finding
active
finding:copy-cat-processes-partial-involutions-are-computationally-universalCopy-cat processes (partial involutions) are computationally universal
Mere copying of tokens between paired positions suffices to simulate all partial recursive functions and model higher-order logics.
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claim
- In game semantics, proofs are generalized copy-cats that conserve information flow; this suggests a deep connection between logic and conservation.
Related by similarity (8)
cosine ≥ 0.65 · no typed edgeEntities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.
- The Geometry of Interaction model shows that simple copying of information between locations suffices for all computation, establishing emergent logic.
- Load-bearing quote from SICP framing computation as spirit-like; grounds the cyberanimism framework
- Partial involutions form a Linear Combinatory Algebra under function application defined by feedback loopsfinding0.782The set of fixed-point free partial involutions on a countable set, with composition via interaction, yields a linear combinatory algebra, hence a universal model of computation.
- Fixed-point free partial injective functions used as simple reversible dynamical processes in Geometry of Interaction.
- Argues that sequence linkages reflect deep necessity, not option, for the system to work.
- Key open problem: foundational definitions for process models that match the role of Turing completeness for functional computation.
- The interactive processes described are reversible in a very strong sense, linking logic and physicsclaim0.756Partial involutions are invertible; the same structures can axiomatize quantum mechanics and analyse entanglement.