The Discovery of the Field: Faraday’s Lines of Force and the Physical Intuition That Came Before the Mathematics.
The source of the “field” and the solid angle 4pi (Paper 02) that recur through the corpus is Michael Faraday (1791-1867). A bookbinder’s apprentice who rose by self-education with almost no formal mathematics, Faraday discovered the physical object “the field” before its mathematics — the lines of force filling space; force is not action at a distance but is transmitted locally through the field at each point. This intuition, first dismissed as “not mathematical,” was later turned by Maxwell into the field equations (1856/1873), and Gauss’s law quantified its flux. Integrating a point source’s field over any closed surface gives, independent of shape, the full solid angle 4pi (surface integral of E dot dA = q/epsilon0, geometric factor 4pi) — the corpus’s 4pi (Paper 02), the quantified version of Faraday’s picture “the number of lines of force through a closed surface.” Faraday’s field is written in the corpus as the EM 2-form F=dA (Paper 92) and the field action (Paper 87). CORE: Faraday supplied the physical object (the field) itself, and Maxwell/Gauss gave it mathematical form — an exemplar of “intuition first, the royal-road mathematics after.” IMPORTANT (scope): a Layer-2 structural/lineage interpretation of established physics (field concept, Gauss’s law, Maxwell’s equations); no new mathematics and no new prediction; physics is not modified. That the intuition “was right” can be said only because it became science through the mathematics; intuition itself is a signature, not a proof (the three-layer discipline). The Universe OS is a Layer-3 non-science lens.
On the making of this work: The ideas and content of this work stem from the author’s own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author’s. Feedback and corrections are sincerely appreciated.
Reference
Yamagishi, Y. (2026). The Discovery of the Field [Paper 93]. Zenodo.
DOI: 10.5281/zenodo.21758537
ORCID: 0009-0006-8587-3450