Time and Space as Relation: Leibniz’s Relationalism, and Not Confusing the Teleology of “the Best” with Least Action.
Are time and space a container (an absolute substance) that holds things, or the relations (orders) among things themselves? Newton took the former (absolute space and time); Gottfried Leibniz took the latter — space is the order of coexistence, time the order of succession (the Leibniz-Clarke correspondence, 1715-16, argued from the identity of indiscernibles and the principle of sufficient reason). This relationalism flows to Mach (Mach’s principle), to Einstein’s general relativity (spacetime as a dynamical, relational object), and to Rovelli’s relational time, resonating directly with the corpus’s Paper 82 (event-based time, the Renko chart). But Leibniz has another face — the principle of “the best of all possible worlds,” often told as the philosophical forerunner of the principle of least action (Maupertuis / Euler). Here lies a TRAP. “The best” is a TELEOLOGY (the world aimed at a purpose), but the corpus’s Paper 84 showed least action is NOT teleology: delta S = 0 is a local condition equivalent to F = ma, and the apparent purpose dissolves into the interference of Feynman’s path integral. Hence the point is the separation of DISTINCT ROOTS (Papers 58/48): (1) Leibniz’s relational time and space (the source of Paper 82, alive) and (2) the teleological motive of “the best” (a beautiful intuition, but NOT the correct understanding of least action, Paper 84) are distinct roots and must not be conflated — even within a single person. Relational time also resonates with, but is distinct from, the corpus’s other times (proper time, thermal time, the coarse-graining arrow = 82/77); Leibniz’s dx is a distant source of the shared alphabet (Cartan, 92); Leibniz heads the author’s “integral brain” lineage. IMPORTANT (scope): a Layer-2 structural interpretation of philosophy of science and the history of mechanics; no new mathematics and no new prediction. 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). Time and Space as Relation [Paper 97]. Zenodo.
DOI: 10.5281/zenodo.21758697
ORCID: 0009-0006-8587-3450