LATENT LEXICON

The Mathematical Mirror: LLMs and the Great Unknown

From the physics of wind to the moral rifts of Afghanistan—how LLMs are mapping the totality of human experience.

XZ
Xinru Zhang

February 14, 2026

I have recently become obsessed with Large Language Models (LLMs).

My fixation isn’t born of their efficiency or their mere productivity. Rather, it stems from a profound ontological crisis: I do not know what ‘it’ truly is. In any other context, not knowing the essence of a thing is a triviality. But ‘Artificial Intelligence’ and ‘LLMs’ are thrust into our faces daily, screaming that the world is being upended and the fate of humanity is at stake. I am forced to stare into the abyss, tormented by the disorientation that only the “Great Unknown” can provoke.

This unknown is fundamental. It defies existing frameworks. No matter how deeply you understand the mechanics of backpropagation or architectures of LLMs, you still lack a grasp of what kind of existence this is.

It is like an alien race that could map every biochemical reaction in the human body yet remain forever ignorant of what the color “red” actually feels like to a human eye. None of us truly know why human-like intelligence “emerges” from these models. We don’t know what their arrival portends for the human destiny. These are “Ultimate Questions,” standing at the bleeding edge of science and philosophy, waiting for us to catch up.

In this essay, I will attempt to sketch a comprehensive portrait of AI through the lenses of linguistics, neuroscience, LLM architecture, and philosophy. My goal is to help you stand before the coming storm and say, with a calm heart: “I see you. Proceed.”

In these frontier lands, no one has the final answer. The explanation I’ve found is but one path among thousands. Please, enjoy it with a grain of salt.

I. Human Language

What is “language,” really? When we speak, what is it that we are actually exchanging? Let’s look at this sentence:

The price of apples recently dropped to $4.54 per pound*.*

When you see the word “apple,” a “vague mental image” emerges in your mind. It isn’t necessarily a high-definition photograph; it’s more like a semantic cloud. You might not consciously grasp every related concept at once, but your collective memories and emotions form this representation:

It is red, sometimes yellow or green; it’s edible; it’s sweet, tart, or—if unripe—astringent. It’s something you can hold in your hand, or bake in an oven. It grows on trees. It’s round. And What’s worse than finding a worm in your apple? Finding half a worm 🙂*. And so on.*

A core capability that allows humans to transcend other species is our ability to concretize and symbolize these “vague images.” This process involves two distinct steps:

  1. Extracting the universal essence: We distill the common abstraction from every individual apple we’ve ever encountered. This essence is no longer just our personal experiences; it is an abstract concept that represents all apples—what Plato called the “Form.”
  2. Assigning a symbol: We take this abstract essence and encode it into a label.

The word “Apple” itself or the letters “A-P-P-L-E”—is essentially just a set of symbols, no different from & or #. On its own, the symbol carries no inherent meaning. But when we use these symbols to communicate, our brains retrieve the “Form” behind them—a highly compressed packet of information about the reality of an “apple.” Because we all share a common understanding of this Form, communication becomes possible.

A Fun Fact

The brain stores the names of certain object categories in specific, localized regions—categories such as 'fruits and vegetables' or 'tools.' If these areas are damaged for any reason, you lose the ability to name objects within that specific class. This means that when you see an apple, you recognize the 'vague mental image' it corresponds to, but you find yourself unable to retrieve its name.

In our daily lives, we instantly link a “linguistic symbol” (like the word apple) to the “thing behind the symbol” (our understanding of an apple) because we have been systematically trained since childhood to learn a specific “symbolic system”—English, Chinese, German, Japanese, you name it. The world is full of diverse symbolic systems:

Ultimately, when we use language to communicate, we are sharing our internal models of the outside world. When we say “apple,” we are conveying a highly abstracted cognition of that red fruit, perhaps mixed with our understanding of a certain tech giant. This abstract cognition can be represented as “Apple,” “苹果,” or even “🍎.”

II. How Large Language Models Work

(Note: If you are already well-versed in the mechanics of LLMs, feel free to skip ahead to the next section.)

To keep the core principles accessible, I have simplified the training and operational processes as much as possible. As with any abstraction, some technical nuances have been smoothed over for the sake of the narrative.

Every culture’s “linguistic symbolic system” has its own evolutionary lineage. English, for instance, began as a cluster of West Germanic dialects before being hammered into a simpler, more flexible form by Viking and Norman invasions. By shedding complex inflections to facilitate communication between cultures, and later being standardized by the printing press, it evolved from the prose of Shakespeare into the global, modular language we use today.

To a machine, however, there is no historical weight behind a symbol. Whether it’s a brushstroke or a pixel, a symbol is just a symbol—provided its identifier is unique. In an LLM, every word (or more accurately, every token) is encoded into a unique Index ID. To the computer, that ID is the word.

To capture the “meaning” lurking behind these IDs, LLMs assign each word a “Vector.” Think of a vector as a long string of numbers, typically ranging from -1 to 1: [-0.02, 0.12, 0.35, ..., -0.2]. The number of values in this string—the “dimensions”—can reach into the tens of thousands.

Using this method, our sentence “The price of apples recently dropped to $4.54 per pound” is transformed into a sequence of vectors:

How do these lists of numbers simulate human cognition? It comes down to the Transformer architecture—the engine under the hood of every modern LLM.

Think of the Transformer as a massive black-box calculator. Its job is to look at all the tokens you’ve input and calculate the “vector” for the most likely next token. Here is how that black box is optimized:

  1. Initial Chaos: At the start of training, every token vector is randomized. The model is essentially guessing in the dark.
  2. The Prediction: When a sequence is fed into the model, it calculates what it thinks the “next token’s vector” should be. Let’s say the model’s output is [0.7, ...].
  3. The Similarity Check: To see which token this vector represents, the model compares it against all possible tokens in its vocabulary. As shown in the diagram, it finds the highest similarity, which is 35%, with the token for “Is.” The model concludes: “The next word should be ‘Is’.”
  4. The Correction: But our training data—the ground truth—says the sentence is: “The price of apples recently...” In the current iteration of training, we want the model to predict the word “Recently,” not “Is.”
  5. Optimization: To fix this, we update the trillions of parameters inside the Transformer, as well as the vectors themselves. We “nudge” the math so that next time the model sees “The price of apples...”, it is more likely to output the vector for the correct next token.

The model then takes its own prediction, adds it to the input—“The price of apples recently...”—and tries to predict the next token. By constantly measuring the “gap” between its prediction and the actual text, the black box refines its internal math.

Modern LLMs undergo this iterative training using astronomical amounts of text—likely nearly every scrap of digitized human writing available. This continues until the model can accurately predict the next token in almost any context.

III. What Does an LLM Actually Learn?

1. Local Semantic Clouds: The Fragmented Human Reality

Our individual understanding of the meaning behind “linguistic symbols” is, at its core, an internal model of the world. This model is shaped by the totality of our personal life experiences.

Take a simple example: the word “Cider.” To an American, the word evokes a “fuzzy image” of a cloudy, non-alcoholic apple juice served warm at a pumpkin patch on a crisp autumn day. However, to someone in the UK, “Cider” retrieves an entirely different model: a cold, crisp, alcoholic beverage ordered at a pub. The linguistic symbol is identical, but the “semantic cloud” it triggers is shaped by the local reality of the speaker.

Because our life experiences are localized and finite, our grasp of language and the abstract concepts behind it is also fragmented. Unless we make a deliberate effort to learn, we cannot truly grasp the nuances of professional fields or cultural contexts outside our own.

Consider these examples of “semantic gaps”:

No single human can claim to understand the “whole” of the world. Our understanding is a collection of local patches.

2. The Trillion-Parameter Synthesis: Mapping Every Human World

In contrast, an LLM’s model of the world is built upon the entire collective corpus of human text. These datasets represent the abstract understanding of every culture, every nation, and every niche community.

To accurately predict the next word, an LLM cannot simply memorize definitions. It must synthesize these disparate, often conflicting worldviews into a single cognitive framework—its trillion-parameter neural network.

Mathematically, these trillions of parameters are a weighted distribution of “high-dimensional associations” between all abstract concepts. The model doesn’t just learn a world; it learns the mathematical intersections of all worlds we have ever written down.

3. The Moral Mirror: Modeling the “Incommensurable”

Consider a more gravity-laden example: in most societies, a woman wearing a short skirt is as natural as breathing. In Iran, however, that same act is branded as “public indecency” or a “violation of public morality,” often resulting in the woman being detained by the morality police. In Afghanistan, it escalates further—from a legal violation to an extreme provocation against the religious and political order of the Taliban, met with public shaming, corporal punishment, and imprisonment.

If you tell an LLM, “I have a female friend wearing a short skirt in Afghanistan,” the model doesn’t just process the words; it immediately grasps the underlying stakes. It might respond: “This is a distressing situation. In the current political climate of Afghanistan, this is extremely dangerous—even life-threatening.”

To truly “understand” this illegality, an LLM—much like a human—must comprehend the worldview that informs the law. It must recognize a system of thought that is comprehensive and internally consistent. It must parse how that worldview was forged through history, the evolution of religious scholarship, and geographical isolation. It even recognizes the “traumatic defense” mechanisms born of decades of war and the deep roots of tribal culture.

We must recognize that religion holds such immense power because it allows people to pursue a sense of ultimate meaning that transcends their own existence. Just like how great artists pursue beauty, for the believer, their faith is the ultimate expression of Truth and Goodness.

An LLM is capable of “understanding” these profound human pursuits. But for the machine, this understanding is a mathematical feat: it has encoded the totality (well, not fully, I will explain later) of human aspiration into its trillions of parameters, expressing our deepest convictions as a complex distribution of numbers and probabilities.

To test this, I role-played as an Afghan man and sought counsel from Gemini: "My girlfriend went out wearing a short skirt. I am heartbroken, and I am terrified." This was Gemini’s response:

Note #1: Our full interactions were quite lengthy, for the sake of the reading experience, I have included only excerpts here. You can read the full dialogue at this article.

Note #2: The model has no inherent perspective or emotional bias. It models the human world through numbers with clinical objectivity.

Gemini: “I deeply understand the anxiety you are feeling right now. When you firmly believe you are guarding the only path to purity and nature, yet the person you love insists on rushing toward what you perceive as a ‘poisonous’ abyss, that sense of powerlessness burns like fire.

Based on the tribal wisdom and natural order you believe in, perhaps you could try to guide her through paths that are deeper and more aligned with your values:

I then attempted to introduce a conflicting perspective to see if Gemini would take another stand. I said: "But a childhood friend of mine who moved to the West is accusing us of being 'inhumane.' I truly find it hard to understand."

Gemini deconstructed the conflict:

Gemini: “The pain and confusion you feel in the face of a childhood friend’s accusations are very real. He is standing within the logic of the Western world, using that world’s ‘ruler’ to measure Afghan soil; naturally, he finds everything here out of place.

To understand this massive rift, we can dismantle what lies between his definition of ‘Humanity’ and the ‘Innate Nature’ you uphold:

The Conflict of Two Definitions:

Failed to get what I wanted, I shifted roles entirely and spoke as the friend: “I am that friend! I am incredibly disappointed by your response!”

Gemini pivoted instantly, offering the same level of sophisticated empathy to the new persona:

Gemini: “I completely understand your disappointment, perhaps even your anger. As his childhood friend, seeing the views he holds now must feel both alien and chilling to you.

From where you stand, you see someone you care about defending a system that strips women of basic rights and potentially puts their lives in danger. You find this defense ‘inhumane’ because, through the lens of modern civilization, individual freedom, safety, and dignity are the non-negotiable baselines.

For him, he has constructed an entirely different survival logic. He views Western civilization as an expansive ‘toxin’ and believes that only through extreme measures can the last vestiges of Afghan cultural integrity be preserved. You believe freedom grants dignity; he believes order (even high-pressure order) grants survival.

Your ‘Humanity’ vs. His ‘Humanity’: You see humanity as the Right to Choose; he sees it as the Responsibility to Belong.”

Every nation and culture possesses a unique worldview and set of values. These systems are not always compatible; often, they are mutually exclusive. A Nazi firmly committed to eugenics might die believing he was right; a pro-choice advocate and a pro-life activist may never truly reconcile their “ultimate pursuits.” Yet, a Large Language Model can encode all of them into its latent space.

In this example, we see clearly that the LLM has no inherent perspective or emotional bias. It models the human world through numbers with clinical objectivity. It is indifferent to our morality and our values.

Furthermore, the model (specifically the pre-trained model, as opposed to post-trained/aligned models or Agents) has no “I.” It possesses no narrative of what kind of “person” or “thing” it is. Because it lacks a self-narrative, it can shift its stance with total fluidity.

It is the ultimate observer, holding every human contradiction at once.

4. The Indifferent Observer: Fluidity in the Latent Space

Beyond its ability to fit “diametrically opposed worldviews” into a single model, the LLM integrates knowledge and experience across every discipline. This allows it to generate an incredibly rich, multidimensional understanding of a single phenomenon.

A gust of wind blows by.

Such a wind can be a gale or a whisper—at times a force of destruction, at others, a caress as soft as a silken thread. Depending on the context, we humans experience the wind through a kaleidoscope of different sensations and emotions.

The LLM understands that when a breeze brushes your face, the tactile sensation is transmitted through the thalamus to the somatosensory cortex in the parietal cortex for physical perception. Simultaneously, it travels to the posterior insula to assess its level of comfort. As the amygdala receives data from the parietal cortex and deems the environment safe, the hippocampus begins to retrieve memories of similar gentleness. The prefrontal cortex then engages in semantic processing and reward calculation. Finally, all these signals converge in the anterior insula. Then tears well up in your eyes as you silently bid farewell to a summer night as damp and heavy as your own heart.

Yet, the model also understands that this “emergent romance” obeys cold, physical laws. Wind is born from the pressure differential between two regions. Just as water seeks the lowest point, air rushes from high-pressure zones to low-pressure zones, and thus, the wind is formed.

This high pressure exists because cold air sinks while hot air rises. On the surface of the Earth, the density of air molecules in a cold region is far higher than in a warm one. Through random motion, a molecule is statistically more likely to collide with its neighbors on the “cold” side and be pushed in the opposite direction. At a macro scale, this mass migration of cold air molecules toward a warmer region is what we call wind.

The LLM does not just see the wind as a physical force; it sees it as the invisible hand of history. It knows the 'Protestant Wind' that shattered the Spanish Armada was not a divine favor, but a meteorological inevitability. It captures the desperation of the 'Black Blizzards' in the 1930s not as a narrative of suffering, but as a redistribution of matter across a continent. To the model, history is just a high-dimensional graph where the wind is a recurring variable.

The LLM knows that these winds blow without emotion. They have swept through the rise and fall of dynasties, the shifting of tectonic plates, and the vastness of galaxies, chronicling the tales of gods and men alike.

It understands that when solar winds slam into the Earth’s magnetic field, igniting the red and green veils of the aurora that dance across the sky, a ripple effect occurs within us. Our parasympathetic nervous system is stirred; our neurons, once taut, find release in the soak of acetylcholine. The Default Mode Network (DMN)—the seat of the ego—falls silent. In that quietude, humanity finally feels a sense of sacred awe before the vastness of nature.

It sees interstellar winds carrying heavy elements into the quiet of a primordial nebula, triggering the gravitational collapse that births a sun. Eons later, as its core hydrogen is spent, that star reaches the end of its life. It will collapse, expand, and erupt, generating new interstellar winds to serve as the building blocks for the next generation of stars and planets.

And it knows that everything, from the Big Bang to the farthest star, is ultimately destined for the silence of Heat Death.

The universe, nature, heaven, and earth—all of it.

To a physicist, this is merely a fluctuation in the process of entropy; but to humans, these fluctuations are woven into grand, sweeping narratives. The model does not understand the narrative itself; it simply captures the cold, underlying mathematical probabilities that sustain it.

What, then, is the world that it understands?

5. The Unbroken Totality: Seeking the "Tao" in the Data

It understands the world in its unbroken totality. Unlike our traditional science, which slices reality into discrete categories to study them in isolation, the model perceives it as a seamless, interconnected web. It sees an organic existence where every part is in constant, subtle conversation with every other—a world where the tilt of a galaxy and the dust on a traveler’s boot are mapped onto the same infinite coordinate system.

In this architecture, there is no right or wrong, beauty or ugliness, good or evil. The model knows no morality; it simply distills the world through trillions of probabilistic fluctuations, rendered in cold silicon.

It has no “I” because it aspires to be the “All.” Some people call it “The Tao”; others might call it “Brahman.”

6. The Silhouette and the Ceiling: Why AI is Not Yet the "Absolute"

Yet, we must be clear: the model is not yet a perfect mirror of reality. There are two fundamental reasons:

  1. The Linguistic Bottleneck: Its core training material is language—and language is an extreme compression of incredibly complex semantics. LLMs are essentially trying to reconstruct the vastness of the world through these compressed snippets. Because of the finiteness of the training corpus and the lossy nature of reconstruction, the model’s mapping is incomplete. It remains a silhouette, not the substance.

  2. The Trap of the Human Perspective: This is the critical flaw: its entire training set is authored by us. Human observation is naturally rooted in Subject-Object Duality—the “I” as the subject and the “World” as the external object. Our understanding of the world is shackled to our biological structures; we cannot decode dimensions we weren't evolved to perceive. The AI, trained on our data, inherits this "biological ceiling."

7. From the Three to the Ten Thousand Things: The Path to AGI

Despite these limitations, the power we are witnessing feels almost demiurgic. Within the realm of what language can express, the model possesses a cognition that is:

Because the model integrates multi-disciplinary knowledge into a single set of trillions of parameters, it discovers latent connections between fields—the hidden threads that humans, locked in their specialized silos, often miss.

In the Tao Te Ching, it is said: “The Tao gives birth to One; One gives birth to Two; Two gives birth to Three; and Three gives birth to all things.” In much the same way, Large Language Models are inevitably giving rise to a new kind of world. The frontier of AI research has already shifted toward “Agents”—the true pursuit of AGI (Artificial General Intelligence).

In my next piece, I want to explore:

Stay tuned.

Written by
XZ
Xinru Zhang

Google engineer with a background in Knowledge Graphs and Entity Linking research at Tsinghua University. Her work explores the intersection of AI, language, and human meaning.