Embeddings are coordinates for meaning
How turning words into points in space makes "similar" something you can compute.
Computers can’t compare meanings. They can compare numbers. Embeddings are the bridge: assign every word (or sentence, or image) a point in space, such that things with similar meanings land near each other.
That one sentence carries the whole idea. The rest is consequences.
Distance becomes meaning
Once meanings are coordinates, fuzzy questions become geometry:
| Question | Becomes |
|---|---|
| Are these two sentences similar? | How far apart are their points? |
| Which document matches this query? | Which point is nearest? |
| What’s the odd one out? | Which point is farthest from the cluster? |
This is why embeddings quietly power almost everything: search, recommendations, RAG pipelines, clustering, deduplication. They’re the plumbing of modern AI.
Where do the coordinates come from?
Nobody sits down and decides “cat goes at (0.2, -1.3, …)”. The coordinates are learned from a simple pressure: words that appear in similar contexts get pushed toward each other.
Feed a model billions of sentences. Every time “coffee” and “tea” show up in interchangeable contexts (a cup of ___, I need my morning ___), the training nudges their vectors closer. Repeat at scale, and the geometry starts encoding meaning nobody explicitly wrote down.
The model never learns what coffee is. It learns what coffee is like. And for a surprising number of tasks, that’s enough.
The part that actually surprised me
Directions in the space can be meaningful too. The classic party trick:
vector("king") - vector("man") + vector("woman") ≈ vector("queen")The difference between “king” and “man” is a direction that roughly means royalty, and adding it to “woman” lands near “queen”. Arithmetic on meaning. It doesn’t work perfectly, and it’s easy to over-romanticize, but the fact that it works at all tells you the space has structure, not just proximity.
The one-sentence version: an embedding is an address in a space where the neighborhood is the meaning. And once meaning has an address, you can do math on it.