Intelligence as Dimensionality Transduction: The Reciprocal Mapping Between High-Dimensional Semantic Manifolds and Low-Dimensional Discrete Symbols

This paper proposes that intelligence is not about computation or prediction, but about **dimensionality transduction**—the continuous back-and-forth conversion between two very different kinds of representation. On one side is the **high-dimensional semantic manifold**: a rich, continuous, and holistic space where meaning lives as a web of sensations, emotions, causal links, and context. On the other side is the **low-dimensional symbolic world**: a sparse, linear, and discrete sequence of words, sounds, or tokens suitable for speaking, writing, or storing.Understanding happens when we **expand** a few thin symbols into a full, thick world of meaning. Expression happens when we **compress** that rich inner world back into a speakable sentence. This framework explains hallucination, the power of compression, and why transformer models resemble the human brain. It also connects directly to our prior work: categorization is the *form* of intelligence (Wang, 2025), while dimensionality transduction is its underlying *mechanism*. This mechanism, in turn, leads to phase transitions in semantic structure—what we called “semantic crystallization”—and may even shed light on quantum nonlocality (Wang, 2026).