Sci - Dimensionless Mathematics: A Pre-Geometric Framework for Closure, Persistence, and Invariant Objecthood
Laboratoire de Chimie Théorique
Abstract
Sci - Dimensionless Mathematics: A Pre-Geometric Framework for Closure, Persistence, and Invariant Objecthood Armstrong Knight — intent-tensor-theory.com This paper formally introduces Dimensionless Mathematics as a proper noun and a named domain of mathematical inquiry, distinct in kind from all classical uses of 'dimensionless' as an adjective in physics and engineering. Classical nondimensionalization operates inside a given geometry, stripping units from equations that already exist in a coordinate frame. Dimensionless Mathematics operates before geometry, asking what conditions must be satisfied for stable structure to exist before spatial or temporal coordinates are treated as fundamental. The framework…
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1Topics & keywords
- Dimensionless quantity
- Invariant (physics)
- Covariance and contravariance of vectors
- Cartesian coordinate system
- Domain (mathematical analysis)
- Axiom
- Covariant transformation