Life, Mind, and Language as Stable Dynamic Patterns

This paper proposes a unified ontological foundation for understanding life, mind, and language as stable dynamic patterns within a state space. Relying on Mazein Mechanics (MM), where impulse is the primary ontological entity and Dynamic Content P [A] serves as a measure of a system's internal complexity, we provide strict formal definitions: (1) Life is any dynamic pattern with non-vanishing content (P ≥ Pmin > 0), positive second variation (δ2P > 0), and locality of interactions; (2) Mind is the capacity of such a pattern to recursively restructure its representational architecture in response to environmental gradients while preserving its identity; (3) Language is not a communication tool, but the operational core of cognition: a system of signs that separates figure from ground, thereby constituting objects. Crucially, to prevent abstract speculation, we anchor the mind level with a central empirical case study: a comparative topological analysis of two neural organization regimes, identified via variational lifting of structural connectomes (C. elegans and Drosophila medulla). We demonstrate that cognitive capacity is not binary but graded, quantifiable via a proposed Rationality Index R. Furthermore, we show that modern Large Language Models (LLMs) fail the ontological criteria for life due to a lack of autonomous persistence. This work serves as a step toward a rigorous science of cognitive entities, unifying physics, biology, and cognitive science through the Operational Set Theory (OST) and Tensor Model of Discrete Dynamics (TMDD) framework.