The post explains the relationship between cosine similarity and concentration ratio for normalized word vectors on high-dimensional spheres. A spherical cap's area ratio to the whole sphere (concentration ratio) reveals why modest cosine similarity values correspond to tiny portions of the sphere, indicating close matches despite counterintuitive high-dimensional geometry.
In high-dimensional word embeddings, cosine similarity measures word relatedness through vector angles. A similarity of 0.656 (49° angle) is considered large because random vectors in 200-dimensional space are nearly perpendicular, making close relationships rare; the canonical word arithmetic example 'king' − 'man' + 'woman' ≈ 'queen' demonstrates this contextual interpretation of similarity.