That article seems like a long way to say something very simple: 1) If you have an n-dimensional space where each dimension means/measures something, then poin

That article seems like a long way to say something very simple: 1) If you have an n-dimensional space where each dimension means/measures something, then points close together in that space will of course be similar in these dimensional qualities. 2) One way to measure closeness/similarity between two points is to consider them as vectors from the origin to the points, then compare the angle (cosine similarity) between the vectors. If the vectors point in the same direction (small angle between them) then the points lie in that same directional region of the n-dimensional space. 3) There are also other ways to measure closeness of points such as the euclidean distance between the points. Cosine similarity tends to work well for high dimensional embedding spaces such as for text embeddings or face embeddings, where distances between different dimensions (e.g. eye-shape vs size-of-nose) are meaningless since these are not euclidian spaces.