Latent Spaces: The Bridge Between Minds and Machines

The mathematics behind embeddings and the metaphors of our thoughts

When Richard Feynman — one of the most brilliant physicists of the 20th century — tried to describe how he thought about complex problems, he found himself struggling. “It’s like asking a centipede which leg comes after which,” he said. “It happens quickly and I’m not exactly sure what flashes and stuff go on in the head.”

What Feynman discovered, in a deeply personal way, was something that sits at the core of both human cognition and modern artificial intelligence: we all inhabit unique latent spaces.

What are embeddings: The technical version

In modern AI architectures, embeddings are dense vector representations of data in a multidimensional space. When a language model processes the word “cat,” it doesn’t simply see five characters but rather a vector of floating-point numbers — say, an array with 768 dimensions — where each dimension captures some semantic aspect of that word.

These vector representations are created through a training process that positions similar words or concepts close to each other in this mathematical space. Proximity is typically measured using cosine or Euclidean distance. Thus, the embedding for “cat” will be closer to “feline” than to “automobile.”

Technically, these structures are products of matrix transformations where:

embedding = input_data × weight_matrix

Models like BERT, Word2Vec, or the embedding layers in architectures like GPT use different approaches to optimize these transformations, but they all share the fundamental goal: creating a latent space where geometry reflects meaningful semantic relationships.

The latent space of the human brain: A constant translation

Now, let’s imagine something fascinating: what if our brains also operated in particular latent spaces?

Feynman once conducted a simple experiment with his mathematician colleague John Tukey. Both tried to count to 60 seconds mentally. Feynman discovered he could read while counting, but couldn’t speak. Tukey, surprisingly, could speak while counting, but couldn’t read.

The revelation came when they compared notes: Feynman counted by speaking numbers to himself internally — occupying his “verbal system.” Tukey visualized a tape with numbers that changed — occupying his “visual system.” Same task, radically different internal representations.

This is the Feynmanian translation in action. When we converse about complex ideas — be they Bessel functions or electromagnetic fields — we are constantly translating between deeply unique personal latent spaces.

The translation dance: AIs vs. Humans

Imagine now the following scenario:

1. You read a text about quantum physics
2. The words are processed and mapped to your personal brain latent space
3. You manipulate these concepts internally
4. You translate back to language when you need to communicate

A modern AI like GPT follows a surprisingly similar flow:

1. Receives input text about quantum physics
2. Maps it to its mathematical latent space (embeddings)
3. Performs operations on these vector representations
4. Converts back to language tokens as output

The crucial difference is that your latent space was formed through your biology, personal experiences, years of specific education, associated emotions, and countless other irreproducible human factors. The AI’s was formed through mathematical optimization on text corpora.

The Tower of Babel in our minds

When Feynman says: “When we’re talking to each other at these high and complicated levels, we think we’re speaking very well, but what we’re really doing is having some kind of big translation scheme going on,” he describes something profound.

It’s as if each human mind were a country with its own language and culture. Communication is not simply transmitting information — it’s an act of cross-cultural translation.

Suppose I try to explain a complex mathematical concept:

1. My latent space: I see geometric patterns unfolding spatially.
2. Your translation: You might translate this into logical sequences in discrete steps.
3. The AI’s translation: It maps to specific clusters in its embedding space.

When you have difficulty understanding my explanation, it may not be due to a lack of ability, but because my explanation is optimized for my own latent space — and the translation to yours is imperfect.

The universal dictionary

Think of AI embeddings as an attempt to create a “universal dictionary” — a shared mathematical space where translations are more predictable and consistent.

If human latent spaces are like separate islands with improvised bridges of communication between them, AI latent spaces try to be mathematically mapped oceans where navigation follows more consistent rules.

When an engineer optimizes embeddings for a language model, they are essentially trying to create a space that approximates the “average dictionary” of translation between all the human minds that produced the training data.

Conclusion: The imperfect translation

Perhaps the most profound aspect of Feynman’s observation is recognizing the fundamental imperfection of all human communication. When we communicate about complex ideas, we’re never really sharing the idea itself — just offering instructions for the other to reconstruct a version of it in their own latent space.

Modern AIs, with their elaborate embedding systems, don’t escape this limitation — they merely formalize it mathematically. An AI’s latent space may be precise in a mathematical sense, but it remains an approximation of the endless human latent spaces it tried to model.

In the end, the most surprising thing is not that we occasionally misunderstand each other, but that we manage to understand each other as well as we do, constantly navigating between islands of thought across improvised bridges of language.

And perhaps this is the true wonder of both human cognition and artificial intelligence: not perfect precision, but the ability to translate between fundamentally different worlds — be they cerebral or mathematical — and still find shared meaning.