An Anchor Theory of Value Sharing: Symmetry and the Structure of Shared Value

This paper proposes an anchor theory of value sharing. The central idea is that shared value is structured by an anchor—the segmented part of a proposition or object that carries the highest subjective value for an agent—and that whether value is preserved or changes depends on the symmetry of the anchor under transformations of time, space, and perspective. Each axis takes the value 1 (symmetry preserved) or 0 (symmetry broken), and value can be shared only while all three axes remain at (1, 1, 1). In vector form, value is written as V = (x, y, z), where x, y, and z denote credibility, narrativity, and importance, and the change induced by a symmetry operation is written as dV = ((dx/dT) dT, (dy/dA) dA, (dz/dS) dS), where the derivative is the rate of change induced by the operation and the differential is the number of operations performed. The correspondence between the axes and the value components is one-to-one both in nature and in history. Value is shared when dV = 0, regardless of whether the value is positive or negative, and dV > 0 or dV < 0 indicates an increase or decrease in the absolute magnitude of subjective value. An anchor can be placed on any proposition or object, so the question is never whether an anchor exists but whether it survives symmetry operations. A central consequence is that objective value is nothing but subjective value that survives symmetry operations; accordingly, the injunction “think objectively” is redefined as “think subjectively in such a way that your valuation survives symmetry operations.” This redefinition has a linguistic basis: numbers are the most symmetry-resistant symbols, and mathematics is the language most resistant to symmetry operations. Mathematical thinking appears objective not because it eliminates subjectivity but because it articulates subjectivity in the most symmetry-resistant language. Science is strong under symmetry operations because it employs numbers; phlogiston employed mathematics but its core was conceived in ordinary language, so its linguistic component lost temporal symmetry while its mathematical findings survived. The theory is applied to a range of phenomena: why scientific propositions can be said, why the lives of great figures can be said while those of ordinary persons cannot, why phlogiston became unsayable, why religion is communicable within a community but not outside it, why products that sell domestically may fail abroad and vice versa, why neglected theories may later be recognized, why changing place can change a life, why misfortune persists when its value is preserved across symmetry operations, and why re-importation can occur through a change in narrativity even when importance remains unchanged. Sayability is treated as one application of the theory—the sharing of linguistic value—rather than as its sole subject. This paper is a proposal for a direction of research rather than a completed theory, and its limitations are explicitly stated.