Embeddings
How computers turn words into coordinates on a map where similar ideas sit close together.
Every word gets coordinates on a giant concept map.
An embedding model converts every word into a list of numbers, placing similar concepts in the same neighborhood.
How many dimensions does a real map have?
A paper map uses two dimensions (X and Y). Real AI embeddings use between 768 and 3,072 dimensions. Each dimension captures a subtle trait: formality, physical size, sentiment, technical depth, or grammatical role.
Distance equals meaning.
The closer two coordinates are in space, the more closely related their concepts are in the real world.
How models measure distance in high dimensions
AI systems use cosine similarity. Instead of measuring physical ruler distance, the system calculates the angle between the two coordinate arrows. An angle of zero means identical meaning, an angle of 90 degrees means unrelated, and 180 degrees indicates opposing concepts.
Math with meaning: the arrow trick.
Because concepts have directions, you can add and subtract words like numbers to solve analogies.
Why analogical directions hold true
In 2013, researchers at Google discovered this property while building Word2Vec. Because the model learned from billions of real sentences, the difference between "man" and "woman" matches the difference between "king" and "queen", "uncle" and "aunt", or "actor" and "actress".
Find what you mean, not just what you type.
Keyword search requires exact matching words. Embeddings match the underlying intent even when every word is completely different.
How Retrieval-Augmented Generation (RAG) uses embeddings
When you ask an AI a question about your documents, a vector database converts your query into an embedding and retrieves the three to five text passages closest to it in semantic space. The AI reads those retrieved chunks to provide an accurate, grounded response.