MATHEMATICAL MODELS IN SCIENCE: BRIDGING DIFFERENCES AND DISCOVERING COMMONALITIES

Abstract

Various scientific disciplines, including biometrics, chemometrics, psychometrics, and econometrics, share a deep connection with statistics but often employ specialized applications. Effective communication across these interdisciplinary boundaries necessitates a common language, and mathematics serves as a universal bridge among the natural sciences. This article centers on the language of mathematics and its role in scientific modeling. The thesis posited here is that mathematical models should be formulated in a manner comprehensible, with some effort, to serious researchers across all disciplines, despite potential cultural barriers. The notion of "understanding" is multifaceted, exemplified by the enigmatic realm of quantum mechanics. While quantum theory is traditionally presented in an abstract language that facilitates calculations, its interpretation remains contentious, posing challenges for researchers outside the physics domain. Notably, quantum mechanics was initially expressed in distinct languages—Schrödinger's wave mechanics and Heisenberg's matrix mechanics—before being mathematically unified. This unification yielded a mathematically elegant yet conceptually intricate theory, accompanied by over 16 partially conflicting interpretations. In the works of Helland (2021) and Helland (2022a), a novel foundation is proposed, potentially more accessible to researchers beyond the quantum community. It introduces conceptual variables denoted as θ, emerging from inquiries like "What will θ be if measured?" Particularly in the discrete case, often central in textbooks and research, precise responses in the form of "θ = u" can be obtained.