E = k·S·D·Λ·C
A universal proportionality defining efficiency in any meaning-bearing system.
Efficiency = k × Semantic Density × Dimensionality × Lambda × Compression
Understanding the Relationship
The Universal Efficiency Law states that efficiency (E) in any information-processingsystem is proportional to the product of four fundamental factors: Semantic Density (S),Dimensionality (D), Lambda/Inverse Latency (Λ), and Compression (C), normalized by a context constant (k).
This isn't an additive relationship — it's multiplicative. This mathematical structure has profound implications:
- Zero in any factor means zero efficiency. A system with perfectcompression but zero semantic content produces nothing useful.
- Improvements compound. Doubling two factors quadruples efficiency. Small optimizations across multiple factors yield exponential gains.
- Balance matters. Systems tend toward equilibrium across factors. Over-optimizing one while neglecting others creates diminishing returns.
The Components
Semantic Density
Proportion of meaningful signal to total data
High semantic density means every piece of data carries meaning. Low density means noise, redundancy, wasted capacity. Whether measuring content quality, signal purity, or information relevance — S captures how much meaning exists per unit of data.
Dimensionality
Degree of discrimination or representational resolution
Dimensionality measures representational resolution — how finely a system can discriminate between different states. High D means nuanced understanding and precise categorization. Low D means coarse, lossy approximations.
Lambda
Inverse latency — responsiveness, 1 ÷ processing time
Lambda captures speed of information flow. Defined as 1/t (inverse of processing time), higher Λ means faster response. Every unit of latency reduces efficiency proportionally — time is a fundamental efficiency cost.
Compression
Ability to represent more meaning in less space
Compression measures information density in storage and transmission. High C means maximum meaning per bit. This extends beyond file compression to conceptual compression — expertise is highly compressed knowledge.
The Context Constant (k)
The context constant k normalizes the equation for specific domains. It accounts for:
- Unit conversions between different measurement scales
- Domain-specific baseline efficiency
- System constraints and physical limitations
In comparative analysis within a single domain, k often cancels out — making the formula useful for relative efficiency comparisons even without precise k calibration.
Quick Reference
| Symbol | Name | Description | If Zero... |
|---|---|---|---|
| S | Semantic Density | Meaningful signal ÷ total data | Pure noise |
| D | Dimensionality | Discrimination resolution | Can't distinguish |
| Λ | Lambda | 1 ÷ processing time | Infinite latency |
| C | Compression | Meaning per unit space | Can't store anything |
Ready to Go Deeper?
Explore individual components or read the full theory.