Connecting Probability Theory to the SEP Engine

Current Focus

This update summarizes how ideas from probability theory—particularly the law of large numbers, Markov chains, and Monte Carlo methods—relate to the ongoing development of the Self‑Emergent Processor (SEP) trading platform. The recent analysis draws on the video The Law of Large Numbers to highlight conceptual links between classical probability and the quantum-inspired approach of the SEP Engine.

Key Takeaways

• Law of Large Numbers: explains how metrics such as coherence, stability, and entropy converge when computed over large datasets.
• Markov Chains: provide a framework for modeling pattern transitions within the SEP Engine, echoing the video's discussion of dependent sequences.
• Monte Carlo Methods: are valuable for backtesting and risk management by simulating trading scenarios under varying market conditions.

Visualizing the Law of Large Numbers

The chart below simulates repeated coin tosses. As the number of trials grows, the sample mean approaches the expected value of 0.5, demonstrating the law of large numbers in action.

Simple Markov Chain Example

Market regimes can be represented as states in a Markov chain. The following chart shows a hypothetical one-step transition matrix for three regimes: Bull, Neutral, and Bear.

Relevance to SEP

The SEP Engine processes OANDA market data and converts it into quantum-inspired patterns. By interpreting pattern evolution through a probabilistic lens, we refine signal generation, improve backtesting via Monte Carlo simulations, and better understand the statistical stability of our metrics. The video underscores these connections by showing how probabilistic models have been applied across physics, search engines, and language processing—parallels that inspire our current engineering efforts.