Natural Language as Compression Format

Shannon's source coding theorem establishes that any source with entropy rate H can be compressed to H bits per symbol without loss, but compression below H inevitably destroys information. Natural language, as a compression format for human intention, is near-optimal for a specific class of information: propositional content, logical relationships, functional specifications. Its semantic bandwidth — carrying denotation, connotation, implication, context simultaneously — vastly exceeds the statistical entropy of the character sequence. But natural language cannot carry the full entropy of every dimension of human knowledge. Embodied intuition, aesthetic judgment, contextual expertise — these reside in patterns of experience that resist verbalization, with entropy rates exceeding what language can encode. The AI interface is therefore a highly efficient compressor for the compressible component of knowledge and a lossy compressor for the incompressible component.