A World That Changes Without Non-Being: The Inner Dimension of Being, and Ontology as a Scientific Research Program

I hold that ontology, too, can be placed under the scientific method: calculate, test, correct when wrong. From the standpoint that being comes first, this paper reads Parmenides' proposition "What is, is, and what is not, is not" as saying being admits no degrees: the amount of being is the same always and everywhere. From this the Eleatics concluded there is neither motion nor plurality; yet the world changes. Representative responses posited a second principle, such as the void or absolute space, or distinguished senses of being, admitting qualified non-being and potentiality. I propose a different kind of reconciliation: keep the amount, and place difference and change in the internal direction toward which being points. In an explicit translation into mathematics, amount-preserving continuous change requires a carrier space of at least two real dimensions for the state, and in the smallest structure composing changes multiplicatively, such continuously differentiable change is generated by the imaginary unit, whose square is −1. The number often introduced as not really existing appears in the smallest structure describing a world that changes without non-being. Under stated conditions, by a known classification, the quaternions remain, with norm-one group isomorphic to SU(2), which describes spin. The hypothesis to be tested takes these conditions and this algebra as the structure of physical being. Finally, the paper identifies by calculation what this choice does not itself guarantee and sets out, as a research program, what must be computed and which results would require its revision or abandonment, inviting participation. Preprint (not peer reviewed). The verification code for the calculations in the appendices is available on Zenodo (see Related works).