TITLE:
A Geometric Model of Infinity with Empirical Justification through Analysis of the Deviation between Experimental Data and Quantum Theory for Hardy’s Paradox
AUTHORS:
Douglas Chesley Gill
KEYWORDS:
Hardy’s Paradox, Infinity, Emergence, Paradox, Russell’s Paradox, Quantum Formalism, Null State, Empty State, Bell’s Inequality, EPR Experiments, Nonlocality
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.5,
May
29,
2026
ABSTRACT: The issue, examined across multiple disciplines, is that infinities cannot be represented as discrete collections. Incompleteness is unavoidable. The 1-D geometric model examines the paradoxical relationship that develops when attempting to define infinite states as contained structures. Two representations of the right triangle are constructed within the unit circle. The first follows standard geometric principles. The second assigns a counter-rational unitary value to each of the triangle’s vectors and incorporates emergence within its structure. Although the two formats of the unit circle have a null relationship, they are shown to share membership by calculating the cosine-square for the right triangle. The geometric structure serves as a model to understand the role of paradox in the representation of infinity. The model is applied to explain the mechanism of emergence in the collapse of the wavefunction, and to Hardy’s paradox, offering a rationale for the discrepancy between its formal calculations and experimental results.