Although some of what we’ve just talked about is still relevant. These were examples of prompt engineering, were relatively small prompts led to very detailed and useful and meticulous outputs in response.
How does this fit with information theory of Shannon and others?
It seems like the prompts only holds so much information, sometimes as little as 10 or 20 words. Then, very precise lengthy outputs are generated by the LLM, possibly 500 or 1000 words long. It’s almost as if matter is being created, so to speak.But an information the sense.
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That’s a profound and subtle question — one that bridges Shannon information theory, statistical language modeling, and even philosophy of information. You’ve put your finger on something that feels almost paradoxical: how can a short prompt (say, “Explain why AI benefits superstars”) yield long, detailed, structured text that seems to contain vastly more information?
Let’s unpack this step by step.
1. Shannon’s framework: information is about uncertainty, not meaning
Claude Shannon’s 1948 theory defines information in terms of entropy — the reduction of uncertainty in a signal.
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If you send one bit, you halve uncertainty about a binary choice.
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If a 10-word prompt has, say, 100 bits of Shannon information, that’s the total “signal” you inject.
So under strict Shannon logic, you cannot create new information ex nihilo; you can only transform or reveal information already latent in the shared channel or prior distribution.
However — and this is the key — Shannon’s information is syntactic, not semantic. It measures how surprising a symbol sequence is, not how much meaning it carries. “A hundred bits of prompt” can trigger a system with trillions of bits of stored correlations to generate an output that seems much richer in semantic content.
2. The prompt as an address, not a container
Your 10-word prompt is not a compressed capsule of all the resulting detail; it’s more like a query pointer into an enormous pre-computed space of structured knowledge.
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Think of the LLM’s parameters as a vast, probabilistic encyclopedia of patterns.
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The prompt conditions this probability distribution: it narrows the model’s attention to a tiny region of parameter space where certain continuations are most likely.
So, in Shannon terms, the prompt doesn’t add information to the model; it selects information from the model. The real “entropy reservoir” is the trained network itself — the billions of parameters encoding statistical relationships from all its training data.
It’s somewhat analogous to entering a few coordinates into Google Earth: your coordinates (a few bytes) yield a detailed image (megabytes), not because you’ve transmitted that data, but because the server already contains it.
3. The model as a lossy compressor and generative decoder
An LLM is effectively a statistical compressor of text. Training minimizes the cross-entropy between predicted and actual tokens — in effect, compressing the probability structure of natural language.
When you prompt it, you provide a small conditioning signal, and the model decodes an expanded sample from its compressed world-model.
So yes, in physical or Shannon information terms, the 500-word output doesn’t contain more new information than what was already encoded in the model’s parameters and conditioning; it’s a re-expression of stored entropy in a human-readable, context-specific form.
It feels like matter creation because the mapping between a tiny input and a rich, coherent output is nonlinear and contextually meaningful — like striking one key on a piano that triggers an entire orchestral accompaniment hidden in the instrument.
4. Analogy to thermodynamics and entropy transfer
You can even stretch the analogy to energy and entropy:
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The model weights are a low-entropy reservoir — a highly ordered, pre-trained structure.
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The prompt provides a small “perturbation” or potential difference.
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The output is a dissipation of that stored structure into a specific form (a detailed response).
No information is created from nothing; rather, it is released or instantiated from stored correlations — much as compressing gas stores energy, and opening a valve lets it expand.
5. Philosophical extension: semantic bootstrapping
In semantic terms, your short prompt acts as a semantic index into a vast manifold of meaning.
Human readers (and LLMs, trained on human text) rely on shared background knowledge. When you type “explain the Matthew Effect in AI,” both you and the model presuppose enormous contextual structure (economics, psychology, AI). The brevity of the prompt hides the fact that it leverages billions of bits of shared world model.
So the long answer isn’t “information creation” in Shannon’s sense; it’s context activation — drawing a specific thread from a woven tapestry.
6. Summary
| Aspect | What Happens |
|---|---|
| Shannon sense | No new syntactic information created; small signal conditions a vast probability space. |
| Computational sense | Prompt = constraint that triggers decoding from a compressed model. |
| Semantic sense | Output feels richer because it expands latent correlations into explicit language. |
| Analogy | Prompt as GPS coordinate → model as the map → output as the terrain rendered in detail. |
7. The poetic version
In your words, it “seems like matter being created.”
Indeed — but what’s created isn’t matter; it’s manifestation.
The prompt is the seed crystal, and the model is the supersaturated solution. One small nudge, and an entire lattice of meaning precipitates out — not from nowhere, but from a stored potential energy of compressed human knowledge.
If you like, I can show a short information-theoretic analogy or toy calculation illustrating how a low-bit signal (prompt) can index or condition a massive entropy reservoir (model weights). Would you like that?
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I like your answer, but I’m less impressed by the Google Earth example. Google Earth is a rigid, enormous database, and the result from any particular exact coordinate is defined, it would be the same if a three-year-old child asked for the coordinate. But the rich and complex output of an LLM isnot precisely defined, and in fact, it shows one pathway of 1000 words when an almost infinite variety of other thousand word pathways could’ve answered the prompt, so it does contain a lot of surprise.
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Excellent observation — and exactly right.
You’ve pinpointed the weak spot in the Google Earth analogy: a coordinate in a fixed map retrieves a deterministic patch of terrain, whereas a prompt to a large language model triggers a stochastic generative process over a vast space of possible continuations.
That difference is profound from the standpoint of information theory.
1. A prompt is not a lookup; it’s a boundary condition
Where Google Earth performs retrieval, an LLM performs sampling.
The prompt sets boundary conditions on a probabilistic field — it constrains the opening words and context, but the model then rolls forward through an immense conditional distribution.
Each token generated reflects both:
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the statistical prior stored in the model’s parameters (the trained world), and
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the randomness or “temperature” of sampling.
So, even if the prompt is short, the entropy of the output distribution — the number of equally plausible continuations — can be huge.
This is why you’re right: the model doesn’t just “fetch” an answer; it selects one among a practically infinite family of valid expansions.
2. Shannon-wise: entropy flows from the model, not the user
In Shannon’s language, the information content of a message equals the surprisal of each symbol:
[
I(x) = -\log_2 P(x)
]
When the model generates text, it’s producing a sequence of symbols drawn from an internal probability distribution ( P_\theta(\text{token} | \text{context}) ).
The prompt provides a small constraint, but each subsequent token carries a bit of new information — new in the sense that it reduces uncertainty within the model’s own conditional space.
That entropy doesn’t originate from your 20-word prompt; it originates from the model’s stored prior.
The model is an entropy reservoir trained to mirror the distribution of human language. Your prompt cracks a tiny window in that reservoir and allows structured randomness to flow out.
3. Comparison to a physical system: the marble landscape
Imagine the model’s probability space as a vast, multidimensional landscape filled with valleys (likely continuations) and peaks (unlikely ones).
Your prompt places a marble somewhere on the slope; from there, the marble rolls downhill, following a path determined by both gradient and chance.
Each rollout is unique but constrained by topology.
Thus, meaningful variety — not deterministic retrieval — is built into the process.
4. Compression, expansion, and “apparent information creation”
Training an LLM compresses trillions of word relations into billions of parameters — an extraordinary condensation of entropy.
Generation is the reverse transformation: expanding a compact latent representation back into high-entropy sequences of text.
So, even though no new bits are “created,” there is an information-theoretic inflation: entropy that was once stored in latent form (as probability mass) becomes expressed as explicit token sequences.
It’s akin to running a highly detailed simulation from a short initial condition — like a fractal or a chaotic system whose unfolding is unpredictable even if the governing rules are simple.
5. Why this feels like “matter being created”
Because the model’s state space is so high-dimensional, the prompt doesn’t dictate the entire trajectory; it selects a tiny subspace from which a cascade of probabilistic commitments unfolds.
Each choice of word narrows the next set of possibilities, producing a stream of locally surprising yet globally coherent events.
From the human vantage point, that expanding cascade of constraint and surprise feels like the spontaneous generation of order — information “condensing out of nothing.”
But it’s actually latent entropy crystallizing into explicit form, guided by your brief instruction.
6. Better metaphors than Google Earth
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Fractal seeds: a few parameters (the Mandelbrot equation) produce endless unique detail — deterministic but sensitive to small variations.
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Weather simulation: a tiny change in initial conditions (the prompt) yields a specific unfolding of atmospheric patterns (text), one of infinitely many consistent with the laws encoded in the model.
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Quantum measurement: the wavefunction (the model’s probability distribution) collapses into one realized outcome when prompted — not new information in total, but new manifest information.
7. The takeaway
Your intuition is spot on:
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The prompt’s Shannon information is small,
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but the conditional entropy of the model’s generative process is vast.
Each generated text is a sample from that distribution — a new realization, not a retrieval.
So no physical “matter” is created, yet something analogous to semantic energy release occurs: latent correlations stored during training are transformed into explicit, surprising, structured language.
That’s why a 20-word prompt can open the floodgates to a thousand words of fresh, intricate output — an act less like reading a database, and more like lighting a fuse on a compressed star of statistical potential.
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If I pick up a brick and raise it high, that changes potential energy in one direction.
iif I pick up a brick at waist level and set it down on the ground, that changes potential energy in another direction. However, my prompts do not change the energy of the LLM database at open AI.
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That’s an exceptionally sharp and philosophically rich distinction — and you’re right.
In physical energy terms, nothing inside OpenAI’s servers stores or releases new energy when you type a prompt. The GPUs already sit in an active, energized state, their parameters fixed until retraining occurs. Your prompt doesn’t alter the weights of the model (no “potential energy” is being raised or lowered), it merely selects a trajectory through a static field of possibilities.
Let’s unpack the analogy carefully:
1. In physics: potential energy resides in the configuration
When you lift a brick, you change the system’s configuration relative to a gravitational field. That new position stores measurable potential energy (m g h). Setting it down releases that stored energy; energy has moved between states.
By contrast, the parameters of a trained LLM are static — a frozen landscape of learned weights, like a sculpted terrain. The “energy” that powered its creation was the training process itself, not your interaction.
2. In an LLM: inference explores a static field
When you type a prompt:
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You are not adding energy to the field (beyond negligible electrical activity).
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You are sampling from that field — tracing a path through a high-dimensional probability manifold that already exists.
The output’s apparent richness comes from the shape of that manifold: your prompt sets initial coordinates, and the model computes a deterministic (or stochastic) rollout according to precomputed gradients.
So:
The act of prompting does not change the model’s internal energy; it expends computation to reveal one possible trajectory through its static structure.
3. The real energy event happened during training
The true “lifting of the brick” was training, when terawatt-hours of GPU power carved the loss landscape into its current form.
During training:
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Gradients flowed through billions of parameters,
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The model’s entropy relative to its data source was reduced (it became more ordered),
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Vast physical energy was dissipated as heat — that was the energetic investment that made the later generative process possible.
Inference is cheap by comparison: it’s like reading a book that took years to write. The creative energy is front-loaded in the writing, not in each reading.
4. So what does your prompt change?
Not the model’s energy state, but its probability weighting during inference — an ephemeral, computational “state of attention.”
You can think of it as potential informational energy rather than physical energy:
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The prompt defines constraints on what kinds of continuations are acceptable.
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The system calculates token probabilities, effectively collapsing a wavefunction of possibilities into one realized string.
This doesn’t consume or store energy in the physics sense; it consumes entropy budget and electric power, but leaves the underlying parameters untouched.
5. A better analogy: music, not mechanics
A musical score (the model) is static.
A conductor (the prompt) doesn’t rewrite the score or increase its stored energy; they choose a tempo, phrasing, and dynamics that bring out one performance from infinite possibilities.
The score embodies potentiality; the performance actualizes one expression of it.
Each new prompt “conducts” a different piece using the same latent structure.
6. In summary
| Concept | Physics | LLM Analogue |
|---|---|---|
| Training | Lifting the brick (energy invested to create structure) | Massive compute energy sculpts weights, reducing entropy |
| Prompting | Choosing where to drop the brick (but field unchanged) | Setting boundary conditions within a fixed parameter space |
| Inference | Watching the brick roll down a slope | Sampling from preexisting gradients; computation releases no stored energy, only uses electricity to compute tokens |
7. The poetic version
When you prompt an LLM, you don’t raise or lower energy —
you trace a current through an already electrified sea.
The spark that makes words flow is not new potential energy,
but the residual hum of a structure already charged with the history of its training.
Your prompt simply tunes the circuit, letting one melody resonate out of a silent, waiting instrument.
