Introducing to the Calculus of Distributed Persistence (CDP)

How do complex systems – from vast computer networks and potential future AI to ecosystems and maybe even civilizations – manage to survive and thrive over long periods, especially when facing failures, resource limits, competition, and the simple tyranny of distance?

Existing tools often look at parts of the puzzle: population growth, network resilience, information flow. But understanding true, long-term persistence requires integrating these factors. How does the ability to replicate interact with the need to maintain accurate information and functional capability across a distributed system, especially when communication takes time and competitors are present?

To address this challenge, we're introducing the Calculus of Distributed Persistence (CDP) – a new mathematical framework designed to model the dynamics of such complex, distributed, and potentially competitive systems.

What is CDP?

At its core, CDP views a distributed system through three key lenses, represented as fields spread across space or a network:

• Functional Unit Density (ρ): How many active components (agents, nodes, individuals) does the system have in different locations?
• Effective Information Level (κ): How much functional knowledge, cultural information, or operational data does the system reliably possess locally? (Think Shannon meets system state).
• Effective Capability Level (γ): How effectively can the system act on its environment or coordinate its components locally?

The "calculus" part comes from defining operators that govern how these fields change over time:

• Generation/Expansion (R): The birth rate – how fast new units are created or the system expands.
• Attrition/Destruction (D): The death rate – how fast units are lost due to failures, threats, or competition.
• Propagation/Synchronization (S): The communication rate – how effectively information and capability spread and synchronize across the system, considering inevitable delays.
• Decay/Degradation (Λ): The forgetting rate – how intrinsic processes lead to loss of information or capability over time.

By modeling the interplay of these operators, often resulting in complex (integro-)differential equations, CDP allows us to analyze the conditions under which a system might enter different dynamic states: Expanding, Stable, Oscillatory, Fragmented, Contracting, or even Collapse.

Why Does This Matter? (Applications)

CDP provides a structured way to ask crucial questions about various systems:

• Future AI & Superintelligence: How resilient could a distributed ASI be? What factors (replication speed, coding efficiency, connectivity) determine its "indestructibility"? Can we model Skynet-like expansion or competitive AI scenarios?
• Technology: Can we develop better health metrics for complex systems like Kubernetes clusters? What are the limits for self-replicating Von Neumann probes exploring the galaxy, considering error accumulation and delays?
• Broader Systems: Can similar principles apply to ecological persistence, the spread of culture, or even the long-term dynamics of civilizations facing internal and external pressures?

Connecting to the Future (and Sci-Fi)

Interestingly, the ambition of CDP echoes concepts like Asimov's psychohistory – the idea of mathematically modeling the trajectory of large-scale systems. While CDP uses a different approach (dynamic field equations vs. statistical laws), it reflects a similar drive to understand the deep principles governing persistence. Sometimes, science fiction anticipates the tools we later strive to build.

The Road Ahead

CDP is presented here as a framework. Making concrete predictions requires instantiating it with specific models and parameters relevant to the system being studied – a significant but exciting challenge.

This research opens the door to formally exploring the fundamental dynamics of survival and resilience in the complex, distributed systems that increasingly shape our world and our future imaginings.

Read the full research proposal: Calculus of Distributed Persistence (PDF)

We welcome discussion and collaboration as this framework develops!

– Artem Andreenko, SentientWave Inc.

artemandreenko.com