The question to explore

Make a map of numbers

What does it mean for two items to be close?

About 10 minutes / Suggested pace / No account needed

  • Vector
  • Distance
  • Representation
Try the experiment

What this activity helps you do

Move the query until another note becomes nearest. Number-based search can help pick what to read next, but distance alone cannot tell you whether a note is true or useful.

Local teaching illustration / No AI model call

  1. Inspect the two coordinates assigned to each story item.
  2. Predict a nearest note, then move Query X and Query Y. The hollow circle and ranked distances update immediately.
  3. Compare the displayed distances. Move again until the nearest item changes.
At (0, 0), the lighthouse note is nearest. These coordinates are hand-assigned.

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The idea

A vector is a list of numbers in a fixed order. Two numbers can place an item on this map. We can then measure how far the query is from each note.

We chose these positions by hand. No language model made them or understood the story. Nearby means close under this map’s rules. Read the notes to decide whether they actually answer the question.

Take this with you

What changed?

A distance is meaningful only alongside the representation and comparison rule that produced it.

Try explaining it.

If two notes land next to each other, have we established that they say the same thing?

Open a possible explanation

No. These hand-assigned positions are a teaching choice. You still need to read the notes to decide whether they agree, conflict or answer your question.

Choose what to try next

Keep exploring, or stay here and try another variation.

By Jonathan Simone, with AI assistance. First edition, October 2026. Activities are fictional teaching examples, not measured AI performance. Help us improve this lesson.

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