Vector Arithmetic

Math on meanings

Here's the most surprising property of word vectors: you can do arithmetic on them, and the results make semantic sense.

This works because the vector for "king" minus "man" captures the concept of "royalty" without the "male" component. Adding "woman" gives us "female royalty" = queen.

Try it yourself

Why this works

Vector arithmetic reveals that word embeddings capture relationships, not just similarities. The direction from "man" to "woman" is similar to the direction from "king" to "queen."

The foundation of modern AI

Word vectors were a breakthrough in the 2010s, but modern LLMs like Claude go much further. They use contextual embeddings where each word's vector changes based on surrounding words.

Still, the core insight remains: meaning can be represented as geometry in high-dimensional space. This is what makes AI language understanding possible.