energetic-scaling

Energetic Scaling: Biology vs. Technology

A publication-quality dual-panel log-log visualization comparing neural efficiency scaling in biology with compute efficiency scaling in technology.

Interactive Version

Open output/energetic_scaling_interactive.html in your browser for an interactive version with hover tooltips.

Key Insights

Left Panel: Biological Allometry

• Neurons per kg vs. body mass reveals clade-specific scaling rules
• Humans are outliers: 86B neurons, Encephalization Quotient (EQ) ~7
• Birds achieve remarkable density (Goldcrest: 3.6×10¹⁰ neurons/kg)
• Reptiles have ~20x fewer neurons than endotherms at same body size
• Power-law slopes differ: mammals ~-0.3, primates flatter (linear scaling)

Right Panel: Tech Scaling (Kurzweil-inspired)

• Compute per dollar has increased ~75 quadrillion-fold (1939–2024)
• Exponential trend continues: ~2x improvement per year
• AI scaling explosion post-2012 (AlexNet → GPT-4 → Grok-4)
• Training FLOPs grew from 10¹⁷ (AlexNet) to 10²⁶+ (frontier 2026)

The Connection

Both panels reveal power laws (straight lines on log-log plots):

• Biology: Energy budget constrains neural investment; humans broke the curve
• Technology: Economic/physical limits drive exponential improvement; AI is the new outlier

Domain	Scaling Rule	Outlier
Biology	Neurons/kg ~ Mass^(-0.3)	Human (EQ~7)
Tech	cps/$ ~ 2^(year/1.5)	AI FLOPs explosion

Data Sources

• Neuronal scaling: Herculano-Houzel et al. (comparative neuroanatomy)
• Metabolic scaling: Kleiber's Law (0.75 exponent)
• Life History Theory: Kaplan, Charnov (Ache/Tsimane forager data)
• Tech price-performance: Kurzweil (2024 update), NVIDIA specs
• AI FLOPs: Epoch AI, scaling reports

Usage

Requirements

pip install matplotlib numpy scipy plotly

Generate Static Charts

cd src && python energetic_scaling.py

Generate Interactive HTML

cd src && python energetic_scaling_plotly.py

File Structure

energetic-scaling/
├── README.md
├── data/
│   └── scaling_data.csv
├── src/
│   ├── energetic_scaling.py
│   └── energetic_scaling_plotly.py
└── output/
    ├── energetic_scaling_highres.png
    ├── energetic_scaling.svg
    └── energetic_scaling_interactive.html

Related Visualizations

• AI Compute Timeline – Training FLOPs growth over time
• Adoption Timeline – Time to mass adoption compression

Together, these three plots show:

1. Compute growth (AI Timeline) → enables scale
2. Adoption compression (Adoption Timeline) → accelerates deployment
3. Efficiency scaling (this plot) → fundamental limits and outliers

License

MIT