What I Learned with John: On the Depth of Language and How to Measure It with Large Language Models and Algorithm (Kolmogorov) Complexity

Language conveys meaning through structures that range from concrete description to abstract generalization. This study introduces a computational framework for measuring linguistic depth by quantifying the algorithmic complexity of semantic networks derived from large language model embeddings. Building on Piagetian and Vygotskian theories of cognitive development, this study propose that abstraction, whether in thought, measurement, or language, reflects the compression of distributed information into coherent, generative structures. We operationalize this principle using Kolmogorov complexity, K(G), estimated via the compressed length of network edge lists. Simulation studies demonstrate that networks derived from factor-structured data exhibit significantly lower K(G) than density-matched random controls, with separation accuracy reaching 94% as factor loadings strengthen. In a controlled linguistic experiment comparing 100 pairs of abstract and concrete phrases matched for syntax and length, abstract expressions produced consistently lower algorithmic complexity (M = 726) than concrete expressions (M = 784), t(194.41) = -3.28, p = .001, d = -0.46. These findings establish that semantic abstraction manifests as network compressibility, i.e., abstract language achieves conceptual depth through structural regularity rather than elaborative detail. The framework unites psychometric network theory, complexity science, and computational linguistics under a single information-theoretic principle, offering a model-agnostic measure of abstraction applicable across psychological networks, natural language, and neural representations. By formalizing the intuition that profound expression achieves economy through structure, K(G) provides both theoretical insight into how meaning is organized and practical methodology for assessing semantic depth in text, psychological data, and artificial intelligence systems.