The Ubiquity of Space-Time Simulation in Modern Computing: From Theory to Practice

This repository contains the academic paper exploring how Ryan Williams' 2025 theoretical result, TIME[t] ⊆ SPACE[√(t log t)], manifests in real-world computing systems.

Paper

Title: The Ubiquity of Space-Time Simulation in Modern Computing: From Theory to Practice
Author: David H. Friedel Jr., Founder, MarketAlly LLC (USA) & MarketAlly Pte. Ltd. (Singapore)
Status: Submitted to arXiv (needing endorsement)

Abstract

Ryan Williams' 2025 result demonstrates that any time-bounded algorithm can be simulated using only O(√(t log t)) space, establishing a fundamental limit on the space-time relationship in computation. This paper bridges the gap between this theoretical breakthrough and practical computing systems. Through controlled experiments and analysis of production systems, we show that space-time tradeoffs following the √n pattern are ubiquitous across databases, machine learning frameworks, and distributed systems. However, we find that practical constant factors range from 100× to 10,000×, primarily due to memory hierarchies and I/O overhead.

Related Repositories

• Experiments & Code: Full implementation, experiments, and interactive dashboard
• Interactive Dashboard: Streamlit app for exploring space-time tradeoffs

Key Findings

1. Theoretical validation: √n space-time patterns confirmed experimentally
2. Massive constant factors: 100× to 10,000× due to memory hierarchies
3. Real-world ubiquity: Found in PostgreSQL, Flash Attention, MapReduce
4. Practical guidance: When to trade space for time (and when not to)

Building the Paper

# Compile the paper
pdflatex main.tex
bibtex main
pdflatex main.tex
pdflatex main.tex

# Compile two-page summary
pdflatex two_page_summary.tex

Citation

Once published on arXiv:

@article{friedel2025ubiquity,
  title={The Ubiquity of Space-Time Simulation in Modern Computing: From Theory to Practice},
  author={Friedel Jr., David H.},
  journal={arXiv preprint arXiv:25XX.XXXXX},
  year={2025}
}

Reading Order

1. Quick Overview: Read executive_summary.md (2 pages)
2. Technical Summary: Read two_page_summary.tex (2 pages, compile to PDF)
3. Full Paper: Read main.tex (25 pages, compile to PDF)
4. Try It Yourself: Visit the experiments repository

Contact

• Email: dfriedel@marketally.ai
• Organization: MarketAlly LLC

License

This paper is licensed under CC BY 4.0. You may share and adapt the material with proper attribution.

Acknowledgments

This work was carried out independently as part of early-stage R&D at MarketAlly LLC and MarketAlly Pte. Ltd. We acknowledge the use of large language models for drafting assistance.