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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
Try the experimentWhat 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.Search systems can rank items by distance between numerical representations. Move the query until a different note comes first. That ranking helps choose what to inspect next; read the note before deciding whether it answers your question.
Local teaching illustration / No AI model call
- Inspect the two coordinates assigned to each story item.
- Predict a nearest note, then move Query X and Query Y. The hollow circle and ranked distances update immediately.
- Compare the displayed distances. Move again until the nearest item changes.
The hollow circle is your query. These are invented coordinates, not embeddings from a model.
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.A vector is an ordered collection of numbers. With two numbers, we can draw an item as a point on a flat map. Put story notes at different points, then measure the distance from a query point to each note. Nearby points become easy to identify.
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.The coordinates in this experiment are assigned by hand. They are not embeddings produced by a language model, and the map does not understand Mira’s story. It teaches one ingredient of a search system: comparing numerical representations. Change the query coordinates and the nearest item can change too. A short distance means closeness under this map’s rules, not that the note is true or useful.
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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.
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Keep exploring, or stay here and try another variation.