Value Fluid Dynamics II: From Scalar Addition to Vector Multiplication -Resonance and Dimensional Explosion in Value Interaction Author: Tatsuya Kem Date: March 27, 2026 Category: Mathematical Physics / Information Theory / Heterodox Economics

This paper develops the second stage of Value Fluid Dynamics (VFD), extending the theory from a thermodynamic model of information condensation and flow to a higher-order mathematical framework of value interaction. We argue that conventional economic systems are fundamentally "scalar": they reduce human value to a one-dimensional quantity and operate through additive exchange. This process strips value of its qualitative structure, resulting in a phenomenon we term "decolorization." In contrast, we propose modeling human value as an infinite-dimensional vector. Interactions between agents are not additive but multiplicative, governed by vector operations. First, we formalize "resonance" as a dot product between value vectors, demonstrating that meaningful interaction depends on directional alignment rather than magnitude alone. Second, we introduce the tensor product as the fundamental operation of value creation, showing that interactions generate entirely new value spaces rather than merely combining existing ones. This shift from scalar addition to vector multiplication implies a radical redefinition of economics, cognition, and creativity, suggesting that value is not conserved but expanded through resonance and dimensional proliferation. 1. Introduction: The Limits of Scalar Economics Modern economic systems operate on a foundational assumption: value is scalar. It is represented as a number, comparable across contexts, and transferable through addition and subtraction. This abstraction enables exchange but imposes a severe constraint-the erasure of structure. A poem, a theorem, and a loaf of bread become commensurable only by undergoing a process of reduction. Their qualitative dimensions-emotion, meaning, and internal structure-are stripped away, leaving a colorless scalar. This is the hidden cost of exchange: decolorization. Within such a system, the total value of interaction is strictly bounded: No matter how profound the interaction, it cannot exceed the sum of its parts. This is not merely a limitation of accounting-it is a limitation of ontology. However, lived human experience contradicts this model. When two minds meet in deep understanding, the result is not additive but transformative. Something qualitatively new emerges. This paper argues that such phenomena require a fundamentally different mathematical description: not scalar addition, but vector multiplication. 2. The Vector Model of Value 2.1 Humans as Infinite-Dimensional Sources We define each human agent as a vector in an effectively infinite-dimensional space: