Navigation and Meta-Trajectories of Intelligences

This manuscript develops a theoretical framework for understanding intelligence as a process of navigation within dynamically evolving spaces of constraints. Moving beyond optimization-based paradigms, it establishes navigation as a more fundamental principle, applicable in contexts where the space of possible configurations is neither fixed nor fully accessible. The core contribution lies in the introduction of a trajectory-based ontology, where intelligences are defined not by states or systems, but by their ability to sustain admissible trajectories under evolving and potentially incompatible constraints. This shift leads to the formalization of path dependence, strong irreversibility, and structural impossibility as intrinsic properties of navigation. Building on this foundation, the manuscript introduces the concept of meta-trajectories, defined as trajectories in the space of trajectories itself. This higher-order structure captures the dynamic transformation, emergence, and disappearance of trajectories, revealing a non-stationary and fragmented space of possibilities. The associated operator of navigation is shown to be non-linear, non-commutative, and non-invertible, reflecting fundamental physical and informational limitations (Wolpert, 2001; Landauer, 1961). A central result is the formulation of a navigation entropy, which quantifies the dispersion, saturation, and collapse of trajectories over time. This entropic perspective establishes a direct link between navigation, thermodynamic irreversibility, and information loss, extending recent developments in stochastic thermodynamics (Seifert, 2012) and the free-energy principle (Friston, 2010). The framework also incorporates multi-level constraint structures, distinguishing local, diffuse, and emergent global regimes, and analyzing their interactions and instabilities. The manuscript further characterizes the limits of navigation through the identification of unreachable trajectories, structural blockages, and conditions of impossibility. These limits are not contingent but arise from the intrinsic incompatibility and evolution of constraints, leading to a non-closed space of trajectories. Finally, a general principle of navigation is established, stating that intelligences evolve by maintaining admissible trajectories within a dynamically transforming, non-closed, and multi-level constraint space, under conditions of irreversibility, partial information, and structural incompatibility. This work contributes to a unified theoretical perspective at the intersection of physics, information theory, and artificial intelligence, opening new directions toward a general theory of meta-navigation and multi-physical intelligence systems