Beyond Gödel: Information-Theoretical Limits of Physical Models and the Principle of Optimal Incompleteness

A new conceptual framework is presented that unifies Gödel’s incompleteness theorems with practical physical modeling through information-theoretic analysis. The method of variables with finite information content demonstrates that every physical model inherits an irreducible uncertainty, representing a “Gödelian barrier” in physics. Models with too few variables are incomplete and yield high uncertainty, while models with an excessive number of variables become computationally intractable despite theoretical completeness. The concept is validated by a systematic analysis of measurements of six fundamental constants across sixty-five scientific publications from the period 2000-2019. The method provides quantitative criteria for model selection, explains systematic discrepancies in precision measurements, and establishes fundamental limits to measurement accuracy independent of improvements in instrumental technology. This work offers researchers a practical tool for assessing model adequacy and understanding why certain physical constants resist precise determination.