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The Space of Meaning

An AI doesn't keep words in drawers, waiting to be looked up. It turns every word into a vector — a long list of numbers you can picture as an arrow reaching into a vast space — and meaning becomes something you can measure: the angle between two arrows.

Not a drawer. A direction.

The shift from a catalog to a model is a shift in what "finding something" even means.

The card catalog

You ask for an exact thing, and there's exactly one drawer it lives in. Spell it wrong and you find nothing. The catalog knows where a book is — never what it's about.

A space of meaning

An LLM turns every word into a vector — a long list of numbers — and sets it somewhere in a vast space. Words that mean similar things land near each other — even if they share no letters. Closeness isn't spelling. It's meaning.

Meaning is the angle between words.

Drag to spin the space. Pick any two words and watch how closely their arrows point the same way.

Drag to rotate · click a word to select
Pick any two words
This little demo doesn’t know “{{ notFound }}” yet — it only knows a small vocabulary. Try one of these:
{{ wordA }} {{ wordB }}
{{ verdict }}

{{ verdictDetail }}

Angle
{{ angleDeg }}°
Cosine similarity
{{ cosine }}
The other 1,497 dimensions

You're seeing 3 directions. The real space has about 1,500. The shimmer is the dimensions we can't draw — yet the angle between your two words barely moves. That stable angle is the meaning.

So how big is this space, really?

In 1,500 dimensions you can fit more distinct meanings than there are atoms in the observable universe.

That vastness is why an AI can hold the meaning of nearly anything you say. It isn't a lookup table — it's the product of decades of work in mathematics, probability, statistics, and computation.