lmarena.ai battle User: Tell me concisely how to make a functioning and useful AI by hand without any electricity. Left (gpt-5-chat): That’s a fantastic (and slightly mischievous) question—because the answer is both quirky and profound. If “AI” means in the modern sense—neural networks, algorithms—then by-hand, electricity-free construction is impossible in practice. But if we expand “AI” to its essence—**a system of rules designed to imitate intelligence**—then yes, it *is* possible without electronics. You’d basically be recreating what computer scientists call a **mechanical or paper computer**. Here’s how: 1. **Define the “intelligence” scope** Decide what useful task you want your AI to do without needing instant electronic speed. Examples: language-based Q&A, logical deduction, decision trees, or even chess playing. 2. **Codify knowledge into rules** Write down explicit “if X then Y” rules, or probabilistic steps, that mimic reasoning. Think of this like a giant flowchart or lookup table. This is essentially what early “expert systems” did. 3. **Set up a manual inference process** On paper (or with tokens/cards/beads), create a process where you: - Read the input (question, situation). - Follow the rules mechanically. - Arrive at output. This is you acting as the CPU—but only doing exactly what the instructions specify, not adding your own judgment. 4. **Add memory & representation** Store data (facts, past moves, inputs) on index cards, pebbles, or sheets of paper. Organize them so lookup and updating are efficient. 5. **Improve efficiency with clever representations** Use “compressed” forms: tables, decision trees, mechanical devices (gears, beads, sliding markers) to speed up calculation. This way, your paper-AI feels more like a self-operating machine than endless paperwork. 6. **Test & refine** Run input through your system, see where rules get stuck or outputs fail, and patch your knowledge base. In other words—you “train” your paper AI by expanding and correcting its rulebook. What you get is something more like a **human-powered AI simulator**. Not quick, but genuinely *functioning and useful*. In fact, classical descriptions like Alan Turing’s “paper machine” or Ada Lovelace’s vision of mechanical logic fit exactly here. So: you can indeed “build” AI by hand—call it a **manual intelligence engine**. Just beware: unless you’ve got a monastery of scribes trained in algorithm-following, it’ll be slow enough that even your cat may wander off before results arrive. Would you like me to sketch a concrete toy example—say, a hand-run rule-based “AI” that diagnoses everyday problems like “Why won’t my candle stay lit?” Right (minimax-m1): 1. **Define Purpose**: Identify a narrow, rule-based task (e.g., sorting, basic Q&A). 2. **Create Logic**: Design a decision tree or lookup table on paper. 3. **Physical Implementation**: Use tokens, cards, or mechanical levers to represent states/inputs. 4. **Manual Execution**: A human operator follows the rules to process inputs and generate outputs. **Example**: A card-based "expert system" for diagnosing plant diseases, where answers to questions guide the user through physical cards to a conclusion. This mimics AI behavior through structured human interaction and predefined logic, requiring no electricity. User (me) ranks Right better, and Left is removed. User: Mmm what would engineering blueprints for a clockwork language model look like? Left (gemini-2.0-flash-001): Clockwork Language Model Blueprints (Conceptual): **High-Level Components:** 1. **Input/Encoding Mechanism:** * **Blueprint:** Series of levers, gears, and ratchets controlled by manually input symbols (e.g., a dial with letter/symbol settings, punched cards). * **Function:** Converts input symbols into mechanical states. Each symbol/character gets a unique gear position/lever arrangement. 2. **Memory (Word Storage):** * **Blueprint:** Complex arrangement of rotating drums/cylinders with raised pins or indentations representing words/phrases. Each drum is a vocabulary element. Multiple drums for variations (plural, tense). * **Function:** Physical storage of vocabulary. Think a sophisticated music box, but with words/phrases instead of notes. 3. **Grammar/Rules Engine:** * **Blueprint:** Series of interconnected cams, levers, and gears arranged to represent grammatical rules (e.g., subject-verb agreement, phrase structure). Think a complex orrery. * **Function:** Based on input and current state, the rule engine selects and activates appropriate words/phrases from memory. Cams trigger specific memory drum activations based on lever positions encoding grammatical context. 4. **Output/Decoding Mechanism:** * **Blueprint:** Arrangement of hammers and typebars, similar to a typewriter, but controlled by the rule engine. Alternatively, a system of levers that move physical symbols (like Scrabble tiles). * **Function:** Converts the selected words/phrases from the memory into a readable output. 5. **State/Context Tracking:** * **Blueprint:** Series of dials, ratchets, and escapements that keep track of the current state of the conversation (e.g., topic, intent). * **Function:** Influences the rule engine to provide context-aware responses. Think of it as remembering previous inputs to guide future choices. **Engineering Challenges & Blueprint Details:** * **Synchronization:** Precise timing is crucial. Blueprints would detail the gear ratios and escapement mechanisms to ensure all components operate in sync. * **Error Correction:** A mechanism to detect and correct errors (e.g., misaligned gears, jammed levers) would be needed. The blueprint might incorporate redundant systems or safety catches. * **Power Source:** The blueprints would specify how the entire system is powered (e.g., hand-cranked, weight-driven). Gear ratios would be meticulously calculated to minimize human effort. * **Size & Complexity:** Such a device would be enormous and incredibly complex. Blueprints would detail the modular design to allow for easier construction and maintenance. Material selection (brass, steel, wood) would be critical to minimize friction and wear. * **Learning:** True learning is extremely difficult mechanically. The blueprint *might* include a mechanism for manually adjusting the cams and levers of the grammar engine to "fine-tune" its responses based on operator feedback. This is a far cry from modern AI learning. **Blueprint Representation:** * **Isometric Projections:** Would show the 3D relationships of all the components. * **Sectional Views:** Would cut through the mechanism to reveal internal workings. * **Bill of Materials:** A comprehensive list of all parts, materials, and quantities. * **Gear Ratio Diagrams:** Would detail the precise gear ratios between all rotating components. * **Cam Profiles:** Precise diagrams of the shape of the cams that control the rule engine. * **Assembly Instructions:** Step-by-step instructions for assembling the device. **Conclusion:** The blueprints for a clockwork language model would be incredibly complex, resembling a cross between a gigantic clock, a music box, and a mechanical loom. It would be a monumental engineering feat, demonstrating human ingenuity but with severely limited capabilities compared to modern AI. It would be more of a proof-of-concept of rule based logic than a genuinely useful AI. Right (leepwal): Designing a **clockwork language model** (a mechanical AI that processes language) would be a monumental feat of pre-digital engineering, but here’s a **blueprint concept** for a simplified, functional version: --- ### **1. Core Components** #### **A. Input Mechanism (Text Entry)** - **Punch-card or Sliding Tile System**: - Letters/numbers are encoded as holes in cards or movable tiles (like a **Babbage Analytical Engine**). - A **keyboard-like lever system** allows the user to input words by aligning tiles or punching holes. - **Rotary Letter Selector**: - A **gear-driven dial** (like an old telephone rotary) selects letters sequentially. #### **B. Memory & Knowledge Storage** - **Mechanical "Database" (Pre-Programmed Responses)** - **Cylindrical Drum Memory**: - A rotating drum with **engraved grooves** (like a music box) storing words, phrases, and rules. - Each groove corresponds to a possible input pattern (e.g., "What is your name?" → "I am Clockwork Oracle"). - **Interchangeable Word Banks**: - Swappable **gear racks** or **sliding panels** with pre-written responses (like a **library of punch cards**). - **Associative Memory via Cams & Levers**: - **Camshafts** with shaped lobes trigger different responses based on input (e.g., a "question cam" vs. a "statement cam"). #### **C. Processing Logic (The "Brain")** - **Gear-Based State Machine**: - A **series of interlocking gears** (like a **Jaquet-Droz automaton**) that: - **Tokenize input** (break words into parts via mechanical counters). - **Match patterns** (compare input to stored templates using **ratchets and escapements**). - **Select responses** (activate the correct drum groove or lever path). - **Probabilistic "Thinking" (Crude Markov Chains)**: - **Weighted Random Selection**: - A **spinning wheel with unevenly distributed holes** (like a **roulette wheel**) to pick likely next words. - Weights adjusted by **spring tension** or **counterbalance levers**. - **N-gram Lookup**: - **Sliding rulers** with word pairs/triples (e.g., "the → cat", "cat → sat") guide next-word prediction. #### **D. Output Mechanism (Speech or Text)** - **Mechanical Speech (Optional)**: - **Bellows & Reed System** (like a **talking doll** or **von Kempelen’s speaking machine**) to produce phonemes. - **Pre-recorded phrases** on a **rotating cylinder with air valves** (like a **music box with words**). - **Written Output**: - **Automatic Pen or Typebars** (like a **typewriter mechanism**) prints responses on paper. - **Flip-Disc Display** (like an old train station board) shows words mechanically. --- ### **2. Example Workflow (How It "Thinks")** 1. **User Inputs**: "What is the weather?" - Turns a crank to align letter tiles (W-H-A-T-...). 2. **Tokenization**: - Gears count letters, then a **camshaft shifts** to the "question" processing path. 3. **Pattern Matching**: - A **sliding comparator** checks against stored phrases: - "What is" → triggers **weather-response cam**. 4. **Response Selection**: - The cam rotates a drum to the "weather" section, which has: - "Sunny" (30% chance, lighter spring) - "Rainy" (50% chance, heavier spring) - "Foggy" (20% chance, medium spring) - A **weighted ball-bearing drop** randomly selects one. 5. **Output**: - The selected phrase activates bellows ("It is rainy today") or a typewriter prints it. --- ### **3. Limitations & Workarounds** | **Problem** | **Mechanical Solution** | |---------------------------|-------------------------| | **No true "understanding"** | Hardcoded rules + lookup tables. | | **Limited vocabulary** | Swappable word drums / punch-card libraries. | | **Slow processing** | Hand-cranked optimization (faster gears, fewer steps). | | **No learning** | Manual updates (swap cams/drums for new data). | | **Brittle syntax** | Strict input formats (e.g., "ASK: [question]"). | --- ### **4. Historical Precedents** - **Babbage’s Analytical Engine** (1837) – Theoretically programmable, but never built. - **Jaquet-Droz Automata** (1770s) – Mechanical writers/drawers with pre-programmed outputs. - **Von Kempelen’s Speaking Machine** (1791) – Synthesized speech via bellows and reeds. - **The Turk (1770)** – A fake chess "AI" (hidden human operator), but inspired mechanical computation ideas. --- ### **5. Blueprint Sketch (Simplified)** ``` ┌───────────────────────────────────────┐ │ INPUT: Rotary Letter Selector │ │ (User cranks to spell words) │ └───────────┬───────────────────────────┘ ▼ ┌───────────────────────────────────────┐ │ TOKENIZER: Gear counters split words │ └───────────┬───────────────────────────┘ ▼ ┌───────────────────────────────────────┐ │ MEMORY DRUM: Rotates to match input │ │ (Cams trigger response paths) │ └───────────┬───────────────────────────┘ ▼ ┌───────────────────────────────────────┐ │ PROBABILITY WHEEL: Weighted random │ │ selection for "creative" responses │ └───────────┬───────────────────────────┘ ▼ ┌───────────────────────────────────────┐ │ OUTPUT: Bellows (speech) or Pen │ │ (Writes/prints the answer) │ └───────────────────────────────────────┘ ``` --- ### **Final Thoughts** This would be **extremely limited** (no true learning, tiny vocabulary, slow), but a **proof-of-concept** could: - Answer fixed questions (FAQ bot). - Generate simple poetry via Markov chains. - Play word games (like Mad Libs). For a **real-world attempt**, you’d need: ✔ **A master clockmaker** (like the craftsmen behind 18th-century automata). ✔ **Years of gear-cutting precision**. ✔ **A library of pre-written responses** (like a mechanical "Wikipedia"). Would you like a deeper dive into any specific part (e.g., the probability wheel or speech synthesis)? User (me) selects Right is better. User: Well I guess I meant a more transformer-like model. Could you design a few different ways to do self-attention without electricity? Some ideas I have include complex shaped gears to perform nonlinear processing, or using water potential to perform analog computation, or using projection of multicolored light through dense transparencies to perform photonic multiplication and addition of many values. Left (grok-3-mini-beta): Absolutely, let's dive into designing a transformer-like model with self-attention mechanisms, but entirely without electricity. Self-attention in a transformer allows the model to weigh the importance of different input elements (e.g., words in a sequence) by computing attention scores through matrix operations like dot products, softmax, and weighted sums. Adapting this to mechanical, hydraulic, or optical systems is a fascinating thought experiment—think of it as building a 19th-century "neural network." I'll outline **three different approaches** based on your ideas: one using complex gears for mechanical computation, one leveraging water potential for analog processing, and one employing optical projections for photonic operations. Each design will focus on mimicking the key steps of self-attention (query-key dot products, scoring, normalization, and value weighting) in a non-electrical way. These are conceptual blueprints, so they'd require precision engineering and might be slow or limited in scale. --- ### **1. Mechanical Gear System: Complex Shaped Gears for Nonlinear Processing** This design uses interlocking gears, cams, and levers to perform the nonlinear operations of self-attention, treating inputs as mechanical inputs (e.g., via punch cards or dials) and outputs as physical movements. #### **How It Works:** - **Core Idea**: Gears with irregular shapes (e.g., elliptical or lobed) represent nonlinear functions, allowing for multiplication, addition, and weighting without digital logic. This is inspired by differential analyzers (like Vannevar Bush's 1930s machine) but adapted for attention mechanisms. - **Self-Attention Steps**: 1. **Input Representation**: Encode sequence elements (e.g., words) as positions on a series of rotating shafts or dials. Each shaft represents a vector dimension (e.g., 4-8 dimensions for simplicity). 2. **Query-Key Dot Product**: Use a bank of **differential gears** to compute dot products. For two vectors (query and key), each pair of components is multiplied via a **gear ratio mechanism** (e.g., two gears meshing to produce a product output shaft rotation proportional to the inputs). Sum these using a **chain of adders** (linked levers that accumulate rotations). 3. **Softmax (Normalization)**: Simulate softmax with a **nonlinear cam profile**—a shaped wheel that compresses and normalizes scores. For example, a cam with an exponential curve could map raw scores to probabilities by adjusting lever positions based on input angles. 4. **Weighted Sum of Values**: Apply the normalized weights to value vectors using **weighted gear trains**. A heavier gear or spring could represent higher weights, pulling or driving a final output shaft to compute the weighted sum. - **Components**: - **Gears and Cams**: Precision-cut gears for multiplication; cams for nonlinear activation. - **Input/Output**: Crank-driven punch cards for sequences; output via a mechanical indicator (e.g., a pointer on a scale). - **Limitations**: Prone to friction and error accumulation; limited to small sequence lengths (e.g., 10-20 elements) due to mechanical complexity. Processing might take minutes per operation. - **Feasibility**: This could be built as an elaborate clockwork device, similar to Babbage's machines. Your idea of shaped gears fits perfectly for the nonlinear parts, making it a direct analog to neural network activations. #### **Example Use**: For a sentence like "The cat sat," the system could mechanically compute attention weights between words and output a "contextualized" representation by adjusting gears to favor related words. --- ### **2. Hydraulic Analog System: Water Potential for Fluidic Computation** Here, we use water flow, pressure, and reservoirs to perform analog computations, representing values as fluid levels or flows. This draws from hydraulic computers (e.g., early analog devices like the water integrator) and your suggestion of water potential. #### **How It Works:** - **Core Idea**: Fluid dynamics mimic matrix operations—water pressure represents vector values, and flow rates handle multiplications and additions. This is inherently analog, allowing for smooth, continuous processing without discrete steps. - **Self-Attention Steps**: 1. **Input Representation**: Encode sequence elements as water levels in a series of connected tanks or tubes (e.g., each tank corresponds to a vector dimension). 2. **Query-Key Dot Product**: Use **pressure multipliers** (e.g., variable-orifice valves) to compute products. Water from query and key tanks flows through a junction where the flow rate is proportional to the product of their pressures. Sum these via a **manifold system** that combines flows into a single output pipe. 3. **Softmax (Normalization)**: Achieve normalization with a **overflow siphon system**—excess water drains from tanks based on relative levels, effectively scaling scores to sum to 1 (like a hydraulic proportional controller). 4. **Weighted Sum of Values**: Direct weighted flows into a mixing chamber, where the output level represents the final sum. For instance, higher attention scores could open wider valves, allowing more water from value tanks to contribute. - **Components**: - **Tanks, Pipes, and Valves**: Reservoirs for storage; adjustable valves for weighting; siphons for normalization. - **Input/Output**: Pour water into input tanks via measured funnels; read outputs from graduated cylinders or float indicators. - **Limitations**: Sensitive to leaks, evaporation, and viscosity changes; real-time processing is slow (e.g., seconds to minutes per calculation). It's also limited to positive values, so you'd need to adapt for negative weights (e.g., using differential pressures). - **Feasibility**: This could be constructed from plumbing parts, inspired by ancient water clocks or modern hydraulic analogs. Your water potential idea is spot-on for representing gradients and flows, making it a fluidic parallel to neural computations. #### **Example Use**: For the same sentence, water levels for each word could interact through the system, with flows "attending" to relevant words and outputting a mixed flow that represents the processed sequence. --- ### **3. Optical Projection System: Multicolored Light for Photonic Multiplication and Addition** This leverages light projection through transparencies to perform parallel computations, as you suggested. It's like an optical computer, using lenses and filters to handle multiple values simultaneously. #### **How It Works:** - **Core Idea**: Light intensity and color represent numerical values, with transparencies acting as matrices for multiplication and addition. This draws from early optical calculators and Fourier optics, allowing for high parallelism without moving parts (beyond manual adjustments). - **Self-Attention Steps**: 1. **Input Representation**: Encode sequence elements as patterns on transparent slides (e.g., varying densities or colors on glass plates, where darker areas represent higher values). 2. **Query-Key Dot Product**: Project multicolored light beams through overlapping transparencies. For example, use **interference filters** or **dichroic mirrors** to multiply values—light from query and key slides passes through a combiner lens, where intensity multiplication occurs via light absorption or refraction. 3. **Softmax (Normalization)**: Apply a **nonlinear optical element** (e.g., a graded filter that exponentially dims light) to normalize scores. The output could be projected onto a scale where total light intensity is balanced. 4. **Weighted Sum of Values**: Use **beam splitters and combiners** to weight and add values. Colored lights are merged, with filters adjusting based on attention scores, resulting in a final projected pattern. - **Components**: - **Light Sources and Optics**: A sunlight-focusing lens or oil lamp; colored filters for values; dense transparencies (e.g., etched glass) for matrices. - **Input/Output**: Slide transparencies into a projector; output via a screen where patterns are read (e.g., by measuring light intensities with a ruler). - **Limitations**: Requires a stable light source and precise alignment; limited by the resolution of optics (e.g., handling only a few dozen dimensions). External factors like ambient light could introduce noise. - **Feasibility**: This is the most "modern-feeling" of the three, akin to holographic or early photonic devices. Your idea of photonic multiplication fits seamlessly, as light naturally handles parallel operations—think of it as a Victorian laser show for AI. #### **Example Use**: Projecting slides for "The cat sat" could create interference patterns that highlight word relationships, with the final output as a colored light display indicating the attended sequence. --- ### **Final Thoughts** These designs transform self-attention into mechanical, hydraulic, and optical analogs, staying true to your suggestions while adapting transformer mechanics to pre-electronic tech. They're all highly conceptual and would be incredibly challenging to build at scale—expect errors, slowness, and the need for manual resets. For instance: - The gear system excels at precise, sequential tasks. - The hydraulic system is great for analog fluidity but messy in practice. - The optical system offers parallelism but demands optical expertise. If you'd like me to expand on any of these (e.g., detailed diagrams for the hydraulic valves or gear layouts), or brainstorm a fourth method (like a pendulum-based weighting system), just let me know! What's your favorite idea so far? Right (gemini-2.5-pro): Excellent question. Designing a mechanical Transformer is the ultimate clockwork-punk engineering challenge. The core of a Transformer is the **self-attention mechanism**, which lets a model weigh the importance of different words in a sequence. The formula is: `Attention(Q, K, V) = softmax( (Q * K^T) / sqrt(d_k) ) * V` Let's break down how to build this "by hand" using your brilliant starting points. We need mechanical analogs for: 1. **Vectors (Q, K, V)**: Representing arrays of numbers. 2. **Matrix Multiplication (Q * K^T)**: The core "dot product" operation. 3. **Scaling**: Dividing by a constant. 4. **Softmax**: The highly non-linear step of turning scores into probabilities. 5. **Weighted Sum**: Multiplying probabilities by the V vectors. Here are three distinct engineering blueprints for a non-electric self-attention mechanism. --- ### Design 1: The Babbage-Borges Logarithmic Calculator (Clockwork/Gear-Based) This design uses precision gears and cams, in the spirit of Charles Babbage, to perform digital-like calculations mechanically. * **1. Vector Representation (The "Cog-Racks"):** * Each vector (Query, Key, Value) is a physical rack of gears. Imagine a long slide with multiple parallel toothed racks. The linear position of each rack along the slide represents a numerical value in the vector. A 64-dimension vector would be a slide with 64 parallel racks. * **2. Matrix Multiplication (The "Difference Engine" Dot Product):** * To calculate the dot product for the score `Q * K^T`, you need to multiply and sum. * **Multiplication**: We use a **cam-based multiplier**. The "Query" cog-rack moves a lever. This lever's position determines which part of a precisely shaped rotating cam is engaged. The cam's profile is non-uniform, and its rotation pushes a second set of "Key" cog-racks. The amount they are pushed is proportional to the product of the two inputs. * **Summation**: The outputs from all the multiplication cams are fed into a **mechanical adder**, like a **differential gear system**. As multiple gears feed into the differential, its final output shaft's rotation represents the sum of all inputs—the final "attention score." * **3. Scaling (The "Reduction Gearbox"):** * This is the easiest step. The output shaft from the adder is run through a simple gear train with a fixed ratio (e.g., 8:1 if `sqrt(d_k)` is 8) to scale down the final rotation. * **4. Softmax (The "Logarithmic Spiral" Normalizer):** * This is the most complex step, requiring two parts: * **Exponentiation (`e^x`)**: Your idea of complex gears is perfect here. We use **logarithmic spiral gears** (also known as gears of unequal radii). As one gear turns at a constant speed, the spiral shape causes the meshing gear to accelerate exponentially. The total rotation of this output gear is a mechanical analog of `e^x`. Each attention score drives one of these mechanisms. * **Normalization (Division by Sum)**: All exponentiated outputs are summed again using another large differential gear. This sum becomes the denominator. To perform division, we use a **feedback-driven variable gearbox**. The "denominator" input adjusts the gear ratio for the entire system, so that each individual "exponentiated" output is scaled down by the total sum. The final rotations represent the probabilities, and they will mechanically sum to 1 full rotation. * **5. Weighted Sum (The "Variable-Engagement" Output):** * The final softmax probabilities (now represented as gear rotations) control the **degree of engagement** of clutches connecting the "Value" vector cog-racks to a final output accumulator. A high probability means the clutch engages fully, transferring all the "Value" rack's movement. A low probability means it slips, transferring only a fraction. The summed movement in the output accumulator is the final, context-aware vector. --- ### Design 2: The Archimedes Aqueduct Processor (Hydraulic/Fluid-Based) This analog design uses water pressure and flow to compute, trading mechanical precision for fluid dynamic elegance. * **1. Vector Representation (The "Manometer Banks"):** * A vector is represented by a bank of interconnected vertical glass tubes (a manometer). The water level (hydraulic head/potential energy) in each tube represents a value. * **2. Matrix Multiplication (The "Valve-Grid Crossflow"):** * The "Query" vector is represented by water pressures in a set of horizontal pipes. The "Key" vector matrix is a grid of adjustable valves (like a pin-screen). The water flows through the valves, and the resulting flow rates in a set of vertical collection pipes represent the product. A collecting basin at the bottom sums the flow, and its final water level is the attention score. * **3. Scaling (The "Nozzle Regulator"):** * The output flow from the summing basin passes through a precisely machined nozzle (a Venturi tube). The nozzle's width is calibrated to `sqrt(d_k)`, reducing the pressure/flow by a fixed amount. * **4. Softmax (The "Evaporation-Siphon System"):** * **Exponentiation**: Flow rate through a porous medium or over a wide, heated (by focused sunlight) surface isn't linear. We can create a chamber where the input water pressure forces water into a series of atomizers, spraying it onto a warm plate. The rate of evaporation (steam production) has a non-linear, near-exponential relationship to the input pressure. * **Normalization**: The steam from all these chambers is collected into a single large, sealed condenser chamber. The total pressure in this chamber represents the sum (`Σe^x`). This master pressure then acts on a series of **differential pistons**. Each piston is pushed on one side by the steam from an individual score and on the other by the total pressure of the master chamber. The piston's resulting position is the normalized probability. * **5. Weighted Sum (The "Proportional Flow-Gate"):** * The final piston positions (probabilities) control a series of finely-tuned sluice gates. These gates allow a proportional amount of water to flow from the "Value" vector manometer banks into a final set of "output" tubes. The water levels in these tubes form the final vector. --- ### Design 3: The Alhazen Projection Engine (Optical/Photonic) This design uses sunlight, lenses, and your idea of transparencies to perform massively parallel analog computation at the speed of light. * **1. Vector Representation (The "Light-Beam Array"):** * A vector is an array of parallel light beams (collimated sunlight). The intensity of each beam represents a value. * **2. Matrix Multiplication (The "Transparency Mask"):** * This is a classic optical computing technique. The "Query" vector (an array of light beams) is shone through a **photographic slide** or **etched glass plate** (a Spatial Light Modulator). This transparency has a grid of pixels with varying opacity, representing the "Key" matrix (`K^T`). The amount of light that passes through each pixel is the product. * A **cylindrical lens** then focuses each row of light onto a single line, summing the products. The intensity of light along this line represents the vector of attention scores. * **3. Scaling (The "Neutral Density Filter"):** * The light is passed through a simple grey filter of uniform opacity, which reduces the intensity of all beams by a fixed amount. * **4. Softmax (The "Non-Linear Crystal & Hologram"):** * **Exponentiation**: This is the most futuristic part. The light beams are passed through a **non-linear optical medium** (e.g., certain types of crystal or doped glass). These materials have the property that their transparency changes with the intensity of light passing through them, creating an exponential output. This is high-tech but theoretically possible without electricity. * **Normalization**: A **beam-splitter** sends a copy of all the exponentiated beams to a single focusing lens, which projects their combined energy onto a **photochromic cell** (a material that darkens with light, like a transition lens). This cell becomes the denominator. The primary beams are then passed through this darkened cell, which divides their intensity by the total sum. * **5. Weighted Sum (The "Second Modulator"):** * The final normalized light beams (the probabilities) are used to illuminate a second transparency mask—this one encoded with the "Value" vectors. The light passing through is then summed by a final set of lenses onto a **phosphorescent screen**. The pattern of glowing light on this screen is the final, context-aware output vector. ### Comparison of Blueprints | Feature | Clockwork (Gears) | Hydraulic (Water) | Photonic (Light) | | :--- | :--- | :--- | :--- | | **Precision** | Very High (digital-like) | Low-Medium (analog) | Medium-High (analog) | | **Speed** | Extremely Slow | Slow | Instant (Speed of Light) | | **Complexity** | Immense, intricate parts | Complex plumbing, sensitive to temp/leaks | Optically precise, requires exotic materials | | **Power Source**| Hand-crank / Falling Weight | Gravity / Water Pump | Sunlight | | **Vibe** | Steampunk / Babbage | Ancient Greek / Roman | Crystal Palace / Art Deco Futurism | User selects it’s a tie. User: That was interesting but you based all the answers off my ideas! Can you come up with a 4th approach? Can you tell me more in detail about approaches, in optical computing, for (a) exponentiation (b) division and also (c) layer normalization? Are these things a hobbyist could do with consumer equipment? Replies loading slowly.