| _version_ | 1866901182186782720 |
|---|---|
| author | Woodward, Vance |
| author_facet | Woodward, Vance |
| contents | <p>This document proposes a foundational shift in mathematical grammar to support Toroidal Scale Dynamics (TSD). Standard mathematics relies on a "Linear Paradigm" where the number line is unbounded and division by zero is undefined, resulting in singularities where physics breaks down. The author proposes a "Cyclic Paradigm" governed by two new axioms: Projective Unity (where 1 equals 0 times Infinity) and the Dipole Law. These axioms treat Zero and Infinity not as "nothing" and "everything," but as reciprocal coordinates on a closed toroidal loop. This framework resolves the algebraic paradoxes of division by zero and provides the rigorous mathematical basis for a finite, cyclic universe where "Infinite" density and "Zero" density are simply opposite sides of the same geometric manifold.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18364876 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Exploring Infinity as a Number: The Mathematical Foundations of Toroidal Scale Dynamics Woodward, Vance Toroidal Scale Dynamics Projective Unity Riemann Sphere Division by Zero Cyclic Mathematics Dipole Law Infinity Number Theory Mathematical Foundations The Wallis Symbol <p>This document proposes a foundational shift in mathematical grammar to support Toroidal Scale Dynamics (TSD). Standard mathematics relies on a "Linear Paradigm" where the number line is unbounded and division by zero is undefined, resulting in singularities where physics breaks down. The author proposes a "Cyclic Paradigm" governed by two new axioms: Projective Unity (where 1 equals 0 times Infinity) and the Dipole Law. These axioms treat Zero and Infinity not as "nothing" and "everything," but as reciprocal coordinates on a closed toroidal loop. This framework resolves the algebraic paradoxes of division by zero and provides the rigorous mathematical basis for a finite, cyclic universe where "Infinite" density and "Zero" density are simply opposite sides of the same geometric manifold.</p> |
| title | Exploring Infinity as a Number: The Mathematical Foundations of Toroidal Scale Dynamics |
| topic | Toroidal Scale Dynamics Projective Unity Riemann Sphere Division by Zero Cyclic Mathematics Dipole Law Infinity Number Theory Mathematical Foundations The Wallis Symbol |
| url | https://doi.org/10.5281/zenodo.18364876 |