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leiden_hybrid_concepts
label: sonnet
community:leiden_hybrid_concepts-run2-c93Continuous vs discrete computability
Contrasts decidability of real closed fields with Gödelian incompleteness of discrete arithmetic via domain theory.
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Claims (1)
- Continuous dynamics inhabit real closed fields (complete, decidable); discrete arithmetic is incomplete and uncomputable.Mathematical argument that continuous biological computation operates in a richer formal domain; suggests computational advantages for consciousness-relevant processing.
Findings (1)
- Continuous functions in Domain Theory reflect that computational processes have access only to finite information at each finite stage.Mathematical principle grounding the formal definition of continuity in domain theory to physical and epistemic constraints on computation.