Qualitative Mathematics: First Supplement. A Grammar That Keeps Growing

This supplement extends the qualitative mathematics introduced in Billions and Billions of Universes. It brings together functional transparency, convergence and divergence, directional coupling, bounds and thresholds, narrowing and widening, deflection, chirality, loops and recursive return, conditionals, waiting and resumption, containment and release, parallel activity, synchronisation, and diffusion. A radial candidate for physical dispersion is also included. The extensions arose through collaborative work on process descriptions and reflection on the grammar itself. Definitions, compositional matrices, worked examples, and reproducible LaTeX code make the proposed notation available for reuse. Qualitative operations and quantitative expressions can be interwoven throughout the same line of reasoning.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-11
DOI
https://doi.org/10.5281/zenodo.22698976
Primary Topic
Mathematics, Computing, and Information Processing
Type
preprint
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preprint

Qualitative Mathematics: First Supplement. A Grammar That Keeps Growing

Daniel Avilés Hurtado
Zenodo (CERN European Organization for Nuclear Research)
Mathematics, Computing, and Information Processing
preprint

Qualitative Mathematics: First Supplement. A Grammar That Keeps Growing

Daniel Avilés Hurtado
preprint en

Abstract

This supplement extends the qualitative mathematics introduced in Billions and Billions of Universes. It brings together functional transparency, convergence and divergence, directional coupling, bounds and thresholds, narrowing and widening, deflection, chirality, loops and recursive return, conditionals, waiting and resumption, containment and release, parallel activity, synchronisation, and diffusion. A radial candidate for physical dispersion is also included. The extensions arose through collaborative work on process descriptions and reflection on the grammar itself. Definitions, compositional matrices, worked examples, and reproducible LaTeX code make the proposed notation available for reuse. Qualitative operations and quantitative expressions can be interwoven throughout the same line of reasoning.

Zenodo (CERN European Organization for Nuclear Research)
Comunidad Autónoma de la Región de Murcia (ES)
Quality Education
Mathematics, Computing, and Information Processing
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