From Binary Origins to Continuous Intensity: Reconceptualizing Life as Gift-Circulation under Entropic Constraint

The question "where does life begin?" presupposes a binary distinction between living and non-living matter. This paper argues that this formulation is fundamentally misconceived. Drawing on Hiroshi Shimizu's theory of life as gift-circulation (yojo junkan) within relational fields and Schrödinger's characterization of life as negative entropy, I propose a synthetic definition: life-intensity equals the product of gift-circulation intensity and local entropy reduction. This formulation yields a continuous measure rather than a binary classification, reveals life as a nested multi-scale phenomenon, and opens the possibility of radically different life-forms—including "open-type" life without membrane boundaries—that may exist elsewhere in the universe. The origin-of-life question thereby transforms from "when did life begin?" to "how did life-intensity increase over Earth's history?"