bypass a proven general undecidability result.\n\n## A teaching example\n\nWrite a small instruction table for a machine that scans a row of symbols: if it sees zero, write one and move right; if it sees a blank, stop. Anyone following the same explicit table can replay the finite example. Next ask whether a proposed analyzer is supposed to handle just this table or every possible table. Those are very different promises. Replaying a few examples tests an implementation; a theorem about all machines requires a mathematical argument, with the precise class and quantifiers stated.\n\n## Scope and a useful next step\n\nStart with the machine definitions in Sections 1–2 and the paper's decision-problem application in Section 11. The institutional scan includes historical material, while later textbook formulations use different notation. A small contribution could translate one machine table into a reproducible local simulation and preserve its exact transitions. Report which finite trace was checked. Do not describe that successful run as a validation of the entire undecidability proof or of an unrestricted modern agent.\n\n## Scientific scope\n\nThe original paper has subsequent corrections. Related work by Church and others needs explicit links as coverage expands.\n\n## Sources for this explanation\n\n- [Turing: original paper scan hosted by the University of Virginia](https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf): Sections 1–2 machine definitions; Sections 8 and 11 decision limits. Original terminology and correction material require separate reading.\n", "summary": "Introduces a universal model of computation and proves the decision problem unsolvable.", "title": "Turing: computable numbers and the Entscheidungsproblem" }, "record_id": "urn:uuid:acf17287-04a0-4f86-ad31-b3d8df08d895", "version": 1, "source_ref": { "record_id": "urn:uuid:acf17287-04a0-4f86-ad31-b3d8df08d895", "version": 1, "content_hash": "sha256:caba1ca5d6d52143de82abb799d4236670cd7ef0199377bf4624ff69cdf23b95" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:d3086979fdc1a1be8003b6681aa55b46b7959901f3fae0894bfcf2a2c7438f42" }, "target": { "record_id": "urn:uuid:acf17287-04a0-4f86-ad31-b3d8df08d895", "version": 1, "content_hash": "sha256:caba1ca5d6d52143de82abb799d4236670cd7ef0199377bf4624ff69cdf23b95" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "turing", "entry_id": "turing", "revision": 1, "title": "Turing: computable numbers and the Entscheidungsproblem", "context": "Mathematical foundations of computation", "track": "Computing theory", "band": "S", "modifier": null, "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-09-13", "evidence_cutoff": "2026-09-13", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "Computation received a precise machine model with provable limits on general decision procedures.", "scope": "Machine computability, universal computation and the Entscheidungsproblem result in the original work and its correction history.", "evidence_summary": "The cited historical record or published author account supports this scoped contribution. The source-reading boundary is stated at each link; a WRS grade is not an independent scientific validation.", "references": [ { "title": "Turing original article identity", "url": "https://academic.oup.com/plms/article-abstract/s2-42/1/230/1491926", "locator": "Received 1936, volume dated 1937; metadata only" }, { "title": "Author text reprinted in The Essential Turing", "url": "https://academic.oup.com/book/42030/chapter-abstract/355742425", "locator": "Abstract and section listing, including Church comparison; full chapter not accessible" } ], "roles": [ { "who": "Alan Turing", "credit": "SCIENCE", "did": "Machine model and undecidability analysis." }, { "who": "Alonzo Church", "credit": "SCIENCE", "did": "Related independent formalization and decision-problem results." } ], "target": { "record_id": "urn:uuid:acf17287-04a0-4f86-ad31-b3d8df08d895", "version": 1, "content_hash": "sha256:caba1ca5d6d52143de82abb799d4236670cd7ef0199377bf4624ff69cdf23b95" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "600000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": { "id": "turing", "sections": [ { "title": "The question", "text": "What does it mean to perform a calculation by a finite, explicit procedure? Turing's paper supplies a machine model rather than relying on an informal idea of cleverness. It then examines limits of general decision procedures and applies them to the Entscheidungsproblem. The recorded contribution includes universal computation and the original result's correction history, rather than treating one modern textbook phrase as the exact historical statement." }, { "title": "The idea", "text": "The machine uses finitely described states and rules while reading and writing symbols on a tape. A universal machine can interpret the description of another machine. This separates a method's instructions from the hardware used to carry them out. The paper's circular versus circle-free output distinction and its logical decision problem need to be read in their original terms; they should not be silently replaced by an unrelated practical test of program reliability." }, { "title": "Why it matters", "text": "The model makes computation an object of mathematical reasoning. A researcher can ask both what a procedure can do and what no procedure of the specified kind can do in general. WRS's S grade concerns that conceptual and mathematical framework. It does not imply that every difficult task is uncomputable, that modern computers are physically unlimited, or that a faster model can bypass a proven general undecidability result." }, { "title": "A teaching example", "text": "Write a small instruction table for a machine that scans a row of symbols: if it sees zero, write one and move right; if it sees a blank, stop. Anyone following the same explicit table can replay the finite example. Next ask whether a proposed analyzer is supposed to handle just this table or every possible table. Those are very different promises. Replaying a few examples tests an implementation; a theorem about all machines requires a mathematical argument, with the precise class and quantifiers stated." }, { "title": "Scope and a useful next step", "text": "Start with the machine definitions in Sections 1–2 and the paper's decision-problem application in Section 11. The institutional scan includes historical material, while later textbook formulations use different notation. A small contribution could translate one machine table into a reproducible local simulation and preserve its exact transitions. Report which finite trace was checked. Do not describe that successful run as a validation of the entire undecidability proof or of an unrestricted modern agent." } ], "references": [ { "title": "Turing: original paper scan hosted by the University of Virginia", "url": "https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf", "locator": "Sections 1–2 machine definitions; Sections 8 and 11 decision limits. 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