Cyclic Measurement: Positional Notation as Ultrametric Time Trees

2026/06/29 by QNFO Research · 1 voice
Mathematics · Physics and Astronomy · #advanced mathematical theories #Quantum Mechanics and Applications #Mathematical and Theoretical Analysis

paper · doi:10.5281/zenodo.21047527

openalex publication_date 2026/06/29 · openalex created_date 2026/06/30 · openalex updated_date 2026/07/01

Abstract

This paper presents three related theses on the structure of measurement, time, and computation. Thesis I argues that positional notation is a rooted tree of nested time-cycles whose native geometry is ultrametric. Thesis II extends this to physics: from the Zitterbewegung of the Dirac electron to cyclic cosmological models, time manifests as a hierarchy of nested cycles, and the Big Bang is a phase boundary, not an origin. Thesis III proposes that the ultrametric tree is a native model of computation where cyclic codes, hierarchical memory, and self-referential measurement form a unified architecture in which the observer is constituted by the act of counting cycles.

Discussions

• New research: Cyclic Measurement in the Calculus of Indications A formal analysis of re-entry and oscillatory structure in Spencer Brown's Laws of Form, revealing fundamental patterns in the algebra [bsky, 0 points, 0 comments]

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