How Geometry Became the Secret Language of Machine Knowledge

A technical explainer explores how computers represent word meaning without storing explicit relationships between concepts. The piece walks through early strategies like tag clouds, where words grouped under shared categories — such as 'Animals' or 'Pets' — begin to express semantic similarity through shared membership. However, using words as tags creates a problem of recursive semantics, where every label itself requires further labeling with no natural stopping point. Researchers ultimately found that assigning words numerical coordinates in a geometric space sidesteps this recursion, allowing meaning to be expressed as measurable distance. The closer two words sit in this space, the more semantically similar they are — a principle that underpins modern language models.