Embeddings and Vector Databases

1. Meaning as Geometry

An embedding model takes a piece of text and turns it into a vector: a long list of numbers, commonly 256 to 3,072 of them. What matters is not the numbers themselves, but where the resulting point lands. Texts with similar meaning land near each other. Take "How do I reset my password?" and "I'm locked out of my account." They share almost no words. Their vectors still sit close together, because the two sentences mean nearly the same thing. And that closeness is something you can actually compute