On the Dynamics of Observation and Semantics
Xiu Li
TL;DR
This work reframes semantic understanding as a physical, bounded process rather than a static latent property, proposing the Observation–Semantics Fiber Bundle in which a high-entropy observation space is projected onto a low-entropy semantic base. The core insight is the Semantic Constant $B$, derived from Landauer's principle, which constrains the complexity of internal transitions and forces the emergence of discrete, compositional symbolic structures. The paper argues that language and logic are ontological necessities—stable, reusable, and combinatorial abstractions that arise to keep computation thermodynamically tractable within finite memory, compute, and energy budgets. Empirically, it connects this theory to language birth and contemporary methods, offering a taxonomy of quotient mappings (loss-based, structure-based, and pure semantic coarse-graining) and explaining the strengths and weaknesses of transformers and GANs through the lens of physical semantics. The framework provides a principled foundation for understanding why scalable intelligence must progress toward a language-like symbolic layer to remain robust under thermodynamic constraints and interventions in a high-entropy world.
Abstract
A dominant paradigm in visual intelligence treats semantics as a static property of latent representations, assuming that meaning can be discovered through geometric proximity in high dimensional embedding spaces. In this work, we argue that this view is physically incomplete. We propose that intelligence is not a passive mirror of reality but a property of a physically realizable agent, a system bounded by finite memory, finite compute, and finite energy interacting with a high entropy environment. We formalize this interaction through the kinematic structure of an Observation Semantics Fiber Bundle, where raw sensory observation data (the fiber) is projected onto a low entropy causal semantic manifold (the base). We prove that for any bounded agent, the thermodynamic cost of information processing (Landauer's Principle) imposes a strict limit on the complexity of internal state transitions. We term this limit the Semantic Constant B. From these physical constraints, we derive the necessity of symbolic structure. We show that to model a combinatorial world within the bound B, the semantic manifold must undergo a phase transition, it must crystallize into a discrete, compositional, and factorized form. Thus, language and logic are not cultural artifacts but ontological necessities the solid state of information required to prevent thermal collapse. We conclude that understanding is not the recovery of a hidden latent variable, but the construction of a causal quotient that renders the world algorithmically compressible and causally predictable.