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Results for “distinction” 9 papers
Information theory. Entropy, capacity and coding bounds Tagged papers: 46.
Cross‑Ratios as Universal Atoms of Meaning: A Projective‑Invariant Framework for Likelihood, Information, and Decision Theory
Dimensionless descriptors such as physical constants, likelihood ratios, and mutual information are central to inference across physics, statistics, and machine learning, yet they are vulnerable to changes of units, model parametrizations, or data distributions. This work bridges projective geometry…
Distinction, Discretisation, and the Cost of Law: A Quantitative Sketch of Approximation Entropy
The deepest question in physics is often posed as "What are the laws?", but a prior question is "What does it cost to state, and to compute with, a law?" Building on the distinction-based formalism of Spencer-Brown's Laws of Form as consolidated in the Quantum Laws of Form (QNFO) programme, and on…
What Makes a Measure “Genuinely Natural”? Bits, Nats, and the Audit of Naturalness Claims in Measurement, Information, and Language
The adjective “natural” is invoked across quantitative sciences to suggest privileged status for units, conventions, or datasets. This paper formalizes three explicit criteria for a measurement convention to be genuinely natural—ratio/relabeling invariance, additivity, and constant‑freedom—and…
Quantum Statistics from the Adelic Product Formula: The Squarefree Origin of the Fermi-Dirac/Bose-Einstein Distinction
Why are there two quantum statistics, and only two, in three spatial dimensions? This paper reads the Bose–Einstein and Fermi–Dirac occupation distributions as the maximum-entropy solutions of one lattice with two multiplicity rules. On the unrestricted integer lattice the Euler factor at each prime…
The Self-Referential Scalar Family: e, the Half-Turn, and the Unification of Information Theory, Statistics, Thermodynamics, and QND Measurement in the Adelic Picture
Standard information theory measures uncertainty at the archimedean place; the adelic program extends it to all completions of the rationals, carrying a p-adic valuation entropy alongside Shannon entropy. This paper shows that the two most familiar distributions of statistical mechanics are already…
ZX Diagrams at the Seam: Spiders, Pauli Webs, Gadgets, and the Cafeteria Problem of Cross-Disciplinary Imports
Diagrammatic languages are the most successful interface between quantum computing and the human mind. The ZX calculus — with its spiders, Pauli webs, and gadgets — is taught as the intuitive picture of quantum processes, and its completeness theorems are among the finest results in the field. Yet…
Information-Theoretic Scale Management
Informational Realism posits that reality’s fundamental layer is informational. This framework axiomatizes a distinction between the complete set of all possible information states, the informational census (\(\Omega\)), and the limited set of physical measurements, the physical poll…
Re‑Founding Information: An Autaxic Ontological Framework with Quantitative Illustrations
The absence of a unified, ontologically grounded theory of information hampers interdisciplinary research, obscures the design of data‑centric technologies, and inflates costs in fields ranging from quantum physics to artificial intelligence. Existing syntactic accounts such as Shannon’s theory and…
Autaxys and its Generative Engine
Prevailing foundational paradigms in science and philosophy encounter significant limitations when addressing the ultimate origin of order, the nature of physical laws, and the genesis of patterned reality from first principles. This article introduces autaxys as a candidate fundamental…
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