Words Become Numbers
Every word in every language maps to a token ID, a number in one shared vocabulary of about 50,000 tokens in GPT-3, the model behind the figures on this page. The same concept gets a different ID in each language. The IDs below are illustrative.
Different Words. Same Destination.
Six languages. Six different words. Six different token IDs. But when these tokens become vectors, they all point to the same neighborhood in meaning-space. The model does not translate. It navigates to where the concept lives.
Numbers Explode Into Dimensions
Each token ID becomes a vector: a list of 12,288 numbers. Each number is a coordinate in a dimension we cannot visualize, but the model navigates fluently.
The Interstellar Problem
In the film Interstellar, the tesseract allowed Cooper to perceive time as a spatial dimension, seeing his daughter's bedroom across all moments simultaneously. We face a similar challenge. How do you show a space with 12,288 dimensions to beings who can only perceive three? The answer is to show shadows, projections, and relationships. We cannot see the space, but we can see what it does.
Meaning Has Geography
In this high-dimensional space, concepts cluster together. Words from different languages that mean the same thing are neighbors. Related ideas form gravitational wells of meaning.
The Geography of Thought
This is a 2D projection of a 12,288-dimensional reality. "Insurance" in English and "seguro" in Spanish are neighbors in this space. No one labeled them as translations. They are neighbors because they appear in similar contexts across billions of sentences. The model learned the map of meaning by walking through language.
The Tesseract of Meaning
Like Cooper in Interstellar perceiving time as space, the model perceives meaning as geometry. Each word exists at coordinates we cannot see, but the model reads them as easily as we read a map.
This is a conceptual model, not a technical specification. The metaphors are simplified to build intuition for how to work with AI effectively. If you want the engineering details (transformers, attention mechanisms, next-token prediction), ask Claude or Perplexity to go deeper.