Measuring meaning with one number

What this lesson shows

Dot product / cosine as an alignment score: multiply-and-add.

The question it opens with

How does the machine measure how near two vectors are?

The walkthrough, in the lesson's own words

• Which word is most like cat? Tap your guess on the map.
• Rotate the arrow. When does the meter hit its peak?
• That shrinking shadow on the dial is the score.
• You'll meet this exact move again in attention and RAG.
• Every arrow here is length 1, so the score measures pure direction, it reaches 1 only when two arrows point the exact same way.
• Nearly 1, cat and dog point almost the same way (just 8° apart), the high score the dial's shadow shows.
• A support bot answers from your company docs and pulls in exactly the right paragraph out of thousands. How does it pick that one?
• It scores your question against every chunk with a dot product, the same multiply-and-add you just rotated, and grabs the highest. This is the retrieval step in RAG, and the same scoring drives attention inside the model.
• Multiply each coordinate, then add, every one is a small agree or disagree.

Key takeaway

Similarity is just multiply-and-add, and it returns in attention and RAG.

What you can do after this lesson

You can explain how a model measures meaning with a dot product.

Where it leads: But these were just two numbers, a toy. A real embedding has hundreds. What do they hold?

This is the written summary. The lesson itself is interactive: you predict, drag and operate the mechanism above, and the reveal answers you.