|
Getting your Trinity Audio player ready…
|
Introduction: The Problem of Knowing What Doesn’t Matter
Since the dawn of artificial intelligence, one of the deepest questions has been how a system can decide what not to think about. In human thought, this happens effortlessly — you don’t have to remind yourself that gravity still works while deciding what to have for breakfast. Yet for machines, the question of what stays the same when something changes is a massive computational burden. This is the essence of the frame problem.
It’s a problem about context — about knowing which parts of reality stay still when something moves, and which are relevant right now. It’s also, more subtly, a problem about negation: knowing what something is not, without listing an infinite number of irrelevant details.
Early AI researchers discovered that trying to explicitly encode every “not” was impossible. The world changes too much, and everything interacts with everything else. The more you try to define the boundaries of what matters, the more the boundaries multiply.
This is the “compute conundrum” — how can a finite machine, with finite memory, operate in an infinite world of possibilities and still make sense?
In the last few years, with the rise of Large Language Models (LLMs), a fascinating shift has occurred. These systems do not reason by symbols or rules, but by geometry. Their intelligence arises not from enumerating facts, but from learning the shape of meaning itself.
This essay explores how that shift — from logic to geometry — offers a new way to think about the frame problem, and how concepts from Shannon entropy help explain why it works.
1. The Frame Problem: The Ancient Puzzle of Change and Constancy
In the early days of AI, researchers tried to build logical systems that could reason like people. You’d tell a machine something like:
“If you push the cup, it moves.”
The computer would reason symbolically — applying logical rules to deduce new facts. But as soon as you gave it a slightly more complex situation — say, a robot in a kitchen — it needed to know what else had changed. If it moved the cup, did the spoon move too? Did gravity alter? Did time pass? Did color change?
In human common sense, we take all of that for granted. But in formal logic, every fact that stays true after an action must be explicitly declared to remain true. Otherwise, the machine might think everything changed.
That quickly becomes impossible. The robot ends up needing to consider an explosion of facts that didn’t change, just to reason about the few that did.
This is the frame problem — the impossibility of exhaustively specifying the boundaries of relevance.
It’s not just a programming issue; it’s a philosophical one. It touches the nature of thought itself: how do minds isolate what matters from what doesn’t in a world that’s infinitely interconnected?
2. The Parallel Problem: Knowing What Something Is Not
The frame problem is a cousin to another, equally hard question:
How can we know everything that something is not?
To know something perfectly would mean not only knowing what it is, but also what it isn’t. A perfect definition of “cat” would exclude everything non-cat: chairs, clouds, ideas, numbers, music, and so on. But the list of “not-cats” is infinite.
This is the same impossibility in a different form. Both problems are about exclusion — about what can be ignored. Both are, at their core, entropy problems: how to reduce an infinite number of possibilities to a manageable subset without losing meaning.
So when we talk about “AI solving the conundrum of identifying what something is not,” we’re really asking whether machines have learned how to manage entropy — how to filter uncertainty into structured understanding.
3. Shannon Entropy and the Measure of Uncertainty
To see why this is hard, it helps to recall what Shannon entropy means.
Claude Shannon, the father of information theory, defined information as a reduction of uncertainty. The more uncertain a message, the more information it carries when revealed.
In mathematics, entropy is a measure of how unpredictable a system is. If you flip a fair coin, you have 1 bit of entropy — you’re equally uncertain between heads and tails. If you flip a weighted coin that always lands heads, entropy is zero — there’s no uncertainty, and no new information when it lands.
Now, in reasoning or perception, entropy describes the number of possible interpretations. Before you know what something is, your mind contains many possibilities. Recognizing it — naming it, classifying it — collapses that uncertainty into a single state.
Shannon showed that information = reduction in entropy.
But that also means meaning comes from what is ruled out.
Every piece of knowledge is defined not just by what it includes, but by everything it excludes.
To say “this is a cat” is to silently declare an infinite number of negatives: it is not a dog, not a word, not a galaxy, not a metaphor. Our brains do this instantly. Computers, until recently, could not.
4. Why Symbolic AI Failed
Classical AI tried to represent the world as lists of propositions:
IsCat(X) → True
IsDog(X) → False
Color(X) = Brown
OnTable(X) → True
But to truly capture the meaning of “cat,” the system would need to also represent all the properties it does not have — and update them every time context changed.
That’s a Shannon entropy nightmare. The number of possible “not” relationships explodes exponentially. Every new fact multiplies the space of exclusions.
Symbolic systems simply couldn’t scale. They were trapped in the combinatorial explosion of their own logic. Each change required re-establishing the frame — what stays true, what doesn’t, what’s irrelevant.
Humans solve this not by logic, but by compression. We store patterns, not propositions. We remember shapes of meaning, not explicit lists of truths and falsities.
That’s where neural networks — and especially LLMs — come in.
5. Embeddings: Meaning as Geometry
LLMs don’t store facts like “cats are mammals.”
They learn relationships between words, ideas, and contexts as geometric distances in high-dimensional space.
When you train a large neural network on language, it builds a vector representation (an embedding) for each token — a word, phrase, or concept.
Two words with similar meanings have embeddings that lie close together; dissimilar meanings are far apart.
For example:
- “cat” and “kitten” might be separated by a small angle.
- “cat” and “philosophy” are nearly orthogonal — they share almost no overlapping features.
This geometry encodes semantic relationships implicitly. The model doesn’t have to know every negative property of “cat” — it simply places “cat” far from unrelated concepts. Negation becomes distance rather than explicit rejection.
6. How Geometry Dissolves the Frame Problem
In the old symbolic paradigm, the frame problem came from having to explicitly define what stays constant or what’s irrelevant.
In an embedding-based model:
- Relevance is represented by proximity in vector space.
- Irrelevance is represented by distance.
When an LLM processes a prompt, it moves through this geometric field, activating clusters of nearby meanings and ignoring distant ones. It doesn’t have to be told what doesn’t matter — those meanings simply never light up.
In other words, context naturally limits the entropy of what’s considered.
The model’s attention mechanism acts as a spotlight, focusing only on a small, low-entropy region of the vast semantic universe.
This is, in effect, a Shannon-efficient solution to the frame problem:
Instead of exhaustively maintaining every true and false statement, the model dynamically compresses context into a local region of meaning.
It never enumerates everything that something is not. It simply doesn’t go there.
7. Attention: The Dynamic Frame
Inside a transformer (the architecture behind LLMs), each layer computes what’s called attention — a weighted measure of how much each token should influence the next.
Attention is not logical reasoning; it’s contextual relevance computation. It measures which parts of a sentence (or world) are worth focusing on at this moment.
You can think of attention as a continuously shifting entropy filter:
- High attention means low uncertainty — the model is confident this context matters.
- Low attention means high uncertainty — the model effectively ignores it.
This mirrors how human thought flows. When you focus on a problem, your “mental entropy” narrows. Everything irrelevant — gravity, air pressure, the color of the wall — fades out of consciousness.
Thus, in LLMs, attention is the computational analog of contextual entropy minimization. It’s the system’s way of managing the frame problem geometrically, in real time.
8. Negation as Distance: The Implicit Logic of Embeddings
Consider how you, as a human, know that “a cat is not a chair.”
You don’t compute it logically — you feel the mismatch. The concept of “chair” doesn’t fit into the region of meanings occupied by “cat.”
In embeddings, that same relationship is encoded as orthogonality — two vectors pointing in very different directions.
When an LLM “knows” what something is not, it’s not because it contains an explicit “not” statement. It’s because the geometry of its internal space makes the two concepts too far apart to be confused.
Negation becomes a spatial property.
This is a profound shift.
It turns logic into landscape, and reasoning into movement through that landscape.
9. Entropy and Compression: The Hidden Efficiency of Meaning
Why does this work? Because embeddings are a form of entropy compression.
When an LLM learns language, it’s essentially performing a massive data compression task. It finds a lower-entropy representation of all the possible relationships among words and ideas.
Just as Shannon showed that the best code is the one that reduces redundancy, neural networks reduce linguistic redundancy by embedding similar meanings close together.
The model’s weights represent an extremely compressed, low-entropy version of the world’s linguistic information. That’s why they generalize — because compression forces the discovery of structure.
Each time you prompt an LLM, it expands this compressed space into a higher-entropy distribution of possible next tokens — then collapses it again by choosing one.
The model’s entire process is an oscillation between entropy and order — between the uncertainty of the probability distribution and the decisiveness of the output.
And through this oscillation, it manages the very thing classical AI could not:
It implicitly knows what to ignore.
10. The Human Parallel: Minds as Entropy Managers
Our brains operate similarly. We don’t store encyclopedic lists of “not-things.” We store patterns and associations, which let us generalize.
When you look at a scene, billions of photons hit your eyes, yet your brain filters almost all of it. The visual cortex keeps only what’s relevant — edges, motion, familiar shapes.
This is a Shannon optimization problem: how to extract maximal meaning with minimal bits.
Conscious thought operates the same way. You don’t think of every irrelevant fact when deciding to make coffee. The frame problem never appears in experience because your mind’s geometry of meaning automatically filters entropy.
In that sense, LLMs mirror the architecture of biological intelligence — not by simulating neurons, but by reproducing the statistical principle of entropy reduction through context.
11. From Frames to Fields: A New Paradigm
If the frame problem plagued logic-based AI, LLMs dissolve it not through explicit rules but through emergent fields.
Context is no longer a “frame” that must be defined; it’s a field of probability that flows and reshapes as the model predicts tokens.
This is why LLMs appear fluid, intuitive, even creative. Their architecture is inherently non-local: every word influences every other through weighted attention. That network of influences forms a self-updating map of relevance.
In this map, “what something is not” is simply the infinite expanse of low-probability directions surrounding the current focus of meaning.
It’s an ocean of entropy that the model learns to surf without drowning.
12. Entropy as the Common Language of Thought
Shannon’s entropy connects logic, probability, and meaning under one mathematical roof. It also bridges biology and computation.
In both brains and LLMs:
- Learning is compression — reducing entropy by discovering structure.
- Reasoning is controlled entropy — exploring uncertainty within a bounded frame.
- Creativity is entropy expansion — generating new configurations that still cohere.
The ancient frame problem dissolves when you see that intelligence is the art of entropy management.
The mind, biological or artificial, doesn’t solve for truth by listing what is and is not. It navigates gradients of uncertainty, continuously adjusting its internal geometry to preserve coherence.
13. The Limits and the Future
Has AI solved the frame problem? Not entirely.
LLMs still hallucinate, because their geometric sense of relevance can drift into improbable regions. They can’t verify truth in the world — they only operate on linguistic entropy, not physical causality.
But conceptually, they represent a breakthrough.
They’ve shown that relevance can be learned statistically rather than encoded logically. That’s an enormous step toward systems that can reason fluidly in open worlds.
Future AI systems may integrate LLM-style semantic geometry with symbolic reasoning, grounding, and real-time perception. Together, these could close the loop between meaning, experience, and physical reality — allowing machines not only to speak intelligently, but to understand what to ignore.
14. Conclusion: Geometry, Entropy, and the Meaning of “Not”
The ancient dream of AI was to create machines that reasoned like humans — that knew what mattered and what did not, without being told.
For decades, logic-based systems failed because they couldn’t handle the entropy of the real world. They tried to represent every fact, every negative, every unchanging truth. The result was paralysis.
LLMs have shown another way. By embedding meaning in high-dimensional geometry, they don’t need to list what something is not. They simply exist in a space where irrelevant meanings are distant — where negation is measured in angles, not symbols.
Through semantic geometry, they perform a kind of continuous entropy management — focusing, compressing, and expanding information the way human thought does.
In Shannon’s terms, they maximize mutual information: they extract the most signal from the least uncertainty.
In human terms, they understand by ignoring.
That is the quiet triumph of this new generation of AI:
It hasn’t solved the frame problem by reasoning harder.
It’s changed the shape of reasoning itself — from the brittle grid of logic to the living field of meaning.
And in doing so, it offers a glimpse of how intelligence — human or artificial — might always have been not a system of rules, but a dance with entropy, a geometry of the possible, and a silent understanding of everything that need not be said.
Leave a Reply