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Work #1547 · Early

On Computable Numbers, with an Application to the Entscheidungsproblem

Alan Turing
1936 · English
Mathematical-logical paper · Mathematical logic / computability theory / Cambridge analytic-mathematical philosophy

Turing's 1936 founding paper of computer science — the Turing Machine and the undecidability of the Entscheidungsproblem

Attribute Fingerprint

Rows where works disagree are highlighted in gold. The full ontology grid is shown.

Attribute On Computable Numbers, with an Application to the Entscheidungsproblem (Early)
Time · Extent Infinite
Time · Ontological Status Substantival
Time · Grain Discrete
Time · Freedom Deterministic
Time · Traversability Linear
Time · Dimensionality One
Time · Direction Uni-directional
Space · Extent Infinite
Space · Ontological Status Substantival
Space · Curvature Flat
Space · Dimensionality Three
Space · Locality Local
Matter · Extent Infinite
Matter · Ontological Status Substantival
Matter · Conservation Conserved
Matter · Dimensionality Three
Matter · Locality Local
Observer · Time Instance Single
Observer · Space Instance Single
Observer · Knowledge Extent Mediated
Observer · Knowledge Retainment Partial
Observer · Physicality Embodied
Observer · Agency Active
Observer · Number Plural
Observer · Metaphysical Agency Impersonal
Observer · Moral Authority Reason
Observer · Theological Method
Energy · Extent Infinite
Energy · Ontological Status Substantival
Energy · Conservation Conserved
Energy · Dispersibility Irreversible
Information · Ontological Status Substantival
Information · Cosmic Conservation Conserved
Information · Personal Conservation Non-conserved
Information · Granularity Discrete

Dimension-by-Dimension Evidence

What each work's passages reveal about its stance on each of the six dimensions.

Time

On Computable Numbers, with an Application to the Entscheidungsproblem

1936 (paper read May, published November). Twenty-three-year-old Turing, then fellow of King's College, Cambridge.

Space

On Computable Numbers, with an Application to the Entscheidungsproblem

Cambridge / Princeton. Turing's intellectual context was Newman's logic course at Cambridge and the contemporary Princeton group (Church, Kleene, Rosser).

Matter

On Computable Numbers, with an Application to the Entscheidungsproblem

Single 36-page mathematical paper. The abstract Turing Machine is the paper's distinctive contribution — a machine of pure mathematical-symbolic operation, with no physical instantiation required.

Observer

On Computable Numbers, with an Application to the Entscheidungsproblem

Early Turing as logician-mathematician. The paper's 'computer' (originally a human following definite rules) is the abstract idealisation that Turing then mechanises.

Energy

On Computable Numbers, with an Application to the Entscheidungsproblem

Founding-logical energies of the 1936 'three-miracle' year (Turing, Church, Post all independently characterised effective calculability).

Information

On Computable Numbers, with an Application to the Entscheidungsproblem

The founding paper of theoretical computer science and of the formal theory of information processing. Every digital computer is in principle a Turing machine.

Internal Tensions

Where each work's argument pulls against itself.

On Computable Numbers, with an Application to the Entscheidungsproblem

The founding paper of theoretical computer science and one of the most-cited mathematical papers of the twentieth century. Together with Church's contemporaneous lambda-calculus paper, established the Church-Turing thesis. Turing's wartime cryptanalytic work at Bletchley Park (Enigma, Tunny) used these abstract ideas in practical machine design; modern computer architectures remain Turing-machine-equivalent.