Dynamic Level Sets
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912934210306048 |
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| author | Fiske, Michael Stephen |
| author_facet | Fiske, Michael Stephen |
| contents | A mathematical concept is identified and analyzed that is implicit in the 2012 paper Turing Incomputable Computation, presented at the Alan Turing Centenary Conference (Turing-100, Manchester). The concept, called dynamic level sets, is distinct from mathematical concepts in the standard literature on dynamical systems, topology, and computability theory. A new mathematical object is explained and why it may have escaped prior characterizations, including the classical result of de Leeuw, Moore, Shannon, and Shapiro that probabilistic Turing machines (with bias $p$ where $p$ is Turing computable) compute no more than deterministic ones. A key mechanism underlying the concept is the Principle of Self-Modifiability, whereby the physical realization of an invariant logical level set is reconfigured at each computational step by an incomputable physical process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22530 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamic Level Sets Fiske, Michael Stephen Computational Complexity Computation and Language Mathematical Physics Dynamical Systems History and Overview 68Q09, 68Q10, 37N99, 37H12 F.2.2; F.1.1 A mathematical concept is identified and analyzed that is implicit in the 2012 paper Turing Incomputable Computation, presented at the Alan Turing Centenary Conference (Turing-100, Manchester). The concept, called dynamic level sets, is distinct from mathematical concepts in the standard literature on dynamical systems, topology, and computability theory. A new mathematical object is explained and why it may have escaped prior characterizations, including the classical result of de Leeuw, Moore, Shannon, and Shapiro that probabilistic Turing machines (with bias $p$ where $p$ is Turing computable) compute no more than deterministic ones. A key mechanism underlying the concept is the Principle of Self-Modifiability, whereby the physical realization of an invariant logical level set is reconfigured at each computational step by an incomputable physical process. |
| title | Dynamic Level Sets |
| topic | Computational Complexity Computation and Language Mathematical Physics Dynamical Systems History and Overview 68Q09, 68Q10, 37N99, 37H12 F.2.2; F.1.1 |
| url | https://arxiv.org/abs/2602.22530 |