The Mechanics of a Large Language Model

The Evolution of Scientific Paradigms

timeline
    title The Evolution of Paradigms: From Solving to Running
    section Antiquity
        Aristotle & Logic : Formalized Rhetoric
        Method : Structural Logic
        Goal : "Is this argument valid?"
        Constraint : Limited to human thought patterns.
    section 1600s - 1900s
        Newton & Mathematics : Calculus & Formulas
        Method : "Solving" Equations
        Assumption : We can find a formula to predict the future (Shortcuts).
        Success : Physics & Engineering (Clockwork Universe).
        Failure : Biology & Society (Too complex for formulas).
    section 1980s - Present
        Wolfram & Computation : Simple Rules & Programs
        Method : "Running" Programs
        Discovery : Simple rules create infinite complexity (Cellular Automata).
        Key Insight : Computational Irreducibility (No shortcuts; must run to know).
        Shift : From "Engineering what we know" to "Mining what exists."

How LLMs (like ChatGPT) Actually Work

graph TD
    subgraph "Input Processing"
    A[Input Text: 'The cat sat on the...'] -->|Tokenization| B(Sequence of Numbers)
    end

    B --> C{The Neural Network}

    subgraph "The 'Black Box' (Training Phase)"
    D[Reads the Entire Internet] -->|Observation| E[Discovering 'Semantic Grammar']
    E -->|Insight| F[Human language has underlying structural rules]
    F -->|Result| G[180 Billion+ Weights Adjusted]
    end

    G -.-> C

    subgraph "Inference Phase (The 'Thinking')"
    C -->|Simple Math Operations| H[Processing Layers]
    H -->|Repeated Billions of Times| H
    H -->|Outcome| I[Probability Distribution]
    end

    I --> J{Next Word Selection}
    J -->|Highest Probability| K["'Mat' (99%)"]
    J -->|Lower Probability| L["'Floor' (0.5%)"]

    K --> M[Output: '...Mat']

    style E fill:#ff9,stroke:#333,stroke-width:2px
    style I fill:#bbf,stroke:#333,stroke-width:2px

The Principle of Computational Equivalence

graph TB
    subgraph "The Hierarchy of Computation"
    direction TB
    C1["Simple Mechanisms
(Light switch, clock)"]
    C2["Sophisticated Computation
(Human Brain, AI, Weather, Rule 30)"]

    C1 -->|Can be predicted/out-computed| C2
    end

    subgraph "The Principle of Computational Equivalence"
    direction TB
    Human[Human Brain]
    AI[Artificial Intelligence]
    Nature[Nature / Physics]

    Human <-->|Equally Sophisticated| AI
    AI <-->|Equally Sophisticated| Nature
    Nature <-->|Equally Sophisticated| Human
    end

    subgraph "The Consequence: Computational Irreducibility"
    direction TB
    Predict[Observer trying to predict the outcome]
    System[The System Running]

    Predict -.-x|Cannot Jump Ahead| Result[Future State]
    System -->|Must run step-by-step| Result

    Note[Insight: We can't predict the AI or Weather
because we aren't smarter than them.
We are equivalent to them.]
    end

    style C2 fill:#ff9,stroke:#333,stroke-width:2px
    style Note fill:#f9f,stroke:#333,stroke-dasharray: 5 5

The Future of Work & Computational Thinking

flowchart TD
    subgraph "The Shift in Human Value"
    direction TB

    Goal[Human Volition / The 'Why']

    subgraph "The 'How' (Mechanism)"
    Coding[Writing Code / Syntax]
    Calc[Calculating / Processing]
    Translation[Translating thoughts to machine code]
    end

    Result[Final Output]

    Goal -->|Previously required| Coding
    Coding --> Result

    Goal -.->|The New Paradigm| Result

    end

    subgraph "The Role of AI"
    AI[AI & Computational Language]

    AI -->|Automates| Coding
    AI -->|Automates| Calc
    AI -->|Automates| Translation

    Goal -->|Input: Computational Thinking| AI
    AI -->|Output: Execution| Result
    end

    style Goal fill:#ff9,stroke:#333,stroke-width:4px
    style AI fill:#bbf,stroke:#333,stroke-width:2px
    style Coding fill:#ddd,stroke:#999,stroke-dasharray: 5 5
    style Calc fill:#ddd,stroke:#999,stroke-dasharray: 5 5
    style Translation fill:#ddd,stroke:#999,stroke-dasharray: 5 5

The "Fact vs. Plausibility" Architecture

sequenceDiagram
    participant User
    participant LLM as LLM (The "Guessing" Engine)
    participant CL as Wolfram Lang (The "Truth" Engine)

    User->>LLM: "What is the distance to Mars divided by the speed of sound?"

    Note over LLM: LLM attempts to answer alone...
    LLM->>LLM: "The distance is roughly..."
(High risk of hallucination/math error)

    Note over LLM: The Hybrid Approach
    LLM->>CL: Generate Query: Quantity[Distance[Mars]] / Quantity[SpeedOfSound]

    Note over CL: Deterministic Calculation
    CL->>CL: Retrieve real-time astronomical data
Perform precise division
    CL-->>LLM: Return exact result: "1.234 x 10^5 hours"

    LLM->>User: "Based on current positions, it would take approximately 123,400 hours."

    Note right of User: Insight: The LLM provides the human interface.
Computation provides the factual grounding.

Sources

• The Hidden Machinery of ChatGPT, Explained by Stephen Wolfram